dynamic characteristics of sandy soils under impact

REPUBLIC OF IRAQ MINISTRY OF HIGHER EDUCATION AND SCIENTIFIC RESEARCH UNIVERSITY OF BAGHDAD, COLLEGE OF ENGINEERING DEPARTMENT OF CIVIL ENGINEERING

DYNAMIC CHARACTERISTICS OF SANDY SOILS UNDER IMPACT LOAD

A THESIS SUBMITTED TO THE COLLEGE OF ENGINEERING OF UNIVERSITY OF BAGHDAD IN A PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN CIVIL ENGINEERING (SOIL MECHANICS AND FOUNDATION ENGINEERING)

BY

BALQEES ABDULWAHID AHMED B.SC. IN CIVIL ENGINEERING, 1995 M.SC. IN CIVIL ENGINEERING, 1998

THUL QA‘DAH 1437

AUGUST 2016

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DEDICATION

To My parents The reason of what I become today Thanks for your great support and encouragements With all love and respect To my brothers Mohammed and Essa To My sisters With all love I am really grateful to all of you

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ACKNOWLEDGEMENTS

First of all, I would like to thank Almighty ALLAH the Merciful for everything wonderful in my life, without his guidance I would never be able to accomplish anything in my whole life. I would like to express my sincere thanks and deepest gratitude to my supervisor Prof. Dr. Adnan Falih Ali AL-Bassri and Prof. Dr. Mohammed Yousif Fattah for their excellent guidance; valuable suggestions, endless support, valuable advice, and encouragement, and I would like to thank them for giving me a lot of their valuable time during the course of this work, for many useful discussions. Therefore, I am really grateful for them. Special thanks for Asst. Prof. Dr. Musab Aied Qissab Al-Janabi, faculty member in the Civil Engineering Department-College of Engineering- University of Al-Nahrain, for his valuable opinions and efforts throughout the preparation of this research. I thank all the people who helped me especially Dr Hayder Amer Al-Baghdadi faculty member in the Civil Engineering Department-College of EngineeringUniversity of Baghdad for his valuable opinions and support and Dr Faris Sadeq Mustafa Al-Saffar, faculty member in the Civil Engineering Department-College of Engineering- University of Baghdad, for his help and efforts by supplying me the physical model. I am also grateful to my best friends Asst. Prof. Maysam Th. AlHadidi, and Asst. Prof. Asma Y. Yahya faculty members in the Civil Engineering Department-College of Engineering- University of Baghdad for their valuable support throughout the preparation of this research. Also, I wish to express thanks to Mrs. Zina M. Deno for her help in the Soil Mechanics Laboratory. Finally, I would like to thank my parents, my brothers Mohammed, and Essa, and my sisters for their help and support.

Balqees Abdulwahid Ahmed 2016

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ABSTRACT

There are many problems in civil engineering deal with the transmission of stress waves through soil due to dynamic load, such as seismic response under earthquake loading, foundation response under dynamic loading (industrial buildings), vibrations in buildings, induced by various sources (pile driving, installation of sheet piles and demolition of buildings, ...etc.), and rail and road traffic. For most designs of such problems, it is very important to investigate the dynamic soil properties especially the shear modulus and the damping ratio. Damping is the energy dissipation through the soil. There are only a few techniques available to determine the damping ratio. Only laboratory tests, such as resonant column and cyclic simple shear tests, but no field testing methods, can be considered as established techniques. The present work includes an experimental study of the behavior of sandy soils having different densities under the action of a single impulsive load. Dry sands of different densities and saturated sand were tested. Sands were implemented in the experimental program. Different falling masses from different heights were conducted using the falling weight deflectometer (FWD) to provide the single pulse energy. The responses of different soils were evaluated at different locations (vertically below the impact plate and horizontally away from it). These responses include; displacements, velocities, and accelerations that are developed due to the impact acting at top and different depth ratios within the soil using the falling weight deflectometer (FWD) and accelerometers (ARH-500A Waterproof, and Low capacity Acceleration Transducer) that are embedded in the soil in addition to soil pressure gauges (KPE-PB) and then recorded using the multi-recorder TMR-200. Based on the experimental test results, the damping characteristics and the behavior of different sandy soils were evaluated. Variation of damping with different parameters was examined, these are; footing embedment, depth ratios (D/B), diameter of the impact plate (B), the applied energy and soil density (dense, medium, and loose) in addition to moisture content (dry or saturated sands).

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Accordingly, empirical equations are proposed to predict the soil damping which is dependent on the frequency ratio (β), shear modulus (G), modulus of elasticity (E), and the modulus of subgrade reaction (K). The results show that the damping ratio is affected by the embedment ratio (D/B). It was found that the damping ratio increases by about 50-150% when the embedment ratio increases from 0 to 2. Also, when the density of the soil increases from loose to dense through a decrease in the void ratio by about 29% and from medium soil to dense by decreasing in the void ratio by 12%, the damping ratio increases by about 30-80% from loose to dense soil and 15-30% from medium to dense soil. Test results reveal that when the falling mass increased by about 100% from the same height fall, the damping ratio decreased by about 10-25% for the case of dense soil, 15-40% for medium soil, and 25-50% for loose. It was found that the damping ratio decreases by about 20-35% when the footing area increases 125%. Although the damping coefficient is increasing when the footing area increased, the damping ratio decreases due to increase in the critical damping coefficient.

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CONTENTS

Abstract ...................................................................................................................... i Contents .................................................................................................................... iii List of Figures ......................................................................................................... vii List of Tables ........................................................................................................... xii Notation .................................................................................................................. xiii Chapter One .............................................................................................................. 1 1. Introduction ........................................................................................................ 1 1.1

General .................................................................................................................... 1

1.2

Impact load ............................................................................................................. 3

1.3

Wave Propagation in Soil Media ............................................................................ 5

1.4

Damping of waves in Soils ..................................................................................... 8

1.5

Objectives of The Study ......................................................................................... 8

1.6

Scope of Study ........................................................................................................ 8

1.7

Outlines of the Research ......................................................................................... 9

Chapter Two ........................................................................................................... 11 2. Review of Literature ........................................................................................ 11 2.1

Introduction ........................................................................................................... 11

2.2

Response of Soil to Impact Load .......................................................................... 11

2.3 Prediction of Dynamic Soil Properties ................................................................. 12 2.3.1 Dynamic shear modulus (G) .......................................................................... 13 2.3.2 Damping of soil ............................................................................................. 15 2.3.2.1 Geometric damping.................................................................................... 19 2.3.2.2 Material damping ....................................................................................... 19 2.3.2.3 Viscous damping........................................................................................ 20 2.3.3 Poisson‘s ratio (ν) .......................................................................................... 20

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2.4 Dynamic Soil-Structure Interaction ...................................................................... 21 2.4.1 Effect of foundation embedment ................................................................... 24 2.4.2 Effect of footing size and shape .................................................................... 27 2.4.3 Effect of soil density ...................................................................................... 28 2.4.4 Effect of soil saturation on the foundation response ..................................... 29 2.5

Concluding Remarks ............................................................................................. 31

Chapter Three ......................................................................................................... 32 3. Experimental Work ......................................................................................... 32 3.1

Introduction ........................................................................................................... 32

3.2 Description of the Soil Model ............................................................................... 33 3.2.1 Raining frame ................................................................................................ 33 3.2.2 Measurement devices .................................................................................... 34 3.3

Soil Types under Consideration ............................................................................ 36

3.4

Sand Preparation Method and Calibration ............................................................ 37

3.5

Impact Test Procedure .......................................................................................... 40

3.6 Measurements of the Dynamic Response ............................................................. 45 3.6.1 The multi-recorder TMR-200 ........................................................................ 45 3.6.2 Acceleration measurement ............................................................................ 47 3.6.3 Pore water pressure measurement ................................................................. 48 3.7

Testing Program .................................................................................................... 50

3.8

Testing Procedure ................................................................................................. 57

Chapter Four........................................................................................................... 60 4. Presentation and Discussion of Test Results ................................................. 60 4.1

Introduction ........................................................................................................... 60

4.2 Behavior of Dry Dense Sandy Soil under Impact ................................................. 60 4.2.1 Amplitude of the impact force ....................................................................... 61 4.2.2 Displacement Response ................................................................................. 62 4.2.3 Response inside the soil medium .................................................................. 64 4.3

Behavior of Dry Medium and Loose Sandy Soils under Impact Load ................. 84

4.4

Summary of Major Conclusions Related to Dry Sand Behavior under Impact .. 106

4.5

Behavior of Saturated Sandy Soils under Impact Load ...................................... 107

Chapter Five .......................................................................................................... 127 5. Prediction of Dynamic Characteristics of Sandy Soil ................................ 127 iv

5.1

Introduction ......................................................................................................... 127

5.2

Dynamic Soil Properties ..................................................................................... 128

5.2.1

Soil modulus of subgrade reaction (K) ........................................................... 128

5.2.2

Soil modulus of elasticity (E) .......................................................................... 128

5.2.3

Shear modulus (G) .......................................................................................... 129

5.3

Soil Mass and Natural Frequency ....................................................................... 129

5.4 A Proposed Methodology ................................................................................... 131 5.4.1 Proposed calculation of natural frequency and mass of soil ....................... 131 5.4.2 Equation of motion of the basic dynamic system ........................................ 132 5.4.3 Soil damping ratio ....................................................................................... 134 5.5

Discussion of Results .......................................................................................... 139

5.6 Modulus of Subgrade Reaction, Modulus of Elasticity, Shear Modulus and Damping Ratios of Sandy Soils of Different Conditions .............................................. 140 5.7

Procedure of Calculations ................................................................................... 145

5.8 Damping behavior of sandy soils ........................................................................ 150 5.8.1 Effect of footing embedment (depth) .......................................................... 150 5.8.2 Effect of footing size ................................................................................... 151 5.8.3 Effect of soil density .................................................................................... 152 5.8.4 Effect of saturation ...................................................................................... 153 5.8.5 Effect of energy of impact ........................................................................... 154 5.9

Shear Modulus of Sandy Soils Undergoing Impact Loading ............................. 154

5.10 Relationship between the Damping Ratio and Shear Modulus .......................... 158 5.10.1 ratio

Relationship between the damping ratio and shear modulus with frequency

5.10.2

Relationship between the damping ratio and stiffness with frequency ratio... 161

160

5.11 Relationship Between the Damping Coefficient and other Factors .................... 162 5.12 Relationship among Modulus of subgrade Reaction, Shear Modulus, and Modulus of Elasticity with Frequency Ratio ................................................................................ 166

Chapter Six ............................................................................................................ 172 6. Conclusions and Recommendations for Future Work ............................... 172 6.1

Introduction ......................................................................................................... 172

6.2

Applicability of the Present Work ...................................................................... 173

6.3

Conclusions ......................................................................................................... 173

6.4

Recommendations for Future Work ................................................................... 177

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References.............................................................................................................. 179 A Appendix A Measurement Devices .............................................................. A-1 A.1

TML Small FWD System ................................................................................... A-1

A.2 The multi-recorder TMR-200 ........................................................................... A-11 A.2.1 Control Unit TMR-211 .............................................................................. A-12 A.2.2 Strain Full Bridge Unit TMR-221 ............................................................. A-17 A.2.3 Connection measurement unit ................................................................... A-25 A.3 ARH-A Waterproof, Low Capacity Acceleration Transducer (ARH-500A) ... A-25 Measurement .......................................................................................................... A-26 A.4 KPE-PB Small Pore Pressure Gauge ................................................................ A-32 Measurement .......................................................................................................... A-32

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LIST OF FIGURES

Figure 1-1 Characteristics and sources of typical dynamic loadings: (a) simple harmonic; (b) complex; (c) impulsive; (d) long-duration (after Clough and Penzien, 2003). ............................................................................................................................ 3 Figure 1-2

Typical loading diagrams: (a) transient loading due to single impact of a hammer; (b) vertical component of ground acceleration due to pile driving (Das and Ramana, 2011)..................................................................................... 4

Figure 1-3 Response ratios due to half-sine pulse (Clough and Penzien, 2003). ............... 4 Figure 1-4

Illustration of vibration transfer during vibratory sheet pile driving, (after Deckner et al., 2012). .......................................................................................... 6

Figure 1-5 Displacement characteristics of different wave types, (Deckner, 2013) .......... 7 Figure 2-1 Typical time history of acceleration in sand (after Chen et al., 1988). ........... 14 Figure 2-2 Decay of vibration amplitude in time domain (after Zhenzhong, 2014). ....... 16 Figure 2-3

Bandwidth method of determination of damping ratio from forced vibration test (Das and Ramana, 2011). ........................................................................... 17

Figure 2-4

Determination of damping ratio from hysteresis loop (Das and Ramana, 2011). ................................................................................................................ 18

Figure 2-5 Geometrical damping of waves emanating from a point source on the surface of a half-space (Andersen, 2003). ..................................................................... 19 Figure 2-6 Experimental setup used by Chen and Chen, (1996). ..................................... 23 Figure 2-7 Accelerations for different plates (after Chen and Chen, 1996). .................... 23 Figure 2-8 Effect of embedment ratio (D/B) on damping ratio for footings on surface of dry sand in terms of increase in damping ratio compared to that for surface footing (after Al-Homoud and Al-Maaitah, 1996). .......................................... 24 Figure 2-9

Effect of footing width on dynamic response in terms of reduction in amplitude (results are given for footing on surface of dry sand for models) (after Al-Homoud and Al-Maaitah, 1996). ....................................................... 27

Figure 2-10 Dependency of distributed spring coefficients and damping ratio on base size; (a) horizontal and vertical spring coefficients; (b) damping ratio (after Kim et al., 2001). .............................................................................................. 28 Figure 2-11 The difference between loose and dense soil with contact points. (after Omidvar et al., 2012). ....................................................................................... 29 Figure 3-1 The setup of the experimental soil model. ...................................................... 34 Figure 3-2 Data acquisition system. ................................................................................. 35

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Figure 3-3 Grain size distribution of the sand. ................................................................. 36 Figure ‎3-4 Preparation of sand layer. a) Sand raining technique b) Preparation of dense sand using tamping. .......................................................................................... 38 Figure 3-5 Density calibration curves for the sand used. ................................................. 39 Figure 3-6 The small FWD system with the standard set with accessories that were used in tests. .............................................................................................................. 41 Figure 3-7 Small FWD main body KFD-100A. ............................................................... 42 Figure 3-8 Exclusive indicator TC-351F. ......................................................................... 43 Figure 3-9 Sample data collected from FWD by using TC-7100 software in impact test. .......................................................................................................................... 44 Figure ‎3-10 Devices for dynamic response measurement. a) The pore water pressure transducer with its catalogue, b) The accelerometer with its catalogue, c) The data logger d) The transducer connection to data logger. ................................. 45 Figure 3-11 System block diagram. .................................................................................. 46 Figure 3-12 The multi-recorder TMR-200 ....................................................................... 46 Figure 3-13 Data of the multi-recorder TMR-200 from tests. .......................................... 47 Figure 3-14 Waterproof, low capacity acceleration transducer (ARH-500A). ................ 48 Figure 3-15 KPE-PB small pore pressure gauge. ............................................................. 49 Figure 3-16 Pressure gauge. ............................................................................................. 50 Figure ‎3-17 The state of impact load on the soil model (a) at surface (b) buried at depth 0.5 B (c) buried at depth B (d) buried at depth 2B. .......................................... 51 Figure ‎3-18 Steps of carrying out test in saturated models a) preparation the physical model for saturated test b) raining technique c) before saturation d) during saturation e) after saturation f) after the test. .................................................... 52 Figure 3-19 Testing program of the physical model. ....................................................... 56 Figure 3-20 Longitudinal section of set-up of the physical model. .................................. 58 Figure 3-21 Steps of preparing the physical model. ......................................................... 59 Figure 4-1 FFT (Fast Fourier Transform) analysis and processing software. .................. 67 Figure 4-2 Test results for DDP10M5H25 model. .............................................................. 68 Figure 4-3 Test results for DDP15M5H25 model. .............................................................. 70 Figure 4-4 Test results for DDP10M10H25 model. ............................................................ 72 Figure 4-5 Test results for DDP15M10H25 model. ............................................................. 74 Figure 4-6 Test results for DDP10M5H50 model. .............................................................. 76 Figure 4-7 Test results for DDP15M5H50 model. .............................................................. 78 Figure 4-8 Test results for DDP10M10H50 model. ............................................................. 80 Figure 4-9 Test results for DDP15M10H50 model. ............................................................. 82 Figure 4-10 Test results for DMP10M5H50 model. ............................................................ 88

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Figure 4-11 Test results for DMP15M5H50 model. ............................................................ 90 Figure 4-12 Test results for DMP10M10H50 model. .......................................................... 92 Figure 4-13 Test results for DMP15M10H50 model. ........................................................... 94 Figure 4-14 Test results for DLP10M5H50 model. .............................................................. 96 Figure 4-15 Test results for DLP15M5H50 model. ............................................................. 98 Figure 4-16 Test results for DLP10M10H50 model. .......................................................... 100 Figure 4-17 Test results for DLP15M10H50 model. .......................................................... 102 Figure 4-18 Test results for SDSP10M5H25 model........................................................... 111 Figure 4-19 Test results for SDSP10M5H50 model............................................................ 112 Figure 4-20 Test results for SDSP15M5H25 model............................................................ 113 Figure 4-21 Test results for SDSP15M5H50 model............................................................ 114 Figure 4-22 Test results for SDSP10M10H25 model. ......................................................... 115 Figure 4-23 Test results for SDSP10M10H50 model. ......................................................... 116 Figure 4-24 Test results for SDSP15M10H25 model. ......................................................... 117 Figure 4-25 Test results for SDSP15M10H50 model. ......................................................... 118 Figure 4-26 Test results of the vertical and horizontal displacement inside the soil medium in saturated case. ............................................................................... 119 Figure 4-27 The excess pore water pressure-time histories at depth B for SDSP10M5H25 model. ............................................................................................................. 121 Figure ‎4-28 The excess pore water pressure-time histories at depth 2B for SDSP10M5H25 model. ............................................................................................................. 121 Figure 4-29 The excess pore water pressure-time histories at depth B for SDSP10M5H50 model. ............................................................................................................. 121 Figure 4-30 The excess pore water pressure-time histories at depth 2B for SDSP10M5H50 model. ............................................................................................................. 121 Figure 4-31 The excess pore water pressure-time histories at depth B for SDSP15M5H25 model. ............................................................................................................. 122 Figure ‎4-32 The excess pore water pressure-time histories at depth 2B for SDSP15M5H25 model. ............................................................................................................. 122 Figure 4-33 The excess pore water pressure-time histories at depth B for SDSP15M5H50 model. ............................................................................................................. 122 Figure 4-34 The excess pore water pressure-time histories at depth 2B for SDSP15M5H50 model. ............................................................................................................. 122 Figure 4-35 The excess pore water pressure-time histories at depth B for SDSP10M10H25 model. ............................................................................................................. 123 Figure 4-36 The excess pore water pressure-time histories at depth 2B for SDSP10M10H25 model. ............................................................................................................. 123

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Figure 4-37 The excess pore water pressure-time histories at depth B for SDSP10M10H50 model. ............................................................................................................. 123 Figure 4-38 The excess pore water pressure-time histories at depth 2B for SDSP10M10H50 model. ............................................................................................................. 123 Figure 4-39 The excess pore water pressure-time histories at depth B for SDSP15M10H25 model. ............................................................................................................. 124 Figure 4-40 The excess pore water pressure-time histories at depth 2B for SDSP15M10H25 ........................................................................................................................ 124 Figure 4-41 The excess pore water pressure-time histories at depth B for SDSP15M10H50 model. ............................................................................................................. 124 Figure 4-42 The excess pore water pressure-time histories at depth 2B for SDSP15M10H50 model. ............................................................................................................. 124 Figure 4-43 The excess pore water pressure-time histories at depth B for the first fifty msec. from the beginning of the impact force. ............................................... 125 Figure 5-1 A lumped parameter vibrating system, (Das and Romana, 2011). ............... 132 Figure 5-2 The applied load-time history. ...................................................................... 133 Figure 5-3 Relationship between damping ratio and embedment ratio in soil of different soil conditions. ................................................................................................ 151 Figure 5-4

Relationship between damping ratio and diameter of footing in dry and saturated soil. .................................................................................................. 153

Figure 5-5 The effect of impact load energy on damping ratio. ..................................... 154 Figure 5-6 The effect of impact load on the shear modulus. .......................................... 155 Figure 5-7

Relationship between the shear modulus and embedment ratio for different soil conditions. ................................................................................................ 156

Figure 5-8

Relationship between the shear modulus and diameter of footing in dry and saturated soil. .................................................................................................. 157

Figure 5-9 Relationship between the shear modulus and damping ratio for different soil conditions........................................................................................................ 159 Figure 5-10 Relationship between the damping ratio multiplied by shear modulus with frequency ratio. ............................................................................................... 161 Figure 5-11 Relationship between the damping ratio multiplied by stiffness with frequency ratio. ............................................................................................... 162 Figure 5-12 Relationship between the damping coefficient and modulus of subgrade reaction. .......................................................................................................... 163 Figure 5-13 Relationship between the damping coefficient and modulus of elasticity. . 164 Figure 5-14 Relationship between the damping coefficient and shear modulus. ........... 165 Figure 5-15 Relationship between the damping coefficient and frequency ratio (beta). 166 Figure 5-16 Relationship between the modulus of subgrade reaction with frequency ratio (beta). .............................................................................................................. 167 Figure 5-17 Relationship between the shear modulus with frequency ratio ( ). ........... 168

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Figure 5-18 Relationship between the modulus of elasticity with frequency ratio ( ). . 169 Figure A-1 TML small FWD system................................................................................ A-5 Figure A-2 Test and inspection data of small FWD main body KFD-100A. ................... A-6 Figure A-3 Test and inspection data of exclusive indicator TC-351F............................. A-8 Figure A-4 Specification of control unit TMR-211. ...................................................... A-12 Figure A-5 Control unit TMR-211. ............................................................................... A-13 Figure A-6 Test and inspection data of control unit TMR-211. .................................... A-14 Figure A-7 Specification of strain full bridge unit TMR-221. ...................................... A-17 Figure A-8 Strain full bridge unit TMR-221. ................................................................ A-18 Figure A-9 Test and inspection data of Strain Full Bridge Unit TMR-221. ................. A-19 Figure A-10 Connection measurement unit. .................................................................. A-25 Figure A-11 Test and inspection data of ARH-500A. ................................................... A-28 Figure A-12 Test and inspection data of ARH-500A. ................................................... A-34

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LIST OF TABLES

Table ‎3-1: Physical properties of the sand used. ................................................................ 36 Table ‎3-2: Chemical properties of the used sand. .............................................................. 37 Table ‎3-3: Physical properties of the prepared sand used in the tests. ............................... 38 Table ‎3-4: Details of the testing program and test designation. ......................................... 53 Table ‎4-1: Summary of load and displacement amplitudes. ............................................ 104 Table ‎4-2: Details of the effect of impact load footing resting on saturated sandy soil testing results. ................................................................................................. 126 Table ‎5-1: Values of frequencies of the impact ( ), frequencies of the vibration foundation-soil system ( ), frequency ratio (β), and the total masses of the foundation-soil system for all cases of study. ................................................. 136 Table ‎5-2: The characteristics of sandy soil (modulus of subgrade reaction, modulus of elasticity, shear modulus and damping ratio) for tested systems. .................. 142 Table ‎5-3: Empirical equations between soil characteristics of sandy soil under impact load. ................................................................................................................ 169 Table A-1: Standard set. ................................................................................................... A-1 Table A-2: Specifications of small FWD main body KFD-100A. ................................... A-2 Table A-3: Specifications of exclusive indicator TC-351F. ............................................ A-3 Table A-4: Specifications of acceleration transducer ARH-500A. ................................ A-27

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NOTATION

Symbol

Meaning

ARH-A B

Waterproof, low capacity acceleration transducer The diameter of the bearing plate Damping coefficient Coefficient of gradation Coefficient of uniformity Critical damping Embedment ratio Relative density Modulus of elasticity Maximum void ratio Minimum void ratio Excess pore water pressure The falling weight deflectometer Shear modulus Specific gravity Modulus of subgrade reaction Stiffness Small pore water pressure gauge Mass of the soil participating in vibration Mass of foundation and machine+ mass of soil participating in vibration Maximum load Radius of loading plate Time of maximum displacement Total soluble salts Time of the end impulse Measurement/ Analysis software The multi-recorder Control Unit Strain Full Bridge Unit Maximum displacement Displacement

Cc Cu D/B Dr E emax emin EPWP FWD G Gs K k KPE-PB ms mt P r t T.S.S. t1 TC-7100 TMR-200 TMR-211 TMR-221 u(t)

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Symbol ̈ ̇ ̅ β γ γdmax γdmin ν τ

Meaning Acceleration Velocity Undamped natural circular Frequency of the vibration foundation-soil system Circular frequency of the impact Frequency ratio Shear strain Maximum dry unit weight Minimum dry unit weight Poisson‘s ratio Shear stress Damping ratio

Note: Any other notation and abbreviation will be explained wherever it appears in the thesis.

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CHAPTER ONE

1. INTRODUCTION

1.1 GENERAL There are two types of forces/loads that may act on soil or the foundation of soil-structure interaction namely, static and dynamic loads. The differences between two types are inertial force (due to accelerated motion), damping, strain rate effect, and oscillation (stress reversals). Dynamic response of a soil can be caused by different loading conditions such as earthquake ground motion, wave action, blast, machine vibration, and traffic movement. Among these, inelastic response is mainly caused by earthquake motions and accidental blasts. Consequently, more research on nonlinear soil behavior has been carried out to study the behavior of soil under dynamic load and especially the soil dynamic properties (soil damping and shear modulus), very little researches are concerned with soil damping characteristics under impact loads. Damping can be defined as the loss of energy within a vibrating or a cyclically loaded system, usually dissipated in the form of heat. The damping ratio is commonly used in geotechnical engineering as a measure for energy dissipation during dynamic or cyclic loading. Damping can be subdivided into two general categories: internal and external. Internal damping denotes the energy dissipation within the material itself, mainly due to microstructural mechanisms. In soils, this is attributed to many factors including inter-particle sliding and friction, structure rearrangement, and pore fluid viscosity. Internal damping is an inherent material property and is therefore commonly referred to as "material damping". External damping indicates energy losses within a structure or a structural member due to factors other than internal friction. This type of damping is therefore not an inherent property of the material and is commonly called "system damping". Internal damping can be subdivided, in turn, into two categories: intrinsic damping and extrinsic damping. While intrinsic damping describes the energy losses at a specific point within the material, extrinsic damping characterizes the global energy loss within a finite volume (Ashmawy et al., 1995). 1

INTRODUCTION

Chapter One

Soils consist of an assemblage of particles having different shapes and sizes which form a skeleton whose voids are usually filled with water and/or air. Hence, soil in general, must be considered as a one phase (dry soil), two-phase (fully saturated soil) or multi-phase (partially saturated soil) material whose state can be described by the stresses and displacements taking place in each phase (Popescu et al., 2006). The soil condition and its property can be quite significant in the consideration on the problems deal with dynamic load in soil-structure interaction. It is very important to understand the behavior of soil under dynamic loads and its properties, how the waves propagate inside the soil media, and the effect of wave propagation on the soil response and its property, and the wave attenuation mechanism inside the soil. Dynamic response of soil subjected to dynamic loads is governed by the dynamic soil properties. The responses obtained for different dynamic loadings needs to be back analyzed to determine the dynamic soil properties (Kumar et al. 2013). The properties that are most important for dynamic analyses are the stiffness, damping ratio, and unit weight. These enter directly into the computations of dynamic response. In addition, the location of the water table, degree of saturation, and grain size distribution may be important, especially when liquefaction is a potential problem. Almost any structure may be subjected to one form of dynamic loading during its lifetime, so, there is awareness that some structures must be designed for dynamic loading as well as static loading. Examples of dynamic loadings are shown Figure (1-1) (Clough and Penzien, 2003). The problems related to the dynamic loading of soils and earth structures frequently encountered by a geotechnical engineer include, but are not limited to the following (Das and Ramana, 2011): 1. Earthquake, ground vibration, and wave propagation through soils. 2. Dynamic stress, deformation, and strength properties of soils. 3. Dynamic earth pressure problem. 4. Dynamic bearing capacity problems and design of shallow foundations. 5. Problems related to soil liquefaction. 2

INTRODUCTION

Chapter One

6. Design of foundations for machinery and vibrating equipment. 7. Design of embedded foundations and piles under dynamic loads. 8. Stability of embankments under earthquake loading.

Figure ‎1-1 Characteristics and sources of typical dynamic loadings: (a) simple harmonic; (b) complex; (c) impulsive; (d) long-duration (after Clough and Penzien, 2003).

1.2 IMPACT LOAD Machine foundations with impact loads are common powerful sources of industrial vibrations. These foundations are generally transferring vertical dynamic loads to the soil and generate ground vibrations which may harmfully affect the surrounding structures or buildings. Dynamic effects range from severe trouble of working conditions for some sensitive instruments or devices to visible structural damage (Svinkin, 2008a).

3

INTRODUCTION

Chapter One

The impact of a hummer on a foundation produces a transient loading condition in the soil, as shown in Figure (1-2a). The load typically increases with time up to maximum value at t = t1 and drops to zero after that. The case shown in Figure (1-2a) is a single pulse load. A typical loading pattern (vertical acceleration) due to a pile-driving operation is shown in Figure (1-2b) (Das and Ramana, 2011).

Figure ‎1-2 Typical loading diagrams: (a) transient loading due to single impact of a hammer; (b) vertical component of ground acceleration due to pile driving (Das and Ramana, 2011). When dealing with impact force problem, it is very important to understand the complete time-history behavior as shown in Figure (1-3), the engineer is usually interested only in the maximum value of response as represented by Points a, b, c, d, and e (Clough and Penzien, 2003).

Figure ‎1-3 Response ratios due to half-sine pulse (Clough and Penzien, 2003). 4

INTRODUCTION

Chapter One

1.3 WAVE PROPAGATION IN SOIL MEDIA Individual particles are excited by a force which transmits the motion to the adjacent particles. As the motion is transmitted from particle to particle, it causes travelling of waves through the material. Wave propagation is defined as the transportation of energy through a medium (soil) without the transportation of any material (Bodare, 1996). An earthquake produces a motion of the ground by the passage of stress waves that originate from the rupture of the stressed earth mass. Waves may also be generated, both at the surface and within the earth, by artificial means, such as blasting, aircraft landings, and bombardment during war. Thus, when a load is suddenly applied to a body, the whole body is not disturbed at the instant of loading. The parts closest to the source of a disturbance are affected first, and the deformations produced by the disturbance are subsequently spread throughout the body in the form of stress waves (Prakash, 1981). Stress wave propagation is of extreme importance in geotechnical engineering, since it allows determination of soil properties such as modulus of elasticity, shear wave velocity, shear modulus; interpretation of test results of geophysical investigation, numerical formulation of ground response analysis and also helps in the development of the design parameters for earthquake resistant structures (Das and Ramana, 2011). Elastic waves that travel from sources of dynamic and produce elastic soil deformations (ground vibrations) which vary in magnitude depending on the intensity of the propagated waves. The responses of structures to ground vibrations depend on the soil-structure interaction. However, under certain circumstances such as a combination of cohesionless soil layers and ground vibrations, elastic waves can be the reason for plastic soil deformations, e.g. liquefaction, densification and soil settlements. The structural response to ground excitation depends on the soil response to waves propagated from the source and soilstructure interaction, as shown in Figure (1-4) (Svinkin, 2008b).

5

INTRODUCTION

Chapter One

Figure ‎1-4 Illustration of vibration transfer during vibratory sheet pile driving, (after Deckner et al., 2012). In an elastic half‐space, there are three principal waves. These waves have different velocities of propagation. The two main wave types are body waves and surface waves as shown in Figure (1-5). 1. Body waves There are two types of stress waves that can propagate through infinite elastic medium compression waves which are called P-waves and shear waves which are called S-waves; however, they travel at different velocities (Das and Ramana, 2011). Another type of wave that can be present in saturated soil, called a Biot wave. This wave is a combination between a compression wave in a fluid and a compression wave in a soil (Davis, 2010). 2. Surface waves There are two common type of surface waves, Rayleigh waves (R‐waves) which are result of interaction of P‐ and S‐waves with the surface (Kramer, 1996), and love waves which have a motion as same as that of the S-waves and that have no vertical displacement only exist when there is a layer of low velocity overlaying a layer of higher velocity. In a homogenous half‐space no Love‐waves are produced (Auersch, 1995).

6

INTRODUCTION

Chapter One

The generation of the impulse wave by the source can vary from a trip hammer blow or at the ground surface, to a buried explosive charge or to an active varied frequency source vibrator. These sources generate P-waves, S-waves and surface waves at different relative amplitudes depending on the dominant wave in the method used. Vertical impact and shallow explosives are very effective in creating P-waves and will dominate the wave content.

Figure ‎1-5 Displacement characteristics of different wave types, (Deckner, 2013) a) P‐wave (a push‐pull motion in the direction of the wave), b) S‐wave (oscillation perpendicular to the propagation direction), c) R‐wave (a sort of combination of P‐ and S‐waves with ellipsoidal particle motion), and d) Love‐wave a snake‐like movement).

7

INTRODUCTION

Chapter One

1.4 DAMPING OF WAVES IN SOILS In an ideal linear elastic material, stress waves travel infinitely, without amplitude change. However, in real materials this type of behavior is not possible; stress waves attenuate with distance. The attenuation is caused by two sources; expansion of the wave front (geometrical damping) and dissipation of energy within the soil itself (material damping) (Kramer, 1996, Lidén, 2012).

1.5 OBJECTIVES OF THE STUDY The main objectives of this research are to predict the soil damping under impact loads. Emphasis will be made on attenuation of waves induced by impact loads through the soil. To achieve the main objectives of the research, several steps are performed as listed below: •

Conducting an experimental investigation on sandy soils to survey how to study the behavior of these soils under the effect of impact loads with different applied kinetic energies.

•

Studying the behavior of soil damping taking into account several factors: soil density (loose, medium, and dense soil), moisture content, the embedment and diameter of the foundation, and the energy of the impact load.

•

Investigation the effect of footing embedment, and footing area on the soil behavior and its dynamic response.

•

Proposing an expression to estimate the damping ratio of the soil depending on different parameters: sand density, state of sand (dry or saturated), load amplitude, footing embedment, contact area of the foundation).

1.6 SCOPE OF STUDY This research is directed to investigate the dynamic soil properties especially the damping of the soil under impact load. Furthermore, the effects of the impact load on the response of the soil-structure interaction are also investigated. To investigate the soil damping under impact load, falling weight deflectometer (FWD) was implemented to achieve the target. It was used to 8

INTRODUCTION

Chapter One

measure impact load amplitude, acceleration, velocity, and displacement. Also, to measure the response of the soil, accelerometers (ARH-500A Waterproof, and Low capacity Acceleration Transducer), soil pressure gauges (KPE-PB) were installed inside the soil media and the multi-recorder TMR-200 was used to record the results. Seventy two dynamic models were conducted. Sixty four tests were conducted on dry sand models and eight models on fully saturated sand under different conditions (load energy, soil density, area of foundation, and embedment ratio of the foundation).

1.7 OUTLINES OF THE RESEARCH The thesis is presented in seven chapters which are: Chapter One gives an introduction to the research including a brief description of the problem, objectives of the research, scope of the research and thesis outline. Chapter Two reviews the previous studies and research works that are related to dynamic response of machine foundations. Chapter Three presents the experimental program which includes detailed description of the physical models as well as the properties of the soil used in the tests, the devices used in the acquisition system and the methodology adopted in conducting different tests. Chapter Four presents the experimental results and trying to present precise explanations for these results. Chapter Five includes presentation of predictions of dynamic characteristics of sandy soil especially the damping characteristics. Proposed equation was developed to calculate the damping rations as well as proposed procedure for calculation of natural frequency and mass of soil participating in vibration is also presented in this chapter. In Chapter Six, the results of soil damping ratio and its relationship with soil characteristic under different condition are presented. Empirical equations are

9

INTRODUCTION

Chapter One

suggested from relationship between soil characteristics and frequency ratio depending on the obtained results. Finally, in Chapter Seven, a summary for the whole research conclusions, as well as suggestions for future studies and researches are presented.

10

CHAPTER TWO

2. REVIEW OF LITERATURE

2.1 INTRODUCTION In this chapter, the previous studies that are concerned with the dynamic response of dry and saturated soils acted upon by dynamic load of machines are presented. Dynamic soil properties and methods of determination are included. Then vibration attenuation and damping are illustrated. The concept of dynamic soil-structure interaction is also presented herein with different factors and parameters that may affect the analysis of machine foundations are considered in this chapter.

2.2 RESPONSE OF SOIL TO IMPACT LOAD Hammer foundations are example of foundations subjected to impact load. In most cases, the hammer foundations respond to impact loads generated by hammers as a single degree of freedom system, and only vertical foundation vibrations have to be considered for analysis of impact machine foundations as sources of industrial vibrations. A real pressure under column footing can be up two times higher than the static pressure due to vibrations from hammer foundations. Accelerations attenuate very fast with distance from the impact machine foundations. Horizontal vibrations to the exterior structures excite by ground vibrations from impact machine foundations are not dangerous for safety of these structures. However, lowfrequency ground vibrations can excite resonant building vibrations at relatively large distances from the hammer foundations (Svinkin, 2008a). Xue et al. (2012) investigated the damage fatigue problem of a hammer foundation system considered with fatigue damage growth and numerical analysis of the influences of damage and vibration on the machine foundation and the 11

REVIEW OF LITERATURE

Chapter Two

ground soil near the foundation block due to the impact of hammer blows were discussed using the concept of damage mechanics based on the interaction between hammer foundation damage and soil ground damage. From analysis of the simulated results, conclusions could be obtained that when a machine foundation is subjected to strong dynamic loading, the dynamic response increases significantly with the degree of damage and this in turn influences the damage propagation both in the foundation and the soil due to the higher stresses concentrating near the foundation areas. Furthermore, the natural frequencies of the hammer foundation system are reduced significantly with the damage growth and as the damping ratio increases significantly. From the numerical investigation of the dynamic properties of damage in the soil ground, it could be seen that the influences of hammer blows on both surface and depth of the soil near the foundation are significant when damage increases. This provides the possibility to work out a method for controlling the damage and its growth in a damaged material, as well as the dynamic response of a damaged structure.

2.3 PREDICTION OF DYNAMIC SOIL PROPERTIES For the dynamic analysis of machine foundations, soil properties, such as Poisson‘s ratio, dynamic shear modulus, and damping of soil, are generally required (Sitharam et al., 2004, Chowdhury and Dasgupta, 2009). For design of machine foundations subjected to vibration, calculation of ground response during an earthquake, analysis of the stability of slopes during an earthquake, and other dynamic analysis of soil, it is required that the shear modulus and the damping ratio of the soil be known. The shear modulus G and the damping ratio ξ of soils are dependent on several factors, such as type of soil, confining pressure, level of dynamic strain, degree of saturation, frequency, and number of cycles of dynamic load application, magnitude of dynamic stress, and dynamic prestrain (Hardin and Black, 1968). The fundamental soil properties such as the shear modulus, modulus of elasticity, and damping ratio are used in the design and evaluation of the behavior of earthen, earth-supported, and earth-retaining structures. In general, the standard soil tests for the determination of the shear modulus, and damping ratio are as follows:

12


Chapter Two

1. Laboratory tests a. Cyclic triaxial tests b. Cyclic simple shear tests c. Cyclic torsional shear tests d. Resonant column test 2. In situ tests a. Seismic reflection test b. Seismic refraction test c. Seismic cross-hole test d. Seismic down-hole and up-hole test.

2.3.1 Dynamic shear modulus (G) The dynamic shear modulus G is the most important soil parameter influencing the dynamic behavior of the soil-foundation system. Together with Poisson‘s ratio, it is used to calculate soil impedance. The measurement of shear modulus depends mainly on the shear wave velocity in all field tests and resonant column test. This method involves the creation of a transient and/or steady-state stress waves (source) and the interpretation of the arrival time and spectral response at one or more locations (receivers). Although, the cyclic test is classified within dynamic test, but there is a difference between the dynamic and cyclic load by the acceleration effect. The shear modulus of a soil in the cyclic simple shear test can be determined as (Das and Ramana, 2011):

2.1

From cyclic torsional simple shear tests, the shear modulus of a specimen tested can be determined as:

13


Chapter Two

2.2

From a cyclic triaxial test, the magnitude of modulus of elasticity (E) can be obtained, the value of shear modulus can be calculated by assuming a representative value of Poisson‘s ration as follows:

2.3

Chen et al. (1988) measured the plate and soil response under low velocity impact. A free-drop impact system was developed to generate the dynamic loading on the plate free surface. The test set-up to determine the wave speed of the sand is shown in Figure (2-1). Three piezoelectric accelerometers were buried in the sand. Figure (2-1) is the recorded response of the accelerometer at various depths. From this figure, the longitudinal wave speed can be evaluated by dividing the distance between two accelerometers by the difference of the arrival times. The shear wave speed cannot be obtained since the shear wave front has not been separated from the longitudinal wave in the time frame of measurements. Thus, a value for Poisson's ratio had to be assumed to evaluate the Young's modulus and shear modulus.

Figure ‎2-1 Typical time history of acceleration in sand (after Chen et al., 1988).

14


Chapter Two

An increase in void ratio results in a decrease in shear modulus. Void ratio is related to soil density. The higher the void ratio, the looser the soil and lower the density. The shear modulus decreases when the soil density decreases. A special note should be made that the density has a minor effect on shear wave velocity (Richart et al., 1970, Zhenzhong, 2014). With every load cycle, the soil structure will deteriorate, pore water pressure will increase and the shear modulus will decrease. This degradation of the soil depends mainly on the number of cycles, the magnitude of the cyclic strain and the characteristics of the soil material (Holeyman, 2002). Degree of saturation affects shear modulus because it changes the matric suction in the soil (Lu and Likos, 2004). The negative pore water pressure induced by suction binds particles together and strengthens soil. Shear modulus is sensitive to degree of saturation at very low and very high degree of saturation, but remains relatively constant at intermediate saturations (Cho and Santamarina, 2001).

2.3.2 Damping of soil Damping plays a significant role in the overall response of soil structure system. Vibrations propagate from a piece of construction equipment through the ground to a distant vibration-sensitive receiver predominantly by means of Rayleigh (surface) waves and secondarily by body (shear and compressional) waves. The amplitude of these waves diminishes with distance from the source. This attenuation is due to two factors: expansion of the wave front (geometrical attenuation) and dissipation of energy within the soil itself (material damping). The rate of geometrical attenuation depends upon the type of wave and the shape of the associated wave front and is a function of mass and inertia of the system. Material damping is generally thought to be attributable to energy loss due to hysteresis, perhaps caused by internal sliding of soil particles (Amick, 1999, Amick and Gendreau, 2000, Chowdhury and Dasgupta, 2009). For dynamic soil analysis, the use of damping ratio is more common than damping. Damping ratio, ξ, is defined as the ratio of damping to critical damping and is dimensionless. Critical damping is derived from the critical condition between over damped condition and under damped condition in single degree of freedom SDOF system vibration theory (ξ =1). The utility of this parameter is based on the ability of the system to absorb dynamic energy and how this will affect the duration and modes of vibration (Zhenzhong, 2014).

15


Chapter Two

Damping is the general term given to the dissipation of energy during cyclic loading or dynamic loading of an inelastic medium. The soil damping characteristics are usually expressed by the hysteretic or material damping ratio. The hysteresis loop produced from the cyclic loading of a typical soil can be described by the path of the loop itself or by two parameters that describe its general shape. The material damping ratio can be determined from free and forced vibration tests on a system (resonant column test). In a free vibration test, the system is displaced from its equilibrium position, after which the amplitudes of displacement are recorded with time (Das and Ramana, 2011).

√

2.4

where δ is logarithmic decrement, and A is the amplitude. The data is plotted in the time domain, Figure (2-2) shows the decay of amplitude over time.

Figure ‎2-2 Decay of vibration amplitude in time domain (after Zhenzhong, 2014). Usually, the damping ratio can be simplified to Equation (2-5) because the damping ratio in soil is very small.

16


Chapter Two

(

)

2.5

In a forced vibration test, this method is applied to the vibration curve in frequency domain. As it is shown in Figure (2-3), it is easy to find out resonant frequency with maximum vibration amplitude and divide the maximum amplitude with √ , so that it can find two corresponded frequency at both sides of resonant frequency. Then, the damping ratio can be approximately calculated using Equation (2-6) if the damping ratio is small.

2.6

in which and = two frequencies of amplitude frequency plot at which the amplitude is equal to 0.707 , =maximum amplitude, and frequency at which amplitude is maximum (resonant frequency).

Figure ‎2-3 Bandwidth method of determination of damping ratio from forced vibration test (Das and Ramana, 2011).

17


Chapter Two

The damping ratio at a given shear strain amplitude from cyclic tests can be obtained from the hysteretic stress-strain properties as shown in Figure (2-4) as follows:

2.7

Figure ‎2-4 Determination of damping ratio from hysteresis loop (Das and Ramana, 2011). As it is mentioned before, there is a difference between cyclic test and dynamic test, so that the resonant column test is the only dynamic test to measure the material damping ratio directly, but it still the laboratory test never represents the actual state because of the disturbance of the specimen and it cannot represent the situation of soil-structure interaction and geometrical damping. Although in-situ testing is being increasingly used as a tool for measuring various soil parameters, but it cannot measure the damping ratio directly. In-situ techniques are nearly always based on the amplitude attenuation equation for harmonic body wave propagation in an infinite elastic homogeneous medium, and the damping ratio is measured by using imperial equations depending on the attenuation factor of displacement. So, there is a need to measure the damping ratio in the laboratory by using large scale model to examine the soil-structure interaction case.

18


Chapter Two

2.3.2.1 Geometric damping In many applications of damping theory, it is important to estimate the vibrations at a given distance from the source. The geometrical damping property describes the decay of amplitude as a function of distance from the source. The decay occurs due to dispersion of wave energy over an increasing volume (Fekadu, 2010). It has been observed that far away from a source to man-made ground vibration, the Rayleigh wave leads to strong vibrations whereas primary, P- and shear, S- waves vanish. Apart of the explanation may be that the majority of the energy transmitted to the ground by a surface source leads to the generation of Rayleigh waves. Another reason lies in the fact that the P- and S- waves spread over the volume thus forming spherical wave fronts whereas Rayleigh waves are abound to the surface, thus spreading like "rings on water" as shown in Figure (2-5). This implies a faster decay of the energy, and hence the displacement amplitudes in the P- and S- waves with the distance from the source than is observed for the Rayleigh wave. The decay of the amplitude of wave due to spreading of the energy over a larger area or volume is denoted as geometrical damping (Andersen, 2003).

a. P-or S-waves

b. Rayleigh wave.

Figure ‎2-5 Geometrical damping of waves emanating from a point source on the surface of a half-space (Andersen, 2003). 2.3.2.2 Material damping Material damping or energy dissipation is the loss of energy due to internal energy dissipation in the material as the soil particles are moved by the propagating wave. Wave energy is transformed to friction heat, and as the energy is converted and ―lost‖ the amplitude of the wave decreases (Heckman and Hagerty, 1978,

19


Chapter Two

Holmberg et. al., 1984, Kramer, 1996). The big difference between material damping and geometric damping is that in material damping, elastic energy is actually dissipated by viscous, hysteretic, or other mechanisms (Kramer, 1996). Material damping is generally thought to be attributable to energy loss due to hysteresis, perhaps caused by internal sliding of soil particles. Material damping in soil is a function of many parameters, including soil type, moisture content and temperature. Clays tend to exhibit a higher damping than sandy soils (Wiss, 1967). The damping ratio for footings on saturated sand is higher than that on dry sand. When soils deform under dynamic loading, energy loss occurs due to rolling and sliding at particle contacts and the creation and deletion of particle contacts. Damping due to these mechanisms is referred to as ―skeleton damping‖ and is the only source of material damping in dry soils. In saturated soils, additional energy loss occurs due to the relative motion between viscous pore fluid and solid particles (Qiu, 2010). 2.3.2.3 Viscous damping When mechanical systems vibrate in a fluid medium such as air, gas, water and oil, the resistance offered by the fluid to the moving body causes energy to be dissipated. The amount of dissipated energy depends on many factors, such as the size and shape of the vibrating body, the viscosity of the fluid, the frequency of vibration, and the velocity of the vibrating body. In viscous damping, the damping force is proportional to the velocity of the vibrating body (Ostadan et al., 2004).

2.3.3 Poisson’s‎ratio‎(ν) As a material is stretched in one direction, it tends to contract in the other direction. This phenomenon is called the Poisson effect. Poisson‘s ratio is usually denoted as ν and is the ratio between the strain, ɛ, in transverse and axial direction of the applied force (Santamarina et al., 2001). It is a fundamental parameter that is difficult to measure and it is usually estimated in engineering calculations. The ratio of horizontal to vertical strain is required to relate moduli and strains in a solid body (Luna and Jadi, 2000). In general, if there is no direct way of obtaining Poisson‘s ratio, ν, it is noted that the elastic response values are not very sensitive to a wide variation in the

20


Chapter Two

values of Poisson‘s ratio; usually, the following values are taken in the absence of specific test results (Richart et al., 1970, Rao, 2011): ν for cohesionless soils = 0.25 to 0.3 ν for cohesive soils = 0.35 to 0.45 Accordingly, an average value of ν = 0.3 for sandy soils was used in this research.

2.4 DYNAMIC SOIL-STRUCTURE INTERACTION Two important characteristics that distinguish the dynamic soil-structure interaction system from other general dynamic structural systems are the unbounded nature and the nonlinearity of the soil medium. Another effect which is also taken into account concerns the interaction of structure with the foundation, which provides both a more realistic boundary condition as well as the damping model due to radiation effect (Rajashekhar Swamy, 2013). Soil- structure interaction (SSI) problems are thus coupled problems as there exist a coupling between the ―action‖ (e.g. the contact pressure) and the ―reaction‖ (e.g. the displacement of the soil-structure interface) along the contact surface by which the former can only be determined jointly with the latter. Mathematically, the soil-structure interaction problem may be formalized through an integral equation where the unknown function is for instance the contact pressure. The term ―interaction‖ is instructive of the meaning of the phenomenon since the ―action‖ depends upon the ―reaction‖. Interaction problems are numerous in physics and engineering. Some of them may be fairly involved (e.g. the well-known three bodies problem of classical mechanics). In engineering, solution of a SSI problem requires an idealization of the behavior of two systems: ―the structure‖ and the ―soil‖ and also of the boundary conditions of the interface (e.g. unilateral constraint, glued/unglued, smooth interface, etc.) (Kotronis et al., 2013). As far as soil modeling is concerned, the so-called Winkler model is one of the most common idealizations of soil response. In statics, the Winkler model is composed by a continuous distribution of linear/nonlinear, non-connected, springs. Among the major shortcomings of Winkler model is its inability to account for the shear stiffness of soils a fact that is responsible of well-known paradoxes (e.g. a continuous, uniformly-loaded beam resting on a Winkler soil undergoes a uniform 21


Chapter Two

settlement, despite experimental evidence shows that the settlement is larger at the center of the beam if compared with that at the edges) (Kotronis et al., 2013). There are two phenomena that occur due to the presence of a dynamically excited structure at a soil site. These phenomena are widely known as kinematic and inertial effects. Kinematic interaction refers to the modification of ground motion relatively to the free-field motion because of the presence of a foundation (averaging of variable ground motions across the foundation slab, wave scattering, and embedment effects). Parameters are: • Size and shape of foundation, and • Depth of foundation Consideration of kinematic interaction means modification of free-field ground motion to the foundation input motion that is the motion imposed at the base of foundations. Inertial interaction effects include inertia characteristics, stiffness and damping of structure and soil, as these parameters affect the overall response of the soil-foundation-structure system under the seismic excitation at the interface between foundation and soil (Spyrakos, 2008). Chen and Chen, (1996) studied the dynamic soil-structure interaction phenomenon involved in a shallow-buried flexible plate under impact loading. This interaction causes load relief on the buried structure. Plexiglass plates were used as the buried flexible roof structure and low-velocity impact loadings were generated on the soil surface as shown in Figure (2-6). Measurements of the interaction loads between the sand and the plate, and the accelerations of the buried plates were conducted. The stiffness of the buried roofs varies by using three different plate thicknesses. Measured acceleration results for each plate are presented in Figure (27), where it is shown that the stiffer plates have accelerations of lower magnitudes. The lowest peak acceleration is found in the thickest (12.6 mm thick) plate. The first peak durations are also shorter for the stiffer plates, and are typically less than 0.1 ms. The stiffer buried plates are observed to experience less load relief, which is contributed to the effects of separation between the soil and the buried plate. Fattah et al., (2013) and Al-Ameri, (2014) simulated the same problem numerically using finite elements.

22


Chapter Two

Figure ‎2-6 Experimental setup used by Chen and Chen, (1996).

Figure ‎2-7 Accelerations for different plates (after Chen and Chen, 1996).

The analysis of the dynamics interaction of soil and structure changes as the specific physical problem changes. There are several categories of problems in the solution of which soil dynamics plays a fundamental role (Banerjee and Butterfield, 1987): i. Machine foundation vibrations, ii. Pile-driving included settlements and vibrations, iii. Traffic and rail induced vibrations, iv. Densification by vibratory or impact loads, v. Wave induced oscillation of offshore structures,

23


Chapter Two

vi. Effects of explosions, and vii. Earthquake engineering. Soil-structure interaction is affected by many factors related to the foundation and soil condition, so the most important parameters that are studied in this research are as follows:

2.4.1 Effect of foundation embedment Al-Homoud and Al-Maaitah, (1996) found that for forced vibration tests, there is an increase in natural frequency and a reduction in amplitude with the increase in embedment depth. On the other hand for free vibration test, the results showed that for different footing models resting on sandy soil, there is an increase in damping ratio with increasing the depth of embedment as shown in Figure (2-8).

Figure ‎2-8 Effect of embedment ratio (D/B) on damping ratio for footings on surface of dry sand in terms of increase in damping ratio compared to that for surface footing (after Al-Homoud and Al-Maaitah, 1996).

Mandal and Roychowdhury (2008) presented the central response of the square raft under the step loading of 100 kN for different depth to width ratios. It was observed that the increase in the depth of embedment yields response of lesser amplitude and higher frequency. Al-Azawi et al. (2006) performed dynamic analysis of machine foundations under vertical excitations. The effect of embedment upon vertical forced vibration of a rigid footing was investigated theoretically. The stiffness and damping of soil 24


Chapter Two

were considered as frequency dependent. It was found that embedment of foundations has a significant effect on the dynamic response. It causes an increase in the dynamic stiffness and damping coefficients and leads to increase the resonant frequency and to decrease the dynamic response of foundation. For a given size and geometry of the foundation, and the soil properties, the stiffness and damping values for an embedded foundation are much higher than those for a surface foundation. The natural frequency of an embedded foundation will be higher and its amplitude of vibration will be smaller compared to a foundation resting on the surface. Increasing the depth of embedment may be a very effective way in reducing the vibration amplitudes (Prakash and Puri, 2006). As a result, embedment plays a significant role on the overall response of the foundation and needs to be carefully evaluated too (Chowdhury and Dasgupta, 2009). Increasing the depth of embedment of foundation may be a very effective way of reducing the vibration amplitudes. The beneficial effects of embedment, however, depend on the quality of contact between the embedded sides of the foundation and the soil. The quality of contact between the sides of the foundation and the soil depends upon the nature of the soil, the method of soil placement and its compaction and the temperature (Prakash and Puri, 2006). Al-Ameri, (2014) found that embedment of footing in sandy soils leads to a beneficial reduction in dynamic response (displacement and excess pore water pressure) for all soil types in different percentages accompanied by an increase in soil strength and he found that the damping ratio increases by a percentage of about 4.0 to 100 % with embedment of footing inside the soil for dense and loose sand, respectively. In addition, the damping ratio of saturated sand is more than that of dry sand by a percentage of about 40.0 to 50.0 % for embedded models. It was also found from experimental work that the measured amplitude forces of footing placed at the surface is less than or approximately equal to that for embedded footing and this response was attributed to the effect of embedment that produces additional confinement to the footing and increase the stability of the footing during vibrations. Bhandari and Sengupta, (2014) concluded that with increase in depth of embedment, there is decrease in value of total vibration response of foundation in vertical direction. This indicates that foundation should be embedded as deep as possible to take benefit of adjoining confining soil to carry energy waves to reduce the total vibration response. But initially at depth equal to 0.5 m, 1.0 m and 1.5 m,

25


Chapter Two

sudden increase in amplitude of vertical vibration was observed. It is mainly because vertical vibration is due to combined effect of vertical and rocking response. If natural frequency of the foundation in rocking response is considered, it was observed that at depths of 0.5 m, 1.0 m and 1.5 m, the natural frequency of the foundation is very close to operating frequency of machine. This creates possibility of resonance which causes increase in amplitude. This condition is arising because of embedment of foundation. For surface foundation, the foundation is free to oscillate in vertical, horizontal and rocking mode. But after introduction to embedment, the surrounding soil restricts free oscillation in rocking mode due to confinement. This has caused decrease in natural frequency for rocking vibration and it becomes nearly equal to operating frequency of machine. This is going to cause resonance in foundation vibration which will affect life of foundation. Hence, either foundation should be embedded deep in soil or its base area should be increased to avoid value of frequency ratio becoming equal to 1. A dynamic numerical analysis of strip machine foundation was carried out by Fattah et al. (2015). The foundation of multiple thicknesses was placed at different depths above a saturated sand with different states (i.e., loose, medium and dense), and vertical harmonic excitation was applied with buildup of the excess pore water pressure being considered. The dynamic analysis was performed numerically using finite element software, PLAXIS 2D. The soil was assumed as an elastic perfectly plastic material obeys Mohr–Coulomb yield criterion. A parametric study was carried out to evaluate the dependency of machine foundation on various parameters including the amplitude of the dynamic load, the frequency of the dynamic load and the embedment of foundation. It was concluded that increasing the embedment ratio causes a reduction in the dynamic response up to a certain embedment depth; when the depth of embedment increases higher than 1 m, the effect become less pronounced and as strength of the soil increases, the effect of embedment depth in reducing dynamic response will decrease also. The vertical displacements decrease obviously by 46, 37 and 40 % for loose, medium and dense sand, respectively, when increasing the embedment of foundation from 0.5 to 1 m, while when the embedment of foundation increases from 1 to 1.5 m, the vertical displacements for loose, medium and dense sand decrease by 45, 38 and 3 %, respectively. Finally, when the embedment of foundation increases from 1.5 to 2 m, the decrements in vertical displacements are also recorded for loose, medium and dense sand by 42, 36 and 18 %, respectively.

26


Chapter Two

2.4.2 Effect of footing size and shape Al-Homoud and Al-Maaitah, (1996) tested many free and forced vertical vibrations models conducted on surface and embedded models for footings on dry and moist poorly graded sand. They found that the contact area has an important effect on amplitude of motion as shown in Figure (2-9). It was found that there is an increase in natural frequency and a reduction in amplitude with the increase in footing base area. Moreover, it was shown that the circular model footing gives low values of dynamic response in comparison to other models. On the other hand, for free vibration test, the results showed that the circular footing gives the highest value of damping ratio among other footings.

Figure ‎2-9 Effect of footing width on dynamic response in terms of reduction in amplitude (results are given for footing on surface of dry sand for models) (after Al-Homoud and Al-Maaitah, 1996). Kim et al., (2001) used a physical model with distributed spring-dashpot elements to model the interactive mechanical behavior between rigid body and ground. The stiffness of the spring-dashpot element was evaluated through the modal analysis of the observed vibration behaviors. The base size effect was clarified quantitatively on damping ratio on plate against diameter of circular base D or width of rectangular base B in Figure (2-10). From Figure (2-10), it is clear that the damping ratio was affected by the base size. It was found that the damping ratio decreases with the increase in base size. This relationship was different between circular base and rectangular base; damping ratio was lower in rectangular base than in circular base from the test cases conducted in the study. The difference

27


Chapter Two

in damping ratio might be attributed to the strain concentration at the corners of rectangular base and associated hysterical strain energy consumption there.

' Figure ‎2-10 Dependency of distributed spring coefficients and damping ratio on base size; (a) horizontal and vertical spring coefficients; (b) damping ratio (after Kim et al., 2001). Nonlinear three-dimensional finite element analysis was carried out by Fattah et al., (2014) to conduct a numerical investigation of the effect of applied impact load on the foundation based on sandy soil using the finite element method by ANSYS (Version 11) computer program. As a case study, a concrete foundation with dimensions (3×3×0.3) m placed on the soil 15 m deep and 9 m away from the edge of foundation was subjected to impact load. A parametric study was carried out to investigate the effect of several parameters including: foundation dimensions (geometry) and amplitude of impact load. It was concluded that as the foundation thickness increases, the time for maximum displacement to take place increases due to geometrical damping induced by the foundation. When the length of foundation increases, the oscillation of vertical displacement decreases, which means that the foundation becomes more stable.

2.4.3 Effect of soil density Al-Ameri, (2014) concluded form his experimental work that the measured amplitude forces for dense sand are greater than that for the loose sand in the case of embedded footings and footing placed at the surface. This behavior was attributed to the fact that in dense sand, the stiffness or the modulus of elasticity is 28


Chapter Two

greater than that for loose sand. It is valuable to state herein that in dense sand, the dynamic load cell can capture the response of force amplitude faster than the loose sand. The results showed that the displacement amplitude for dry dense sand models is less than that of dry loose sand models for footing placed on surface or embedded footings and he attributed this behavior to the increase in the stiffness and the modulus of elasticity of dense sandy soil that makes the soil stiffer and resist vibrations as well as to it could be attributed to the trench and sidewall effects. Omidvar et al., (2012) investigated the response of sand under high strain rate and they found that several factors that affect the stress-strain response one of them is the initial void ratio whereas loose sand grains have fewer contact points compared to dense sand as shown in Figure (2-11).

Less contact points in loose sand.

More contact points in dense sand.

Figure ‎2-11 The difference between loose and dense soil with contact points. (after Omidvar et al., 2012).

2.4.4 Effect of soil saturation on the foundation response Pore water pressure properties under dynamic loading play significant role on variation of soil deformation and strength. It is the key for dynamic effective stress analysis method (Tang et al., 2014). Soil is a porous medium with voids often filled with a fluid, e.g. water. The behavior of such a two-phase material is important for many engineering problems.

29


Chapter Two

Especially considering dynamic loading, fully saturated soil can show a different behavior compared to dry soil or drained conditions with no development of excess pore pressure. This behavior can be important for the process of pile driving, analysis of liquefaction phenomena as well as earthquake loading (Grabe et al., 2014). Al-Homoud and Al-Maaitah, (1996) found that there is an increase in natural frequency and a reduction in amplitude with the increase in degree of saturation of sandy soil subjected to vertical forced vibration loading. On the other hand, for free vibration test, the results showed that for different footing models resting on sandy soil, there is an increase in damping ratio with increase in the degree of saturation, as well as the damping ratio of footing on saturated sand is higher than that on dry sand. Livaoglu and Dogangun, (2007) investigated the effect of degree of saturation on the shear modulus and damping parameters of sand. It was concluded that the dynamic stiffness and damping characteristic are substantially independent of saturation ratio in the range of 25 to 75%. However, by approaching the full saturation state, the values of modulus fall sharply and damping of loose samples increases dramatically from corresponding values of unsaturated levels. Abd Al-Kaream, (2013) conducted an experimental work to study the effect of vertical vibration of a machine on the response of saturated sand prepared at three relative densities (35, 60 and 80%). The type of dynamic load was cyclic of amplitudes 0.4, 0.6 and 0.8 kN and with frequencies of 0.16, 0.5, 1.0 and 2.0 Hz. From the experimental test results, it was found that, the excess pore water pressure increases with increasing load amplitude, frequency, and relative density. In addition, the rate of change of the pore water pressure increases about 30.0 % as the load amplitude increases from 0.4 to 0.6 kN while it increases only 21.0 % when the load amplitude increases from 0.6 to 0.8 kN under the same frequency and relative density. Al-Ameri (2014) and Fattah et al. (2016) concluded from the experimental physical model that the excess pore water pressure increases with increasing the relative density of the sand, the amplitude of dynamic loading and the operating frequency. In contrast, the rate of dissipation of the excess pore water pressure during dynamic loading is more in the case of loose sand. It was concluded from the numerical analysis that the rate of increase in pore pressure becomes faster and faster with increase in the loading amplitude and increasing the relative density of

30


Chapter Two

sandy soil. The excess pore water pressure ratio is always reduced with depth and the maximum values near the surface of the soil. They found from their experimental results that the maximum values of displacement amplitude for saturated dense sand models are almost more than those for dry dense sand models for surface and embedded footing. They were attributed this behavior to the increase in the pore water pressure during dynamic load that causes reduction in the inter particle forces between solid particles of the soil skeleton hence causing an increase in displacement response. Another reason for this behavior could be the short period during vibration that prevents solid particles from interlocking with each other to rearrange their skeleton to resist the applied dynamic loading. It is expected that for a long period of vibration, the displacement amplitudes of dry and saturated sand could converge to each other.

2.5 CONCLUDING REMARKS From the presented literature review, the following conclusions can be drawn: 1. Very little researches were concerned with soil damping characteristics under impact loads. 2. The response of the soil under the dynamic load is affected by different parameters such as amplitude and type of force, geometry and size of footing, soil state and condition, type of dynamic loading … etc. 3. The behavior of foundation subjected to dynamic loads is highly dependent on the type of machine as well as operating frequency, soil state, and depth of embedment and method of analysis. 4. The measurement of response inside the soil media is not significantly taken into consideration in vertical direction under the dynamic loads or in horizontal direction distance away from the dynamic loads. Accordingly, further experimental investigations are necessary to study the damping characteristics for sandy soil with different mechanical properties under impact loads. In this study, a trial will be made to determine an expression which can be used to estimate the damping ratio of the soil depending on different parameters including: the sand density, state of sand (dry or saturated), load amplitude, distance from the dynamic source, contact area of the foundation, .etc.). 31

CHAPTER THREE

3. EXPERIMENTAL WORK

3.1 INTRODUCTION Physical modeling of interesting geotechnical problems has helped in clarifying behaviors and failure mechanisms of many civil engineering systems. Physical modeling in a laboratory may be used to test the mechanics associated with a range of natural problems that have direct to geotechnical participation together with the mechanisms that set these problems. Close control over material properties and well defined boundary conditions in physical models that declaration parametric studies to be managed (Davies et al., 2010). In this chapter, a small scale model is implemented to simulate a physical model of machine foundation resting on a dry or saturated soil media under impact load. The details of the test specimens, materials, measurement and the outline of the experimental program are described in this chapter. The dynamic system is the soil medium through which waves propagate outward from sources of impact load. The input signal of the system is the impulse response of the ground at the place of installation of a machine foundation; the output signal is the dynamic response of a location of interest situated on a foundation receiving impulse or within the soil stratum. This chapter concentrates on describing the engineering properties of the sand used in the study and to outline the equipment and testing program used in this research. The chapter begins with a description of the soil model and the properties of the sand used, preparation method and calibration of apparatuses used in this study. Descriptions of the impact test procedure, and equipment used to measure the dynamic response inside the soil medium are included. The testing program consists of two major parts. The first part is devoted to dry sand models with total number of tests of 64. The tests were performed in loose, medium, and dense soil state under impact load with different energy forces. Two 32

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footing sizes were adopted and the models were tested at the surface of the soil and at a depth of 0, 0.5B, B, and 2B (where B is the diameter of the footing). The second part is concerned with saturated sand models with total number of 8 models, the same parameters were taken into consideration except that the models were prepared from dense sand only and the footing tested is placed at the surface only. All the experimental tests are conducted at the Soil Mechanics Laboratory of the Civil Engineering Department of the University of Baghdad. The total number of the tests carried out is 72 models.

3.2 DESCRIPTION OF THE SOIL MODEL In this study, systematic experiments are performed to investigate the dynamic response of foundation on a soil medium under the effect of impact load. Figure (3-1) shows the setup that was used to carry out tests, it consists of a steel box with walls made of plates (2 mm) thick and a base as a soil container, and the falling weight deflectometer (FWD) to apply impact loads on the soil model with a base bearing plate of two sizes which is dealt with as a shallow foundation on the soil under impact load. The steel box consists of two parts with dimensions; length of (1200 mm), width of (1200 mm) and height of (800 mm). Each part has a height of (400 mm) and strengthened from the outside with loops of (40 mm) right angle (2 mm) thick spaced at (1330 mm) in the tangential direction.

3.2.1 Raining frame The "raining technique and tamping" used to deposit the soil in the testing tank at a known and a uniform density was adopted in preparing the tested soil. The device consists of a steel hopper, with dimensions of (1200 mm in length, 300 mm in width and 450 mm in height) which is ended with an inclined funnel mounted above the testing tank and used as a hopper to pour the testing material from different heights through two rollers. In order to facilitate the horizontal movement of the steel tank, a simple sliding system was prepared for this purpose.

33

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Two rollers for adjusting the height Sliding rail

Sand raining box

The falling weight deflectometer (FWD) Wires connecting the accelerometer to the data logger

Two part steel container

Steel frame

Figure ‎3-1 The setup of the experimental soil model.

3.2.2 Measurement devices The vertical impact load tests are conducted to simulate different impact loads using different falling masses (5 kg or 10 kg) with different dropping heights (250

34

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mm or 500 mm). Two sizes of the base bearing plate were used; with diameter equal 100 mm or 150 mm. The response of the soil under impact load was measured by installing four accelerometers; two in the vertical direction at depths equal to B and 2B where B is the diameter of the base bearing plate that was used in the test. Other two accelerometers were used in the horizontal direction at determined distances from the source of the impact load at B and 2B from the plate center and buried at a depth of 10 mm from the surface. Two pore water pressure transducers in the condition of saturation were installed in the vertical direction at depths of B and 2B. The system of acquisition data was utilized so that all data could be scanned and recorded automatically, as shown in Figure (3-2). To examine the boundary effect for testing setup, a single test was performed for the case of the highest impact load and it was found that there is no reasonable dynamic response at the boundary of the model.

Accelerometers and pore water pressure data logger TMR-200

Windows-PC to record the results of the TMR-200

The data logger of the impact load TC-351F

Figure 3-2 Data acquisition system. 35

Windows-PC to record the results of the impact load

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3.3 SOIL TYPES UNDER CONSIDERATION The soil used for the model tests is clean sand, passing through sieve No. 10 and retaining on sieve No. 100. It was brought from Kerbelaa (Al-Ekhether region). Figure (3-3) shows the grain size distribution of the test sand. Physical properties of the sand are presented in Table (3-1). Table (3-2) shows the chemical properties to make sure that there are no soluble salts that might affect the results.

Figure 3-3 Grain size distribution of the sand. Table ‎3-1: Physical properties of the sand used. Property

Value

Unit

Standard of the test

Specific Gravity, Gs

2.65

----

ASTM D 854

Coefficient of gradation, Cc

0.79

----

Coefficient of uniformity, Cu

2.94

----

USCS-soil type

SP

----

Maximum dry unit weight, γdmax

17.8

kN/m3

ASTM D 2049-69

Minimum dry unit weight, γdmin

14.9

kN/m3

ASTM D4254-00

Maximum void ratio (emax)

0.7447

----

---------

Minimum void ratio (emin)

0.4605

----

---------

36

ASTM D 422 and ASTM D 2487

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Table ‎3-2: Chemical properties of the used sand. Property

Value

Unit

Standard of the test

Total soluble salts (T.S.S.)

0.35%

----

BS 1377:1990 Part 3

Sulphate content (SO3)

0.23%

----

Earth Manual (1984)

pH value

8.06

----

Chloride content (Cl)

150

mg/l

3.4 SAND PREPARATION METHOD AND CALIBRATION Tamping and raining technique were used to prepare the sand in the test tank. Table (3-3) shows the physical properties of the soil used in the tests. In order to achieve a uniform layer with a desired density, the raining technique was used to prepare the sandy soil model as shown in Figure (3-4a). This process was implemented using a pre-manufactured steel hopper and steel tank (manufactured by Al-Saffar, 2015) through a repeated horizontal movement of the hopper which was controlled manually on the steel tank. The height of drop and the rate of discharge of the sand mainly affect the density of the sand layer in the raining method (Turner and Kulhawy, 1987). Two rollers fixed at the top of the box were used to adjust the height of the raining device to control the height of the free fall of the sand. Several trials with different heights of fall were performed in order to achieve the desired relative density. In each trial, samples collected in small metal tins of known volumes positioned at several places in the test tank were used to check the density. After calculating the density, the void ratios of the sand and the relative density (Dr) as a function of the height of fall, the results are presented in graphs as shown in Figure (3-5). From this figure, the height of fall can be directly interpreted analogous to the required relative density. For dry tests, three types of density were tried; loose, medium and dense. To prepare the loose state of sand with relative density of 30%, the height of the free fall will be 200 mm as obtained from Figure (3-5). After filling the raining box (tank) with sand and choosing the proper height of drop (200 mm), the sand was poured into the test tank. The soil layer was prepared in (6) layers with (100 mm) constant height for each one to attain the last elevation of (600 mm) from the bottom of container, and the same procedure is followed for preparing medium sandy soil with a relative density of 55% depending on Figure (3-5) and choosing the suitable height for free fall of sand, which was 600 mm. For preparation of

37

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dense sand, the same procedure is followed, and then tamping is made with a hammer of 15 kg weight four times at the surface of each layer as shown in Figure (3-4b), the thickness of each layer was 5 cm to prepare dense sand at a relative density of 80%. Table ‎3-3: Physical properties of the prepared sand used in the tests. Property Dense state relative density, Dr, %

Value 82.0

Unit ----

Medium state relative density, Dr, %

55.0

----

Loose state relative density, Dr, %

30.0

----

Dry unit weight in dense state

17.2

kN/m3

Dry unit weight in medium state

16.37

kN/m3

Dry unit weight in loose state

15.66

kN/m3

Saturated unit weight in dense state

20.52

kN/m3

Void ratio at dense state

0.5114

----

Void ratio at medium state

0.5881

----

Void ratio at loose state

0.6601

----

(a)

(b)

Figure ‎3-4 Preparation of sand layer. a) Sand raining technique b) Preparation of dense sand using tamping.

38

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Figure ‎3-5 Density calibration curves for the sand used.

39

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Chapter Three

3.5 IMPACT TEST PROCEDURE In this research, the falling weight deflectometer (FWD) was used to apply impact loads on the soil model. The small FWD system with the standard set with options Measurement/ Analysis Software TC-7100, additional weight (10 kg), and loading plate of 150 mm diameter were used as shown in Figure (3-6). This equipment is capable of measuring the applied impact force-time history, displacement –time history at the soil surface, the modulus of elasticity of the soil, and the coefficient of subgrade reaction. During each test, the acceleration-time history was measured at different depths utilizing accelerometers transducers (ARH-A waterproof, low capacity acceleration transducer (ARH-500A)) type as well as the pore water pressure using a pore-water pressure transducer (KPE-PB small pore water pressure gauge). The basic structure of the FWD system consists of the main unit with built-in accelerometer (KFD-100A) as shown in Figure (3-7) and the indicator (TC-351F) as shown in Figure (3-8). The details of the FWD system are recorded in Appendix A. The indicator records the maximum load value, maximum displacement value and the analyzed coefficient of subgrade reaction and subgrade modulus. Various analysis results can be recorded and stored in the memory card. The data recorded in the memory card can be taken into a PC directly or via the indicator. The indicator system is capable of getting the reading every 0.05 msec. In addition, in this research, the load, acceleration, velocity, displacement waveform, O-P time (in case of load: time between the start point of loading and the maximum value point, in case of displacement: time between the start point of loading of displacement and the maximum value point of displacement), and time product are stored in the PC in addition to the analysis results from the indicator because the measurement/processing software (TC-7100) was used as shown in Figure (3-9). This system drops the weight of the small FWD main body by free fall and measures the impact load and displacement using the load cell and the accelerometer. Displacement is measured by integrating the measurement value in the accelerometer twice. The measurement/processing software (TC-7100) is required for a measurement system that uses a PC. In this system, the data transferred to the indicator is transferred to the PC as it is via the indicator.

40

EXPERIMENTAL WORK

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Carrying case Exclusive indicator TC-351F Small FWD main body KFD-100A The additional weight 10 kg The additional base bearing plate 150 mm

Figure ‎3-6 The small FWD system with the standard set with accessories that were used in tests.

41

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Figure ‎3-7 Small FWD main body KFD-100A.

42

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Figure ‎3-8 Exclusive indicator TC-351F.

43

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Figure ‎3-9 Sample data collected from FWD by using TC-7100 software in impact test.

44

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3.6 MEASUREMENTS OF THE DYNAMIC RESPONSE Figure (3-10) shows four accelerometers (ARH-500A Waterproof, Low capacity Acceleration Transducer) to measure acceleration in the sand and two small soil pressure gauges (KPE-PB) to measure pore water pressure in saturation condition, buried in the sand. They are connected to the multi-recorder TMR-200 to analyze the data measured by the transducers.

(a)

(b)

(c) (d) Figure ‎3-10 Devices for dynamic response measurement. a) The pore water pressure transducer with its catalogue, b) The accelerometer with its catalogue, c) The data logger d) The transducer connection to data logger.

3.6.1 The multi-recorder TMR-200 The multi-recorder TMR-200 series is a small multi-channel data recording system enabling combination of various measuring units according to measurement purposes. The testing objects are analog input such as stress, load, pressure, acceleration, etc. using strain gauges and strain gauge based transducers and digital input/output such as CAN, etc. up to 80 channels. The configuration of TMR-200 series is shown in Figure (3-11). As presented in Figure (3-12) the requirement for this research is Control Unit TMR-211 and Strain Full Bridge Unit TMR-221to read 45

EXPERIMENTAL WORK

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the acceleration and pore water pressure and it is capable of getting the reading every 0.02 msec and it is suitable for the response of the soil under impact load. Figure (3-13) presents sample of the data from one the tests. The details of Control Unit TMR-211 and Strain Full Bridge Unit TMR-221 are recorded in Appendix A.

Figure ‎3-11 System block diagram. Control Unit TMR-211

Strain Full Bridge Unit TMR-221

Figure ‎3-12 The multi-recorder TMR-200

46

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Figure ‎3-13 Data of the multi-recorder TMR-200 from tests.

3.6.2 Acceleration measurement Figure (3-14) shows ARH-A waterproof, low capacity acceleration transducer (ARH-500A). It is installed in water or ground or embedded in concrete. The rigid waterproof structure makes this transducer suitable for use in an adverse

47

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environment or for outdoor use. The details of the ARH-500A transducer are recorded in Appendix A.

Type

Weight

SI

Gravitation

(g)

ARH-500A

AR-50H

18

*Unit: mm Figure ‎3-14 Waterproof, low capacity acceleration transducer (ARH-500A).

3.6.3 Pore water pressure measurement Figure (3-15) shows the KPE-PB small pore water pressure transducer that is used in this research which is suitable to measure pore water pressure underground. This transducer is utilized to measure pore-water pressure inside the soil model at different depths during impact. The dual construction of this transducer is not affected by lateral pressure which offers an accurate measurement. Features: • Small, lightweight • Easy handling • Dual structure not affected by the outer lateral pressure 48

EXPERIMENTAL WORK

Chapter Three

• Replaceable filters The pore pressure gauge enables highly accurate measurement on condition that the mesh in the filter and the space between the pressure-sensing surface and the filter are filled with water. The filter must be installed on the main body of the pressure gauge according to the following procedures. Details of KPE-PB small pore pressure gauge and installation procedure are given in Appendix A. The attached filter is supplied with its mesh ventilated and impregnated with water as follows: 1. Pouring water into a vessel and putting the pressure gauge and packed filter in the water as shown in Figure (3-16). 2. Removing the filter cap. 3. Unpacking the filter and installing it on the gauge. The cap is put on and screwed to fix the filter. The work of the steps 1 to 3 above must be done in the water.

Unit: mm (weight apparatus = 4.5 gm) Figure ‎3-15 KPE-PB small pore pressure gauge.

49

EXPERIMENTAL WORK

Chapter Three

Figure ‎3-16 Pressure gauge.

3.7 TESTING PROGRAM The testing program consists of two major parts. The first part is devoted to dry sand models with a total number of tests of 64. The tests were performed in loose, medium and dense soil state. Two bearing plate sizes, 100 mm or 150 mm were used and the models were tested at the surface of the soil and at a depth of 0.5B, B, and 2B where B is the diameter of the bearing plate as shown in Figure (317). The impact load is applied by dropping the mass of 5 kg or 10 kg from a height of 500 mm or 250 mm. The details of abbreviation for the tested samples as well as example of models naming are explained in Table (3-4). The second part is concerned with saturated sand models with total number of 8 models. The models were prepared from dense sand only using a bearing plate size 100 mm or 150 mm at surface, and the same details for the impact load. In these tests, first, the tank is lined from inside with PVC blanket to prevent leakage of water and then a grid (net) of perforated PVC pipes with (20 mm) in diameter was placed at the base of the tank. As in dry tests, raining technique was used to fill the tank with soil and then tamping with 15 kg hammer at the surface of each 50 mm layer. After that, the soil medium was saturated from the bottom by connecting the PVC net to a water supply, where water flowed through it and streamed in the upward direction. Meanwhile, the flow was maintained uniform and laminar by controlling the head and the discharge of water supply; after that, saturation was achieved by submerging the sand layer for about 10 hours, as shown in Figure (318). Figure (3-19) shows the testing program.

50

EXPERIMENTAL WORK

Chapter Three

(a)

(b)

(c)

(d)

Figure ‎3-17 The state of impact load on the soil model (a) at surface (b) buried at depth 0.5 B (c) buried at depth B (d) buried at depth 2B.

51

EXPERIMENTAL WORK

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(a)

(b)

(c)

(d)

(e)

(f)

Figure ‎3-18 Steps of carrying out test in saturated models a) preparation the physical model for saturated test b) raining technique c) before saturation d) during saturation e) after saturation f) after the test.

52

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Table ‎3-4: Details of the testing program and test designation.

No.

Test designation

Soil state

1

DLSP10M5H50

Dry

Loose

at surface

Size of bearing plate (mm) 100

2

DL0.5bP10M5H50

Dry

Loose

at 0.5 B

100

5

500

3

DLbP10M5H50

Dry

Loose

at B

100

5

500

4

DL2bP10M5H50

Dry

Loose

at 2B

100

5

500

5

DMSP10M5H50

Dry

Medium

at surface

100

5

500

6

DM0.5bP10M5H50

Dry

Medium

at 0.5 B

100

5

500

7

DMbP10M5H50

Dry

Medium

at B

100

5

500

8

DM2bP10M5H50

Dry

Medium

at 2B

100

5

500

9

DDSP10M5H50

Dry

Dense

at surface

100

5

500

10

DD0.5bP10M5H50

Dry

Dense

at 0.5 B

100

5

500

11

DDbP10M5H50

Dry

Dense

at B

100

5

500

12

DD2bP10M5H50

Dry

Dense

at 2B

100

5

500

13

DLSP15M5H50

Dry

Loose

at surface

150

5

500

14

DL0.5bP15M5H50

Dry

Loose

at 0.5 B

150

5

500

15

DLbP15M5H50

Dry

Loose

at B

150

5

500

16

DL2bP15M5H50

Dry

Loose

at 2B

150

5

500

17

DMSP15M5H50

Dry

Medium

at surface

150

5

500

18

DM0.5bP15M5H50

Dry

Medium

at 0.5 B

150

5

500

19

DMbP15M5H50

Dry

Medium

at B

150

5

500

20

DM2bP15M5H50

Dry

Medium

at 2B

150

5

500

21

DDSP15M5H50

Dry

Dense

at surface

150

5

500

22

DD0.5bP15M5H50

Dry

Dense

at 0.5 B

150

5

500

23

DDbP15M5H50

Dry

Dense

at B

150

5

500

24

DD2bP15M5H50

Dry

Dense

at 2B

150

5

500

Soil density

Impact loading state

53

The The dropping height mass of drop (kg) (mm) 5 500

EXPERIMENTAL WORK

Chapter Three

Table 3-4: Continued.

No.

Test designation

Soil state

25

DLSP10M10H50

Dry

Loose

at surface


26

DL0.5bP10M10H50

Dry

Loose

at 0.5 B

100

10

500

27

DLbP10M10H50

Dry

Loose

at B

100

10

500

28

DL2bP10M10H50

Dry

Loose

at 2B

100

10

500

29

DMSP10M10H50

Dry

Medium

at surface

100

10

500

30

DM0.5bP10M10H50

Dry

Medium

at 0.5 B

100

10

500

31

DMbP10M10H50

Dry

Medium

at B

100

10

500

32

DM2bP10M10H50

Dry

Medium

at 2B

100

10

500

33

DDSP10M10H50

Dry

Dense

at surface

100

10

500

34

DD0.5bP10M10H50

Dry

Dense

at 0.5 B

100

10

500

35

DDbP10M10H50

Dry

Dense

at B

100

10

500

36

DD2bP10M10H50

Dry

Dense

at 2B

100

10

500

37

DLSP15M10H50

Dry

Loose

at surface

150

10

500

38

DL0.5bP15M10H50

Dry

Loose

at 0.5 B

150

10

500

39

DLbP15M10H50

Dry

Loose

at B

150

10

500

40

DL2bP15M10H50

Dry

Loose

at 2B

150

10

500

41

DMSP15M10H50

Dry

Medium

at surface

150

10

500

42

DM0.5bP15M10H50

Dry

Medium

at 0.5 B

150

10

500

43

DMbP15M10H50

Dry

Medium

at B

150

10

500

44

DM2bP15M10H50

Dry

Medium

at 2B

150

10

500

45

DDSP15M10H50

Dry

Dense

at surface

150

10

500

46

DD0.5bP15M10H50

Dry

Dense

at 0.5 B

150

10

500

47

DDbP15M10H50

Dry

Dense

at B

150

10

500

48

DD2bP15M10H50

Dry

Dense

at 2B

150

10

500

Soil density


54


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No.

Test designation

Soil state

Soil density


49

DDSP10M5H25

Dry

Dense

at surface


50

DD0.5bP10M5H25

Dry

Dense

at 0.5 B

100

5

250

51

DDbP10M5H25

Dry

Dense

at B

100

5

250

52

DD2bP10M5H25

Dry

Dense

at 2B

100

5

250

53

DDSP15M5H25

Dry

Dense

at surface

150

5

250

54

DD0.5bP15M5H25

Dry

Dense

at 0.5 B

150

5

250

55

DDbP15M5H25

Dry

Dense

at B

150

5

250

56

DD2bP15M5H25

Dry

Dense

at 2B

150

5

250

57

DDSP10M10H25

Dry

Dense

at surface

100

10

250

58

DD0.5bP10M10H25

Dry

Dense

at 0.5 B

100

10

250

59

DDbP10M10H25

Dry

Dense

at B

100

10

250

60

DD2bP10M10H25

Dry

Dense

at 2B

100

10

250

61

DDSP15M10H25

Dry

Dense

at surface

150

10

250

62

DD0.5bP15M10H25

Dry

Dense

at 0.5 B

150

10

250

63

DDbP15M10H25

Dry

Dense

at B

150

10

250

64

DD2bP15M10H25

Dry

Dense

at 2B

150

10

250

65

SDSP10M5H50

Sat.

Dense

at surface

100

5

500

66

SDSP10M5H25

Sat.

Dense

at surface

100

5

250

67

SDSP15M5H50

Sat.

Dense

at surface

150

5

500

68

SDSP15M5H25

Sat.

Dense

at surface

150

5

250

69

SDSP10M10H50

Sat.

Dense

at surface

100

10

500

70

SDSP10M10H25

Sat.

Dense

at surface

100

10

250

71

SDSP15M10H50

Sat.

Dense

at surface

150

10

500

72

SDSP15M10H25

Sat.

Dense

at surface

150

10

250

55


56

Bearing plate size (10 cm)

Falling mass 5 kg from height of drop = 500 mm




Dense


Dense


At (B)

Loose


At (2B)



Medium

Sand State

Dry

Depth of Measurements

Figure ‎3-19 Testing program of the physical model.

At surface

At (0.5 B)



Depth of Measurements

At surface

Saturated

Experimental Program

Chapter Three

EXPERIMENTAL WORK

EXPERIMENTAL WORK

Chapter Three

3.8 TESTING PROCEDURE The following steps describe the testing methodology: 1. Preparing the layers of sand which have a total depth of 400 mm (100 mm for each) as mentioned before depending on the required relative density. 2. Installing the accelerometers at the center of the sand layer in the vertical direction under the centroid of the bearing plate at a depth of (B) or (2B) according to the size of bearing plate. 3. In state of saturation, the pore water pressure gauge is installed at the center of the sand layer in the vertical direction under the centroid of the bearing plate at a depth of (B) or (2B) according to the size of bearing plate. 4. Installing the accelerometer in the horizontal direction near the surface at a depth of (10 mm). 5. Leveling the surface and installing the FWD at the center of the model surface and checking if it is perpendicular to the surface of the model. 6. Adjusting the data logger reader and the exclusive indicator TC-351F of the FWD to get zero readings. 7. Releasing the striking mass and the resulted response will be recorded and presented on a PC. Figure (3-20), shows a schematic diagram showing the longitudinal section of set-up of the physical model, and showing the location of transducers used, while Figure (3-21) shows some steps of preparing the physical model.

57

EXPERIMENTAL WORK

Chapter Three

Personal computer ( setting, monitor, measurement results display, analysis process, etc.)

Analysis of data

The Multi-Recorder TMR-200

2B

Exclusive indicator TC-351F

B 10 mm

B B

B

400 mm

1200 mm

Figure ‎3-20 Longitudinal section of set-up of the physical model.

58

EXPERIMENTAL WORK

Chapter Three

Figure ‎3-21 Steps of preparing the physical model.

59

CHAPTER FOUR

4. PRESENTATION AND DISCUSSION OF TEST RESULTS

4.1 INTRODUCTION A series of (72) laboratory tests were conducted to analyze the response sandy soils subjected to impact loads with different amplitudes. Two sizes bearing plate were used and the plate was placed at the surface of the model embedded at different depths to study the response of soil under impact load different situations.

of of or in

Tests are divided into two main groups, the first group includes (64) models performed on dry sands of different relative densities (dense, medium, and loose), while the second group consists of 8 models performed on saturated dense sand, as mentioned in Chapter Three. Amplitude of the impact load and the corresponding dynamic response of soil including acceleration, velocity, and displacement under the impact load are presented in this chapter. These parameters are expected to affect the soil damping. Displacements of certain points in the vertical and horizontal directions within the soil medium are presented. These points are located at distances of B and 2B from the source of the impact (B = diameter of the plate).

4.2 BEHAVIOR OF DRY DENSE SANDY SOIL UNDER IMPACT Impact tests were carried out on loose, medium, and dense dry sandy soils with different loading parameters. Two bearing plate sizes, 100 mm or 150 mm were used, the plate was placed at the soil surface or at depths of 0.5B, B, or 2B.

60

Chapter Four

PRESENTATION AND DISCUSSION OF TEST RESULTS

The impact load was applied by dropping a mass of 5 kg or 10 kg from a height of 250 mm or 500 mm. Test results are presented in Figures (4-2) to (4-17). These results resemble the load-time history, displacement, acceleration, and velocity as a function of time as shown in parts (a, b, and c) of each figure for each response, respectively. All these responses are measured under the plate directly. Parts (d and e) of each figure show the variation of vertical displacement (beneath the plate) and horizontal displacement (at a distance from the edge of the plate) with the variation of depth of bearing plate (0, 0.5B, B, and 2B). The displacement inside the soil medium was obtained by using FFT analysis and processing software (visual log-data analysis software DFA-7610) to get the velocity and displacement from acceleration results as shown in Figure (4-1). The function of the falling weight deflectometer (FWD) is adopted by dropping freely a mass from a certain height over a plate (used to be at top of soil surface or embedded within the soil) and at the same time recording the impact load-time history developed in the load cell that is attached to the top of the plate. Several notes can be drawn from Figures (4-2) to (4-17), as illustrated in the following sections.

4.2.1 Amplitude of the impact force Results of impact force-time history are plotted and shown in part ―a‖ of each plot. Examining the figures reveals that: a. In case of dense sand, the impact force-time curves are almost ideally harmonic in nature, but of a single pulse, with or without a negative phase (though it is of a very short duration as compared to the positive pulse duration). This negative phase might resemble the rebound of the soil-structure to the falling mass. The system in such a case is acting as an elastic body responding to the impact load as in the case of beam impact or pile impact formula (Clough and Penzien, 2003). b. When the plate diameter is relatively small (100 mm) and the falling mass is relatively low (smaller height of fall), the system behavior can be described as follows: if the plate is mounted at the top of the soil surface, the resulting pulse is of relatively smaller amplitude (smaller maximum impact force) than all other cases of plate depth. For any other depth of the impact plate (0.5B, B, and 2B), the amplitudes and duration of the pulses are almost identical. This leads to an 61

Chapter Four


observation, that is, the active mass of the soil that is contributing to the response is less and no confining is to be encountered and hence, the absorbed energy is expected to be of larger magnitude which results in lower values of the peak impact force amplitude. If the plate diameter is relatively larger (150 mm), the falling mass is greater and the height of fall, at the same time, is also larger (500 mm), the foundation soil system responds similarly to the impact, thus, resulting in almost identical harmonic pulses. This means that the excited soil mass becomes larger enough to overcome the effect of confinement. This behavior can be seen clearly when comparing the impulsive force-time history of two cases at the same time, that is, when the plate diameter is 150 mm, for the same falling mass and height of fall, it is observed that the impulse amplitudes are always larger from those when the plate diameter is only 100 mm. This behavior supports the justification of effects of the active mass reacting to the impact force. As an example, in case of DD2bP10M5H25 model, the maximum peak impact is about 2200 N but for DD2bP15M5H25 model, the peak is 2300 N, for DD2bP10M10H25 model, the maximum peak is almost 3600 N, while for DD2bP15M10H25 model, the peak is about 3700 N. The differences are small but they exist. c. A one common tendency can also be noticed, that is the amplitude of the impact pulse force increases with the increase of the energy of the hammer, i.e., the weight and height of fall. d. The figures also highlight one more tendency, that is, the time for peak impulse to occur, is affected mainly by the magnitude of the falling mass rather than other factors, since it is noticed that the time for peak impulse in case of 10 kg falling mass is always more than that in case of 5 kg by about 12% in most cases. The height of fall has insignificant effect on the peak response time while the plate diameter has a minor effect on this time in case of low energy of the falling mass (250 mm).

4.2.2 Displacement Response The term displacement response refers to top soil surface displacement under impact force in the vertical direction (measured under the center of the impact plate); these responses are shown at the lower segment of part (a) of each figure. There are common trends associated with impact and used to be as a common behavior, these are:

62

Chapter Four


a. Maximum displacement occurs always when the impact plate is located at top soil surface, as the impact plate is embedded at deeper locations, the surface displacement reduces. This tendency is related to the increase in the compressible layer subjected to impact loads. When the embedment depth increased, this will lead to increasing the overburden pressure which in turn leads to rebound and increasing in the points of contact between particles and more uniform contact pressure which results in increasing in the stiffness of the sandy soil. The reductions in the values of displacement when the plate is embedded at 2B as compared to the case when the plate is located at top soil surface ranges from 40-45% in most cases except when the plate diameter is 100 mm and acted upon by 5 kg falling mass from 250 mm height where the reduction in displacement is about 50% for the two cases of plate depths. The same observation was noticed by Al-Homoud and Al-Maaitah, (1996), Mandal and Roychowdhury , (2008), Al-Azawi et al., (2006), Prakash and Puri, (2006), , Bhandari and Sengupta, (2014), and Fattah et al., (2015). They attributed this trend to the trench effect (the normal and shear stresses resulting from the overlying soil restrict the vertical movement and thus reducing the settlement of the foundation base by increasing its vertical stiffness) and sidewall effects (part of the applied load is transmitted to the ground through shear stresses along the vertical sides of the footing when the sides are in contact with the surrounding soil). b. At the same energy of impact, the displacement reduces with the increase of footing diameter (hence, footing area). The reduction in displacement was found to be ranging from 30% to 40% when the plate is located at the top soil surface. If the plate is embedded at a depth of 2B, the difference becomes in the range from 30% to 35%. It is worthwhile to declare that, the area of impact plate is increased by 125% as compared to the reduction in displacements which are mentioned above. Al-Homoud and Al-Maaitah, (1996), and Fattah et al., (2014) found the same trend, that is, when the area of foundation increases, the oscillation of vertical displacement decreases, which means that the foundation becomes more stable and the reduction in response for large contact area is attributed to the reduction in the stresses due to large contact area. Al-Homoud and Al-Maaitah, (1996) found that there is an increase in natural frequency and reduction in amplitude with the increase in footing base area. The increase in natural frequency is verified in this study.

63

Chapter Four


The special notes that are related to the dynamic behavior of foundation-soil system are: a. The peak response occurs during the active phase of the pulse (within the phase of forced vibration), this means that the frequency of the applied load ( ̅) is less than the natural frequency of the soil-foundation system (ω) or (

̅

).

b. When the impact plate is embedded at a depth of 2B below the top surface of the soil, the peak response occurs within a relatively short duration after the peak impulse occurs (at a time lag of 22% to 35% of the time of peak impulse). The maximum phase angle (time lag) occurs always when the impact plate is located at the top surface of the soil. The time lag is found to be ranging from 40% to 65% of the time of peak impulse. The time of the peak impulse range from 8.05 msec to 11.35 msec, and the time of the peak response range from 11.25 msec to 17.0 msec. As an example in case of DDSP10M10H50, the time of the peak impulse is about 9.85 msec, and the time of the peak response is about 16.2 msec, while in case of DD2bP10M10H50 the time of the peak impulse is about 10.1 msec and the time of the peak response is about 13.4 msec. This means that, although the peak response is still within the active phase of the impact but however, the frequency ratio (β) is approaching a value near to 1.0 ( ̅ approaches ). c. It is important to notice from figures in part ―b‖ of each plot that, the pulse wave velocity at the end of the active phase of the impulse is always having low magnitude or sometimes approaching to zero. This means that although the displacement response occurs at the end of the active phase of loading however, the maximum response never occur during the free vibration phase (after the end of the impulse). Such a tendency proves that the dynamic response vanishes quickly due to large absorption of the energy. d. The acceleration of the pulse curve is noticed from figures in part ―c‖ to vanish at the end of the pulse interval in most cases as the pulse velocity dose.

4.2.3 Response inside the soil medium Four accelerometers (ARH-500A) were installed inside the soil to measure acceleration response under the impact load. Two accelerometers were installed at the center of the sand layer in the vertical direction under the centroid of the bearing plate at depths of (B) and (2B) according to the size of the bearing plate, and the 64

Chapter Four


other two accelerometers were installed in the horizontal direction at a depth of 10 mm at a distance of (B) and (2B) from the edge of the bearing plate. From the obtained acceleration, processing software was used to carry out FFT to get the velocity and displacement as shown in Figure (4-1). In this chapter, the maximum amplitudes of displacement of the response of these points in the vertical and horizontal directions were presented to make a comparison of displacement inside the soil under the effect of impact load, and to clarify the response of the soil in the vertical and horizontal directions. In general, at a certain distance in the vertical or horizontal direction within the soil medium as shown in parts d, e, f, g, h, and i of Figures (4-2) to (4-9), it can be seen that the displacement increases with the increase of the amplitude of load in all directions. The main conclusion that is drawn from the experimental work carried out on dry dense sandy soils is that: The displacement response (vertical and horizontal) always follow the same behavior (decreasing with depth irrespective of the depth of impact plate) as the behavior of static load (live loads or surcharge) with depth follow the conventional Bousinesq distribution. Bousinesq equation is used to solve the problem of stress distribution produced at any point in a homogeneous, elastic, and isotropic medium as the result of a point load applied on the surface of an infinity large half space. There are common trends associated with impact which are used to be as a common behavior for both cases (displacement in vertical and horizontal directions inside the soil medium), these are: a. In case of vertical displacement inside the soil medium, the figures reveal that the displacement vanish rapidly with depth; at a depth of B the displacement decreases to about 70% less than the surface displacement. The reduction in displacement at a depth B was found to be about 65% when the plate diameter is 100 mm, but when the area of bearing plate is increased by about 125% for the same impact energy, the reduction will be about 70%. It is noticed that the response becomes of negligible values (10% of the maximum response) at a depth of 2B below the footing (as shown in parts d of each figure). b. The displacement in the horizontal direction at a distance B away from the edge of the bearing plate is reduced by about 75% in case when the plate is at the surface while when the plate is embedded, the reduction in displacement will be about 85% for all conditions of tests on dense soil.

65

Chapter Four


It is clear that the response becomes of negligible values (10% of the maximum response when the plate is placed at the surface and 5% when the plate is embedded in the soil) at a distance of 2B away from the bearing plate (as shown in parts e of each figure). c. It can be seen from parts e, f, g, and h from each figure, that there is a time lag between the displacement in the vertical direction and the horizontal direction, and that is because the P-waves are the fastest, they will arrive first, followed by the S-waves.

66

Chapter Four


(a) Part of the acceleration results

(b) The integration processes to get the velocity and displacement Figure ‎4-1 FFT (Fast Fourier Transform) analysis and processing software.

67


Chapter Four

150

2500

Depth of bearing plate

Depth of bearing plate Acceleration (m/s2)

2000

1500

Force (N)

0 0.5B B 2B

100

0 0.5B B 2B

1000

50

0 0

10

20

30

-50

-100

500

-150

Time (msec)

0

10

0 30

20

1

-500

2

3

4

Time (msec)

0.6 Depth of bearing plate 0 0.5B B 2B

0.4 Velocity (m/s)

0

Displacement directly beneath the plate (mm)

(b) acceleration-time history

0.2

0 0

10

-0.2

(a) force-time history with displacement-time

20

30

Time (msec)

(c) velocity time-history

history Distance away from the edge of the bearing plate (cm)

0

1

2

3

4

0

8

12 Depth of bearing plate 16

0

4

8

12

16

0.4

4

Displacement (mm)

Depth below the center of the bearing plate (cm)

Displacement (mm) 0

0.8

1.2 Depth of bearing plate 1.6

0 0.5B B 2B

0 0.5B B 2B

2

20

(d) displacement variation in vertical direction

(e) displacement variation in horizontal direction

Figure ‎4-2 Test results for DDP10M5H25 model.

68

20


Chapter Four

1.2 Displacement at B below the plate 2B below the plate

0.8

Displacement at a horizontal distance a way from the edge of bearing plate

Displacement (mm)

Displacement (mm)

1.2

0.4

0

-0.4

0

10

20

30

0.4

0

-0.4

40

at distance B at distance 2B

0.8

0

10

Time (msec)

20

30

40

50

40

50

40

50

40

50

Time (msec)

(f) The bearing plate at surface 1.2

Displacement at B below the plate 2B below the plate


Displacement (mm)

Displacement (mm)

1.2

0.8

0.4

0


0.8

0.4

0

0

10

20

30

40

0

10

20

30

Time (msec)

Time (msec)

(g) The bearing plate embedded at 0.5 B depth 1.2 Displacement at B below the plate 2B below the plate 0.8

0.4

0

0

10

20

30


Displacement (mm)

Displacement (mm)

1.2

0.4

0

40


0.8

0

10

Time (msec)

20

30

Time (msec)

(h) The bearing plate embedded at B depth 1.2 Displacement at B below the plate 2B below the plate 0.8

0.4

0

0

10

20

30

40

Time (msec)


Displacement (mm)

Displacement (mm)

1.2


0.8

0.4

0

0

10

20

30

Time (msec)

(i) The bearing plate embedded at 2B depth Figure ‎4-2 continued.

69


Chapter Four

120


2500


Force (N)

Acceleration (m/s2)

0 0.5B B 2B

2000

0 0.5B B 2B

80

1500

40

0 0

5

10

15

20

25

-40

1000

-80

-120

Time (msec)

500

(b) acceleration-time history 10

20

1

2

3

Time (msec)

Depth of bearing plate 0 0.5B B 2B

0.4

0.3

Velocity (m/s)

0

0 30


0.5

0

0.2

0.1

0 0

5

10

-0.1

(a) force-time history with displacement-time

15

20

25

Time (msec)

(c) velocity time-history

history 1

2

Distance away from the edge of the bearing plate (cm)

3

0

10

20

0

0.4

10

20


Displacement (mm)

Depth away from the center of the bearing plate (cm)

Displacement (mm) 0 0

0.8

1.2

Depth of bearing plate 1.6

0 0.5B B 2B

2

30



Figure 4-3 Test results for DDP15M5H25 model.

70

30


Chapter Four

1.2

1.2 Displacement at a horizontal distance a way from the edge of bearing plate

at depth 2B

Displacement (mm)

Displacement (mm)

Displacement at B below the plate 0.8

0.4

0


0.8

0.4

0

0

5

10

15

20

25

0

10

20

30

40

30

40

30

40

30

40

Time (msec)

Time (msec)

(f) The bearing plate at surface. 1.2 Displacement at B below the plate 2B below the plate 0.8

0.4

0

0

5

10

15

20


Displacement (mm)

Displacement (mm)

1.2

0.4

0

25


0.8

0

10

Time (msec)

20

Time (msec)

(g) The bearing plate embedded at 0.5 B depth. 1.2 Displacement at a horizontal distance a way from the edge of bearing plate


Displacement (mm)

Displacement (mm)

1.2

0.8

0.4

0

0

5

10 15 Time (msec)

20

0.4

0

25


0.8

0

10

20 Time (msec)

(h) The bearing plate embedded at B depth. 1.2 Displacement at B below the plate 2B below the plate 0.8

0.4

0

0

5

10

15

20

25


Displacement (mm)

Displacement (mm)

1.2


0.8

0.4

0

0

Time (msec)

10

20

Time (msec)

(i) The bearing plate embedded at 2B depth. Figure ‎4-3 Continued.

71


Chapter Four

150


4000

Force (N)

Acceleration (m/s2)

0 0.5B B 2B

3000

0 0.5B B 2B

100


50

0 0

10

20

30

-50

2000 -100

-150

Time (msec)

1000


20

2

4

6

Time (msec)


0.4

Velocity (m/s)

0

0 30


0.6

0

0.2

0 0

10

-0.2

20

30

Time (msec)

(a) force-time history with displacement-time (c) velocity time-history

history


1

2

3

4

5

0

6

4

8

12

16

0

0

0.4

4

Displacement (mm)


Displacement (mm) 0

8

12

0.8

1.2


Depth of bearing plate 16

1.6

0 0.5B B 2B

0 0.5B B 2B

2

20




72

20


Chapter Four

2.5


2


Displacement (mm)

Displacement (mm)

2.5

1.5 1


1.5 1 0.5

0.5 0

2

0

0

10

20

30

40

0

10

20

30

40

50

40

50

40

50

40

50

Time (msec)

Time (msec)

(f) The bearing plate at surface. 2.5 Displacement at B below the plate 2B below the plate

2

Displacement (mm)

Displacement (mm)

2.5

1.5 1 0.5 0


2


1.5 1 0.5

0

10

20

30

0

40

Time (msec)

0

10

20

30

Time (msec)

(g) The bearing plate embedded at 0.5 B depth. 2.5


2


Displacement (mm)

Displacement (mm)

2.5

1.5 1


1.5 1 0.5

0.5 0

2

0

0

10

20

30

40

0

10

20

30

Time (msec)

Time (msec)

(h) The bearing plate embedded at B depth. 2.5 Displacement at B below the plate 2B below the plate

2 1.5 1 0.5 0


Displacement (mm)

Displacement (mm)

2.5

2


1.5 1 0.5

0

10

20

30

40

0

0

Time (msec)

10

20

30

Time (msec)


73


Chapter Four

120


4000

0 0.5B B 2B

80

0 0.5B B 2B

3000

Force (N)

Acceleration (m/s2)


2000

40

0 0

10

20

30

-40

-80

-120

Time (msec)

1000

(b) acceleration-time history 0.5

10

20

1

2

3

4

Time (msec)

0 0.5B B 2B

0.4

Velocity (m/s)

0

0 30



0

0.3

0.2

0.1

0 0

10

-0.1

20

30

Time (msec)


history


1

2

3

0

4

10

20

0

0

0.4

Displacement (mm)


Displacement (mm) 0

10

20

0.8

1.2



0 0.5B B 2B

0 0.5B B 2B

2

30




74

30



1.2

0.8

0.4

0

0

10

20


Displacement (mm)

Displacement (mm)

Chapter Four

1.2

0.8

0.4

0

30


0

10

Time (msec)

20

30

40

30

40

30

40

30

40

Time (msec)


1.2


Displacement (mm)

Displacement (mm)

(f) The bearing plate at surface.

0.8

0.4

0

1.2

0.8

0.4

0

0

10

20

30


40

0

10

20

Time (msec)

Time (msec)

(g) The bearing plate embedded at 0.5 B depth. 1.2


Displacement (mm)

Displacement (mm)

1 Displacement at B below the plate 2B below the plate

0.8

0.4

0.8


0.6 0.4 0.2

0

0

10

20

30

0

40

Time (msec)

0

10

20

Time (msec)

1


1.2


Displacement (mm)

Displacement (mm)

(h) The bearing plate embedded at B depth.

0.8

0.4

0.8


0.6 0.4 0.2

0

0

10

20

30

40

0

0

Time (msec)

10

20

Time (msec)


75


Chapter Four

200

4000



Acceleration (m/s2)

2000

0 0

10

20

30

-100

1000

-200

0

10

0 30

20

2

-1000

4

6

Time (msec)

Time (msec)



0.6

Velocity (m/s)

0


Force (N)

3000

100

0.4

0.2

0 0

10

-0.2

20

30

Time (msec)


history

Distance away from the edge of bearing plate (cm) 0

Displacement (mm) 1

2

3

4

5

4

8

12

16

0

6

0

0.4 4

Displacement (mm)

Depth away from the center of bearing plate (cm)

0

8

12

0.8

1.2



1.6

0 0.5B B 2B

0 0.5B B 2B

2

20

(e) displacement variation in horizontal direction Figure 4-6 Test results for DDP10M5H50 model.


76

20


Chapter Four


1.5 1 0.5

Displacement (mm)

Displacement (mm)

2


1.6 1.2 0.8 0.4

0 -0.5


0

20

40

0

60

0

20

40

60

80

60

80

60

80

60

80

Time (msec)

Time (msec)

(f) The bearing plate at surface. 2


1.6 1.2 0.8


Displacement (mm)

Displacement (mm)

2


1.2 0.8 0.4

0.4 0

1.6

0

0

10

20

30

0

20

40

Time (msec)

Time (msec)

(g) The bearing plate embedded at 0.5 B depth. 2


1.6


Displacement (mm)

Displacement (mm)

2

1.2 0.8


1.2 0.8 0.4

0.4 0

1.6

0

0

10

20

30

0

20

40

Time (msec)

Time (msec)

(h) The bearing plate embedded at B depth. 2


1.6 1.2 0.8

1.6


1.2 0.8 0.4

0.4 0


Displacement (mm)

Displacement (mm)

2

0

0

10

20

30

40

0

20

40

Time (msec)

Time (msec)


77


Chapter Four

200


4000

0 0.5B B 2B


Acceleration (m/s2)

Force (N)

3000

100

2000

0 0

10

20

30

-100

1000 -200

10

0 30

20

1

-1000

2

3

0.6


0.4

Velocity (m/s)

0


0

Time (msec)


0.2

0 0

10

20

30

4

Time (msec)

-0.2

Time (msec)


history


1

2

3

0

4

10

20

0

0.4

Displacement (mm)



10

20

0.8

1.2



0 0.5B B 2B

0 0.5B B 2B

2

30




78

30


Chapter Four


0.8

0.4

0

-0.4


Displacement (mm)

Displacement (mm)

1.2


0.8

0.4

0

0

10

20

30

40

50

0

10

20

30

40

50

40

50

40

50

40

50

Time (msec)

Time (msec)

(f) The bearing plate at surface. 1.2

Displacement at B below the plate 2B below the plate 0.8

0.4

0


Displacement (mm)

Displacement (mm)

1.2


0.8

0.4

0

0

10

20

30

40

0

10

20

30

Time (msec)

Time (msec)

(g) The bearing plate embedded at 0.5 B depth. Displacement at a horizontal distance 0.8 a way from the edge of bearing plate


Displacement (mm)

Displacement (mm)

1.2

0.8

0.4

0


0.4

0

-0.4 0

10

20

30

40

50

0

10

20

30

Time (msec)

Time (msec)

(h) The bearing plate embedded at B depth. Displacement at B below the plate 2B below the plate 0.8

0.4

0


Displacement (mm)

Displacement (mm)

1.2

0.4

0

0

10

20

30

40


0.8

0

Time (msec)

10

20


79

30

Time (msec)


Chapter Four

200


6000 100


Force (N)

4000

Acceleration (m/s2)

0 0.5B B 2B

0 0

10

20

30

-100

-200

2000 -300

Time (msec)


20

2

4

6

8

Time (msec)

1.2


0.8

Velocity (m/s)

0

0 30


0

0.4

0 0

10

-0.4

20

30

Time (msec)

(a) force-time history with displacement(c) velocity time-history

time history Displacement (mm) 0

2

4

6


8

0

0

8

12

16

0.4

Displacement (mm)

Depth (cm)

4

8

12


4

0

0 0.5B B 2B

0.8

1.2


0 0.5B B 2B

2

20




80

20


Chapter Four

3 Displacement at a horizontal distance a way from the edge of bearing plate


Displacement (mm)

Displacement (mm)

3

2

1

0

0

20

40


2

1

0

60

0

20

Time (msec)

40

60

40

60

40

60

40

60

Time (msec)




Displacement (mm)

Displacement (mm)

3

2

1

0

1

0

0

20

40


2

60

0

20

Time (msec)

Time (msec)

(g) The bearing plate embedded at 0.5 B depth. 3 Displacement at a horizontal distance a way from the edge of bearing plate


Displacement (mm)

Displacement (mm)

3

2

1

0

0

20

40

1

0

60


2

Time (msec)

0

20

Time (msec)

(h) The bearing plate embedded at B depth. 3 Displacement at a horizontal distance a way from the edge of bearing plate


Displacement (mm)

Displacement (mm)

3

2

1

0

0

20

40

60

Time (msec)


2

1

0

0

20

Time (msec)


81


Chapter Four

200


8000

0 0.5B B 2B


6000

Force (N)

100

0 0.5B B 2B

4000

0 0

10

20

30

-100

-200

2000

Time (msec)

(b) acceleration-time history 0.8 10

20

30


0 1 2 3 4

0 0.5B B 2B

0.6

Velocity (m/s)

0

Displacement (mm)

0

0.4

0.2

0 0

5

Time (msec)

10

-0.2

20

30

Time (msec)



2

3


5

0

10

20

0

0.4

Displacement (mm)


0 0

10

20


0.8

1.2


30

0 0.5B B 2B

2




82

30


Chapter Four

1.6

1.6

1.2


0.8

0.4

0

Displacement (mm)

Displacement (mm)


0.8

0.4

0

0

10

20

30

40


1.2

50

0

10

20

30

40

50

40

50

40

50

40

50

Time (msec)

Time (msec)

(f) The bearing plate at surface. 1.6


1.2


Displacement (mm)

Displacement (mm)

1.6

0.8

0.4

0

0.8

0.4

0

0

10

20

30

40


1.2

50

0

10

20

30

Time (msec)

Time (msec)

(g) The bearing plate embedded at 0.5 B depth. 1.6 Displacement at B below the plate 2B below the plate

1.2


Displacement (mm)

Displacement (mm)

1.6

0.8

0.4

0

0

10

20

30

40

0.8

0.4

0

50


1.2

0

10

Time (msec)

20

30

Time (msec)

(h) The bearing plate embedded at B depth. 1.6 Displacement at a horizontal distance a way from the edge of bearing plate


1.2

Displacement (mm)

Displacement (mm)

1.6

0.8

0.4

0

0

10

20

30

40

50


1.2

0.8

0.4

0

0

Time (msec)

10

20

30

Time (msec)

(i) The bearing plate embedded at 2B depth.

Figure ‎4-9 Continued.

83

Chapter Four


4.3 BEHAVIOR OF DRY MEDIUM AND LOOSE SANDY SOILS UNDER IMPACT LOAD Since the height of falling mass was found to have insignificant effects on the global behavior of both impulse-time shape and the displacement (qualitatively not quantitatively), it was preferred to take into account the case of 500 mm height of fall only which is considered as representative for other cases of height of fall (250 mm). Plots of the experiment results are presented in Figures (4-10) to (4-13) for medium sand and (4-14) to (4-17) for loose sand. Examinations of these figures show the behavior presented here after: 1. The impact load-time history is also of a single pulse but has no ideal sine shape. In case of medium sand, it almost vanishes or becomes of negligible value at the end of the impulse-time history when the impact plate is embedded at large depths while it ends at a magnitude equals or near to the magnitude of the weight of the falling hammer when the footing is placed at the top surface or embedded at a shallow depth. 2. When the impact load acts on a footing resting on loose sand, the impulse forcetime history ends at values near to the weight of the falling hammer irrespective of other parameters (magnitude of the hammer weight or the footing diameter). This tendency ensures the idea that, no reflection of the impulsive wave from the far boundaries is encountered (for both medium and loose sands), so that, the boundaries act as a free support (at the base) having no or negligible stiffness. 3. The amplitude of the impulsive wave was found to be: a. Decreasing as the density of supporting medium (soil) decreases. The lowest amplitudes of the impulsive wave are found to be in models of loose soil for all cases of impact plate diameter, weight of the falling mass and height of fall of the hammer. In case of 100 mm diameter of impact plate, the reduction in impulse force amplitude from dense to loose sand ranges between 60%-70% (keeping other parameters unchanged) while in case of 150 mm impact plate, the reduction is about 45%-55%. This tendency is a common behavior of impulsive force amplitude magnitude since the magnitude of impulse is stiffness dependent. Stiffer soils tend to act as solids with high rebound capability. 84

Chapter Four


b. As the impact plate diameter increases, the magnitude of the impulsive amplitude increases also by about 30-40% in case of medium sand and by about 50-60% in case of loose soil. This tendency is attributed to the fact that the soil stiffness is related to two factors, degree of confinement which increases with the footing area and the magnitude of the excited mass which depends, also upon the footing area. c. As the energy of impact increases (due to an increase in the weight of the falling hammer), the amplitude of the impact increases also. A 100% increase in the weight results in an increase in the impulse amplitude by about 55-80% in case of medium sand and by about 45-55% in case of loose sand. This tendency is related to the fact that the impulse amplitude is energy dependent. The energy, meanwhile, decreases as the density also decreases that is, looser soils contribute more in energy dissipation though the magnitude of dissipation is less than the increase associated with the mass of falling hammer. 4. Response of soil (displacement) during impulse: Figures of soil-foundation response show that: a. The maximum response occurs either at the end of impulse time interval or within the free vibration phase (after vanishing of impulse). This behavior could be justified to the fact that the frequency ratio (β) (which is equal to ̅

( ) that is, frequency of applied load to the natural frequency of the foundation soil system) becomes more than 1.0. Since ̅ is almost unchanged or its variation is minor; therefore, ω might be decreasing as the soil becomes more loose. Such a justification should follow that the stiffness reduces in large magnitudes as the soil density reduces. This might be a reasonable justification which will be highlighted in the following chapter. Such a tendency results in lower natural frequency of the soil-foundation system and therefore, ̅ will be larger and hence β becomes larger than unity. b. An important note can be highlighted from the plots, that is, higher displacement response is found to occur when the impact plate (footing) is placed at the top surface of the supporting soil (medium or loose). As the footing becomes deeper, the displacement response decreases down to a depth equals to twice the footing width (2B). This can be justified according

85

Chapter Four


to the degree of compaction of soil and hence, the excited soil mass during impact; that is, as the soil becomes looser, the excited mass reduces significantly while for deeper footing, the soil is naturally compacted and the excited mass starts to increase and the soil becomes more stiff. These results are compatible with the findings of Al-Homoud and AlMaaitah, (1996) found that for forced vibration tests, there is an increase in natural frequency and a reduction in amplitude with the increase in embedment depth. The results are also in a greement with those of Mandal and Roychowdhury (2008) who presented the central response of the square raft under the step loading of 100 kN for different depth to width ratios. It was observed that the increase in the depth of embedment yields response of lesser amplitude and higher frequency. c. One more notice is also recorded, that is, at the end of the impulsive-time period, the soil particles; still possess both velocity and acceleration in most cases. This behavior can result in higher responses (displacements) during the free vibration phase. This tendency was concluded earlier at this paragraph. 5. Finally, the vertical displacements within the soil medium are found to decrease with depth and follow the conventional Bousinesq equation, which is, following different paths, therefore they reduce with depth. This tendency is related to the larger void ratio which increases according to the results in unpredictable mechanisms of soil particles during impulse wave propagation. Ultimately, the responses were noted to vanish at depths below the footing especially at a depth equals to 2B by about 85-90% reduction in displacement caused by the impact load. As shown in parts (d, e, f, g, h, and i) from Figures (4-10) to (4-17) there are common trends associated with impact for both cases (displacement in vertical and horizontal directions inside the soil medium) for both medium and loose sand, these are: a. In case of loose and medium sand, the reduction in the vertical displacement inside the soil medium at a depth B was about 30-55% for medium sand and 25-30% for loose sand and that when the plate diameter is 100 mm and falling mass 5 kg from a height of 500 mm. When the falling weight is increased 100% (falling mass 10 kg from a height of 500 mm), the reduction will be about 20-30% for medium sand and by about 10-13% for loose sand, but when the area of bearing plate increases to about 125 % for the same

86

Chapter Four


force energy, the reduction will be about 35-45% and 25-40% for medium and loose sand, respectively (as shown in parts d of each figure). It is important to notice that the reduction in vertical direction in dense soil was higher than the reduction in loose and medium soil and it is about 50% and that is due to the fact that the void ratio of dense soil is smaller than in medium or loose sand. b. In general, the reduction in displacement in the horizontal direction at a distance B away from the edge of the bearing plate was of negligible values (10% of the maximum response when the plate is at the surface and 5% when the plate is embedded in the soil). Finally, the peak amplitudes of impulsive force during impact, impact duration and maximum responses together with their duration are summarized in Table (4-1).

87


Chapter Four

200

2000



Acceleration (m/s2)

100

1200

0 0

10

20

30

-100

800 -200

400

Time (msec)


10

20

30 4

8

12

16

20

Time (msec)


1.2

Velocity (m/s)

0


1.6

0

0.8

0.4

0 0

10

-0.4

20

30

Time (msec)



4

8

12

16

Distance away from the edge of bearing plate (cm)

20

0

0

4

8

12

16

0

4

Displacement (mm)


Force (N)

1600

8

12

2

4


16

6

20



Figure 4-10 Test results for DMP10M5H50 model.

88

20


Chapter Four



12

Displacement (mm)

Displacement (mm)

16

8

4

0

2

0

0

10

20

30

40


4

50

0

20

40

60

80

Time (msec)

Time (msec)



12


Displacement (mm)

Displacement (mm)

16

8

4

0


4

2

0

0

10

20

30

40

50

0

20

40

60

40

60

40

60

Time (msec)

Time (msec)



12


Displacement (mm)

Displacement (mm)

16

8

4

0

0

10

20

30

40


4

2

0

50

0

20

Time (msec)

Time (msec)



12

Displacement (mm)

Displacement (mm)

16

8

4

0

0

10

20

30

40

50


4

2

0

0

Time (msec)

20

Time (msec)


89


Chapter Four

150


2500


Force (N)

Acceleration (m/s2)

0 0.5B B 2B

2000

0 0.5B B 2B

100

1500

50

0 0

10

20

30

-50

1000

-100

500

Time (msec)



10

0 30

20

4

8

12

Time (msec)

0 0.5B B 2B

0.8

Velocity (m/s)

0


0

0.6

0.4

0.2

0 0

10

-0.2

20

30

Time (msec)


time history


Displacement (mm) 2

4

6

8

10

0

12

10

20

0

Displacement (mm)


0 0

10

20


2

4


0 0.5B B 2B

0 0.5B B 2B

30

6




90

30


Chapter Four

2


8

Displacement (mm)

Displacement (mm)

10

6 4


1.2 0.8 0.4

2 0


1.6

0

0

10

20

30

40

50

0

10

20

30

40

50

40

50

40

50

40

50

Time (msec)

Time (msec)

(f) The bearing plate at surface 2 Displacement at a horizontal distance a way from the edge of bearing plate


8

Displacement (mm)

Displacement (mm)

10

6 4


1.2 0.8 0.4

2 0

1.6

0

0

10

20

30

40

50

0

10

20

30

Time (msec)

Time (msec)

(g) The bearing plate embedded at 0.5 B depth 2 Displacement at B below the plate 2B below the plate

8

Displacement (mm)

Displacement (mm)

10

6 4


1.6 1.2 0.8 0.4

2 0


0

10

20

30

40

0

50

0

10

Time (msec)

20

30

Time (msec)

(h) The bearing plate embedded at B depth 2


8


Displacement (mm)

Displacement (mm)

10

6 4


1.2 0.8 0.4

2 0

1.6

0

0

10

20

30

40

50

0

10

Time (msec)

20

(i) The bearing plate embedded at 2B depth Figure ‎4-11 Continued

91

30

Time (msec)


Chapter Four

300


4000


Force (N)

3000

0 0.5B B 2B

200

0 0.5B B 2B

2000

100

0 0

10

20

30

-100

-200

1000

Time (msec)


20

5 10 15 20 25

Time (msec)

0 0.5B B 2B

2

1.5

Velocity (m/s)

0



0 30

0

1

0.5

0 0

10

-0.5

20

30

Time (msec)



10

15


25

0

4

8

12

16

0

1

4

Displacement (mm)


0 0

8

12


0 0.5B B 2B

2

3

4


20

0 0.5B B 2B

6




92

20


Chapter Four


16

Displacement (mm)

Displacement (mm)

20


8


4

2

4 0

0

20

40

0

60

0

20

Time (msec)

40

60

80

Time (msec)

(f) The bearing plate at surface. 6 Displacement at a horizontal distance a way from the edge of bearing plate

16 12


8

Displacement (mm)

Displacement (mm)

20


4

2

4 0

0

0

20

40

60

0

20

40

60

80

100

80

100

80

100

Time (msec)

Time (msec)



16

Displacement (mm)

Displacement (mm)

20

12 8


4

2

4 0

0

0

20

40

60

0

20

40

60

Time (msec)

Time (msec)



16

Displacement (mm)

Displacement (mm)

20

12 8


4

2

4 0

0

20

40

60

Time (msec)

0

0

20

40 60 Time (msec)


93


Chapter Four

200


4000

0 0.5B B 2B


Acceleration (m/s2)

Force (N)

3000

100

2000

0 0

10

20

30

-100

1000

-200

Time (msec)

0

10

0 30

20

4

8

12

16

Time (msec)


1.6

0 0.5B B 2B

1.2

Velocity (m/s)

0



0.8

0.4

0 0

10

-0.4

20

30

Time (msec)


time history Displacement away from the edge of bearing plate (mm) 0

4

8

12


16

0

0

10

20

Displacement (mm)

0

Depth (cm)

10

20


2

4


0 0.5B B 2B

0 0.5B B 2B

30

6




94

30


Chapter Four


12

Displacement (mm)

Displacement (mm)

16

8

4

0

0

10

20

30

40


3

2

1

0

50


0

20

Time (msec)

40

60

80

60

80

60

80

60

80

Time (msec)



12

Displacement (mm)

Displacement (mm)

16

8

4

0

0

10

20

30

40

2

1

0

50


3

0

20

Time (msec)

40

Time (msec)



12


Displacement (mm)

Displacement (mm)

16

8

4

0

2

1

0

0

10

20

30

40


3

50

0

20

40

Time (msec)

Time (msec)



12

Displacement (mm)

Displacement (mm)

16

8

4

0

0

10

20

30

40

50


3

2

1

0

0

Time (msec)

20

40

Time (msec)


95


Chapter Four

300


1600

0 0.5B B 2B


1200

Force (N)

200

0 0.5B B 2B

800

100

0 0

10

-100

400

20

30

Time (msec)


20

5 10 15 20 25

Time (msec)

0 0.5B B 2B

1.6

Velocity (m/s)

0

0 30



0

1.2

0.8

0.4

0 0

10

20

30

Time (msec)



5

10

15

20


25

0

4

8

12

16

0

4

Displacement (mm)


0

8

12

16

2

4


Depth of bearing plate 0 0.5B B 2B 6

20



Figure 4-14 Test results for DLP10M5H50 model.

96

20


Chapter Four

4


16


Displacement (mm)

Displacement (mm)

20

12 8


3

2

1

4 0

0

0

20

40

60

80

0

20

40

60

80

100

80

100

80

100

80

100

Time (msec)

Time (msec)



16

Displacement (mm)

Displacement (mm)

20

12 8 4 0

0

20

40

60

2

1

0

80


3

0

20

40

60

Time (msec)

Time (msec)



16

Displacement (mm)

Displacement (mm)

20

12 8


3

2

1

4 0

0

0

20

40

60

80

0

20

40

60

Time (msec)

Time (msec)

(h) The bearing plate embedded at B depth. 4 Displacement at B below the plate 2B below the plate

16

Displacement (mm)

Displacement (mm)

20

12 8 4 0

0

20

40

60

80

Displacement at a horizontal distance a way from the edge of bearing plate at distance B 3 at distance 2B 2

1

0

0

20

Time (msec)

40

60

Time (msec)


97


Chapter Four

300


2000


1200

100

0

800

0

10

-100

400

20

30

Time (msec)

0

10

0 30

20

-400

4

8

12

16

Time (msec)


1.6

Velocity (m/s)

0



1.2

0.8

0.4

0 0

10

20

30

Time (msec)



4

8

12


16

0

0

10

20

0

Displacement (mm)


Force (N)

200

0 0.5B B 2B

1600

0 0.5B B 2B

10

20

2

4


Depth of bearing plate 0 0.5B B 2B 6

30




98

30


Chapter Four



Displacement (mm)

Displacement (mm)

12

8

4

0

0

10

20

30

40

2

1

0

50


3

0

20

Time (msec)

40

60

80

60

80

60

80

60

80

Time (msec)



Displacement (mm)

Displacement (mm)

12

8

4

0

2

1

0

0

10

20

30

40


3

50

0

20

40

Time (msec)

Time (msec)



Displacement (mm)

Displacement (mm)

12

8

4

0

0

10

20

30

40

2

1

0

50


3

0

20

Time (msec)

40

Time (msec)




Displacement (mm)

Displacement (mm)

12

8

4

0

2

1

0

0

10

20

30

40

50


3

0

20

40

Time (msec)

Time (msec)


99


Chapter Four

400


2000

0 0.5B B 2B

300

0 0.5B B 2B

1600

1200 Force (N)

Acceleration (m/s2)


100

0 0

800

10

20

30

-100

-200

400

Time (msec)

0

10

0 30

20

-400

10

20

30

40

Time (msec)

2.5


2

Velocity (m/s)

0



1.5

1

0.5

0

0

10

20

30

Time (msec)



20

30


40

0


4

8

12

16

0

0 0.5B B 2B

Displacement (mm)


0 0

8

12

2

4


16

6

20




100

20


Chapter Four


Displacement (mm)

Displacement (mm)

30

20 Displacement at B below the plate 2B below the plate 10

0

0

20

40

60

80

2

0

100


4

0

20

40

Time (msec)

60

80

100

Time (msec)

(f) The bearing plate at surface. Displacement at a horizontal distance a way from the edge of bearing plate

Displacement (mm)

Displacement (mm)

4


30

20

10

0

0

20

40

60

2

1

0

80


3

0

20

Time (msec)

40

60

80

60

80

60

80

Time (msec)

(g) The bearing plate embedded at 0.5 B depth. Displacement at a horizontal distance a way from the edge of bearing plate

Displacement (mm)

Displacement (mm)

4


30

20

10

0

0

20

40

60

2

1

0

80


3

Time (msec)

0

20

40

Time (msec)

(h) The bearing plate embedded at B depth. Displacement at a horizontal distance a way from the edge of bearing plate

Displacement (mm)

Displacement (mm)

4


30

20

10

0

0

20

40

60

80


3

2

1

0

0

Time (msec)

20

40

Time (msec)


101


Chapter Four

300


3000


Force (N)

Acceleration (m/s2)

0 0.5B B 2B

2000

0 0.5B B 2B

200

100

0 0

10

20

30

-100

1000 -200

Time (msec)


10

20

10

20

30

Time (msec)

0 0.5B B 2B

1.6

Velocity (m/s)

0


0 30


0

1.2

0.8

0.4

0 0

10

20

30

Time (msec)



10

15

20

25


30

0

10

20

10

20

0

Displacement (mm)


0 0


2

4


0 0.5B B 2B

0 0.5B B 2B 6

30




102

30


Chapter Four



16

Displacement (mm)

Displacement (mm)

20

12 8 4 0

0

20

40

60

2

1

0

80


3

0

20

Time (msec)

40

60

80

60

80

60

80

60

80

Time (msec)



16


Displacement (mm)

Displacement (mm)

20

12 8


3

2

1

4 0

0

0

20

40

60

0

20

40

Time (msec)

Time (msec)



16

Displacement (mm)

Displacement (mm)

20

12 8 4 0

0

10

20

30

40

2

1

0

50


3

Time (msec)

0

20

40

Time (msec)



16


Displacement (mm)

Displacement (mm)

20

12

8


3

2

1

4

0

0 0

10

20

30

40

50

0

Time (msec)

20

40

Time (msec)


103


Chapter Four

Table ‎4-1: Summary of load and displacement amplitudes. No.

Test Designation

Max. amplitude of load (N)

Duration of load (msec)

Max. displacement (mm)

Time of max. displacement (msec)

1

DLSP10M5H50

1069

26.35

24.9

26.35

2

DL0.5bP10M5H50

1075

25.95

21.693

25.95

3

DLbP10M5H50

1190

25.60

19.6

25.6

4

DL2bP10M5H50

1244

25.70

16.007

25.55

5

DMSP10M5H50

1316

25.35

18.4

25.35

6

DM0.5bP10M5H50

1359

25.00

14.495

25

7

DMbP10M5H50

1467.4

24.70

11.3

21.95

8

DM2bP10M5H50

1575

24.69

10.1

21.25

9

DDSP10M5H50

2829

19.10

5.399

14.45

10

DD0.5bP10M5H50

3173

17.95

3.877

12.55

11

DDbP10M5H50

3293

17.65

3.397

12.1

12

DD2bP10M5H50

3409

17.20

2.934

11.65

13

DLSP15M5H50

1730

24.25

15.158

24.25

14

DL0.5bP15M5H50

1740

24.15

12.31

24.2

15

DLbP15M5H50

1766

23.95

11.476

24.15

16

DL2bP15M5H50

1813

23.75

11.015

23.95

17

DMSP15M5H50

1977

24.00

10.151

24

18

DM0.5bP15M5H50

1979

23.85

8.332

21.2

19

DMbP15M5H50

2088

23.75

7.726

20.5

20

DM2bP15M5H50

2144

23.5

6.785

19

21

DDSP15M5H50

3320

18.65

3.509

13.1

22

DD0.5bP15M5H50

3408

17.80

2.533

12.4

23

DDbP15M5H50

3571

17.00

2.188

11.5

24

DD2bP15M5H50

3692

16.40

1.988

10.95

104


Chapter Four

Table ‎4-1: Continued. No.

Test Designation





25

DLSP10M10H50

1550

25.3

35.511

25.3

26

DL0.5bP10M10H50

1603.35

24.95

32.16

24.95

27

DLbP10M10H50

1728

25.00

30.406

24.85

28

DL2bP10M10H50

1798

25.00

28.34

24.6

29

DMSP10M10H50

2280

24.90

24.204

24.9

30

DM0.5bP10M10H50

2406.8

24.45

19.644

24.45

31

DMbP10M10H50

2709

24.25

17.1627

24.25

32

DM2bP10M10H50

3004

24.35

14.779

23.45

33

DDSP10M10H50

5166

23.80

6.755

16.2

34

DD0.5bP10M10H50

5457

23.20

6.182

15.4

35

DDbP10M10H50

5636

22.45

5.271

14.35

36

DD2bP10M10H50

5669

22.00

4.331

13.4

37

DLSP15M10H50

2467

24.10

25.766

24.1

38

DL0.5bP15M10H50

2617

23.70

21.656

24

39

DLbP15M10H50

2731

23.95

20.637

23.95

40

DL2bP15M10H50

2762

23.75

18.717

23.75

41

DMSP15M10H50

3080

24.00

15.141

23.5

42

DM0.5bP15M10H50

3241

23.50

12.995

23.35

43

DMbP15M10H50

3553

23.45

10.777

21

44

DM2bP15M10H50

3878

23.35

9.179

19.85

45

DDSP15M10H50

5753

22.45

4.361

14.25

46

DD0.5bP15M10H50

6005

21.65

3.754

13.55

47

DDbP15M10H50

6102

22.25

3.3885

13.25

48

DD2bP15M10H50

6300

21.30

2.997

12.65

105


Chapter Four

Table ‎4-1: Continued. No.

Test Designation





49

DDSP10M5H25

1840

19.00

3.964

14.85

50

DD0.5bP10M5H25

2212

17.85

2.806

12.55

51

DDbP10M5H25

2261

17.75

2.402

12.00

52

DD2bP10M5H25

2270

17.70

1.980

11.6

53

DDSP15M5H25

2113

17.95

2.700

13.55

54

DD0.5bP15M5H25

2240

17.55

1.790

12.00

55

DDbP15M5H25

2300

17.25

1.550

11.65

56

DD2bP15M5H25

2378

16.90

1.303

11.25

57

DDSP10M10H25

3082

25.20

5.102

17.00

58

DD0.5bP10M10H25

3377

24.00

3.884

15.20

59

DDbP10M10H25

3532

23.95

3.300

14.50

60

DD2bP10M10H25

3606

23.70

2.772

13.85

61

DDSP15M10H25

3581

24.65

3.117

14.95

62

DD0.5bP15M10H25

3553

24.25

2.364

14.15

63

DDbP15M10H25

3616

24.05

2.024

13.75

64

DD2bP15M10H25

3716

23.95

1.800

13.25

4.4 SUMMARY OF MAJOR CONCLUSIONS RELATED TO DRY SAND BEHAVIOR UNDER IMPACT 1. In case of dense sand, the impact force-time curves are almost ideally harmonic in nature; but of a single pulse, with a negative phase. This negative phase might resemble the rebound of the soil-structure to the falling mass; the system in such a case is acting as an elastic body responding to the impact load. In case of medium sand, no such tendency is being observed, the impulse force-time pulse is no longer being a sine pulse, and that is, the soil is acting as a visco-elastic medium. The impact forces do not end to zero but instead end to values equal to the static weight of the falling mass or less, that is, no rebound.

106

Chapter Four


2. The frequency ratio becomes more than 1.0 in case of medium or loose sand because the maximum response occurs either at the end of impulse time interval or within the free vibration phase (after vanishing of impulse), while in case of dense sand, the peak response occurs during the active phase of the pulse (within the phase of forced vibration). This means that the frequency of the applied load ( ̅) is less than the natural frequency of the soil-foundation system or

3. For all conditions of the soil, the maximum displacement occurs always when the impact plate is located at top soil surface, as the impact plate is embedded at deeper locations, the surface displacement reduces, and the reduction in the displacement occurs when the area of the plate increases due to the decrease in pressure. 4. The displacement response inside the soil medium in the vertical direction is found to be decreasing with depth which follows the conventional Bousinesq equation. The same behavior was found for all conditions of soil as the behavior under static loads (live load or surcharge) with depth. It is noticed that the response becomes of negligible values at a depth of 2B below the footing. Different paths of reduction were followed according to the soil density; this tendency is related to the void ratio of the soil. 5. In general, it is noticed from Table (4-1) that the time period (duration of load) increases by about 30-45% when the soil density decreases. When the stiffness is decreasing, the time period for the load is also increasing.

4.5 BEHAVIOR OF SATURATED SANDY SOILS UNDER IMPACT LOAD Prior to highlighting the behavior of saturated sandy soils, it is important to mention that experiments were carried out on saturated dense sand only. Medium and loose sandy soils show no stability during saturation, that is, once the soil is allowed to be fully saturated, the soil particles collapse due to loss of frictional resistance between them leading to excessive settlements of the top surface of the soil and hence losing the ability of the soil to support the FWD in its original position. Therefore, tests were found to be possible in case of saturated dense sands only.

107

Chapter Four


Tests were carried out for a single case of position of the impact plate, that is, the impact plates were placed at the top surface of the soil only. Two cases of footing diameter and height of fall of the hammer were implemented, namely, 100 mm and 150 mm plate diameter and 250 mm and 500 mm height of fall, respectively. Test results are plotted and presented in Figures (4-18) to (4-21) for a hammer weight of 5 kg and Figures (4-22) to (4-25) for the case of 10 kg hammer weight. The impulse force-time histories and the displacement-time histories are shown in part (a) of each figure while the acceleration-time history and velocity time-history are shown in part (b) and (c), respectively. The displacement variations along the depth are shown in part (d) and along the horizontal direction at the soil surface in part (e) of each figure. Two piezometers were installed below the impact plate for pore water pressure measurement during impact, namely at depths of B and 2B. The following behavior of soil-foundation system is noticed: 1. The impulsive waves (force-time histories) were found to be of a single pulse of half sine wave. Some cases were found to be of no negative phase of the pulse while few of them showed a minor negative phase. Such a tendency reveals that a fully saturated dense sandy stratum behaves as an ideal continuous solid irrespective of its density due to the relatively low void ratios (absence of voids) which tend to cause reflections and refractions of the impulsive waves thus, resulting in the ideal solid-impact behavior. 2. As the sandy soil stratum becomes saturated, the resulting impulse waves were found to be having peaks smaller than the corresponding dry stratum for all cases of study under consideration. The reduction of impulse peaks were found to be about 14% in cases where the impact plate is of 100 mm diameter and about 22% in cases of impact plate of 150 mm diameter (in comparison to the case of dry dense sandy soils). This tendency is attributed to the fact that the voids are filled with water and hence less interaction of particles. 3. However, the peak displacement responses in case of saturated sands were found to be always larger than those displacements in the corresponding dry soil. The increase in responses was found to be larger as the energy of the falling hammer increases (weight and height of fall). When the weight of hammer or the height of fall are doubled (from 5 kg to 10 kg or from 250 mm to 500 mm, 108

Chapter Four


respectively), the differences in peak response were found to be ranging from 35% to 40% as compared to those of dry soil condition. If both factors are doubled, the difference exceeds 60%. This behavior is related to the possibility of higher dissipation of the energy that occurs when the soil is saturated where the angle of repose reduces. Thus, resulting in attenuation, collapse and reorientation of the soil particles to form a mass of more stability and hence higher energy absorption. 4. The peak response (displacement) was found to occur always in the forced vibration phase lagging behind the peak impulsive force at a time difference of 40% to 60% related to the time of peak impulsive force. This tendency ensures that the natural frequency of the soil-foundation system (ω) is always larger than the frequency of the applied impulse ( ̅), that is, ( ̅ ) is less than unity. This behavior proves that either the stiffness or the damping increases when the dry sandy soil becomes fully saturated. The same behavior was also noticed in case of dry soil (qualitatively). 5. Parts (d) and (e) from Figures (4-18) to (4-25) and Figure (4-26) show the variation of vertical and horizontal responses (displacements) beneath or beside the impact plate, respectively, the displacement follows the same behavior under the static surcharge that is, governed by Boussineq equation (qualitatively), and it can be noticed from parts (d) of the figures that the vertical displacement in saturated soil is higher than the dry soil by about 20-50% at a depth B from the bearing plate. According to Biot (1956), there are two compressive waves and one shear wave through the saturated medium; the fluid wave (transmitted through the fluid) and the frame wave (transmitted through the soil structure), although there is a coupled motion of the fluid and the frame waves and that makes the displacement to be larger in the saturated soil. For the horizontal displacement, it is clear from parts (e) of the figures that the displacements in saturated sands are less than the displacements in dry state for the same condition. That is because of two reasons, first, the shear wave is concerned, the pore water has no rigidity to shear and the second, because the voids are filled with water and hence less interaction of particles due to the role of water as a lubricant between particles. Figures (4-27) to (4-42) show the excess pore water pressure-time histories measured by the pore water pressure transducers (KPE-PB) located at depths of B and 2B below the center of the bearing plate. It is noticed that the positive values in

109

Chapter Four


the figures indicate that the pore water pressure builds up in the soil. It is clear that the measured excess pore water pressure increases with the increase in the amplitude of load for tests at depth B, but the excess pore water pressure vanishes at a depth of 2B. In addition, it can be noticed that the change in size of the bearing plate has an important effect under the same falling mass and the same height of drop. In brief, the excess pore water pressure within the soil medium is found to be a function of two main parameters, energy of impact (hammer mass and height of fall) and the area of footing which is subjected to the impact (impact plate). An increase in the impact area results in a reduction of the excess pore water pressure for cases of unchanged energy of the impact, 125% increase of the plate area (diameter is changed from 100 mm to 150 mm) results in about 50-60% reduction in the pore water pressure. This tendency is logical since the pressure should reduce by about 56% (at least) from static laws; the extra decrease is the dissipation of energy between the sand particles. Meanwhile an increase in the height of fall from 250 mm to 500 mm (100% increases in energy) results in about 25% increase in excess pore water pressure which is also logical since the soil particles contribute to the energy dissipation. The results are also in agreement with those of Abd AlKaream, (2013), and Fattah et al. (2016) who found that, the excess pore water pressure increases with increasing load amplitude of harmonic type. In all cases, this behavior is encountered at a depth of B below the footing. Most of the impact energy dissipates beyond this depth to vanish almost completely at 2B. A summary of the maximum excess pore water pressure at a depth B with corresponding load amplitude is given in Table (4.2). Finally, as shown in Figure (4-43) in all cases, the peak excess pore water pressures are found to lag behind the peak impact force but still within the period where the impact force is acting (the forced vibration phase) which also ensures the thoughts that the medium is acting as a continuous medium or solid having less than unity ( is larger than ̅ ) and damping ratios are low in magnitudes.

110


Chapter Four

150

100

2000

Acceleration (m/s2)

Dry Sat. 1600

Force (N)

Dry Sat.

1200

800

50

0 0

10

20

30

-50

-100

-150

400

Time (msec)

0

10

0 30

20

1 2 3 4 5

Time (msec)

0.6 Dry Sat. 0.4

Velocity (m/s)

0



0.2

0 0

10

-0.2

20

30

Time (msec)

(a) force-time history with displacement(c) velocity-time history

time history 1

2

3

4


5

0

4

8

12

16

0

4

0.4

Displacement (mm)



8

12

16

0.8

1.2

1.6

Dry Sat.

Dry Sat.

20

2



Figure 4-18 Test results for SDSP10M5H25 model.

111

20


Chapter Four

200 Dry Sat.

3000 100

Acceleration (m/s2)

Dry Sat.

Force (N)

2000

0 0

10

20

30

-100

1000 -200

Time (msec)


20

2

4

6

8

Time (msec)

Dry Sat. 0.8

Velocity (m/s)

0

0 30


1.2

0

0.4

0 0

10

-0.4

20

30

Time (msec)


time history 2

4

6


8

0

4

8

12

16

0.4

4 0.8

Displacement (mm)



8

12

1.2

1.6

16

Dry Sat.

Dry Sat.

20

2




112

20


Chapter Four

120

2500

80

Acceleration (m/s2)

Dry Sat. 2000

Force (N)

Dry Sat.

1500

40

0 0

10

20

30

-40

1000

-80

-120

500

Time (msec)


20

1

2

3

4

Time (msec)

Dry Sat. 0.4

Velocity (m/s)

0

0 30


0.6

0

0.2

0 0

10

-0.2

20

30

Time (msec)


time history 1

2

3


4

0

10

20

0

0.4

Displacement (mm)



10

20

0.8

1.2

1.6

Dry Sat.

Dry Sat. 2

30




113

30


Chapter Four

200 Dry Sat.

4000 Dry Sat.

Acceleration (m/s2)

100

Force (N)

3000

2000

0 0

10

20

30

-100

1000

-200

Time (msec)


10

20

1 2 3 4 5

Time (msec)

Dry Sat. 0.6

Velocity (m/s)

0

0 30


0

0.4

0.2

0 0

10

-0.2

20

30

Time (msec)


time history 1

2

3

4

5

Distance away from the edge of the bearing plate (cm) 0

10

20

0

0.4

10

Displacement (mm)



20

0.8

1.2

1.6

Dry Sat.

Dry Sat. 2

30




114

30


Chapter Four

150 Dry Sat.

4000 100

Acceleration (m/s2)

Dry Sat.

Force (N)

3000

2000

50

0 0

10

20

30

-50

-100

1000

-150

Time (msec)


20

2

4

6

8

Time (msec)

0.8 SD SS 0.6

Velocity (m/s)

0

0 30


0

0.4

0.2

0 0

10

-0.2

20

30

Time (msec)


time history 2

4

6


8

0

4

8

12

16

0

4

0.4

Displacement (mm)



8

12

16

0.8

1.2

1.6

Dry Sat.

Dry Sat.

20

2




115

20


Chapter Four

200 Dry Sat.

6000 Dry Sat.

Acceleration (m/s2)

100

Force (N)

4000

0 0

10

20

30

-100

2000

-200

Time (msec)


10

20

2 4 6 8 10

Time (msec)

Dry Sat. 0.8

Velocity (m/s)

0

0 30


0

0.4

0 0

10

-0.4

20

30

Time (msec)


time history 2

4

6

8


10

0

4

8

12

16

0.4

4

0.8

Displacement (mm)



8

12

1.2

1.6 16

Dry Sat.

Dry Sat.

20

2




116

20


Chapter Four

120 Dry Sat.

4000

80

Acceleration (m/s2)

Dry Sat.

Force (N)

3000

2000

40

0 0

10

20

30

-40

-80

-120

1000

Time (msec)


10

20

1 2 3 4 5

Time (msec)

SS SD 0.4

Velocity (m/s)

0

0 30


0

0.2

0 0

10

-0.2

20

30

Time (msec)


time history 1

2

3

4


5

0

10

20

30

0

0.4

Displacement (mm)



10

20

0.8

1.2

1.6

Dry Sat.

Dry Sat.

30

2




117


Chapter Four

200 Dry Sat.

8000 Dry Sat.

Acceleration (m/s2)

100

Force (N)

6000

4000

0 0

10

20

30

-100

-200

2000

Time (msec)


20

2

4

6

8

Time (msec)

SS SD 0.8

Velocity (m/s)

0


1.2

0 30

0

0.4

0 0

10

-0.4

20

30

Time (msec)

(a) force-time history with displacement(d) velocity-time history

time history 2

4

6


8

0

10

20

0.4

0.8

Displacement (mm)



10

20

1.2

1.6

Dry Sat.

Dry Sat.

30

2

(e) displacement variation in vertical direction

(f) displacement variation in horizontal direction


118

30


Chapter Four

3

Displacement at B below the plate 2B below the plate 2

1

0


Displacement (mm)

Displacement (mm)

3


2

1

0

0

10

20

30

40

0

10

20

30

40

Time (msec)

Time (msec)

(a) Test results for SDSP10M5H25 model. 3



Displacement (mm)

Displacement (mm)

3

2

1

0

1

0

0

10

20

30

40


2

50

0

20

40

60

Time (msec)

Time (msec)

(b) Test results for SDSP10M5H50 model. 3 Displacement at B below the plate 2B below the plate 2

1

0

0

10

20

30


Displacement (mm)

Displacement (mm)

3


2

1

0

40

Time (msec)

0

10

20

30

40

50

Time (msec)

(c) Test results for SDSP15M5H25 model. 3

Displacement at B below the plate 2B below the plate 2

1

0


Displacement (mm)

Displacement (mm)

3


2

1

0

0

10

20

30

40

50

Time (msec)

0

20

40

Time (msec)

(d) Test results for SDSP15M5H50 model. Figure 4-26 Test results of the vertical and horizontal displacement inside the soil medium in saturated case.

119

60


Chapter Four

3

3


1

0

Displacement (mm)

Displacement (mm)

Displacement at a horizontal distance a way from the edge of bearing plate at distance B at distance 2B

2

1

0

0

10

20

30

40

0

20

40

60

Time (msec)

Time (msec)

(e) Test results for SDSP10M10H25 model. 3

3

Displacement (mm)

Displacement (mm)

Displacement at a horizontal distance a way from the edge of bearing plate 2 Displacement at B below the plate 2B below the plate 1

0

0

10

20

30

40

1

0

50


2

0

20

Time (msec)

40

60

80

60

80

60

80

Time (msec)

(f) Test results for SDSP10M10H50 model. 3 Displacement at a horizontal distance a way from the edge of bearing plate


Displacement (mm)

Displacement (mm)

3

2

1

0


2

1

0

0

10

20

30

40

50

0

20

40

Time (msec)

Time (msec)

(g) Test results for SDSP15M10H25 model. 3



Displacement (mm)

Displacement (mm)

3

2

1

0


2

1

0

0

10

20

30

40

50

0

20

40

Time (msec)

Time (msec)

(h) Test results for SDSP15M10H50 model. Figure ‎4-26 continued.

120


Chapter Four

Excess pore water pressure (kPa)

30

20

10

0

-10 0

100

200

300

Time (msec) Figure 4-27 The excess pore water pressure-time histories at depth B for SDSP10M5H25 model.


30

20

10

0

-10 0

100

200

300

Time (msec) Figure ‎4-28 The excess pore water pressure-time histories at depth 2B for SDSP10M5H25 model.


30

20

10

0

-10 0

100

200

300

400

Time (msec) Figure 4-29 The excess pore water pressure-time histories at depth B for SDSP10M5H50 model.


30

20

10

0

-10 0

100

200

300

400

Time (msec) Figure 4-30 The excess pore water pressure-time histories at depth 2B for SDSP10M5H50 model.

121


Chapter Four


30

20

10

0

-10 0

20

40

60

80

100

Time (msec)

Figure 4-31 The excess pore water pressure-time histories at depth B for SDSP15M5H25 model. Excess pore water pressure (kPa)

30

20

10

0

-10 0

20

40

60

80

100

Time (msec)

Figure ‎4-32 The excess pore water pressure-time histories at depth 2B for SDSP15M5H25 model.


30

20

10

0

-10 0

100

200

300

Time (msec)


30

20

10

0

-10 0

100

200

300

Time (msec)

Figure 4-34 The excess pore water pressure-time histories at depth 2B for SDSP15M5H50 model.

122


Chapter Four


30

20

10

0

-10 0

100

200

300

400

Time (msec)


30

20

10

0

-10 0

100

200

300

400

Time (msec)



30

20

10

0

-10 0

200

400

600

Time (msec)


30

20

10

0

-10 0

200

400

600

Time (msec)


123

Chapter Four



30

20

10

0

-10 0

100

200

300

Time (msec)


30

20

10

0

-10 0

100

200

300

Time (msec)

Figure 4-40 The excess pore water pressure-time histories at depth 2B for SDSP15M10H25 model. Excess pore water pressure (kPa)

30

20

10

0

-10 0

100

200

300

Time (msec)


30

20

10

0

-10 0

100

200

300

Time (msec)


124


Chapter Four

30

Excess PWP (kPa)

Excess PWP (kPa)

30 20 10 0

20 10 0 -10

-10 0

10

20

30

40

0

50

10

(a) SDSP10M5H25 model Excess PWP (kPa)

Excess PWP (kPa)

40

50

30

20 10 0 -10

20 10 0 -10

0

10

20

30

40

50

0

10

Time (msec)

20

30

40

50

Time (msec)

(c) SDSP15M5H25 model.

(d) SDSP15M5H50 model.

30

30

Excess PWP (kPa)

Excess PWP (kPa)

30

(b) SDSP10M5H50 model.

30

20 10 0

20 10 0 -10

-10 0

10

20

30

40

0

50

10

20

30

40

50

Time (msec)

Time (msec)

(e) SDSP10M10H25 model.

(f) SDSP10M10H50 model.

30

30

Excess PWP (kPa)

Excess PWP (kPa)

20

Time (msec)

Time (msec)

20 10 0

20 10 0 -10

-10 0

10

20

30

40

0

50

10

20

30

40

50

Time (msec)

Time (msec)

(g) SDSP15M10H25 model.

(h) SDSP15M10H50 model.

Figure 4-43 The excess pore water pressure-time histories at depth B for the first fifty msec. from the beginning of the impact force.

125


Chapter Four

Table ‎4-2: Details of the effect of impact load footing resting on saturated sandy soil testing results.

No.

Max. Duration amplitude Test designation of load of load (msec) (N)



PWP at depth B (kPa)

1

SDSP10M5H50

2389

19.5

6.38

15.5

20

2

SDSP10M5H25

1590

20.65

4.509

16.25

16

3

SDSP15M5H50

2586

18.8

4.518

14.7

9

4

SDSP15M5H25

1716

20.15

3.563

15.9

6

5

SDSP10M10H50

4019

24.3

8.788

17.3

28

6

SDSP10M10H25

2747

25.4

6.402

18

22

7

SDSP15M10H50

4665

23.45

6.653

16.9

13

8

SDSP15M10H25

2900

24.65

4.944

18.1

11

126

CHAPTER FIVE

5.

PREDICTION OF DYNAMIC CHARACTERISTICS OF SANDY SOIL

5.1 INTRODUCTION The measurements of damping ratio using a laboratory test by means of resonant column, cyclic simple shear test, cyclic triaxial test and other tests are well established. For resonant column test, a linear viscoelastic constitutive soil model is assumed, and the damping ratio is calculated using either free vibration decay or half-power bandwidth methods. With a lower frequency torsional shear or cyclic triaxial tests, the damping ratio is calculated directly from the hysteresis in the stress-strain curve [e.g., Hardin and Drnevich (1972), Seed et al. (1986), and Vucetic and Dobry (1991)], but there is doubt about the effect of specimen disturbance on the measured values (Rix et al., 2000). In situ measurements cover a larger volume of soil than do laboratory tests on small specimens. Engineers and seismologists have used borehole seismic methods such as cross hole or downhole tests to measure the attenuation of body waves (Hoar and Stokoe, 1984; Redpath and Lee, 1986; Mok et al., 1988; Jongmans, 1990; Stewart, 1992; Gibbs et al., 1994; Liu et al., 1994). The damping ratio is computed from particle motion attenuation measurements using several approaches, for example, amplitude decay with distance. Field tests on instrumented full-scale shallow foundation are, in principle, the most appropriate approach to the calibration and verification of analytical methods for specific projects, but the cost of such experiments is high and the control of soil parameters and the assessment of their effects on foundation behavior are difficult. Another choice is to attain small-scale laboratory models. Because of the difficulty to obtain damping ratio under impact load (large strain level), this chapter presents a proposed equation depending on the energy dissipated from single degree of freedom SDOF system. 127

Chapter Five


5.2 DYNAMIC SOIL PROPERTIES 5.2.1 Soil modulus of subgrade reaction (K) The modulus of subgrade reaction (K) was measured directly by the (FWD), described in Chapter Three, which is based on the following equation for soil under consideration (operation manual):

5.1

where: coefficient of subgrade reaction (MN/m3), obtained by TML small FWD system, maximum load (N), maximum displacement (mm), radius of loading plate (mm), diameter of loading plate, R=2r (mm), and diameter of standard loading plate (ϕ 300 mm).

5.2.2 Soil modulus of elasticity (E) The soil modulus of elasticity was measured by the (FWD) which was based on the following equation (operation manual):

5.2

where: E = subgrade modulus (MN/m2) obtained by TML small FWD system, P = maximum load (N), D = maximum displacement (mm),

128

Chapter Five


r = radius of loading plate (mm), and ν = Poisson‘s ratio (0.30, changeable).

5.2.3 Shear modulus (G) The shear stress (τ) is related to the shear strain (γ) by the following equation (Atkinson, 2007): 5.3 where: Shear modulus (MN/m2). For isotropic material, the shear modulus, G can be calculated using the following equation:

5.4

5.3 SOIL MASS AND NATURAL FREQUENCY According to Prakash (1981), Clough and Penzien (2003), and Das and Ramana (2011), the circular natural frequency (ω) in the vertical mode of the foundation-soil system can be determined using the theory of vibration. The equation of motion, with behavior as an undamped mass-spring system, is:

√

5.5

where: soil spring constant (N/m), and total mass of foundation and machine (kg).

129

Chapter Five


The theory of vibration for spring–mass–dashpot systems considers the spring to be weightless and accordingly, Equation (5-5) has been derived. This theory can be applied to foundation vibrations only if the mass of the soil participating in the vibration can also be included (Rao, 2011).

5.6

√

where: mass of the soil participating in vibration (kg). In case of machine foundations, the mass of soil, , participating in vibration needs to be determined. There have been several approaches suggested to determine the effective or equivalent mass of soil, , in calculating the natural frequency (Rao, 2011). The choice of any method still remains the designer‘s preference. It is usually related to the mass of soil in the pressure bulb. The value of generally varies between zero and m. In other word, the total mass (m) varies between m and 2 m in most cases. Barkan (1962) suggested that the mass of the vibrating soil should lie between (2/3) to (1.5) times the total mass of the vibrator and foundations. Unfortunately, the size of the co-vibrating body of a soil cannot be determined exactly as yet because it depends on frequency and influenced by the size of the base area of the vibrator (foundation) and by the elastic properties of the soil (spacing) (Punmia et al., 2005). The investigations carried out by various research workers have confirmed the fact that a certain mass of soil vibrates with the foundation, and this should be accounted for in the analysis. There is, however, no agreement on the magnitude of the effective mass of the soil participating in vibration (Punmia et al., 2005). Adam and Adam (2003), presented a mechanical modeling of the dynamic plate load test with falling weight deflectometer (FWD). They derived an equation to calculate the additional weight to device (mass of soil) for cohesive soils which is, however, small as compared to the mass of the device, and they neglected the mass of soil for cohesionless soils.

130


Chapter Five

5.4 A PROPOSED METHODOLOGY In this section, a procedure is proposed to calculate the damping ratio.

5.4.1 Proposed calculation of natural frequency and mass of soil For dense sand as can be seen in Figures (4-2) to (4-17) in part ―a‖, the impact-time curves are almost ideally single half-sine-wave impulse and the peak response occurs during the active phase of the forced vibration, hence, the natural frequency can be calculated based on the frequency of the load as follows (Clough and Penzien, 2003):

̅

̅

5.7

where: time of maximum displacement (sec), frequency of the vibration foundation-soil system (rad/sec), and ̅

frequency of the impact (rad/sec).

And the total mass (mass of foundation and machine + mass of soil participating in vibration) can be calculated from the undamped response, including the transient as well as the steady-state terms, given by (Clough and Penzien, 2003):

̅

where: maximum load (N), maximum displacement (m), and ̅

frequency ratio ( ).

131

5.8


Chapter Five

The previous procedure cannot be used for medium and loose sand because, in general, the peak response occurs in the free vibration phase, therefore, the mass of soil is considered to be neglected because the soil is not dense and cohesionless, and the natural frequency can be calculated from Equation (5-5).

5.4.2 Equation of motion of the basic dynamic system The basic equation of motion for a single degree of freedom system (SDOF) as shown in Figure (5-1) can be written as follows: ̈ where ̈ ̇

̇

5.9

are acceleration, velocity, and displacement, respectively,

the equivalent soil mass and foundation ( damping coefficient (

),

),

spring constant ( ), and the force (N).

𝑓 𝑡

𝑓 𝑡

Figure ‎5-1 A lumped parameter vibrating system, (Das and Romana, 2011).

132


Chapter Five

For short-duration loads, the maximum displacement amplitude depends principally upon the magnitude of the applied impulse ∫

and is not

strongly influenced by the form of the loading impulse (Clough and Penzien, 2003). In this research, the soil damping, which is expressed by energy loss per cycle, can be found using the following proposed equation which is based on the principle that ―the impulse or momentum of the falling mass is equal to the momentum of the equivalent soil system‖ as follows:

∫ ̈

∫ ̇

5.10

Or

∫

∫ ̈

∫ ̇

∫

5.11

where: t1 = time of the end of impulse (sec), as shown in the Figure (5-2). 2000

Load (N)

1500

1000

500

𝑡1 0 0 -500

5

10

15

20

25

30

Time (msec) Figure ‎5-2 The applied load-time history.

Carrying out the necessary numerical integrations of all parts of Equation (511), the expression for the damping coefficient can be given as follows:

133


Chapter Five

∫

̈

∫ ∫

∫

̇

5.12

5.4.3 Soil damping ratio Damping ratio is defined as the damping coefficient (c) divided by the critical damping coefficient (cc) as follows (Clough and Penzien, 2003):

5.13

For the case under consideration, the impact load was applied as a half sine wave. Accordingly, damping ratio may be defined alternatively as the energy loss per cycle divide by the critical damping coefficient and evaluated as follows:

5.14

where 5.15 and

is the circular natural frequency of the foundation-soil system, and

.

Accordingly, and based on the test results of all case studies which were presented in Chapter Four, the natural frequency ( ) of each system of foundationsoil medium is calculated based on the output results given in Chapter Four and hence, with the use of frequency of the applied load ( ̅), the frequency ratio β is calculated and presented-together with ̅ and β in Table (5-1). Moreover, the mass is also calculated based on the proposed procedure of Chapter Five as shown for each case of test in the last column of Table (5-1). Several cases of analysis are presented in this chapter, these are: a. How the frequency of the applied load is obtained for dense and medium sandy soils, 134

Chapter Five


b. How the frequency of the system (foundation-soil) is derived for cases where the peak response occurs in the forced vibration and free vibration phases and finally, c. Two cases of mass evaluation are also presented in details. Examples of calculations are presented in article 5.7. Finally, to fulfill the main objective of the present work, that is, evaluation of damping for different sandy soil conditions, the damping ratios are evaluated on the basis of the important factors presented in Table (5-1). These are ̅ , and . Some are functions of the applied energy ̅ while others are function of the foundation-soil interaction ( and ). The total mass could be a function of the foundation-soil or the foundation only.

135

Chapter Five


Table ‎5-1: Values of frequencies of the impact ( ̅ ), frequencies of the vibration foundation-soil system ( ), frequency ratio (β), and the total masses of the foundation-soil system for all cases of study.

No.

Test designation

̅ (measured) (rad/sec)

1

DLSP10M5H50

119.2

37.8

3.15

10.00

2

DL0.5bP10M5H50

121.1

40.6

2.983

10.00

3

DLbP10M5H50

122.7

44.9

2.73

10.00

4

DL2bP10M5H50

122.2

50.9

2.40

10.00

5

DMSP10M5H50

123.9

48.8

2.54

10.00

6

DM0.5bP10M5H50

125.7

55.9

2.25

10.00

7

DMbP10M5H50

127.2

65.8

1.93

10.00

8

DM2bP10M5H50

127.2

72.14

1.76

10.00

9

DDSP10M5H50

164.5

270.3

0.61

12.68

10

DD0.5bP10M5H50

175.0

325.6

0.54

13.53

11

DDbP10M5H50

177.9

341.3

0.52

14.52

12

DD2bP10M5H50

182.7

356.7

0.51

15.89

13

DLSP15M5H50

129.6

72.0

1.79

11.00

14

DL0.5bP15M5H50

130.1

80.2

1.62

11.00

15

DLbP15M5H50

131.2

83.6

1.57

11.00

16

DL2bP15M5H50

132.3

86.5

1.53

11.00

17

DMSP15M5H50

130.9

94.1

1.39

11.00

18

DM0.5bP15M5H50

131.7

103.9

1.27

11.00

19

DMbP15M5H50

132.3

110.8

1.19

11.00

20

DM2bP15M5H50

133.7

119.8

1.12

11.00

21

DDSP15M5H50

168.5

311.2

0.54

17.14

22

DD0.5bP15M5H50

176.5

330.2

0.53

21.61

23

DDbP15M5H50

184.8

361.6

0.51

21.71

24

DD2bP15M5H50

191.6

382.2

0.50

22.00

136

(Eq. 5-5) or (Eq. 5-7) (rad/sec)

̅

(Eq. 5-8) (kg)


Chapter Five


No.

Test designation


25

DLSP10M10H50

124.2

38.1

3.26

10.00

26

DL0.5bP10M10H50

125.9

40.8

3.09

10.00

27

DLbP10M10H50

125.7

43.5

2.89

10.00

28

DL2bP10M10H50

125.7

45.9

2.73

10.00

29

DMSP10M10H50

126.2

56.0

2.25

10.00

30

DM0.5bP10M10H50

128.5

63.9

2.01

10.00

31

DMbP10M10H50

129.6

72.5

1.79

10.00

32

DM2bP10M10H50

129.0

82.3

1.57

10.00

33

DDSP10M10H50

131.9

255.8

0.52

20.35

34

DD0.5bP10M10H50

135.4

272.5

0.49

20.55

35

DDbP10M10H50

139.9

297.9

0.47

20.58

36

DD2bP10M10H50

142.7

326.1

0.44

20.62

37

DLSP15M10H50

130.4

65.9

2.00

11.00

38

DL0.5bP15M10H50

132.6

74.1

2.025

11.00

39

DLbP15M10H50

131.2

77.6

2.00

11.00

40

DL2bP15M10H50

132.3

81.9

2.00

11.00

41

DMSP15M10H50

130.9

96.2

1.96

11.00

42

DM0.5bP15M10H50

133.7

106.5

1.99

11.00

43

DMbP15M10H50

133.9

122.4

1.79

11.00

44

DM2bP15M10H50

134.5

138.6

1.70

11.00

45

DDSP15M10H50

139.9

300.9

0.46

24.81

46

DD0.5bP15M10H50

145.1

318.6

0.46

26.71

47

DDbP15M10H50

141.2

333.0

0.42

26.93

48

DD2bP15M10H50

147.5

349.2

0.42

28.55

137

(Eq. 5-5) or (Eq. 5-7) (rad/sec)

̅

(Eq. 5-8) (kg)


Chapter Five


No.

Test designation


49

DDSP10M5H25

165.3

257.8

0.64

12.35

50

DD0.5bP10M5H25

175.9

324.7

0.54

13.12

51

DDbP10M5H25

176.9

346.6

0.51

13.62

52

DD2bP10M5H25

177.5

364.2

0.49

15.00

53

DDSP15M5H25

175.0

288.7

0.61

16.60

54

DD0.5bP15M5H25

179.0

344.6

0.52

18.38

55

DDbP15M5H25

182.1

357.2

0.50

20.21

56

DD2bP15M5H25

185.9

372.6

0.49

22.76

57

DDSP10M10H25

124.7

244.9

0.51

18.41

58

DD0.5bP10M10H25

130.9

282.5

0.46

18.55

59

DDbP10M10H25

131.2

302.2

0.43

19.59

60

DD2bP10M10H25

132.6

321.1

0.41

20.57

61

DDSP15M10H25

127.4

292.8

0.44

22.41

62

DD0.5bP15M10H25

129.6

314.5

0.41

24.96

63

DDbP15M10H25

130.6

326.3

0.40

27.27

64

131.2

343.0

0.38

28.01

65

DD2bP15M10H25 SDSP10M5H50

161.1

244.3

0.66

11.08

66

SDSP10M5H25

152.1

234.5

0.65

11.32

67

SDSP15M5H50

167.1

260.3

0.64

14.93

68

SDSP15M5H25

155.9

239.3

0.65

14.86

69

SDSP10M10H50

129.3

233.9

0.55

14.69

70

SDSP10M10H25

123.7

225.4

0.55

14.84

71

SDSP15M10H50

133.9

237.8

0.56

21.84

72

SDSP15M15H25

127.4

219.7

0.58

21.45

138

(Eq. 5-5) or (Eq. 5-7) (rad/sec)

̅

(Eq. 5-8) (kg)

Chapter Five


5.5 DISCUSSION OF RESULTS a. Frequencies and frequency ratios For all case studies, it can be seen that the frequency of impact load is always at high level ranging between about 120 rad/sec to about 180 rad/sec, which is between 19 and 29 Hz. Higher values of load frequencies are expected in cases of dense sandy soil which acts as a solid medium. An important note can be highlighted, that is, these load frequencies are almost compatible with the frequencies of the most common earthquakes of high risk. This leads to a conclusion that care should always be taken in designing a foundation-soil system to allow for better resistance to impulse or explosion due to air raids or other sources. Concerning frequencies of the foundation-soil system, a major and important conclusion is to be highlighted, that is; dense sands result always in natural frequencies having higher values than those of the applied loads. As a result, the frequency ratio β will be less than unity and hence, the soil response when acted upon by an impact is of low peak and dissipates quickly before the applied energy dissipates, therefore, the damping of soil is expected to be significant. This conclusion highlights why compaction of the foundation soil is important. On the other hand, medium or loose sandy soils are always associated with circular frequencies lower than those of the applied load and hence, β values are larger than unity. This leads to an important conclusion also, that is, the response continues to occur beyond the time period for the energy of load to dissipate and hence, the peak response is larger and a second or third shock or impulse or earthquake will be fatal since two peaks can occur simultaneously resulting in magnification of the settlement or displacements, then, collapse of the foundation. As a result, damping is either low or insignificant. It can be noticed that for the footing embedded in soil of medium density at a depth of 2B, the frequency ratio (β) is approaching a value near to 1.0, this means that the natural frequency of foundation is very close to the operating frequency of equipment and this creates possibility of resonance and causing an increase in the amplitude and may cause resonance in the foundation which will affect life of the foundation as noticed by Bhandari and Sengupta, (2014). b. Effective masses of the system

139

Chapter Five


The total mass of the system is varying between a value equal to the weight of footing and machine (FWD) (soil has no contribution) for the cases of loose sandy soils up to values near or exceed 150% of the weight of FWD in case of dense sandy soil. One very important conclusion can be drawn, that is, the results support previous thoughts and ideas that are the effective soil mass depends on the frequency of the load and is influenced by the size of the base area of the vibrator (foundation) and by the elastic properties of the soil. It can be seen from the results of dense soil models that the soil mass for DDSP10M5H50 model equals about 30% of the weight of FWD, for DDSP15M5H50 model, it equals about 66.67% of the weight of FWD, and for DDSP15M10H50 model, it equals about 150% of the weight of FWD.

5.6 MODULUS OF SUBGRADE REACTION, MODULUS OF ELASTICITY, SHEAR MODULUS AND DAMPING RATIOS OF SANDY SOILS OF DIFFERENT CONDITIONS As mentioned earlier, a procedure is developed for evaluation of the soil stiffness and damping ratio. Accordingly, the obtained values of subgrade reaction, elastic and shear modulus and damping ratios for different soil and loading conditions are evaluated and presented in Table (5-2). Examples of calculations are also presented in this chapter. The major conclusions drawn from all the values given in Table (5-2) and based on each test are summarized as follows: a. The modulus of subgrade reaction for loose sandy soils is not exceeding 4000 kN/m3, this leads to low values of Young‘s and shear modulus (Young‘s modulus is always less than 1000 kN/m3 and the shear modulus is accordingly less than 400 kN/m2). This leads to two main conclusions, the stiffness is absolutely low, that is, low values of circular natural frequency which in turn makes the frequency ratios for most known dynamic forces to exceed unity. Therefore, the peak response of the footing when acted upon by dynamic loads usually takes long period. Accordingly, two or more successive pulses could cause great damage to the system, especially earthquake base excitation. The second conclusion is that such kind of soils possesses low values of damping (not to exceed 10%). This means that a dynamic force is expected to be

140

Chapter Five


highly effective and could result in large responses (displacement and settlement) of the footings. b. The response of a saturated dense soil usually possess large values of modulus of subgrade reaction, modulus of elasticity and shear modulus (can be about 10 times those of loose soils) but still, these soils are noticed to be having low values of damping ratios (still less than 10%). Accordingly, first it is important to take into account any possible dynamic force acting on the system (impacts or earthquakes) since due to action that could take place, excessive static settlement can occur when the pore water pressure dissipates and second, along the load duration, the dynamic force could result in large displacements leading to local and even general shear failure. c. Dense sandy soils usually possess relatively large values of modulus of subgrade reaction (exceeding 20000 kN/m3 and may be about 50000 kN/m3). Accordingly, Young‘s and shear modulus become normally above 10000 kN/m2. This means that both P and S waves of an earthquake or the wave induced by machine to be travelling at high velocities (since the wave velocity

√ ), that

is, the dynamic magnification factors (representing dynamic amplification effect of harmonically applied load (

)), especially in cases of impact or

explosions, are less than 2.0 or at least close to unity. Such a tendency provides good supporting system to vibrating equipment and machines. The damping ratios in cases of dense sandy soil are found to be large enough (could exceed 10%) to prevent successive reflections and refractions of the dynamic waves of a pulse and hence, reducing the foundation-soil responses. d. Finally, it is found that the modulus of elasticity and shear modulus of sandy soils, as expected, are functions not only of the relative density of the soil but they are also function of the magnitude of the dynamic force acting on the footing and the size and depth of the footing. Hence, it is very clear to notice that vibration isolation is considered to be effectively reliable due two reasons, large stiffness values and large damping ratios. Loose sands or generally saturated sands are noticed to be less affected by isolating the machine, that is vibrating and supported by a footing resting on such a media. Deep footings possess higher natural frequencies and hence less affected by dynamic forces. 141


Chapter Five

Table ‎5-2: The characteristics of sandy soil (modulus of subgrade reaction, modulus of elasticity, shear modulus and damping ratio) for tested systems.

K

E

G

%

(kN/m3)

(kN/m2)

(kN/m2)

(Eq. 5-13b)

DLSP10M5H50

1822

497

191

2.66

2

DL0.5bP10M5H50

2103

574

221

3.62

3

DLbP10M5H50

2577

735

283

5.31

4

DL2bP10M5H50

3298

861

331

7.27

5

DMSP10M5H50

3035

829

319

6.03

6

DM0.5bP10M5H50

3979

1086

418

7.18

7

DMbP10M5H50

5511

1505

579

8.17

8

DM2bP10M5H50

6618

1807

695

8.77

9

DDSP10M5H50

22239

6071

2335

8.25

10

DD0.5bP10M5H50

34735

9483

3647

8.81

11

DDbP10M5H50

41142

11232

4320

9.95

12

DD2bP10M5H50

49312

13462

5178

10.42

13

DLSP15M5H50

3229

882

339

3.05

14

DL0.5bP15M5H50

3999

1092

420

4.17

15

DLbP15M5H50

4354

1220.303

469

4.99

16

DL2bP15M5H50

4657

1238.416

476

5.61

17

DMSP15M5H50

5511

1504

579

4.21

18

DM0.5bP15M5H50

6720

1835

706

5.22

19

DMbP15M5H50

7647

2088

803

5.69

20

DM2bP15M5H50

8941

2441

939

6.14

21

DDSP15M5H50

26770

7308

2811

5.38

22

DD0.5bP15M5H50

38074

10394

3998

6.19

23

DDbP15M5H50

46177

12606

4849

6.47

24

DD2bP15M5H50

52546

14345

5517

6.85

No.

Test designation

1

142


Chapter Five

Table ‎5-2: Continued.

K

E

G

%

(kN/m3)

(kN/m2)

(kN/m2)

(Eq. 5-13b)

DLSP10M10H50

1852

506

195

0.90

26

DL0.5bP10M10H50

2116

578

222

2.18

27

DLbP10M10H50

2412

658

253

3.57

28

DL2bP10M10H50

2693

735

283

5.38

29

DMSP10M10H50

3998

1091

420

5.05

30

DM0.5bP10M10H50

5199

1419

546

6.13

31

DMbP10M10H50

6699

1829

703

7.08

32

DM2bP10M10H50

8627

2355

906

7.83

33

DDSP10M10H50

32458

8861

3408

7.49

34

DD0.5bP10M10H50

37464

10228

3934

7.95

35

DDbP10M10H50

45380

12389

4765

8.96

36

DD2bP10M10H50

55550

15165

5833

9.82

37

DLSP15M10H50

2709

740

284

1.49

38

DL0.5bP15M10H50

3419

933

359

2.22

39

DLbP15M10H50

3744

1022

393

3.23

40

DL2bP15M10H50

4175

1140

438

4.36

41

DMSP15M10H50

6057

1653

636

2.65

42

DM0.5bP15M10H50

6706

1831

704

3.56

43

DMbP15M10H50

9328

2547

979

4.29

44

DM2bP15M10H50

11954

3263

1255

5.11

45

DDSP15M10H50

37326

10189

3919

4.15

46

DD0.5bP15M10H50

45260

12356

4752

4.68

47

DDbP15M10H50

50952

13909

5349

5.12

48

DD2bP15M10H50

59477

16237

6245

5.80

No.

Test designation

25

143


Chapter Five


K

E

G

%

(kN/m3)

(kN/m2)

(kN/m2)

(Eq. 5-13b)

DDSP10M5H25

19700

5378

2069

8.95

50

DD0.5bP10M5H25

33457

9134

3513

9.97

51

DDbP10M5H25

39946

10905

4194

10.62

52

DD2bP10M5H25

48650

13282

5108

12.41

53

DDSP15M5H25

22142

6045

2325

6.69

54

DD0.5bP15M5H25

35407

9666

3718

7.03

55

DDbP15M5H25

41976

11459

4408

7.82

56

DD2bP15M5H25

51637

14097

5422

8.36

57

DDSP10M10H25

25637

6999

2692

8.47

58

DD0.5bP10M10H25

36901

10074

3875

9.17

59

DDbP10M10H25

45424

12401

4769

10.30

60

DD2bP10M10H25

55213

15073

5797

11.00

61

DDSP15M10H25

32506

8874

3413

5.03

62

DD0.5bP15M10H25

42525

11609

4465

5.97

63

DDbP15M10H25

50549

13799

5308

6.44

64

DD2bP15M10H25

58412

15946

6133

6.69

65

SDSP10M5H50

15892

4339

1669

9.42

66

SDSP10M5H25

14966

4086

1571

9.77

67

SDSP15M5H50

16195

4421

1700

6.43

68

SDSP15M5H25

13627

3720

1431

7.17

69

SDSP10M10H50

19409

5299

2038

8.15

70

SDSP10M10H25

18211

4972

1912

9.02

71

SDSP15M10H50

19839

5416

2083

4.81

72

SDSP15M15H25

16597

4531

1743

6.09

No.

Test designation

49

144


Chapter Five

5.7 PROCEDURE OF CALCULATIONS Five examples have been chosen for loose, medium, dense dry sand and saturated sand to clarify the calculations as follows: Example (5-1): For DLSP10M5H50 model, the following test results were obtained: P (maximum load) =1069 N, D (maximum displacement) =24.9 mm, r (radius of loading plate) = 50 mm, t1 (time of the end of impulse) = 26.35 msec, ∫ ̈

,∫

,∫

, ∫

.

Spring constant,

√

∫

√

̈

∫ ∫

∫

̇

145

̇


Chapter Five

Example (5-2): For DMSP10M5H50 model, the following test results were obtained: P (maximum load) = 1316 N, D (maximum displacement) = 18.4 mm, r (radius of loading plate) =50 mm, t1 (time of the end of impulse) = 25.35 msec, ∫ ̈

,∫

,∫

, ∫

̇

.

Spring constant,

√

√

∫

̈

∫ ∫

∫

̇

Example (5-3): For DDSP10M5H50 model, the following test results were obtained: P (maximum load) = 2829 N, D (maximum displacement) = 5.399 mm, r (radius of loading plate) =50 mm, t1 (time of the end of impulse) = 19.1 msec, ∫ , ∫

̇

, ∫

,∫

̈

, t (time of maximum displacement)

= 14.45 msec. 146


Chapter Five

Spring constant, ̅

̅ ̅

̅

(

)

(

∫

)

∫ ∫

(

)

̈

∫

̇

147


Chapter Five

Example (5-4): For SDSP10M5H50 model, the following test results were obtained: P (maximum load) = 2389 N, D (maximum displacement) = 6.38 mm, r (radius of loading plate) =50 mm, t1 (time of the end of impulse) = 19.5 msec, ∫ ,∫

̇

,

∫

,

,

,

∫

t

(time

̈ of

maximum

displacement) = 15.5 msec.

Spring constant, ̅

̅

̅

(

) (

)

148


Chapter Five

∫

̈

∫ ∫

∫

̇

Example (5-5): For DDSP15M5H50 model, the following test results were obtained: P (maximum load) = 3320 N, D (maximum displacement) = 3.509 mm, r (radius of loading plate) =75 mm, t1 (time of the end impulse) = 18.65 msec, ∫ , ∫ ,

̇

, ∫

∫

,

displacement) = 13.1 msec.

Spring constant, ̅

̅ ̅

149

t

(time

̈ of

maximum


Chapter Five

̅

(

)

(

∫

)

∫ ∫

(

)

̈

∫

̇

5.8 DAMPING BEHAVIOR OF SANDY SOILS The damping characteristics of sandy soils were determined to be functions of footing depth, soil density, degree of saturation of the soil and the applied energy to the soil. These are described as follows:

5.8.1 Effect of footing embedment (depth) A parametric study on the effects of D/B ratio (depth/diameter) on the damping ratios of different soils and loading conditions is carried out and the results are plotted and presented in Figure (5-3). The plots reveal that, for all soil conditions and footing diameters, the damping is a direct function of D/B ratio and is found to increase with the increase of D/B. This tendency is related to the increase of soil density as D/B increases, hence the soil tends to behave as a solid medium which activates both viscous and strain damping. This rate of increase of damping ratio is noticed to be smaller for cases of large diameter of impact plates.

150


Chapter Five

The same tendency was found by Al-Homoud and Al-Maaitah, (1996), Al-Azawi et al. (2006), Prakash and Puri, 2006, and Al-Ameri, (2014). Dropping Mass 5 kg Diameter of Bearing Plate 15cm

Dropping Mass 5 kg Diameter of Bearing Plate 10cm Loose Medium Dense

Loose Medium Dense

0.12

Damping ratio

Damping ratio

0.12

0.08

0.04

0.08

0.04

0 0

0.5

1

1.5

0

2

0

D/B

1.5

2

(b) Mass=5 kg, plate diameter =150 mm Dropping Mass 10 kg Diameter of Bearing Plate 15cm

Dropping Mass 10 kg Diameter of Bearing Plate 10cm

Loose Medium Dense

0.12

Loose Medium Dense

Damping ratio

Damping ratio

1

D/B

(a) Mass=5 kg, plate diameter =100 mm

0.12

0.5

0.08

0.04

0.08

0.04

0

0 0

0.5

1

1.5

2

D/B

0

0.5

1

1.5

D/B

(c) Mass=10 kg, plate diameter =100 mm

(d) Mass=10 kg, plate diameter =150 mm

Figure ‎5-3 Relationship between damping ratio and embedment ratio in soil of different soil conditions.

5.8.2 Effect of footing size As shown in Figure (5-3), the impact plate (footing) diameter seems to have a reverse effect on the damping ratio of sandy soil for all cases of soil conditions, embedment depth and energy of impact. It was found that an increase in the footing area by about 125% results in a decrease in the damping ratio by 20-35%. This means that the damping behavior of sandy soils is more influenced by the stiffness 151

2

Chapter Five


of the corresponding soil rather than the vibrating mass (foundation-soil mass). An increase in the footing diameter results in an increase of the stress bulb of soil and hence the mass. Though the mass simultaneously increases, however, its rate of increase is less than that of the stiffness and therefore, the natural frequencies of the foundation-soil system increases and hence, the system becomes more sensitive to the active energy of the load causing vibration. It can be noticed from examples (5-3) and (5-5) that the coefficient of damping in DDSP15M5H50 model is higher than that in the DDSP10M5H50 model due to the coefficient of damping which is a measure of vibration energy dissipated within the soil and carried away by spreading waves. These waves are generated at every point on the soil-foundation interface so that in general, the coefficient of damping increases with increasing the area of contact that is, increasing the geometrical damping. The same conclusion was reached by Al-Azawi et al. (2006). A very important notice is to be mentioned, that is, though the damping coefficient is found to increase as the contact area of footing increases but, meanwhile, the critical damping values increases also but slightly larger, this variation leads to the unexpected decrease in the damping ratio , that is, the damping increases as the footing area increases while at the same time the damping ratio decreases. That was previously concluded by Kim et al. (2001).

5.8.3 Effect of soil density It was found that the void ratio (or packing density) has a significant effect on damping. It is clear from Figure (5-3) that the damping ratio decreases with the void ratio increase because; when the void ratio increases, both types of damping decrease, material damping and geometric damping. Material damping decreases because of decrease in friction between particles. Geometrical damping decreases because the energy that is generated from the load transfers to displacement. During earthquakes, soft soils experience strong shaking effect than others which cause damage to structures constructed in such areas. This tendency occurs since these soils amplify the shaking effect due to the fact that such type of soils possess small stiffness values which in turn results in amplifying displacement to conserve the same input energy. Accordingly, loose or soft soil has a low damping when it is subjected to a dynamic action compared to stiff or dense soils.

152


Chapter Five

5.8.4 Effect of saturation

0.1

0.1

0.08

0.08

Damping ratio

Damping ratio

Plots of the effects of soil saturation on the damping behavior of sandy soil are shown in Figure (5-4). These plots reveal that saturated soils always possess larger damping ratios than dry ones irrespectively of all other conditions of loading or geometry. This phenomenon is true since a saturated soil tends to behave as a real viscous medium than dry soils. However, for the scope of the present work, the increase in damping ratios were found to be about 10-20% in case of saturated soils as compared to the dry soil. These results are compatible with Qiu (2010), AlHomoud and Al-Maaitah (1996), and Livaoglu and Dogangun (2007).

0.06

0.04

Dropping Height 250 mm Falling Mass 5 kg

0.02

0.06

0.04


0.02

Sat. soil Dry soil

Sat. soil Dry soil 0 5

10

15

20

0

25

5

Diameter of footing (cm)

15

20

25

(b) Height= 250 mm, mass= 10 kg

0.1

0.1

0.08

0.08

Damping ratio

Damping ratio

(a) Height= 250 mm, mass= 5 kg

0.06

0.04


0.02

10


0.06

0.04


0.02

Sat. soil Dry soil

Sat. soil Dry soil 0

0 5

10

15

20

25

5

10

15

20



(c) Height= 500 mm, mass= 5 kg

(d) Height= 500 mm, mass= 10 kg

Figure ‎5-4 Relationship between damping ratio and diameter of footing in dry and saturated soil. 153

25


Chapter Five

5.8.5 Effect of energy of impact The energy of impact is a function of two factors, falling mass and height of fall. As shown in Figure (5-5), the damping ratio of a sandy soil is highly influenced by the energy of impact, that is, impacts having low energy of the applied dynamic load experienced larger damping ratios in sandy soils as compared to the cases of impact having large energies. This tendency is a common property or phenomenon of sandy soil, such that, a dynamic load of low energy excites less mass of soil and causes minor disturbance in the structure orientation of the soil particles, that is, no collapse and the foundation-soil system acts as a solid medium which retains its geometry and hence possessing higher tendency to dissipate the propagating impact wave, and hence, experiencing larger damping activity. 0.14

0.14

Diameter of Bearing Plate 150 mm Falling weight 5kg from height 250mm Falling weight 5kg from height 500mm Falling weight 10kg from height 250mm Falling weight 10kg from height 500mm

0.12

Damping ratio

Damping ratio

0.12

0.1

0.08

0.1

0.08

Diameter of Bearing Plate 100 mm Falling weight 5kg from height 250mm Falling weight 5kg from height 500mm Falling weight 10kg from height 250mm Falling weight 10kg from height 500mm

0.06

0.04

0.06

0.04 0

0.5

1

1.5

2

D/B

0

0.5

1

1.5

D/B

(b) different falling masses and 150 mm

(a) different falling masses and 100 mm diameter of bearing plate

diameter of bearing plate

Figure ‎5-5 The effect of impact load energy on damping ratio.

5.9 SHEAR MODULUS OF SANDY SOILS UNDERGOING IMPACT LOADING It is known that the modulus of subgrade reaction of soils, stiffness and hence the shear modulus are properties of soil that depend upon general soil conditions, that is, compaction (density) and the degree of saturation. It was tried in this study to have some understanding of shear modulus variation of sandy soil undergoing

154

2


Chapter Five

impact. Results of several tests are categorized in more than one category and presented in the plots shown in Figure (5-6), (5-7), and (5-8). The plots reveal that both loose and medium dry sandy soils in addition to the saturated sand are usually having no variation or slight changing in stiffness characteristics, that is, shear modulus, irrespectively of the case of loading and its characteristics. Dry dense sand however experienced a noticeable improvement during impact especially when the footing is placed at larger D/B ratios. The size of footing is noticed to have an influence on the shear modulus of dry dense sand where the shear modulus was found to increase by 40-90% for loose and medium soil and about 10-20% for dense soil as the plate area increases by 125%. This tendency is related to the increase in the degree of confinement as the diameter of footing increases. The shear modulus was found to be highly affected by the energy of impact where it was found that, a dynamic load possessing higher energy (height of fall or mass) results in a noticeable rebound of the impact wave, that is, an increase in the combined footing-soil stiffness (k) which in turn results in an increase of the soil shear modulus (G).

6000

Shear modulus (kN/m2)


6000

4000

Diameter of Bearing Plate 100 mm

2000

Falling weight 5kg from height 250mm Falling weight 5kg from height 500mm Falling weight 10kg from height 250mm Falling weight 10kg from height 500mm

4000

Diameter of Bearing Plate 150 mm

2000

Falling weight 5kg from height 250mm Falling weight 5kg from height 500mm Falling weight 10kg from height 250mm Falling weight 10kg from height 500mm

0 0

0.5

1

1.5

2

0 0

D/B

0.5

1

1.5

D/B

(a) Plate diameter = 100 mm

(b) Plate diameter = 150 mm

Figure ‎5-6 The effect of impact load on the shear modulus.

155

2


Chapter Five

8000

8000

Dropping Mass 5 kg Diameter of Bearing Plate 150 mm

Loose Medium Dense

6000




4000

2000

0 0

0.5

1

1.5

Loose Medium Dense

6000

4000

2000

0

2

0

0.5

D/B

(a) Mass= 5 kg, plate diameter = 100 mm

1.5

2

(b) Mass= 5 kg, plate diameter = 150 mm 8000

8000


Dropping Mass 10 kg Diameter of Bearing Plate 100 mm Loose Medium Dense

6000



1

D/B

4000

2000

0 0

0.5

1

1.5

2

D/B

Loose Medium Dense

6000

4000

2000

0 0

0.5

1

1.5

D/B

(c) Mass= 10 kg, plate diameter = 100 mm

(d) Mass= 10 kg, plate diameter = 150 mm

Figure ‎5-7 Relationship between the shear modulus and embedment ratio for different soil conditions.

156

2


Chapter Five

5000

5000 Dropping Height 500 mm Falling Mass 5 kg

Sat. soil Dry soil

4000




3000

2000

1000

0 5

10

15

20

Sat. soil Dry soil

4000

3000

2000

1000

0

25

5


10

(a)

25

5000

Dropping Height 250 mm Falling Mass 10 kg Sat. soil Dry soil



20

(b)

5000

4000

15


3000

2000

1000

4000

3000

2000


1000

Sat. soil Dry soil

0 5

10

15

20

25


0 5

10

15

20


(c)

(d)

Figure ‎5-8 Relationship between the shear modulus and diameter of footing in dry and saturated soil.

157

25

Chapter Five


5.10 RELATIONSHIP BETWEEN THE DAMPING RATIO AND SHEAR MODULUS It was found earlier that the relationship between the damping and shear modulus of sandy soil is affected by several factors when the soil is subjected to an impact. These factors are, footing depth (D/B ratio), type of soil (degree of compaction) and the magnitude of energy of the falling mass during impact. Accordingly, these variables are assembled together and presented in plots as in Figure (5-9). Examinations of these plots show two major notes, first, dense sandy soils with footing placed at any depth within it, show a stable behavior as a linear structure, that is, since the soil is dense, it is having less possibilities of soil particles tend to collapse, a dynamic load represented by impact tends to densify the soil rather than changing the structure or orientation of particles, therefore, causing the shear modulus to increase. Meanwhile, the system starts to behave as a solid continuum where both viscous damping and strain damping become distinguished structure properties, hence an increase in the shear modulus of a dense dry sand by about 60% to 120% (caused by an impact) results in an increase in the damping ratio of the sandy soil system by about 20% to 25%. Loose dry sandy soils show instability in the system behavior, that is, a single impulsive impact generally causes densification of the soil particles which in turn results in a limited increase in the shear modulus; however, this limited increase in the shear modulus (less than 25%) causes the damping to increase by more than 200% in most cases. Medium sandy soils show a behavior ranging between that of dense and loose sand where impact causes the shear modulus to increase by about 100% and accordingly, damping ratios increase by 50% to 75%. An increase in the embedment ratio (D/B) causes the sandy soil layer to act as a solid medium which in turn results in an increase in soil density and hence the damping ratio increases. In general, one can notice that the damping ratio increases with increasing of the shear modulus for all test results as shown in Figure (5-9).

158


Chapter Five

One more common tendency can be noticed, in general, the damping ratio increases with the increase of the shear modulus in a logarithmic relationship depending on the embedment effect and size of the bearing plate.

0.14

Damping ratio

0.12

0.1

0.08

0.06

The size of bearing Plate 100 mm Loose soil under falling weight 5 kg from 500 mm Medium soil under falling weight 5 kg from 500 mm Dense soil under falling weight 5 kg from 500 mm Dense soil under falling weight 5 kg from 250 mm

0.04

0.02 0

2000

4000

6000


(a) Plate diameter = 100 mm, mass = 5 kg

Damping ratio

0.12

0.08


0.04

0 0

2000

4000

6000


(b) Plate diameter = 150 mm, mass = 5 kg Figure ‎5-9 Relationship between the shear modulus and damping ratio for different soil conditions.

159


Chapter Five

Damping Ratio

0.12

0.08


0.04

0 0

2000

4000

6000

Shear Modulus (kN/m2)

(c) Plate diameter = 100 mm, mass = 10 kg The size of bearing Plate 150 mm Loose soil under falling weight 10 kg from 500 mm Medium soil under falling weight 10 kg from 500 mm Dense soil under falling weight 10 kg from 500 mm Dense soil under falling weight 10 kg from 250 mm

Damping Ratio

0.12

0.08

0.04

0 0

2000

4000

6000

Shear Modulus (kN/m2)

(d) Plate diameter = 150 mm, mass = 10 kg Figure ‎5-9 Continued.

5.10.1 Relationship between the damping ratio and shear modulus with frequency ratio The damping ratio multiplied by shear modulus can be expressed as a power or exponential relationship with frequency ratio (

̅

) as shown in Figure (5-10)

with correlation factor (R = 0.936 for power relationship and R = 0.925 for exponential relationship). 160


Chapter Five

a. Power relationship with R = 0.936:

5.16

b. Exponential relationship with R = 0.925:

5.17 where: G in kN/m2, and ξ is in decimals.

ξ.G (kN/m2)

700 600

y = 549.84e-1.57x R² = 0.8556

500

y = 72.304x-1.933 R² = 0.8765

400

Power (Damping ratio.G and beta)

300

Expon. (Damping ratio.G and beta)

200 100 0 0

0.5

1

1.5

2

2.5

3

3.5

Frequency ratio (β)

Figure 5-10 Relationship between the damping ratio multiplied by shear modulus with frequency ratio.

5.10.2 Relationship between the damping ratio and stiffness with frequency ratio Figure (5-11) demonstrates the relationship between the damping ratio multiplied by the stiffness with frequency ratio (

̅

) with a correlation factor (R

= 0.976 for power relation and R = 0.972 for linear relation) as follows: 161


Chapter Five

c. Exponential relationship with R = 0.955:

5.18

d. Power relationship with R = 0.946:

5.19

Damping‎ratio.‎Stiffness‎(ξ.k)‎(N/m)

where: k in N/m, and ξ is in decimals.

90

y = 69.326e-1.667x R² = 0.9114

80 70

y = 8.0686x-2.01 R² = 0.8958

60 50 40

Expon. (Damping ratio.k and beta)

30

Power (Damping ratio.k and beta)

20 10 0 0

0.5

1

1.5

2

2.5

3

3.5


Figure 5-11 Relationship between the damping ratio multiplied by stiffness with frequency ratio.

5.11 RELATIONSHIP BETWEEN THE DAMPING COEFFICIENT AND OTHER FACTORS According to the test results of the present work, some relationships between damping coefficient and shear modulus, modulus of subgrade reaction, modulus of

162


Chapter Five

elasticity, and frequency ratio and (5-14).

can be drawn as shown in Figures (5-12), (5-13),

The same relationships (power or linear) among the damping coefficient and shear modulus, modulus of subgrade reaction, and modulus of elasticity was found but with different factors having values of the characteristics with correlation factor (R = 0.976 for power relation and R = 0.972 for linear relation) as follows: 1. Relationship between the damping coefficient and the modulus of subgrade reaction: e. Power relationship with R = 0.976: 5.20 f. Linear relationship with R = 0.972: 5.21 where: c in N.sec/m, and K in kN/m3.

Damoing coefficient (c) (N.sec./m)

12000

y = 0.0157x1.2174 R² = 0.9527 y = 0.149x - 21.585 R² = 0.9453

10000 8000 6000 4000

Power (c&K)

2000

Linear (c&K)

0 0

10000

20000

30000

40000

Modulus of subgrade reaction

50000

60000

70000

(kN/m3)

Figure 5-12 Relationship between the damping coefficient and modulus of subgrade reaction.

163


Chapter Five

2. Relationship between the damping coefficient and modulus of elasticity: a. Power relationship with R = 0.976: 5.22 b. Linear relationship with R = 0.972: 5.23 where: c in N.sec/m, and E in kN/m2.

Damping coefficient (c) (N.sec./m)

12000

y = 0.0764x1.2174 R² = 0.9525

10000

y = 0.5457x - 21.44 R² = 0.9453

8000

6000 4000 Linear (c&E)

2000

Power (c&E) 0 0

2000

4000

6000

8000

10000

Modulus of elasticity

12000

14000

16000

18000

(kN/m2)

Figure 5-13 Relationship between the damping coefficient and modulus of elasticity. 3. Relationship between the damping coefficient and shear modulus: a. Power relationship with R = 0.976: 5.24

164


Chapter Five

b. Linear relationship with R = 0.972: 5.25 where: c in N.sec/m, and G in kN/m2.


12000

y = 1.4188x - 21.44 R² = 0.9453

10000

y = 0.2444x1.2174 R² = 0.9525

8000

6000

4000 Linear (c&G)

2000

Power (c&G) 0 0

1000

2000

3000

4000

Shear modulus

5000

6000

7000

kN/m2

Figure ‎5-14 Relationship between the damping coefficient and shear modulus. Figure (5-15) shows relationship between the damping coefficient and the frequency ratio (β) with power and exponential forms as follows: 1. Power relationship with R = 0.971 5.26 2. Exponential relationship with R = 0.957 5.27 where: c in N.sec/m.

165


Chapter Five

10000


9000

y = 1456.4x-1.898 R² = 0.9421 y = 10640e-1.539x R² = 0.9167

8000 7000

6000 Expon. (c&beta)

5000

Power (c&beta) 4000 3000 2000 1000 0 0

0.5

1

1.5

2

2.5

3

3.5


Figure 5-15 Relationship between the damping coefficient and frequency ratio (beta).

5.12 RELATIONSHIP AMONG MODULUS OF SUBGRADE REACTION, SHEAR MODULUS, AND MODULUS OF ELASTICITY WITH FREQUENCY RATIO According to test results, relationship among modulus of subgrade reaction, shear modulus, and modulus of elasticity with frequency ratio was obtained in a power or exponential form. These relations indicate that increasing the stiffness leads to decreasing in the frequency ratio under impact load as follows: 1. Relationship between the modulus of subgrade reaction with Figure (5-16):

as shown in

a. Power relationship with R = 0.968: 5.28

166


Chapter Five

b. Exponential relationship with R = 0.939: 5.29 where K in kN/m3.

Modulus of subgrade reaction kN/m3

70000 60000

y = 12055x-1.517 R² = 0.9364

50000

y = 57655e-1.21x R² = 0.8811

40000

Power (K&Beta)

30000

Expon. (K&Beta) 20000 10000 0 0

0.5

1

1.5

2

2.5

3

3.5


Figure 5-16 Relationship between the modulus of subgrade reaction with frequency ratio (beta). 2. Relationship between the shear modulus and

as shown in Figure (6-17)

a. Power relationship with R = 0.968: 5.30 b. Exponential relationship with R = 0.939: 5.31 where G in kN/m2.

167


Chapter Five

7000

Shear Modulus (G) kN/m2

6000

y = 6051.7e-1.21x R² = 0.8809

5000

y = 1265.8x-1.517 R² = 0.9363

4000

Power (G&Beta) 3000

Expon. (G&Beta)

2000 1000 0 0

0.5

1

1.5

2

2.5

3

3.5


Figure 5-17 Relationship between the shear modulus with frequency ratio ( ).

3. Relationship between the modulus of elasticity with

as shown in Figure (5-18)

a. Power relationship with R = 0.968: 5.32 b. Exponential relationship with R = 0.939 5.33 where E in kN/m2.

168


Chapter Five

Modulus of elasticity (E) (kN/m2)

18000 16000

y = 3291x-1.517 R² = 0.9363

14000

y = 15734e-1.21x R² = 0.8809

12000 10000 8000 6000 4000 2000 0 0

0.5

1

1.5

2

2.5

3

3.5


Figure 5-18 Relationship between the modulus of elasticity with frequency ratio ( ). Finally, it can be seen from the previous empirical equations that the frequency ratio is very important in the impact load and dependent on many factors like energy force, diameter of the footing, the position of the embedment of the foundation, and of course on the density of the soil. Table (5-3) presents review on the empirical equations presented in this chapter. These relations are valid to dry and saturated sandy soils. Table ‎5-3: Empirical equations between soil characteristics of sandy soil under impact load.

Dependent

in decimals

in decimals

Variables

Equation

, and

(R)

0.936

, and

0.925

169

Chapter Five



Dependent

in decimals

in decimals

Variables ,

and

,

and

Equation

(R)

0.955

0.946

0.976

0.972

0.976

0.972

0.976

0.972

0.971

0.957

0.968

0.939

0.968

170

Chapter Five



Dependent

Variables

Equation

(R)

0.939

0.968

0.939

171

CHAPTER SIX

6. CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK

6.1 INTRODUCTION The present study evaluates the response of dry and saturated sands acted upon by impact loads using the falling weight deflectometer (FWD) to impose impact on the soil model with a base bearing plate of two sizes. The condition is dealt with as a shallow foundation on sandy soil under impact. In order to investigate the response of soil and footing to dynamic loading, a physical model was used. Total of (72) models were conducted. The parameters that were taken into consideration are related to amplitude of loading (falling mass 5 kg, or 10 kg falling from a height of 250 mm, or 500 mm), footing parameter (size of bearing plate 100 mm or 150 mm and depth of embedment (D/B = 0, 0.5, 1, 2)), soil conditions (relative density (loose, medium, or dense) and degree of saturation (dry or fully saturated)). Soil damping, which is expressed by an energy loss per cycle, was evaluated using a developed empirical equation based on the principle that the impulse or momentum of the falling mass is equal to the momentum of the equivalent soil system. Many empirical equations are proposed in this study implemented relationships among the damping coefficients with the frequency ratio (β), shear modulus (G), modulus of elasticity (E), and modulus of subgrade reaction (K) were derived in addition to relationships between the damping ratio multiplied by stiffness or by shear modulus and the frequency ratio (β).

172

Chapter Six

CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK

6.2 APPLICABILITY OF THE PRESENT WORK The present work, which deals with the dynamic behavior of sandy soil under single impact load, clarifies the response of soil and foundation to impact loading condition. The present work cannot be considered as a complete study of the response of machine foundations to dynamic loading (in addition to the data available in literature), which are restricted to the number of variables studied especially for the measurements of response inside the soil media. Hence, the limitations within the testing program are:  The circular bearing plate is considered as a rigid circular steel footing,  The soil is a poorly graded (uniform) sand, and  The dynamic load is due to single impact load only.

6.3 CONCLUSIONS Based on experimental work carried out during this study and for the test conditions encountered in these tests, the following main conclusions can be listed as follows: 1. Damping of soil is a function of several factors: a. Type and magnitude of load, b. Size of foundation, c. Depth of foundation (embedment ratio), d. Relative density of sand, and e. Degree of saturation. 2. The frequency ratio (frequency of the impact/ frequency of the vibration foundation-soil system) is very important factor in problems deal with impact load. 3. The amplitude of the force-time history for dense soil under impact load is ideally harmonic with a single pulse, while in case of medium and loose soil, the impact load time history is also of a single pulse but has no ideal sine shape. The impulse almost vanishes or becomes of negligible value at the end of the impulse-time history in case of medium sandy soils while it ends at a magnitude equals or near to the magnitude of the weight of the falling hammer in case of sand of loose density.

173

Chapter Six


4. When the area of the bearing plate (footing) is increased by 125%, the following points are obtained: a. The amplitude of the force-time history will be increased. It will increase by about 50-60% for loose sand, 30-40% for medium sand, and 10-15% for dense sand. This tendency is attributed to the fact that the soil stiffness is related to two factors, degree of confinement which increases with the footing area and the magnitude of the excited mass which depends, also upon the footing area. b. The displacement response reduces in case of dry and saturated soil due to reduction in the stresses caused by the increase of contact area. The response reduces by about 30-45% for dry sand and 20-30% for saturated sand. c. The excess pore water pressure is reduced by about 50-60%. This tendency is logical since the pressure should reduce by about 56% (at least) from static laws. d. An increase in the natural frequency of the soil-foundation system (ω) by about 70-100% for loose sand, 60-90% for medium sand, and 5-15% for dense sand due to the increase in the soil stiffness. e. An increase in the value of the total active mass for dense soil by about 3050% due to increasing the volume of bulb of the soil participating in vibration. f. An increase in the modulus of subgrade reaction, modulus of elasticity, and shear modulus by about 40-90% for loose and medium soil and by about 1020% for dens soil, because the soil stiffness is related to two factors, degree of confinement which increases with the footing area and the magnitude of the excited mass which depends also upon the footing area. g. A decrease in damping ratio by about 20-35% due to the increase in the critical damping which is increased because of increases in the active mass and natural frequency. 5. Increasing footing embedment depth results in the followings: a. Amplitude of the force-time history increases by about 10-30%. due to increase in the degree of confinement with the increasing in the embedment.

174

Chapter Six


b. The displacement response of the soil will decrease by about 25-35% for loose sand, 35-40% for medium sand, and by about 40-50% for dense sand due to increase in the overburden pressure when the embedment depth increased which leads to increasing in the stiffness of the sandy soil. c. Increasing the natural frequency of the soil-foundation system (ω) by about 20-45%. For surface foundation, the foundation is free to oscillate in vertical, horizontal and rocking modes. But, when embedding a footing, the surrounding soil restricts oscillation due to confinement which leads to increasing the natural frequency, moreover, soil density increases with depth because of compaction, that is, tendency to behave as a solid medium. d. Increase in the value of total active mass for dense soil by about 10-25% hence, increasing amplitude of the force-time history and creating more wave travel paths. e. An increase in the modulus of subgrade reaction, modulus of elasticity, and shear modulus by about 50-100% due to the increase in soil density. f. An increase in the damping ratio by about 50-150% due to the increase of soil density as D/B increases, hence the soil tends to behave as a solid medium which activates both viscous and strain damping. 6. Variation of soil density leads to a variation of the soil characteristics and response as follows: a. When the falling weight of the hammer increased by about 100%, the impulse amplitude will increasing by about 70-80% in case of dense sand, 55-80% in case of medium sand and by about 45-55% in case of loose sand. This tendency is related to the fact that the impulse amplitude is energy dependent. The energy, meanwhile, decreases as the density also decreases, that is, looser soils contribute more in energy dissipation though the magnitude of dissipation is less than the increase associated with the mass of falling hammer. b. In case of 100 mm diameter of impact plate, the reduction in impulse force amplitude from dense to loose sand ranges between 60%-70%, while in case of 150 mm impact plate, the reduction is about 45-55% due to tendency of impulsive force amplitude magnitude since the magnitude of impulse is

175

Chapter Six


stiffness dependent. Stiffer soil tends to act as solids with high rebound capability. c. The displacement of the soil decreases by about 70-85% when the density of the soil is increased due to the decreasing in the void ratio. d. Increasing in the soil density leads to the increase in the natural frequency of the soil-foundation system (ω) by about 300-600% due to the increase of the soil stiffness. e. When the soil density changes from loose or medium to dense, the modulus of subgrade reaction, modulus of elasticity, and shear modulus increases by about 500-1000% due to decreasing in the void ratio which makes the soil to be stiffer. f. The damping ratio increases by about 20-80% when the soil density is varied from loose to dense since the waves will be generated at every point at the soil-foundation interface so that a higher void ratio leads results in less contact points in addition to less contact between particles, that makes the material damping and geometrical damping to reduce. 7. The damping ratio decreases when the load energy increases by about 10% for dense soil, 15—20% for medium soil, and 25-50% for loose soil. Low energy excites less mass of soil and causes minor disturbance in the structure orientation of the soil particles, that is, no collapse and the foundation-soil system acts as a solid medium which retains its geometry and hence possessing higher tendency to dissipate the propagating impact wave, and hence, experiencing larger damping activity. 8. The displacement response (vertical and horizontal) always follow the same behavior (decreasing with depth irrespective of the depth of impact plate) as the behavior of static load (live loads or surcharge) with depth following the conventional Bousinesq equation with different paths according to void ratio. 9. A comparison between dry and saturated soil condition reveals that: a. Amplitude of the force-time history decreases in case of saturated condition by about 10-22% since the voids are filled with water which leads to less contact points between particles.

176

Chapter Six


b. The displacement increases in the saturated condition by about 20-60% because there are two compressive waves through the saturated medium, the fluid wave and the frame wave with a coupled motion of the fluid and the frame waves and that makes the displacement to be higher in the saturated soil. c. The natural frequency of the soil-foundation system (ω) decreases in case of saturated sand by about 10-25%, since the voids are filled with water which restricts the soil form vibration. d. The modulus of subgrade reaction, modulus of elasticity, and shear modulus all decrease in case of saturated soil by about 30-50%. e. The damping ratio was found to be of higher values in case of saturated sands by about 10-20% since a saturated soil tends to behave as a real viscous medium. f. The horizontal displacement within the soil medium at a distance B away from the edge of the footing decreases in saturated and dry sands but the reduction in displacement in the saturation condition is higher than in dry condition that is due to two reasons: first, if the shear wave is concerned; pore water has no rigidity to shear and the second the voids are filled with water and hence less interaction of particles due to the role of water as a lubricant between particles. 10. The excess pore water pressure increases by about 40% as the amplitude of the impact force increases due to the increase of the contact pressure.

6.4 RECOMMENDATIONS FOR FUTURE WORK The following recommendations are suggested for future work: 1. Adopting full scale experiments with measurements of acceleration, velocity, and displacement in the surrounding soils and studying the scale effect on damping. 2. Studying the attenuation of body waves, dynamic response of soils and damping using other different types of dynamic force source such as machine vibration and earthquake base excitations. 3. Investigation of damping in dry and saturated clays to evaluate expressions for defining the damping ratio. 177

Chapter Six


4. The test program can be used to study the effects of different degrees of saturation. 5. The test program can be used to evaluate damping ratios within the soil medium using pressure cells inside the soil medium instead of the accelerometer to evaluate the energy loss inside the soil medium. 6. Carrying out numerical study using FE programs to analyze the problem and to carry out parametric study using different damping ratio values.

178

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 Gibbs, J. F., Boore, D. M., Joyner, W. B., and Fumal, T. E. (1994): "The Attenuation of Seismic Shear Waves in Quaternary Alluvium in Santa Clara Valley, California", Bulletin of Seismological Society of America, 84(1), pp.76– 90, Cited by Rix et al. (2000).  Grabe, J., Hamann, T., and Chmelnizkij, A. (2014): ―Numerical Simulation of Wave Propagation in Fully Saturated Soil Modeled as a Two-Phase Medium‖, Proceedings of the 9th International Conference on Structural Dynamics, EURODYN, pp. 631-637.  Hardin, B. O., and Black, W. L. (1968). "Vibration Modulus of Normally Consolidated Clays", Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 94, No. SM2, pp. 353-369.  Hardin, B. O., and Drnevich, V. P. (1972):. "Shear Modulus and Damping in Soils." Journal of Soil Mechanics and Foundation Division, 98(7), pp. 667–692.  Heckman, W.S. and Hagerty, D.J. (1978). "Vibrations Associated with Pile Driving", Journal of the Construction Division, Vol. 104, No. CO4, December 1978, pp. 385‐394  Hoar, R. J., and Stokoe, K. H., II. (1984). ‗‗Field and Laboratory Measurements of Material Damping of Soil in Shear.‘‘ Proc., 8th World Conference on Earthquake Engineering, Prentice-Hall, Englewood Cliffs, N.J., Vol. III, pp. 47– 54.  Holeyman, A.E. (2002): "Soil Behavior under Vibratory Driving", Proceedings of the International Conference on Vibratory Pile Driving and Deep Soil Compaction, 9-10 September 2002, Louvain-la-Neuve, Belgium, pp. 3-19.  Holmberg, R., Arnberg, P.W., Bennerhult, O., Forssblad, L., Gereben, L., Hellman, L., Olsson, K., Rundqvist, G., Sjöberg, C., Sjökvist, K. & Wallmark, G. (1984): "Vibrations generated by traffic and building construction activities. Swedish Council for Building Research", Stockholm, Sweden, Cited by Deckner (2013).  Jongmans, D. (1990): "In-Situ Attenuation Measurements in Soils.", Engineering Geology, 29, pp. 99–118.

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 Kim, Y.S., Miura, K., Miura, S., and Nishimura M., (2001): "Vibration Characteristics of Rigid Body Placed on Sand Ground", Soil Dynamics and Earthquake Engineering, Vol. 21, No. 1, pp. 19-37.  Kotronis, P., Claudio, T., St´ephane, G. (2013): "Soil-Structure Interaction", ALERT Doctoral School 2013, the Alliance of Laboratories in Europe for Research and Technology, Germany.  Kramer, S.L. (1996): ―Geotechnical Earthquake Engineering‖, Prentice‐Hall, New Jersey, USA.  Kumar, S. S., Krishna, A. M., Dey, A. (2013): ―Parameters Influencing Dynamic Soil Properties: A Review Treatise‖, National Conference on Recent Advances in Civil Engineering; November 15-16th, 2013, pp.1-10.  Lidén, M., (2012): ―Ground Vibrations due to Vibratory Sheet Pile Driving‖, M.Sc. Thesis, Division of Soil- and Rock Mechanics, Department of Civil and Architectural Engineering, Royal Institute of Technology, Stockholm.  Liu, H. P., andWarrick, R. E.,Westerlund, R. E., and Kayen, R. E. (1994): "In Situ Measurement of Seismic Shear-Wave Absorption in the San Francisco Holocene Bay Mud by the Pulse-broadening Method", Bulletin of Seismological Society of America, 84(1), PP. 62–75, Cited by Rix et al. (2000).  Livaoglu, R. and Dogangun, A. (2007): "Effect of Foundation Embedment on Seismic Behavior of Elevated Tanks Considering Fluid–Structure-Soil Interaction", Soil Dynamics and Earthquake Engineering, Vol. 27, No. (9), pp. 855-863.  Lu, N., and Likos, W.J., ( 2004): "Unsaturated Soil Mechanics", John Wiley & Sons, INC.  Luna, R. and Jadi, H. (2000): ―Determination of Dynamic Soil Properties Using Geophysical Methods‖, Proceedings of the First International Conference on the Application of Geophysical and NDT Methodologies to Transportation Facilities and Infrastructure, St. Louis, MO, December 2000, pp.1-15.  Mandal, J. J., and Roychowdhury, S. (2008): ―Response of Rectangular Raft Foundations under Transient Loading‖, Proceedings, 12th International

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Conference of International Association for Computer Methods and Advanced in Geomechanis (IACMAG), India, pp. 524-530.  Mok, Y. J., Sa´nchez-Salinero, I., Stokoe, K. H., II, and Roesset, J. M. (1988). ‗‗In Situ Damping Measurements by Crosshole Seismic Method.‘‘ Earthquake Engineering and Soil Dynamics II–Recent Advances in Ground Motion Evaluation, Geotech. Spec. Publ. No. 20, J. L. Von Thun, ed., ASCE, New York, pp. 305–320.  Omidvar, M., Iskander, M. and Bless, S. (2012), "Stress-Strain Behavior of Sand at High Strain Rates", International Journal of Impact Engineering. Vol. 49, pp. 192-213.  Ostadan, F., Deng, N., and Roesset, J. M. (2004): ―Estimating Total System Damping for Soil- Structure Interaction Systems‖, Proceedings Third UJNR Workshop on Soil-Structure Interaction, Menlo Park, California, USA, pp. 1-33.  Popescu, R., Prevost, J. H., Deodatis, G. and Chakrabortty, P. (2006): ―Dynamics of Nonlinear Porous Media with Applications to Soil Liquefaction‖, Soil Dynamics and Earthquake Engineering, 26, pp. 648-665.  Prakash, S. (1981): ―Soil Dynamics‖, McGraw-Hill, New York.  Prakash, S., and Puri, K. V. (2006): ―Foundation for Vibrating Machines‖, Special Issue, of the Journal of Structural Engineering, SERC, and Madras, India, pp. 1-38.  Punmia, B. C., Jain, A. K., Jain, A. K. (2005) ―Soil Mechanics and Foundations‖ Luxima Publications (P) Ltd.  Qiu, T., (2010): "Analytical Solution for Biot Flow–Induced Damping in Saturated Soil during Shear Wave Excitations", Journal of Geotechnical and Geoenvironmental Engineering, ASCE, November, Vol. 136, No. 11 pp. 15011508.  Rajashekhar Swamy H. M., (2013): "Non-linear Dynamic Analysis of Soil Structure Interaction of Three Dimensional Structure for Varied Soil Conditions", Ph.D. Thesis, Department of Civil Engineering Manipal Institute of Technology, Manipal University, India.

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 Rao K., N. S. V. (2011), "Foundation Design Theory and Practice", John Wiley and Sons (Asia) Pte Ltd.  Redpath, B. B., and Lee, R. C. (1986): "In-situ Measurements of Shearwave Attenuation at a Strong Motion Recording Site" Earthquake Notes, 57, 8, Cited by Rix et al. (2000).  Richart, F. E., Woods, R. D. & Hall, J. R. (1970): ―Vibrations of Soils and Foundations‖, Prentice‐Hall, Engelwood Cliffs, USA.  Rix, G. J. Lai, C. G., and Spang Jr., A. W., (2000): "In Situ Measurement of Damping Ratio Using Surface Waves", Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol.126, No.5, PP 472-480.  Santamarina, J. C., Klein, K. A., Fam, M. A. (2001): ―Soils and Waves‖, Wiley and Sons Ltd, Chichester.  Seed, H. B., Wong, R. T., Idriss, I. M., and Tokimatsu, K. (1986): "Moduli and Damping Factors for Dynamic Analysis of Cohesionless Soils." Journal of Geotechnical Engineering, ASCE, Vol.112, No. 11, pp. 1016–1032.  Sitharam, T., Govindaraju, L. and Sridharan, A. (2004), "Dynamic Properties and Liquefaction Potential of Soils", Current Science, 87, No. 10, pp.1370-1378.  Spyrakos, C. C. (2008): ―Dynamic Soil-Structure Interaction: Historical Development and Modern Practice‖, Laboratory for Earthquake Engineering, School of Civil Engineering, National Technical University.  Stewart, W. P. (1992): "In Situ Measurement of Dynamic Soil Properties with Emphasis on Damping." Ph.D. dissertation, University of British Columbia, Vancouver, Cited by Rix et al., (2000).  Svinkin, M. R., (2008a): ―Dynamic Effects of Impact Machine Foundations‖, Geotechnical Earthquake Engineering and Soil Dynamics IV, © 2008 ASCE, pp. 1-17.  Svinkin, M. R., (2008b): ―Soil and Structure Vibrations from Construction and Industrial Sources‖, the Sixth International Conference on Case Histories in Geotechnical Engineering, Omni Press, Arlington, Virginia, pp. 1-14.

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 Tang, Y., Zhou, J., Ren, X., Yang, Q. (2014): ―Dynamic Response and Deformation Characteristic of Saturated Soft Clay under Subway Vehicle Loading‖, Springer Environmental Science and Engineering, Science Press Ltd, Beijing and Springer-Verlag Berlin Heidelberg.  TML Small FWD System: ―Operation Manual‖, Tokyo Sokki Kenkyujo Co., Ltd.  Turner J. R. and Kulhawy F. H., (1987), "Experimental Analysis of Drilled Foundations Subjected to Repeated Axial Loads under Drained Conditions", Report EL-S32S, Electric Power Research Institute, Palo Alto, California.  Vucetic, M., and Dobry, R. (1991): "Effect of Soil Plasticity on Cyclic Response." Journal of Geotechnical Engineering, ASCE, 117(1), pp. 89–107.  Wiss, J.F. (1967): "Damage Effects of Pile Driving Vibration", Highway Research Board Record, No. 155, pp. 14‐20.  Xue, X., Ren, T., and Zhang, W., (2012): ―Analysis of Fatigue Damage Character of Soils under Impact Load‖, Journal of Vibration and Control, pp. 1– 10.  Zhenzhong W.U., (2014): ―Measuring Dynamic Properties of Wind Turbine Foundation Soil in Resonant Column - Issues and Challenges‖, M.Sc. Thesis, Civil and Environmental Engineering at the University of Wisconsin – Madison, United States.

187

A Appendix A MEASUREMENT DEVICES

A.1 TML SMALL FWD SYSTEM FWD-Light, which is a TML-type small FWD system as shown in Figure (A1) with dimensions, is easy to handle and carry, and capable of measuring the coefficient of subgrade reaction (K-value) and subgrade modulus (E-value) over a short period of time. The following Table (A-1) shows components and standard accessories of set. Table (A-2) and (A-3) shows the specifications of small FWD main body KFD-100A and specifications of exclusive indicator TC-351F respectively. Test and inspection data of small FWD main body KFD-100A and exclusive indicator TC-351F are shown in Figures (A-2) and (A-3) respectively. Table A-1: Standard set.

Components 1. Small FWD main body: KFD-100A

1

2. Exclusive indicator: TC-351F

1

3. Portable aluminum carrying case

1

4. 32MB compact flash memory card

1

5. Memory card adaptor

1

6. Data acquisition software for TC-351F: TC-7351

1

Standard accessories 1. AC power package: CR-1870 2. 5m cable (7-pin 5-pin) 3. Operation manual 4. Certificate of guarantee 5. Inspection sheet A-1

‎A

Appendix A

Table A-2: Specifications of small FWD main body KFD-100A. Dimensions of loading plate

φ100×15(thick)mm

Mass of weight

5 kg

Falling height

50-530mm

Falling method of weight

Lever (with stopper)

Measuring range Load cell

0.7-20kN

Displacement transducer

0-2.5mm

Sensor Load cell

Strain gauge based load cell 1 point Capacity 20kN（allowable over load 150％）

Acceleration transducer

Strain gauge based Acceleration transducer 1 point Capacity 500m/s2（allowable over load 300％）

Data acquisition No. of measuring points

2 points (load and acceleration)

Measuring accuracy

±(0.1%rdg+2digit) (at 23±5°C)

Data memory

800 data/point

Sampling speed

50μsec

Trigger function

By data (load value), pre-trigger recording

Interface Exclusive

2-wire serial transfer

No. of external displacement sensors

2 points at maximum

Power source

Supplied by Exclusive indicator TC-351F

Environment

-20

-

+60°C,

85%

RH

or

less

condensation) Height

Approx. 1100mm

Wight

Approx. 15kg (including 5kg weight)

A-2

(no

‎A

Appendix A

Table A-3: Specifications of exclusive indicator TC-351F. Liquid crystal display 128×64 dots

Display

Content of display Monitor

Load, Acceleration, * Acceleration of external displacement sensor, Time Analysis

Analysis result Maximum load, Maximum displacement, *Maximum displacement of external sensor, Coefficient of subgrade reaction (KTML), Subgrade modulus (ETML)

Indicates results of four measurements including last three measurements Stored data indication

Stored data indication Stored data in specified file number in memory card Indicated including stored data of three continual measurements

File management

File management of stored data Deletion of stored data in specified file number Formatting of memory card

Real time clock

Year, Month, Day, Hour, Minute, Second

Accuracy

±2sec/day (at 23±5°C)

Memory card

Storing result of analysis

Card standard

Conforms to PC Card Standard (Type II)

Card type

Compact flash memory card (with card adapter) or ATA flash memory card

Card capacity

8-128 M byte

Data format

CSV

Data memory

Storing and reading out measurement results

A-3

‎A

Appendix A

Table ‎A-3: Continued. Number of stored

data Approximately 7,500 measurement results (With 2 external displacement sensors: approximately 5,700 measurement results)

Data maintained period

Approximately 10 days (with fully-charged internal backup battery)

Interface

When using optional measurement/analysis software TC-7100

Standard

RS-232C

Function

Receiving control command, Sending measured data, Output to exclusive printer

Power source(battery)

Nickel hydride secondary battery

Continual operation

Approx. 32 hours or 1000 times measurements (at 23±5°C). In case of measuring 30 times/hour by standard configuration without options with fully charged battery

Vibration

tolerance 30m/s2 (at 50Hz 0.6mmp-p)

Drip-proof

IP-54 (with cover installed)

Environment

-10 - +50°C, less than 85%RH (no condensation)

Dimensions

150(W)×120(H)×265(D)mm（excluding projected parts）

Weight Approx.

3kg

A-4

‎A

Appendix A

(a) Small FWD main body KFD-100A

(b) Exclusive indicator TC-351F

Figure A-1 TML small FWD system

A-5

‎A

Appendix A

Figure A-2 Test and inspection data of small FWD main body KFD-100A.

A-6

‎A

Appendix A

Figure A.2 Continued.

A-7

‎A

Appendix A

Figure A-3 Test and inspection data of exclusive indicator TC-351F.

A-8

‎A

Appendix A

Figure A-3 Continued.

A-9

‎A

Appendix A


A-10

‎A

Appendix A


A.2 THE MULTI-RECORDER TMR-200 The multi-recorder TMR-200 series is a small multi-channel data acquisition system enabling combination of various measuring units according to measurement purposes. The testing objects are analog input such as stress, load, pressure, acceleration, etc. using strain gauges and strain gauge based transducers and digital input/output such as CAN, etc. in vehicle onboard measurement  Combination of a plentiful and various sensor input/output units for strain, temperature, voltage, CAN, etc.  The maximum measurement of 80 channels  100kHz high speed sampling  USB and LAN interfaces  Vibration tolerance and small size suitable for vehicle onboard  Battery operation  Data recovery at power interruption and measurement restart at power recovery

A-11

‎A

Appendix A

 Various settings, monitoring and measurement result display with the display unit In this research two parts was used according to the purpose of the research control unit TMR-211and strain full bridge unit TMR-221 as follows:

A.2.1 Control Unit TMR-211 Figure (A-4) and (A-5) shows the specification and explanation of control unit TMR-211 respectively. Figures (A-6) shows test and inspection data of control unit TMR-211.

Figure A-4 Specification of control unit TMR-211.

A-12

‎A

Appendix A

Figure A-5 Control unit TMR-211.

A-13

‎A

Appendix A

Figure A-6 Test and inspection data of control unit TMR-211.

A-14

‎A

Appendix A


A-15

‎A

Appendix A


A-16

‎A

Appendix A

A.2.2 Strain Full Bridge Unit TMR-221 Figure (A-7) and (A-8) shows the specification and explanation of strain full bridge unit TMR-221 respectively. Figures (A-9) shows test and inspection data strain full bridge unit TMR-221.

Figure A-7 Specification of strain full bridge unit TMR-221.

A-17

‎A

Appendix A

Figure A-8 Strain full bridge unit TMR-221.

A-18

‎A

Appendix A

Figure A-9 Test and inspection data of Strain Full Bridge Unit TMR-221.

A-19

‎A

Appendix A


A-20

‎A

Appendix A


A-21

‎A

Appendix A


A-22

‎A

Appendix A


A-23

‎A

Appendix A


A-24

‎A

Appendix A

A.2.3 Connection measurement unit Using the accessory control cable ―CR-6460‖ to connect one end to the unit port on the back of the control unit and another end to the control port on the back of the measurement unit as shown in Figure (A.10).

Figure A-10 Connection measurement unit.

A.3 ARH-A WATERPROOF, LOW CAPACITY ACCELERATION TRANSDUCER (ARH-500A) The ARH-A acceleration transducer has a waterproof structure. It is installed in water or ground or embedded in concrete. The rigid waterproof structure makes this transducer suitable for use in an adverse environment or for outdoor use. The specification of acceleration transducer is listed in Table (A-4) and the test and A-25

‎A

Appendix A

inspection data of four acceleration transducers that used in this research are shown in Figure (A-11).

Measurement 1. The transducer is calibrated with a constant voltage excitation type strainmeter using the supplied cable. The rate output and sensitivity shown on the test data are found with an instrument gauge factor 2.00 (In case of using TML data logger, its coefficient should be set to 1.000). 2. One end of the supplied cable is usually supplied without connector plug. The cable is connected to a strainmeter or its switching box by screwing or soldering. In case of using NDIS 7-pin connector plug, refer to the following connection layout. (N.B. The shield wire of the cable is not connected to the transducer body).

3. Set necessary measuring parameters to a strainmeter, recorder, computer, etc. (For strainmeter, for example, initial balancing, sensitivity adjustment, settings of unit, coefficient and measure mode, initial value measurement and so on.) 4. Take note of the polarity of measured value. If acceleration is generated in the + side of arrow mark of the transducer, the measured value is in the + polarity.

5. In ordinary measurement, it is recommended that the strainmeter is previously set to direct measure mode in physical unit. In case of strain reading, acceleration can be found using the following equation. A-26

‎A

Appendix A

Acceleration = Measure Value × Calibration Coefficient [ m/s2 ]

[ ×10-6 ]

[ m/s2/1×10-6 ] ---- International system of units (SI)

[G]

[ ×10-6 ]

[ G/1×10-6]

---- Gravitational system of units

6. In case that the cable is extended under constant voltage excitation, correct the lowering of sensitivity using the following equation.

{

}

where ɛ0 = Real value after correction

[ m/s2 ] [ G ] [ µ ]

ɛ = Measured value

[ m/s2 ] [ G ] [ µ ]

R = Input resistance of transducer

[Ω]

r = Resistance value of extended cable (Total resistance at input)

[Ω]

Sectional area of wire of extended cable (mm2) Total resistance value per meter

(Ω)

0.05

0.08

0.3

0.35

0.5

0.63

0.44

0.12

0.11

0.071

Table A-4: Specifications of acceleration transducer ARH-500A. 500m/s2

Capacity

0.5mV/V(1000×10-6 strain)

Rateped Output Non-linearity

1%RO

Frequency response range

DC~520Hz

Natural frequency

870Hz

Allowable temperature range

-10 ~ +50°C

Over load

300%

Input/Output resistance

120Ω

Recommended exciting voltage

Less than 2V

Allowable exciting voltage

5V

Water pressure resistive

500kPa

Weight

85g

Input/Output cable :φ3.2mm 0.08mm2 4-core shielded vinyl cable 5m Input/Output cable is grounded to the body.

A-27

‎A

Appendix A

Figure A-11 Test and inspection data of ARH-500A.

A-28

‎A

Appendix A


A-29

‎A

Appendix A


A-30

‎A

Appendix A


A-31

‎A

Appendix A

A.4 KPE-PB SMALL PORE PRESSURE GAUGE It small size pore water pressure gauge suited to measuring pore water pressure under the ground in model experiment for a short term. The test and inspection data of two pore water pressure gauge that used in this research are shown in Figure (A-12).

Measurement 1. One end of the supplied cable is usually supplied without connector plug. The cable is connected to a strain meter or its switching box by screwing or soldering. In case of using NDIS 7-pin connector plug, refer to the following connection layout.

2. The pore pressure gauge is calibrated with a constant voltage excitation type strain meter with its input/output cable connected to the strain meter. The rated output and sensitivity shown on the test data are found with the instrument gauge factor 2.00. (In case of using TML data logger, its coefficient should be set to 1.00.) 3. Set necessary measuring parameters to a strain meter, recorder, computer, etc. (For strain meter, for example, initial balancing, sensitivity adjustment, setting of unit, coefficient and measure mode, initial value measurement and so on.) 4. Measured values are in + side for increase of pressure. When a reverse polarity is required, change connections between B and D (green and white) on the strain meter terminal. 5. In ordinary measurement, it is recommended that the strain meter is previously set to measure directly in physical unit. In case of strain reading, pressure can be found using the following equation. Pressure = Measure Value × Calibration Coefficient A-32

‎A

Appendix A

[ kPa, MPa ]

[ ×10-6 ]

[kPa, MPa /1×10-6 ]

The calibration coefficient is a value obtained by dividing the rated capacity (kPa, MPa) by the the rated output (×10-6). It is found in the test data supplied. 6. In case that the cable is extended under constant voltage excitation, correct the lowering of sensitivity using the following equation

{

}

where ɛ0 = Real value after correction

[kPa, MPa] [ µ ]

ɛ = Measured value

[kPa, MPa] [ µ ]

R = Input resistance of transducer

[Ω]

r = Resistance value of extended cable (Total resistance at input)

[Ω]

Sectional area of wire of extended cable (mm2) Total resistance value per meter

(Ω)

A-33

0.35

0.05

0.08

0.3

0.35

0.5

1.00

0.63

0.44

0.12

0.11

0.071

‎A

Appendix A

Figure A-12 Test and inspection data of ARH-500A.

A-34

‎A

Appendix A


A-35

‫الخالصة‬

‫هنان العدٌد من المشاكل فً الهندسة المدنٌة المتعلمة بأنتمال موجات االجهاد خالل التربة نتٌجة‬ ‫الحمل الدٌنامٌكً‪ .‬مثال ذلن االستجابة الزلزالٌة نتٌجة الهزة االرضٌة او رد فعل االساس تحت تأثٌر‬ ‫الحمل الدٌنامٌكً (المبانً الصناعٌة) او االهتزاز فً المبانً الناتج من مصادر مختلفة مثل (إنشاء‬ ‫الركائز أو انشاء الركائز اللوحٌة او هدم المبانً ‪...‬الخ) وكذلن السكن الحدٌدٌة و حركة المرور على‬ ‫الطرق‪.‬‬ ‫من المهم جدا خالل التصمٌم لهكذا نوع من المشاكل عمل تحرٌات للتربة لمعرفة خصائصها‬ ‫الهندسٌة وخاصة معامل المص ونسبة االخماد‪.‬‬ ‫االخماد هو تبدد الطالة خالل التربة‪ .‬فً الولت الحاضر الٌوجد سوى عدد للٌل من التمنٌات‬ ‫المتوفرة الٌجاد نسبة االخماد‪ .‬فً الفحوصات المختبرٌة ٌوجد فمط فحص العمود الرنان‬ ‫(‪ (Resonant column‬وفحص المص البسٌط الدوري (‪ )Cyclic simple shear‬و الٌوجد‬ ‫فحوص مولعٌة ٌمكن اعتبارها الٌجاد نسبة االخماد‪.‬‬ ‫فً هذا البحث تم عمل دراسة عملٌة عن تصرف التربة الرملٌة بكثافات مختلفة تحت تأثٌر‬ ‫حمل صدمً مفرد‪ .‬التربة المستخدمة فً الفحوص كانت تربة جافة بمختلف الكثافات ومشبعة بكثافة‬ ‫عالٌة‪ .‬تم تجهٌز الرمل وفك برنامج مختبري‪ .‬تم تسلٌط اوزان مختلفة من ارتفاعات مختلفة على‬ ‫التربة بواسطة جهاز الحمل السالط ‪ FWD‬للحصول على طالة الحمل الصدمً على التربة‪ .‬تم لٌاس‬ ‫استجابة التربة التً تتضمن االزاحة والسرعة والتعجٌل نتٌجة الحمل الصدمً على سطح التربة‬ ‫حسب مولع االساس او على اعماق مختلفة بأستخدام ‪ FWD‬وكذلن تم دفن المتحسسات فً داخل‬ ‫التربة لمٌاس التعجٌل ( ‪ARH-500A Waterproof, and Low capacity Acceleration‬‬ ‫‪ )Transducer‬بأالضافة الى المتحسسات التً تمٌس ضغط ماء المسام (‪ (KPE-PB‬وٌتم تسجٌل‬ ‫نتائج المتحسسات بأستخدام المارئ (‪.)TMR-200‬‬ ‫تم الحصول على خصائص االخماد لكثافات مختلفة من الترب الرملٌة باالعتماد على الفحوص‬ ‫المختبرٌة‪ .‬لمد وجد ان هنان اختالفا ً فً نسبة االخماد مع المتغٌرات المختلفة للفحص التً اعتمادها‬

‫فً الفحوص والتً تتضمن نسبة عمك االساس (عمك االساس‪ /‬لطر االساس) و لطر االساس و‬ ‫ممدار الموة المسلطة وكذلن كثافة التربة (رمل كثٌف او رمل متوسط الكثافة او رمل للٌل الكثافة)‬ ‫بأالضافة الى المحتوى المائً (تربة رملٌة مشبعة)‪.‬‬ ‫وفما لذلن وباالعتماد على النتائج المختبرٌة تم التراح معادالت وضعٌة الٌجاد لٌمة اخماد‬ ‫التربة والتً تعتمد على نسبة التردد و معامل المص و معامل المرونة و معامل رد فعل التربة‬ ‫التحتً‪.‬‬ ‫لمد بٌنت النتائج ان نسبة االخماد تتأثر بنسبة عمك االساس )‪ )D/B‬بحوالً ‪ %005-05‬عندما‬ ‫ٌزداد ممدار نسبة عمك االساس من ‪ 5‬الى ‪ .2‬كذلن عندما تزداد كثافة التربة من تربة رملٌة للٌلة‬ ‫الكثافة الى تربة رملٌة عالٌة الكثافة و ذلن بأنخفاض نسبة الفراغات بٌن جزٌئات التربة ‪ %22‬و من‬ ‫رمل متوسط الكثافة الى رمل عالً الكثافة بنسبة فراغات ‪ %02‬فأن االخماد ٌزاد تمرٌبا ‪%05-05‬‬ ‫من التربة للٌلة الكثافة الى التربة عالٌة الكثافة و تمرٌبا ‪ %05-00‬من الترب متوسطة الكثافة الى‬ ‫عالٌة الكثافة‪.‬‬ ‫نتائج الفحوص بٌنت ان عند زٌادة الكتلة السالطة بنسبة ‪ %055‬من نفس مسافة السموط فأن‬ ‫نسبة االخماد تمل تمرٌبا بنسبة ‪ %20-05‬لحالة التربة عالٌة الكثافة و ‪ %05-00‬لحالة تربة متوسطة‬ ‫الكثافة و ‪ %05-20‬لحالة للٌلة الكثافة‪ .‬كما وجد ان نسبة االخماد تمل تمرٌبا بنسبة ‪ %00-25‬عند‬ ‫زٌادة مساحة االساس بنسبة ‪ .%020‬على الرغم من ان معامل االخماد ٌزٌد مع زٌادة مساحة‬ ‫االساس لكن نسبة االخماد تمل نتٌجة زٌادة معامل االخماد الحرج‪.‬‬

‫جمهىريت العراق‬ ‫وزارة التعليم العالي والبحث العلمي‬ ‫جامعت بغداد_كليت الهندست‬ ‫قسم الهندست المدنيت‬

‫الخصائص الذيناميكية للحرب الرملية جحث جأثير‬ ‫حمل صذمي‬

‫االطروحة‬ ‫مقذمة الى كلية الهنذسة في جامعة بغذاد كجزء من المحطلبات‬ ‫لنيل درجة الذكحىراه في فلسفة الهنذسة المذنية‬ ‫)اخحصاص ميكانيك الحربة وهنذسة األسس(‬

‫أعداد‬

‫بلقيس عبذالىاحذ احمذ‬ ‫بكالىريىس هندست مدنيت ‪0220‬‬ ‫ماجستير هندست مدنيت ‪0220‬‬

‫ذو القعدة ‪0007 /‬‬

‫آب ‪2016/‬‬