EMBEDMENT EFFECT ON THE BEARING

EMBEDMENT EFFECT ON THE BEARING CAPACITY OF SPREAD FOOTING IN SAND 1

Mary Ann ADAJAR,

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Tadashi DAIMON, 3Osamu KUSAKABE

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Faculty, Dept. of Civil Engineering, DLSU-Manila Masteral Graduate, Kusakabe Laboratory, Tokyo Institute of Technology 3 Professor, Tokyo Institute of Technology

ABSTRACT: The main concern of this study was to verify the embedment effects on the bearing capacity of spread footing under pure vertical and combined loadings through experimental program using the centrifuge technology. It was also included in the scope the determination of the possible location and shape of slip plane of the surrounding soil. A series of centrifuge tests were conducted using dry Toyoura sand for the model ground. The model footing was made of rigid steel whose dimensions are 40 mm x 40 mm x 15 mm (Length x Width x Height) with a column attached to it whose dimensions are 10mm x 10mm x 75mm. Two (2) vertical loading tests and four (4) combined vertical and horizontal tests were performed using a depth of embedment–width (D/B) ratios of 1.0 and 1.5. The conclusions drawn from the test results are: 1.) in pure vertical loading, the increase in effective overburden pressure at the foundation base due to embedment led to an increase in vertical bearing capacity. The values derived from the test data were in good agreement with the values derived using the Vesic’s formula. 2.) Under vertical loading condition, the ground seemed to have failed by punching shear as indicated by load intensity-displacement curve and ground deformation. 3.) In combined loading, the shape of the yield surface as described by the load path in (V,H) plane is a parabolic ellipsoid. For each depth-width (D/B) ratio, the maximum Hu/Vu was achieved when Vo/Vu was close to 0.60 with a slightly higher Hu/Vu value when D/B is greater. 4.) As indicated by the load-displacement curve and ground deformation, the mode of failure of the ground under combined loadings was general shear failure. KEYWORDS: bearing capacity, spread footing, centrifuge test, slip plane 1. INTRODUCTION It is an important aspect in the design of spread footings to understand the behavior of surrounding soil when footings are subjected to vertical and eccentric loads. The conventional method of footing design requires that footing must possess sufficient safety against failure and settlement must be kept within the allowable value. These requirements are dependent on the bearing capacity. To have a safe design, the bearing pressure on the underlying ground has to be kept within the allowable bearing values and eccentricity must satisfy the criterion of less than 1/6 of the footing width (e < B/6) so as to avoid tension between the foundation and the soil (Coduto, 2001). This is the reason why footings subjected to large overturning or rotation also require large footing dimensions which sometimes become uneconomical. If the underlying ground has sufficient bearing resistance, this will result in smaller footing dimensions and low construction cost. There are several factors which contribute to an increase in bearing capacity and these are: the depth of embedment of the footing, the relative density of the 1

ground and the shape of footing. In this study, we take into account the effect of depth of embedment in the bearing capacity of spread footing. There are several previous studies that discussed the characteristics of bearing capacity and its interrelated factors. A study made by Horvath (2000) discussed the effect of depth of embedment in calculating the gross ultimate bearing capacity of shallow foundations using the formulas presented by Terzaghi, Meyerhof, Hansen and Vesic. The results of the study suggest that the Hansen and Vesic solutions are more conservative to use in situations where embedment may control design because they assign a relatively greater proportion of gross bearing capacity to embedment. Adajar (2002) in her Masteral thesis investigated the effect of depth of embedment on the design of spread footing. Based on the said study, the passive earth pressure exerted by surrounding soil, the weight of the overlying soil and the self-weight of the column/footing constitute the righting moment that counteracts the applied overturning moment and is dependent on the depth of embedment. The greater depth of embedment resulted in a greater resistance against overturning. Pu and Ko (1988) made an experimental investigation of bearing capacity in sand by centrifuge footing tests and proved that ultimate bearing capacity is defined not only on the basis of peak bearing pressure but also in relation to the footing penetration required to reach the capacity. Footing penetration equal to ten percent (10%) or twenty percent (20%) of footing width became a more realistic criterion for defining ultimate bearing capacity. Ohmaki et al. (1998), in his study on the characteristics of bearing capacity of shallow foundations on soft cohesive ground, proved that an application of horizontal load led to an increase in the subgrade reaction on the passive side and a decrease on the active side of the foundation, the results of the test values showed good correspondence with the values obtained using the Rankine earth pressure formula. The results of the study on lateral response of square embedded foundation in dry sand made by Gadre and Dobry (1998) demonstrate that passive forces account for more than half of the ultimate lateral capacity of embedded footing. The studies of behavior of footing under combined loadings are also relevant, since this loading case is directly applicable to this study. Gottardi et al. (1999) provided information on the behavior of footing under combined loadings and the results of the tests are interpreted in the context of hardening plasticity theory. The shape of yield surface in ( V, M/2R. H ) space is well described by a parabolic ellipsoid. Punrattanasin’s (2003) study on the sheet pile foundation behavior and its capacity on sand under combined loading also provide a good reference material in terms of loading procedures and analysis of results. Comparison between square footing and sheet pile foundation in terms of the vertical, horizontal and moment capacity was the main focus of his study and a newsophisticated combined loading apparatus was developed for this purpose. The same loading apparatus was used in the experimentation process of this research study. 1.1 Objectives of the Study The objective of the research study described in this paper is to verify the embedment effects on the bearing capacity of spread footing under pure vertical and combined loadings through experimental program using the centrifuge technology. It is also the purpose of this research to determine the location and shape of slip plane of the surrounding soil.

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2. EXPERIMENTAL PROGRAM 2.1 The Centrifuge Technology Centrifuge testing is a useful tool in geotechnical engineering for it provides better understanding of the geotechnical events and processes. It enables the study and analysis of design problems using geotechnical materials. It is an economical way of correctly reproducing and observing the stresses and gravity effects on the small-scale models and the results are extrapolated to the full-scale prototype situation using well-established scaling laws. This concerns physical modeling of geotechnical events comparable to what might exist in the prototype. The model is a reduced scale of the prototype. In centrifuge technique, soil models placed at the end of a centrifuge arm are accelerated and subjected to an inertial radial acceleration field similar to gravitational acceleration field but many times stronger than earth’s gravity (Schofield, 1980; Taylor, 1995). The inertial stresses in a centrifuge model induced by rotation about a fixed axis correspond to gravitational stresses in the prototype. In this study, the Tokyo Institute of Technology Mark III Centrifuge was used throughout the experimentation process. The centrifuge is a beam type having a pair of parallel arms that hold two platforms. One arm is used to support the loading system. The other is for counterbalance weights. Fig. 1 shows the schematic drawing of the Mark III Centrifuge. All centrifuge tests were performed at 30g centrifugal acceleration. Therefore, all linear measurements like model dimensions and displacements were multiplied by 30 while forces in the model were multiplied by 302 = 900 to obtain the corresponding prototype values. 2.2 The Model Ground Dry, dense Toyoura sand with a target relative density of 75% was used in all centrifuge experiments. Physical properties of the Toyoura sand are given in Table 1. The sand sample for the underlying ground was prepared by air pluviation using a hopper suspended from an overhead crane. This method is usually employed when uniform dry sand is required. Density of the model sand ground is controlled by both pouring height and pouring rate volume (Vaid and Negussy, 1988). The fall height is controlled by increasing the distance between the hopper and the surface of the sand in the container while the flow rate is controlled by varying the size and characteristics of the orifices through which the sand will flow. The height of the hopper above the deposited sand was periodically adjusted with the rise of sand surface to keep the falling height constant. After the height of sand reached the bottom of footing level, the sand surface was leveled and the loading apparatus with the model footing was attached to the container. The preparation of the backfill sand was done using a special hopper with a slant tubular orifice because of the limitation in space. In each test, the sand density was directly measured from the weight of sand per volume in the container. Throughout the experiment, the initial void ratio and the density of each test were determined by measuring the mass and volume of the model sand.

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Fig. 1 Schematic Drawing of the Mark III Centrifuge at Tokyo Institute of Technology Table 1 Physical Properties of Toyoura Sand (after Punrattanasin, 2003) Type Specific Gravity D50 (mm) D30 (mm) D10 (mm) Coefficient of Uniformity Coefficient of Curvature Maximum Void Ratio, emax Minimum Void Ratio, emin

Toyoura Sand 2.645 0.19 0.16 0.14 1.56 0.95 0.973 0.609

2.3 The Model Column/Footing The model footing is square with dimensions of 40mm x 40mm x 15mm (Length x Width x Thickness) attached to a square column with dimensions of 10mm x 10mm as shown in Fig. 2. It is made of rigid steel material and a very thin rubber mat was glued to the base of the footing to have a smooth surface to minimize the effect of frictional resistance. Using the 30g centrifugal acceleration, this simulates a prototype footing dimensions of 1.2 x 1.2 x 0.45m (L x W x T) and prototype column 0.30 x 0.30 m. The model column/footing was placed inside the circular steel container with internal dimensions of 585.6mm in diameter and 400mm in height (Fig. 3). The dimensions of this container are much larger than the dimensions of the model column/footing thereby eliminating any boundary effect for this slow cyclic loading. The steel container has a specially opened door to give ease in slicing of the model ground.

Fig. 2 Model Column/Footing Used in Experimental Study

Fig. 3 Steel Container with Specially Opened Door 4

2.4 The Loading Apparatus In this study, a combined loading apparatus for centrifuge test developed by Punrattanasin as shown in Fig. 4 was used throughout the experiment with the aim of investigating the performance of the footing under vertical and combined horizontal and vertical loadings. A key aspect of this loading apparatus is its ability to generate a system that any combination of vertical, horizontal and moment load as well as displacement paths can be applied to footings with high precise force, position, orientation and configuration under high centrifuge operation. This loading apparatus will be fitted to the 0.9 x 0.9 m swinging platform of the Mark III centrifuge. The loading apparatus uses a system of jacks to apply vertical and horizontal load, Cambridge Load Transducers to measure the applied loads and Linear Variable Differential Transformers (LVDTs) to measure the footing displacement and rotation. The system was designed to operate at maximum of 50g operational acceleration. A detailed description and operating technique of this loading apparatus is provided by Punrattanasin et al. (2003).

Fig. 4 General View of the Loading Apparatus 2.5 Experimental Procedure The test program consisted of 6 centrifuge loading tests as presented in Table 2 under a 30g centrifugal acceleration for each test. Two (2) vertical loading tests and four (4) combined horizontal and vertical loading tests were conducted. When the sand for the underlying ground was already prepared, the loading apparatus was bolted onto the top of the container with the model footing attached to it. The model footing was then lowered down to the sand surface level by command from computer program, after which the backfill sand was poured until it reached the desired embedment level. The vertical loading tests were carried out on two cases with depth–width ratio D/B (D: depth of embedment, B: width of footing) of 1.0 and 1.5. The centrifuge speed was increased gradually and once it reached the required acceleration, the model footing was loaded inflight at the rate of 0.1mm/sec until failure. The Cambridge load cell and the LVDTs measured the magnitude of the applied vertical load and vertical displacement respectively. The maximum vertical capacity of the model footing was then determined from the loaddisplacement curve. Combined horizontal and vertical loading test were conducted by varying the D/B ratio and initial vertical load (Vo). Two (2) tests were carried out with D/B ratio of 1.0 and varying Vo/Vu ratio of 0.30 and 0.60 and another two (2) tests were done with D/B ratio of 1.5 and Vo/Vu ratio also of 0.30 and 0.60. Here, Vu is defined as the maximum vertical load for a given D/B ratio obtained from the pure vertical loading tests. The model footing was placed in the model ground using the same procedure as in the vertical loading tests. After the centrifuge acceleration reached 30g, the vertical load 5

was applied until it reached Vo/Vu ratio of 0.30. With the vertical displacement fixed, the horizontal load was then applied simultaneously with the vertical load until failure. The applied loads (horizontal and vertical) and the horizontal displacement were measured by the load cells and LVDTs respectively. After reaching the maximum horizontal load, the model footing was unloaded and was moved back to its initial horizontal position and the application of vertical load and penetration was continued until it reached the Vo/Vu ratio of 0.60, after which the footing was then loaded horizontally using the same procedure as the previous test. The maximum horizontal load, Hu was determined from the loaddisplacement curve and the shape of yield surface was described from the horizontal loadvertical load curve. After each test event, the model ground was saturated with water and completely drained to enable the slicing procedure of the model ground. The model ground was sliced in vertical section to observe the deformation of the ground and determine the shape of slip plane. Fig. 5 showed the actual experimental procedure. Depth-Width Ratio D/B 1.0 1.5

Air pluviation method for sand beneath footing

Table 2 Test Conditions Vertical Test Horizontal Test Vo/Vu = 0.30 H=0 V1 H1A V2

Air pluviation for backfill sand

Draining of the model ground after saturation

H2A

Horizontal Test Vo/Vu = 0.60 H1B H2B

Steel container with the model footing and loading apparatus on one arm of the centrifuge machine, counterweights on the other arm.

Slicing of the model ground

Fig. 5 Actual Experimental Procedure

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3. TEST RESULTS AND DISCUSSIONS 3.1 The Vertical Loading Tests Fig. 6 showed the relationship between vertical load and vertical displacement. The loaddisplacement curve for each vertical test increased steadily without any peak or apparent yield point. The maximum vertical load (Vu) was taken as the load at the intersection of the tangent to the load-displacement curve at the origin and the tangent to the curve after the gradient substantially reduced. Table 3 presented the summary of vertical test results. The test data showed an increase in vertical bearing capacity as D/B ratio increases. An increase in embedment corresponds to an additional effective overburden pressure that results in an increase in shear strength of the model ground at the base of the footing. The maximum vertical load capacity as indicated by the test data is in good agreement with the calculated values using the Vesic formula (Eq. 1) for calculating the ultimate bearing capacity for footing in sand. qu = DNqSqdq + 0.5 BN S d (1) where: = unit weight of sand D = depth of embedment of footing B = width of footing Nq, N = bearing capacity factors which are functions of angle of internal friction of sand,ø Sq, S = shape factors, Sq = 1 + (B/L) tan ø and S = 1- 0.4(B/L) dq, d = depth of embedment factors dq = 1 + 2(D/B)tanø(1-sinø)2 when D/B 1 1 + 2 arctan (D/B) tanø(1-sinø)2 when D/B > 1 d = 1 The formula developed by Vesic is based on theoretical and experimental findings, which take into account the effect of other, related factors like depth of embedment (Coduto, 2001). The comparison between the calculated values using Terzaghi and Vesic formulas and the values derived from the test data was presented in Fig. 7. The photographs of the vertical sections of the ground showing the slip failure plane were shown in Fig. 8. For each test, it can be seen that vertical movement of the footing is not accompanied by visible soil bulging at the surface of the ground. Lateral displacement of the surrounding ground and beneath the footing is considerably minimal than the vertical settlement of footing. This observation and shape of load-displacement curve indicate that ground failed by punching shear for each vertical test. For V2 tests, the deformation beneath the footing penetrates to about the footing width while horizontal range of ground deformation was wider as a result of increase in depth of embedment. Table 3 Summary of Vertical Loading Tests D/B Vu (kN) Relative Density % V1 V2

1.0 1.5

5.8 6.9

76.1 75.5

7

10.0

8.0

9.0

7.0 6.0

7.0

Vertical Load (kN)

Vertical Load (kN)

8.0

6.0 5.0 4.0 3.0

V1 (D/B = 1)

2.0

V2 (D/B = 1.5)

5.0 4.0 3.0

Vesic Terzaghi Test Data

2.0 1.0

1.0 0.0 0

5

10

15

20

25

30

35

Vertical Displacement (mm)

Fig. 6 Load-displacement Curve for Vertical Loading Test

0.0 -

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

Depth-Width Ratio (D/B)

Fig. 7 Comparison between test values and calculated values

D/B = 1.0

At 4cm from center of footing

At 3 cm from center of footing

At edge of footing

At edge of column

D/B = 1.5



At edge of footing

At edge of column

Fig. 8 Slip Plane under Vertical Loading

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3.2 The Horizontal Loading Tests Table 4 summarizes the results of horizontal loading tests. It was observed from the test data that greater D/B and Vo/Vu ratios produced a greater maximum horizontal capacity (Hu). In such case, the larger the applied vertical load on the footing, the smaller was the eccentricity of the resultant force at the base. Thus, the effective area of the footing increased which led to an increase in the shear strength at the base of the footing. This shear strength and the passive earth pressure mobilized in the embedded part of the column and footing resisted the applied horizontal force. Since passive earth pressure increases with depth, the greater the depth of embedment of footing, the greater the passive resistance and therefore resulted to a greater horizontal bearing capacity. Fig. 9a showed the horizontal load plotted against the horizontal displacement for each D/B ratio with initial vertical load. The maximum horizontal capacity was taken as the horizontal load when the curve reached the peak value. Fig. 9b showed the curve of horizontal load versus the vertical load, demonstrating that as the horizontal load increases and later decreases towards the end of the test, the vertical load continuously reduces. Expressing the results in (V,H) plane and presented in terms of dimensionless parameters Hu/Vu and Vo/Vu (Fig. 10), the curve described the load path of the yield surface in the shape of a parabolic ellipsoid. This is similar to what is previously observed by Gottardi and Butterfield (1993, 1999) for strip and circular footings on sand. For each D/B ratio, the maximum Hu/Vu was achieved when Vo/Vu was close to 0.60 with a slightly higher Hu/Vu value when D/B is greater. The photographs taken after the loading tests were shown in Fig. 11. Bulging of the ground surface due to lateral movement on the sides of the column/footing was observed especially for the case of D/B = 1.5. This indicates that passive resistance of surrounding ground was mobilized upon the application of the horizontal load. The slip plane described near the face of the column reached to a horizontal range of almost three times the width of footing. Based from the loaddisplacement curve and shape of ground deformation, the ground seemed to have failed by general shear. Table 4 Summary of Combined Vertical and Horizontal Loading Tests H1A H1B H2A H2B Depth-Width (D/B) 1.0 1.0 1.5 1.5 Max. Vertical Load, Vu (kN) 5.8 5.8 6.9 6.9 Initial Vertical Load, Vo (kN) 1.87 3.79 2.21 4.19 Vo/Vu 0.3 0.6 0.3 0.6 Max. Horizontal Load, Hu (kN) 0.71 1.2 1.03 1.71 2.5

2.5

H 1A ( D / B = 1.0 wit h V = 0 .3 V u) H 1B ( D / B = 1.0 wit h V = 0 .6 V u) H 2 A ( D / B = 1.5 wit h V = 0 .3 V u) H 2 B ( D / B = 1.5 wit h V = 0 .6 V u)

2

Horizontal Load (kN)

2

1.5

1

1.5

1

0.5

0.5

0

0 0

5

10

15

Ho r i z o nt al D i sp lacement ( mm)

20

25

0

1

2

3

4

5

6

Vertical Load (kN)

(a) (b) Fig. 9 Results of Combined Vertical and Horizontal Loading Tests 9

0.50 0.45 0.40

D/B = 1.0

0.35

D/B = 1.5

Hu/Vu

0.30 0.25 0.20 0.15 0.10 0.05 0

0.2

0.4

0.6

0.8

1

1.2

Vo/Vu

Fig.10 Load Path of the Yield Surface in (V,H) Plane D/B = 1.0



At edge of footing

At edge of column

3B

D/B = 1.5



At edge of footing

At edge of column

Fig. 11 Slip Plane under Combined Vertical and Horizontal Loading

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4. CONCLUSIONS The results of a series of centrifuge tests on model square footing under pure vertical and combined loadings were presented on this paper. Based on the analysis of results, the following conclusions were reached: a.) In pure vertical loading, the increase in effective overburden pressure at the foundation base due to embedment led to an increase in vertical bearing capacity. The values from the test data were in good agreement with the values derived using Vesic’s Formula for calculating the ultimate bearing capacity. b.) Under vertical loading condition, the ground seemed to have failed by punching shear as indicated by load-displacement curve and ground deformation. c.) In combined loading, the shape of the yield surface as described by the load path in (V,H) plane is a parabolic ellipsoid. For each depth-width (D/B) ratio, the maximum Hu/Vu was achieved when Vo/Vu was close to 0.60 with a slightly higher Hu/Vu value when D/B is greater. d.) As indicated by the load-displacement curve and ground deformation, the mode of failure of the ground under combined loadings was general shear failure. REFERENCES Adajar, M.Q. (2002), The Effect of Depth of Embedment on the Design of Spread Footing, Masteral Thesis, De La Salle University, Manila, Philippines. Coduto, D.P. (2001) Foundation Design Principles and Practices, 2nd ed., Prentrice-Hall Inc., Upper Saddle River, New Jersey. Horvath, J.S. (2000): Coupled Site Characterization and Foundation Analysis Research Project: Rational Selection of ø for Drained Strength Bearing Capacity Analysis, Research Report No. CE/GE-00-1, http://www.engineering.manhattan.edu/civil/CGT/pubs/cegeoo3.pdf Gadre, A. and Dobry, R. (1998), Lateral Response Square Embedded Foundation in Dry Sand, Centrifuge 98, Vol. 1, pp. 465–470. Gottardi, G. and Butterfield, R. (1993), On the Bearing Capacity of Surface Footings on Sand Under General Planar Loads, Soils and Foundations, Vol. 33, pp. 68-79. Gottardi, G. and Butterfield, R. (1999), Plastic Response of Circular Footings on Sand Under General Planar Loading, Geotechnique, Vol. 49, pp. 453-469. Kita, K. and Okamura, M. (1998), Bearing Capacity Test, Centrifuge 98, Vol. 2, pp. 1067-1975. Ohmaki, S. et.al. (1998), Characteristics of Bearing Capacity of Shallow Foundations on Soft Cohesive Ground, Centrifuge 98, Vol. 1, pp.453-458. Pu, J.L. and Ko, H.Y. (1988), Experimental Determination of Bearing capacity in Sand by Centrifuge Footing Tests, Centrifuge 88, pp. 293-299. Punrattanasin, P. et.al. (2003), Development of Combined Loading Apparatus for Centrifuge Test, International Journal of Physical Modelling in Geotechnics 4, pp. 1-13. Schofield, A.N. (1980), Cambridge Geotechnical Centrifuge Operations, Geotechnique 30, Vol. 3, pp. 227-268. Taylor, R.N. (1995), Geotechnical Centrifuge Technology, Blackie Academic and Professional. 11

Ueno, K. (1998), Methods for Preparation of Sand Samples, Centrifuge 98, Vol. 2, pp. 1047-1055.

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