Software of Seismic Response and Liquefaction ...

Caldynsoil: Software of Seismic Response and Liquefaction Potential of a Soil Deposit B. Sbartai & K. Fillali LMGHU laboratory, University of August 20 1955-Skikda, Road el-hadeik, 21000 Skikda Algeria.

Abstract The purpose of this paper is to present the program “Caldynsoil” that we developed in the Matlab® to analyze the seismic response of a saturated soil deposit and the estimation of its liquefaction potential using a total stress approach. For this purpose, we used an equivalent linear method with concentrated masses associated with the three hyperbolic laws of Hardin and Drnevich, Rambert and Osgood and Masing to take into account the nonlinear behavior of soil and deduce the maximum shear stress required for calculation of the cyclic stress ratio (RCS). To estimate the risk of liquefaction of the soil profile, the calculation of cyclic resistance ratio (RCR) is required. To this end, we integrated three approximate methods based on in-situ tests SPT (Blake), CPT (Robertson and Wride) and VS (Andrus and Stokoe). The addition of graphical user interface software has facilitated the use of a program enabling interactive input and editing data. Some examples are presented to demonstrate program effectiveness and performance Keywords: liquefaction, Matlab, soil, earthquake. 1. INTRODUCTION At the time of an earthquake, the constraints of cyclic distortions developed in a layer of soil can cause a partial or total loss of its structural capacity. If a layer of soil loses its structural capacity completely, we say that it liquefied. The sands and the saturated silts none compacted are the most susceptible to liquefy. As the movement of soil causes an increase of the interstitial pressure, the resistance of soil decreases until canceled. This phenomenon can cause catastrophic effects on the constructions built on liquefiable soils. The earthquakes of Nigata in Japan (1964), of Mexico City (1985), of Boumerdes city (2003) and Asnam city (1980) are the examples for which the liquefaction of the sands caused considerable damages. Seen the complexity and the difficulty of the arithmetic techniques used in our studies, we were obliged to think on the conception of an efficient computing program that offers us a gain in the time and a good precision in calculations. To this effect, a computing program under Matlab® environment (2007) [Matlab® & Simulink® Release (2007)] has been developed to calculate the seismic response as well as the evaluation of the potential of liquefaction of a soil deposit (sand, silt, gravel, clay. etc.). This approach requires the determination of the shearing constraint developed by the seismic solicitation τa and the cyclic resistance of soil shearing τl. For the determination of τa, an equivalent linear dynamic analysis with concentrated masses has been used to adjust (iterative procedure) the module of shearing and the factor of soil damping according to the level of the resulting shearing deformation because the constraintdeformation diagram of the soil layer is nonlinear with dissipation of energy by hysteresis to every cycle. In this study, the behavior of soil has been represented by three hyperbolic relations. For the determination τl, the abacus of Seed [Seed and al (1985)] based on the SPT test has been used. The report of the two constraints permits the definition of safety factor opposite the risk of liquefaction (FS) that allows us to localize the depths of soil susceptible to be liquefied.

Various efforts have been globally made to develop software systems that quantify the liquefaction of deposit soils due to natural hazards like earthquakes. The most well known tools for the estimation of potential liquefaction of soils include Novliq, Liquiter (Geostru) and LiquefyPro. All these software are based on approached methods for the calculus of cyclic shear stress. The goal of this work is the presentation of the program conceived CALDYNASOL in our survey, that is a program that permits to analyze the seismic response of a soil deposit on the one hand (determination of the cyclic constraint of shearing) and the potential of liquefaction on the other hand. Three hyperbolic laws are integrated there, the one of Hardin and Drnevich [Hardin and Drnevich, (1972)], Rambert and Osgood and Masing [Jenning, (1964)] to concretize the concepts of the linear equivalent method with concentrated masses. This software is composed of two main modules, one to calculate the seismic response of the soil deposit and the other to estimate the potential of liquefaction. The software uses the most recent concepts as: • Numerical analysis: The algorithm of numerical integration of Newmark- Beta is used for the resolution of the system of differentials coupled equations. • Graphics: A main graphic interface with menu and dialogue boxes including three secondary interfaces for the storage under form of data base of the accelerogram, the geotechnical characteristic of soil and the curves of resistance to the liquefaction with the possibility to update any data base at any moment. • Soil: Linear equivalent method with concentrated masses and the behavior’s hyperbolic laws of Hardin and Drnevich, Rambert and Osgood and Masing for the analysis of the seismic response of the soil deposit and the speed’s wave of shearing methods of Robertson and Wrides 1998, the approximate method SPT of Blake (1999) and simplified method of Seed [Seed and al (1971)] and other to estimate the liquefaction potential.. 2. METHODOLOGY OF CALCULATION 2.1 Main Interface The graphic interface of the software facilitates the use of the program and permits the input and an interactive edition of data; the graphic or numeric outputs can be exploited directly or saved in a file for an ulterior use. The software is composed in general of four interfaces (main and secondary). The main interface as in figure 1 is divided in general in three groups that can be illustrated like follows: • Geotechnical characteristics of the layers of the massif: to input and exploit the parameters of soil saved in the data base that can be called by any application. • General data: to input and exploit relative data to a specific application • Results of calculation: for the display of the numeric or graphic results • A menu for the registration and loading of the applications • A menu that calls the interfaces of update of the data bases 2.2 Interface of Update of the Geotechnical Characteristic of Soils This interface permits to insert, to save and to update the different types of soils with their geotechnical characteristic to load them thereafter by the main program for possible treatments. It is composed of two main groups (Fig 1):

Figure 1. Main interface of the computing program “Caldynsoil”.

(a) Group geotechnical parameters of soil : it is composed of fields of type "unwinding list" for the display and the selection of the list of the existing soils in the data base, "input fields" for the input, the modification and the display of the selected characteristics of the soil. (b) Group list of the accelerograms: The field "list of the accelerograms» permits to select the accelerogram that is going to be proposed in the main interface for their use in the calculation (Fig 2):

Figure 2. Interface Update of the geotechnical characteristics of soil.

2.3 The Update Interface of the Accelerogram This interface is composed of three groups and a menu (Fig 3): (a) Group display of the accelerogram: Include three subgroups: • The subgroup "Attached and display of data" contains two fields of type " Stationary list" who serve like support of display of the neat and the abscissa of the accelerogram, and two input fields to input or to modify data.

• The subgroup "Characteristics of the earthquake" contains some input fields to input the relative characteristics of the inserted earthquake. • The subgroup "Check from the registered accelerogram» the value of the maximal amplitude of the acceleration and the time during which it is reached are extracted of the registration basis and compare to those seized by the user to ascertain the accurateness of the input data. (b) Group interval of tracing: Limit the interval of presentation of the accelerogram by the pulled values from the three input fields: beginning, step and end.

Figure 3. Interface of update of the accelerogram.

(c) Group update of data: It is composed of seven buttons (Fig 4):

Figure 4. Subgroup update of data.

2.4 Interface of Update of the Resistance Curves to the Liquefaction This interface is composed of three groups and a menu (Fig 5): (a) Group display and input of data: Contains two fields of type "Stationary list" which serve like support of display of the neat and the abscissa of the resistance curve, and two input fields to seize or to modify data. (b) Group tracing of the graph: Contains a button that permits the tracing of the diagram, two fields of type "Unwinding list" which serve to modify the color of the graph and the thickness of the line and a checkbox permitting either to display several curves on a same graph or on different graphs (Fig 5). (c) Group update of data: It is composed of six buttons (Fig 5): • Button "New" : for the resetting of all fields • Button "Add" : for the addition of a point • Button "Deletion": to suppress a point of the curve • Button "Modification" : to modify the coordinates of a point of the curve • Button "Erase": to empty the fields after display • Button "Display list": to redisplay the list after having erased.

Figure 5. Interface update of the resistance curves to the liquefaction.

3. EXAMPLE OF APPLICATION Marina's district localizes to be quoted on the north of San Francisco in California. Following the earthquake of Loma Prieta 17/10/1989, some important damages have been recorded there although it is located to more than100 Km of the epicenter as, liquefaction of soils, cracking and settlement at different places. The American geological survey (Reston, VA) done, has include five CPT polls to measure the vertical settlements caused by the earthquake (Bennett 1990). Bardet and Kapuskar (1991) in their study achieved nine CPTs polls to the level of Marina's district. The stratigraphy of Marina's district is generally composed of three deposit of sand distinct (Holzer and O'Rourke 1990) left like follows: • The zone is composed of a mainly beach sand deposit that spreads on a depth of 8m and surmounts a layer of clay. • The central zone is composed of a sandy deposit to silted sand that has been put in place in 1912 without compaction (Rollins and McHood 1998) that spreads on a depth of 8m and surmounts a layer of clay. • The west zone is composed of a deposit of dune sand that spreads on 11m depth and surmounts a layer of clay. Authors G. Zhang, P.K. Robertson, and R.W.I. Brachmen exploited these data to value the risk of liquefaction and the post-liquefaction displacements and found that the layers that are probably liquefiable are to 2.5-4.5m and 7m. After having introduced data in the program, we have used two methods to estimate the potential of liquefaction, the method simplified CPT of Seed and Idriss (1982) and the dynamic method with the hyperbolic models of Hardin and Drnevich, Rambert and Osgood and Masing. For the calculation of the liquefaction potential we used the results of one of the tests available CPT of the East zone of Marina's district where the profiles of the peak resistance (qc) and the lateral rubbing (fs) are represented below on the figure 6:

Figure 6. Profile of the peak resistance and the lateral rubbing according to the depth.

3.1 Assessment by the CPT Method of Seed and Idriss (1982) The gotten graphic and analytic results are presented below. Table 1. Evaluation of the liquefaction potential by the CPT method of Robertson and Wride (1998). ࣌ᇱ࢜૙ Z qc fs PL CN qc1n qc1ncs IC KC RCR RCS FS (m) (Kpa) (Kpa) (Kpa) (%) 1,76 3 984,38 43,70 26,43 1,70 67,73 94,95 2,07 1,40 0,159 0,086 1,84 11,72 1,95 4 453,13 30,71 29,30 1,70 75,70 90,91 1,91 1,20 0,149 0,086 1,73 13,99 2,26 4 609,38 31,89 33,91 1,70 78,36 93,23 1,90 1,19 0,155 0,086 1,80 12,53 2,30 1 796,88 7,09 34,50 1,70 30,55 30,55 2,15 1,00 0,075 0,086 0,88 60,83 2,99 1 953,13 10,63 41,01 1,56 28,06 28,06 2,18 1,00 0,073 0,100 0,73 73,67 3,41 1 718,76 10,63 44,98 1,49 29,12 50,57 2,23 1,74 0,092 0,106 0,86 61,92 3,99 6 328,13 56,69 50,39 1,41 24,21 49,26 2,33 2,03 0,091 0,113 0,80 67,51 4,98 5 546,88 36,61 59,73 1,29 81,88 101,74 1,95 1,24 0,177 0,122 1,45 22,51 5,52 6 328,13 44,88 64,79 1,24 68,91 84,61 1,94 1,23 0,136 0,125 1,08 43,44 5,79 5 781,25 41,34 67,31 1,22 77,13 92,81 1,91 1,20 0,154 0,127 1,21 34,65 6,02 6 250,00 46,06 69,48 1,20 69,36 86,44 1,96 1,25 0,140 0,128 1,09 42,97 6,44 4 687,50 27,17 73,45 1,17 72,93 90,02 1,94 1,23 0,147 0,130 1,13 39,84 6,98 8 203,13 62,60 78,51 1,13 52,90 69,47 2,01 1,31 0,111 0,132 0,84 64,13 7,67 5 390,63 53,15 84,98 1,08 88,99 104,38 1,88 1,17 0,185 0,134 1,38 25,76 7,98 2 187,51 41,34 87,89 1,07 57,50 84,09 2,10 1,46 0,135 0,135 1,00 50,21

According to the figure 7, the layers that seem to represent a risk of liquefaction are those situated in 2.3m, 3m, 3.41m, 4m and to 7m with probability of liquefaction respectively equal to 51.28%, 65.48%, 52.44%, 58.60% and 55.48%.

Figure 7. Profile of the safety factor according to the depth.

3.2 Assessment by the Dynamic Method: Model of Hardin and Drnevich According to the unavailability of the accelerogram of LOMA PRIETA having a maximal acceleration of 0.135g, we are going to submit the massif to the earthquake of LANDERS of the 28/06/1992 registered from the station of YERMO composing 34.9N AND 116.8W of magnitude 7.4 and having a maximal acceleration of 1.332 m/s2 (0.135g). The gotten graphic and analytic results are presented below. Table 2. Evaluation of the liquefaction potential by the dynamic method (Model of Hardin and Drnevich). ࣌ᇱ࢜૙ fs CN qc1n qc1ncs IC KC RCR RCS FS Prob Z qc τmax (m) (Kpa) (Kpa) (KPa) (Kpa) (%) 0,88 3984,38 43,70 13,22 1,02 1,9 67,7 94,85 2,0 1,40 0,15 0,07 2,06 8,40 3 67,73 7 1,40 0,15 94 0,09 73 1,653 16,0 1,76 3984,38 43,70 26,43 2,55 1,6 94,95 2,0 9 75,73 7 1,20 0,14 96 0,12 67 1,221 33,85 1,86 4453,13 30,71 27,87 3,41 1,6 90,90 1,9 7 0 1 99 23 1,235 33,04 1,95 4453,13 30,71 29,30 3,55 1,6 75,7 90,91 1,9 1,20 0,14 0,12 5 78,30 1 1,19 0,15 99 0,12 10 1,279 30,94 2,11 4609,38 31,89 31,61 3,85 1,6 93,22 1,9 1 78,36 0 1,19 0,15 53 0,11 18 1,295 29,86 2,26 4609,38 31,89 33,91 4,07 1,5 93,23 1,9 8 30,56 0 1,00 0,07 54 0,12 98 0,596 84,90 2,28 1796,88 7,09 34,20 4,35 1,5 30,55 2,1 8 30,55 5 1,00 0,07 54 0,12 73 0,593 84,80 2,30 1796,88 7,09 34,50 4,38 1,5 30,55 2,1 7 5 5 54 70 0,554 87,21 2,65 1796,88 7,09 37,76 5,03 1,5 29,2 29,24 2,1 1,00 0,07 0,13 3 28,04 7 1,00 0,07 44 0,13 31 0,529 89,22 2,99 1796,88 7,09 41,01 5,74 1,4 28,06 2,1 9 29,76 8 1,71 0,09 34 0,14 94 0,626 82,26 3,20 1953,13 10,63 42,99 6,33 1,4 51,00 2,2 6 9 2 23 69 0,618 83,44 3,41 1953,13 10,63 44,98 6,80 1,4 29,1 50,57 2,2 1,74 0,09 0,15 4 24,82 3 2,00 0,09 20 0,15 02 0,603 84,33 3,70 1718,76 10,63 47,69 7,28 1,4 49,68 2,3 1 24,29 1 2,03 0,09 14 0,15 24 0,580 85,49 3,99 1718,76 10,63 50,39 7,90 1,3 49,26 2,3 8 1 3 10 57 1,225 33,77 4,49 6328,13 56,69 55,06 8,37 1,3 85,2 104,62 1,9 1,23 0,18 0,15 3 81,88 101,74 1,9 4 1,24 0,17 65 0,15 21 1,116 41,18 4,98 6328,13 56,69 59,73 9,56 1,2 9 70,38 5 1,22 0,13 79 0,16 97 0,844 63,27 5,25 5546,88 36,61 62,26 10,19 1,2 85,75 1,9 7 68,90 3 1,23 0,13 86 0,16 35 0,818 66,28 5,52 5546,88 36,61 64,79 10,91 1,2 84,61 1,9 4 77,81 4 1,20 0,15 63 0,16 73 0,915 57,09 5,66 6328,13 44,88 66,05 11,28 1,2 93,42 1,9 3 6 1 58 98 0,918 57,75 5,79 6328,13 44,88 67,31 11,49 1,2 77,1 92,81 1,9 1,20 0,15 0,16 2 69,93 1 1,24 0,14 43 0,17 96 0,820 65,23 5,91 5781,25 41,34 68,40 11,74 1,2 86,89 1,9 1 69,30 5 1,25 0,14 10 0,17 06 0,826 65,54 6,02 5781,25 41,34 69,48 11,90 1,2 86,44 1,9 0 6 6 01 02 0,873 60,54 6,23 6250,00 46,06 71,46 12,23 1,1 73,9 90,86 1,9 1,23 0,14 0,17 9 72,93 4 1,23 0,14 97 0,16 04 0,879 61,20 6,44 6250,00 46,06 73,45 12,55 1,1 90,02 1,9 7 53,73 4 1,30 0,11 78 0,16 99 0,660 79,57 6,71 4687,50 27,17 75,98 12,90 1,1 70,16 2,0 5 8 0 21 93 0,652 80,07 6,98 4687,50 27,17 78,51 13,38 1,1 52,9 69,47 2,0 1,31 0,11 0,16 4 90,70 105,86 1,8 1 1,17 0,19 12 0,16 94 1,136 39,54 7,33 8203,13 62,60 81,74 13,70 1,1 1 88,93 104,38 1,8 8 1,17 0,18 03 0,16 73 1,107 41,94 7,67 8203,13 62,60 84,98 14,39 1,0 9 9 8 58 83 0,803 67,55 7,82 5390,63 53,15 86,43 14,76 1,0 57,9 84,46 2,1 1,46 0,13 0,16 8 57,58 0 1,46 0,13 60 0,16 98 0,801 67,50 7,98 5390,63 53,15 87,89 14,95 1,0 84,09 2,1

According to the figure 8, the layers that seem to represent a risk of liquefaction are those situated between 2.28m-4m, 5.25m-6.98m and to 7.82m with most elevated probabilities of liquefaction valued to 87.22% for the first interval, 80.04% for the second and 67.50% for the layer situated to 7.82m. For the rest of the layers soil behaves like a non liquefiable clay (IC>2.6) since F>1% and the Chinese criteria is not verified (FC>15%).


3.3 Assessment by the Dynamic Method: Model of Masing The gotten graphic and analytic results are presented below. Z (m)

Table 3. Evaluation of the liquefaction potential by the dynamic method (Model Masing). qc fs τmax KC RCR RCS FS CN qc1n qc1ncs IC ࣌′࢜૙ Kpa) (Kpa) (KPa) (Kpa)

0,88 1,76 1,86 1,95 2,11 2,26 2,28 2,30 2,65 2,99 3,20 3,41 3,70 3,99 4,49 4,98 5,25 5,52 5,66 5,79 5,91 6,02 6,23 6,44 6,71 6,98 7,33 7,67 7,82 7,98

3984,3 3984,3 4453,1 4453,1 4609,3 4609,3 1796,8 1796,8 1796,8 1796,8 1953,1 1953,1 1718,7 1718,7 6328,1 6328,1 5546,8 5546,8 6328,1 6328,1 5781,2 5781,2 6250,0 6250,0 4687,5 4687,5 8203,1 8203,1 5390,6 5390,6

43,70 43,70 30,71 30,71 31,89 31,89 7,09 7,09 7,09 7,09 10,63 10,63 10,63 10,63 56,69 56,69 36,61 36,61 44,88 44,88 41,34 41,34 46,06 46,06 27,17 27,17 62,60 62,60 53,15 53,15

13,22 26,43 27,87 29,30 31,61 33,91 34,20 34,50 37,76 41,01 42,99 44,98 47,69 50,39 55,06 59,73 62,26 64,79 66,05 67,31 68,40 69,48 71,46 73,45 75,98 78,51 81,74 84,98 86,43 87,89

1,03 2,87 4,22 4,44 4,75 5,09 5,27 5,31 5,77 6,81 7,39 8,26 8,46 9,64 9,31 11,15 11,67 13,51 13,94 14,34 14,67 14,84 15,06 15,71 15,45 16,70 15,93 17,79 18,18 18,84

1,93 1,69 1,67 1,65 1,61 1,58 1,58 1,57 1,53 1,49 1,46 1,44 1,41 1,38 1,33 1,29 1,27 1,24 1,23 1,22 1,21 1,20 1,19 1,17 1,15 1,14 1,11 1,09 1,08 1,07

67,73 67,73 75,70 75,70 78,36 78,36 30,55 30,55 29,24 28,06 29,79 29,12 24,89 24,21 85,28 81,88 70,30 68,91 77,86 77,13 69,90 69,36 73,93 72,93 53,78 52,90 90,73 88,99 57,98 57,50

94,85 94,95 90,90 90,91 93,22 93,23 30,55 30,55 29,24 28,06 51,00 50,57 49,68 49,26 104,62 101,74 85,75 84,61 93,42 92,81 86,89 86,44 90,86 90,02 70,16 69,47 105,86 104,38 84,46 84,09

2,0 2,0 1,9 1,9 1,9 1,9 2,1 2,1 2,1 2,1 2,2 2,2 2,3 2,3 1,9 1,9 1,9 1,9 1,9 1,9 1,9 1,9 1,9 1,9 2,0 2,0 1,8 1,8 2,1 2,1

1,40 1,40 1,20 1,20 1,19 1,19 1,00 1,00 1,00 1,00 1,71 1,74 2,00 2,03 1,23 1,24 1,22 1,23 1,20 1,20 1,24 1,25 1,23 1,23 1,30 1,31 1,17 1,17 1,46 1,46

0,15 0,15 0,14 0,14 0,15 0,15 0,07 0,07 0,07 0,07 0,09 0,09 0,09 0,09 0,18 0,17 0,13 0,13 0,15 0,15 0,14 0,14 0,14 0,14 0,11 0,11 0,19 0,18 0,13 0,13

0,078 0,108 0,151 0,151 0,150 0,150 0,154 0,154 0,152 0,166 0,171 0,183 0,177 0,191 0,169 0,186 0,187 0,208 0,211 0,213 0,214 0,213 0,210 0,214 0,203 0,212 0,194 0,209 0,210 0,214

2,04 1,47 0,99 0,98 1,03 1,03 0,49 0,49 0,48 0,44 0,53 0,50 0,51 0,47 1,10 0,95 0,74 0,65 0,73 0,72 0,65 0,65 0,71 0,69 0,55 0,52 0,97 0,88 0,64 0,63

Prob (%) 8,63 21,8 50,7 50,9 47,2 47,1 91,3 91,3 91,4 93,6 88,6 90,7 89,9 92,0 41,9 53,9 72,9 80,2 73,1 74,3 79,9 80,1 75,5 77,2 87,7 89,4 51,9 59,7 80,8 82,0


According to the figure 9, the layers that seem to represent a risk of liquefaction are those situated between 2.28-3.99m and 4.98-7.98m, with a middle liquefaction probability of about 91.14% and 74.61%. For the rest of the layers soil behaves like a non liquefiable clay (IC>2.6) since F>1% and the Chinese criteria is not verified (FC>15%). 3.3 Assessment by the Dynamic Method: Model of Rambert and Osgood The gotten graphic and analytic results are presented below. Table 4. Evaluation of the liquefaction potential by the dynamic method (Model Rambert and Osgood). fs τmax Z qc Prob ࣌ᇱ࢜૙ CN qc1n qc1ncs IC KC RCR RCS FS (Kpa) (Kpa) (KPa) (Kpa) (m) (%) 0,88 3984,38 43,70 13,22 0,51 1,93 67,73 94,85 2,07 1,40 0,1594 0,0388 4,110 0,93 1,76 3984,38 43,70 26,43 1,38 1,69 67,73 94,95 2,07 1,40 0,1596 0,0522 3,060 2,43 1,86 4453,13 30,71 27,87 2,36 1,67 75,70 90,90 1,91 1,20 0,1499 0,0848 1,767 13,26 1,95 4453,13 30,71 29,30 2,61 1,65 75,70 90,91 1,91 1,20 0,1499 0,0891 1,681 15,25 2,11 4609,38 31,89 31,61 2,77 1,61 78,36 93,22 1,90 1,19 0,1553 0,0877 1,772 13,16 2,26 4609,38 31,89 33,91 2,98 1,58 78,36 93,23 1,90 1,19 0,1554 0,0880 1,766 13,28 2,28 1796,88 7,09 34,20 3,11 1,58 30,55 30,55 2,15 1,00 0,0754 0,0909 0,830 64,87 2,30 1796,88 7,09 34,50 3,14 1,57 30,55 30,55 2,15 1,00 0,0754 0,0909 0,830 64,90 2,65 1796,88 7,09 37,76 3,16 1,53 29,24 29,24 2,17 1,00 0,0744 0,0836 0,890 59,53 2,99 1796,88 7,09 41,01 3,86 1,49 28,06 28,06 2,18 1,00 0,0734 0,0942 0,779 69,49 3,20 1953,13 10,63 42,99 4,09 1,46 29,79 51,00 2,22 1,71 0,0923 0,0952 0,970 52,48 3,41 1953,13 10,63 44,98 4,84 1,44 29,12 50,57 2,23 1,74 0,0920 0,1076 0,855 62,61 3,70 1718,76 10,63 47,69 4,64 1,41 24,89 49,68 2,31 2,00 0,0914 0,0973 0,939 55,16 3,99 1718,76 10,63 50,39 5,61 1,38 24,21 49,26 2,33 2,03 0,0910 0,1112 0,818 65,96 4,49 6328,13 56,69 55,06 4,73 1,33 85,28 104,62 1,94 1,23 0,1865 0,0859 2,170 7,20 4,98 6328,13 56,69 59,73 6,27 1,29 81,88 101,74 1,95 1,24 0,1779 0,1049 1,696 14,88 5,25 5546,88 36,61 62,26 6,39 1,27 70,30 85,75 1,93 1,22 0,1386 0,1026 1,352 27,01 5,52 5546,88 36,61 64,79 8,02 1,24 68,91 84,61 1,94 1,23 0,1363 0,1237 1,102 42,07 5,66 6328,13 44,88 66,05 8,20 1,23 77,86 93,42 1,91 1,20 0,1558 0,1241 1,255 32,07 5,79 6328,13 44,88 67,31 8,61 1,22 77,13 92,81 1,91 1,20 0,1543 0,1279 1,207 34,97 5,91 5781,25 41,34 68,40 8,76 1,21 69,90 86,89 1,95 1,24 0,1410 0,1281 1,101 42,15 6,02 5781,25 41,34 69,48 8,95 1,20 69,36 86,44 1,96 1,25 0,1401 0,1289 1,087 43,17 6,23 6250,00 46,06 71,46 8,82 1,19 73,93 90,86 1,94 1,23 0,1497 0,1234 1,214 34,55 6,44 6250,00 46,06 73,45 9,45 1,17 72,93 90,02 1,94 1,23 0,1478 0,1287 1,149 38,75 6,71 4687,50 27,17 75,98 8,88 1,15 53,78 70,16 2,00 1,30 0,1121 0,1169 0,959 53,43 6,98 4687,50 27,17 78,51 10,03 1,14 52,90 69,47 2,01 1,31 0,1112 0,1278 0,870 61,28 7,33 8203,13 62,60 81,74 8,93 1,11 90,73 105,86 1,88 1,17 0,1903 0,1092 1,742 13,80 7,67 8203,13 62,60 84,98 10,58 1,09 88,99 104,38 1,88 1,17 0,1858 0,1245 1,492 21,07 7,82 5390,63 53,15 86,43 10,77 1,08 57,98 84,46 2,10 1,46 0,1360 0,1246 1,092 42,80 7,98 5390,63 53,15 87,89 11,40 1,07 57,50 84,09 2,10 1,46 0,1353 0,1297 1,043 46,53

According to the figure 10, the layers that seem to represent a risk of liquefaction are those situated between 2.28m-3.9m and 6.71-7m., with most elevated probabilities of liquefaction valued to 69.49% for the first interval and 61.28% for the second. For the rest of the layers soil behaves like a non liquefiable clay (IC>2.6) since F>1% and the Chinese criteria is not verified (FC>15%).


On the figure 11, we present a comparison between the four used methods, and we recognize well in this example that the simplified method underestimates the potential of liquefaction in relation to the dynamic methods.

Figure 11. Profile of the safety factor gotten by the four methods according to the depth.

4. CONCLUSION In this work, we tried to give a brief presentation of the program “Caldynsoil” in its first version, it treats in general the cases nonlinear concretized by the integration of the equivalent linear analysis with concentrated masses and the hyperbolic models of Hardin and Drnevich, Rambert and Osgood and Masing. This program can be especially an effective tool for the researchers who work in the domains of the dynamics of soils or structures, it facilitates the fast generation of the numeric and graphic results and it is also expandable to other methods and nonlinear models that we will do our best to concretize them in the second version of program.

REFERENCES Hardin B.O., Drnevich V.P. (1972). Shear modulus and damping in soils: design equations and curves. Journal of Soils Mechanics and Foundation Division – ASCE 98:7, 667-692. Jenning P.C. (1964). Periodic Response of General Yielding Structure. Journal of the Engineering Mechanics Division, ASCE 90: EM2. Matlab® & Simulink® Release (2007), Matrix Laboratory Language. Seed H. B., Idriss I.M. (1971). Simplified procedure for evaluating soil liquefaction potential. Journal of Soil Mechanics and Foundations Division - ASCE. 97:SM9, 1249-1273. Seed H. B., Tokimatsu K.., Harder L.F. and Chung R. M. (1985). The influence of SPT procedures in soil liquefaction resistance evaluations. J. Geotech. Engrg., ASCE, 111: 12, 1425–1445. Robertson P. K.., Wride C.E. (1998). Evaluating cyclic liquefaction potential using the cone penetration test. Can. Geotech. J. 35:3, 442–459. Bardet J.P., Kapuskar M. (1991). Site investigation of the Marina District of San Francisco in September 1990. Report to the National Science Foundation, University of Southern California. Bennett M.J. (1990). Ground deformation and liquefaction of soil in the Marina District. Chapter D of Effects of the Loma Prieta Earthquake on the Marina District, San Francisco, California. U.S. Geological Survey Open-File Report 90–253, U.S. Geological Survey, Reston, VA. D1–D36. Holzer, T.L., O’Rourke, T.D. 1990. Effects of the Loma Prieta earthquake on the Marina District, San Francisco, California. U.S. Geological Survey, U.S. Geological Survey, Reston, VA. Open-file report 90–253. Rollins, K.M., McHood , M.D. 1998. Comparison of computed and measured liquefaction-induced settlements in the Marina District, San Francisco. The Loma Prieta, California, Earthquake of October 17, 1989 – Liquefaction. U.S. Geological Survey Professional Paper 1551-B, U.S. Geological Survey, Reston, VA. pp. B223–B240. Blake T. F. 1999. Recommended Procedures for Implementation of DMG Special Publication 117, Guidelines for Analyzing and Mitigating Landslide Hazards in California, Southern California Earthquake Center, University of Southern California. Seed, H.B., Idriss I.M. (1982). Ground motions and soil liquefaction during earthquakes. Berkeley, CA: Earthquake Engineering Research Institute.

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m Titre : ESTIMATION DU RISQUE DE LIQUEFACTION D’UN DEPOT DE SOL SOUS SOLLICITATION SISMIQUE Sujet : Auteur : e Mots clés : Commentaires : Date de création : 27/04/2012 23:16:00 N° de révision : 13 Dernier enregistr. le : 24/06/2012 22:47:00 Dernier enregistrement par : e Temps total d'édition :97 Minutes Dernière impression sur : 24/06/2012 22:47:00 Tel qu'à la dernière impression Nombre de pages : 11 Nombre de mots : 4 194 (approx.) Nombre de caractères : 23 068 (approx.)