INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING Volume 3, No 2, 2012 © Copyright by the authors - Licensee IPA- Under Creative Commons license 3.0

Research article

ISSN 0976 – 4399

Comparison between Experimental and Finite Element Modeling Data for Triaxial Undrained Cyclic Tests in Compression on HOSTUM Sand Seyed Hassan Golmaei1, Marc Boulon2 1 Sari Agriculture Sciences and Natural Resources University, Sari, Iran 2 GRENOBLE University, France [email protected] doi:10.6088/ijcser.201203013040

ABSTRACT Finite elements modeling data is fitted to the results of experimental undrained monotonic and cyclic isotropic triaxial tests. The model can predict the accumulation strain /stress, and pore pressure in undrained state. For determination of material constants, the first cycle (loading-unloading) is performed step-by-step, using Hardening-Soil model for undrained soil, then for the cycles greater than one, the Behavior of the soil is simulated as a pseudo creep (Soft-Soil-Creep model, here) where the number of cycles N is considered equivalent time. The prediction of model is compared with experimental results from monotonic and cyclic undrained isotropic triaxial tests. Good correlation exists between predicted and experimental response. Keywords: Triaxial undrained, cyclic tests, Hostum sand; Pseudo cyclic creep model, Explicit model, PLAXIS. 1. Introduction The evolution of civil engineering constructions at sea, has highlighted the need to develop a method for calculating foundation structure at sea, for taking into account the repeated action of waves and wind.The behavior prediction of structures under cyclic loading requires a good knowledge of the behavior of an element of the soil, under cyclic loading in homogenous conditions. This knowledge is a necessary basis for each method of calculation of structure, for example finite element method. In this study, it is limited to consideration of the cyclical behavior of sands. It has been proposed further that the case of a slow loading during which the soil is loaded in quasi-static, inertial forces is not involved in the analysis of the phenomenon. In undrained conditions the application of cyclic loading leads to the accumulation of pore pressure and modification of the soil module to the change of the effective mean stress. 1.1 EXPLICIT Versus IMPLICIT Method In the Finites Elements (F.E.) calculation of the accumulation due to cyclic loading two different numerical strategies can be considered: the Implicit and Explicit methods. For highcyclic loading in general explicit models are the better choice. They treat the process of accumulation under cyclic loading similar to a process governed by viscosity. The number of cycles N replaces the time(9). Application of boundary value problems with cyclic loading can be studied numerically by means of finite element method (FEM).The so-called IMPLICIT method, where in each cycle is calculated with a constitutive model and many strain increments, is not applicable for a number of cycles N higher than 50 because of the

Received on September 2012 Published on November 2012

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Comparison between Experimental and Finite Element Modeling Data for Triaxial Undrained Cyclic Tests in Compression on HOSTUM Sand Seyed Hassan Golmaei, Marc Boulon

accumulation of numerical errors and the huge calculation effort. In this case the so-called EXPLICIT method is superior to the IMPLICIT one. An explicit model treats the accumulation of residual strains under cyclic loading similar to the problem of creep under constant loads (9). Metals, especially under high temperatures, exhibit simultaneously the phenomena of creep and viscoplasticity. The former is essentially a redistribution of stress and / or strains with time under elastic material response while the latter is a time dependent plastic deformation. Experimental observations cannot distinguish between the two phenomena and their separation has been largely an analytical convenience rather a physical requirement (5). The explicit model has been used in a combined numerical strategy consisting of implicit and explicit schemes for the solution of accumulation problems in the engineering practice. Numerical processes, as described in this work, allow the simultaneous description of both effects. Three modes of operation have been distinguished in the modes of material routines. 1- explicit schemes for the solution of accumulation problems in the engineering practice. Initial equilibrium and first cycle .The explicit model has been used in a combined numerical strategy consisting of implicit and The accumulation model implemented into the FE program , PLAXIS has been utilized by HSM (hardening soil model). 2- recoding mode from the first cycle, the strain amplitude can be used for the calculation of the second cycle and for control cycles. 3- Pseudo-creep mode :In this mode the explicit calculation of accumulation according to SSCM (Soft Soil Creep Model) is carried out.

Own weight of soil

Averag e load

Recording cycle

Explicit creep

Figure Error! No text of specified style in document..1: Assignment of calculation steps and program modes for the calculation of cyclically loaded Geotechnical structure

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Comparison between Experimental and Finite Element Modeling Data for Triaxial Undrained Cyclic Tests in Compression on HOSTUM Sand Seyed Hassan Golmaei, Marc Boulon

The present study focus on finite element modeling of undrained monotonic and cyclic triaxial tests. This is done by industrial software (PLAXIS here). The results of modeling and experimental data found in literature are compared by curve fitting. 2. Materials and Methods Cyclic tests were carried out by IOANNIS THANOPLOUS [8] to 200 cycles on the undrained condition in HOSTUM sand. The series of cyclic triaxial compression tests on the undrained condition was conducted following the drained compression test to 200 cycles. peak

Figure Error! No text of specified style in document..2: the mean position of the cycle and cyclical amplitude is defined by using the two variables reduced by σm and ω (8). Is the value of the deviator to the rupture during the test as defined monotonic under compression Is the maximum value of axial stress during the cycle. Is the minimum value of the axial stress during the cycle. The parameters and ω are calculated from the stress to the rupture defined during the crushing monotonically, under compression. Cyclic tests were carried out by LOANNIS THANOPLOUS to 200 cycles on the undrained condition in HOSTUM sand. The series of cyclic triaxial compression tests on the undrained condition was conducted following the drained compression test to 200 cycle. For all these tests the initial effective lateral stress is equal to 200 kPa. Table 1: The mean level σ3 and cyclical amplitude ω are defined by comparison to the deviator rupture drained, (σ1 – σ3)peak (8). (

)

18.0

750

kPa

16.0

480

kPa

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Comparison between Experimental and Finite Element Modeling Data for Triaxial Undrained Cyclic Tests in Compression on HOSTUM Sand Seyed Hassan Golmaei, Marc Boulon

Table 2: The tests performed on six simple of HOSTUM sand in undrained condition are: (8) (

)

18.0 to18.3

16 to 16.4

ESSAI

ω

Monotone 75% 25% 0.75 0.25 25% 25% Monotone

0.25 0.25

0.25 0.50 0.75 0.50

0.25 0.25 0.25 0.50

25% 50% 75% 50%

25% 25% 25% 50%

For comparison between experimental data under undrained compression condition and Finite- Element calculation, Plaxis Package 2D Version 8.2 has been used (6). The Hardening-Soil model has been used for simulation of undrainedtriaxial test, and then the Soft-Soil-Creep model is used for simulation of a creep model. A triaxial test can simply be modeled by means of an axisymmetric geometry of unit dimension (1m x 1m), that represent a quarter of soil specimen, Figure 2.2 These dimensions are not realistic, but they are selected for simplicity. The dimension of the model does not influence the results, provided that the soil weight is not taken into account. In this configuration the stresses and strains are uniformly distributed over the geometry. The deformation magnitudes in x – and y - directions of the top right hand corner correspond to the horizontal and vertical strains, respectively. The left hand side and the bottom of the geometry are axes of symmetry. At these boundaries the displacements normal to the boundaries are fixed and the tangential displacements are kept free to allow for „smooth‟ movements. The remaining boundaries are fully free to move.

Figure Error! No text of specified style in document..3: Simplified configuration of a triaxial test. International Journal of Civil and Structural Engineering Volume 3 Issue 2 2012

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Comparison between Experimental and Finite Element Modeling Data for Triaxial Undrained Cyclic Tests in Compression on HOSTUM Sand Seyed Hassan Golmaei, Marc Boulon

3. Results and Discussion 3.1 Isotropically Consolidated Undrained Monotonic Compression Tests Preliminary to the undrained cyclic triaxial tests, in order to determine material constants, curve fitting for correlation between the experimental and F.E. modeling data, for two series of undrained monotonic triaxial tests (compression) were performed .The specimens were consolidated under isotropic effective stress 200 kPa. Comparison between model prediction and experimental results under monotonic loading on Hostum sand are shown in figures 3.1 – 3.2. In figs 3.1 a – 3.2 a, the peak friction angle (PFA, RC), the drain line slope 1:3, the critical state line (CSL, DC) are plotted. In both figures, the path representing the state of stresses goes back to drained loading surface. The evolutions of pore water pressure are presented in Figs 3.1 c – 3.2 c. A drained behavior of sand that would first contracting (u increasing) and secondly dilating (u decreasing) are shown in both figures. From the comparison it can be concluded that model data, reasonably well, predict experimental data. Table 3 resumes the required material constant for applying pseudo - creep mode. Table 3: Materials Properties according to Harding Soil Model KPa =18.3 e=0.45 [kPa] [kPa] [kPa] m 45000 45000 135000 0.5 = 200 kPa = 16.3 e = 0.5 23000 23000 69000 0.5

C[kPa] 0.1

Φ[Degree] Ψ[Degree] 42 23.5 0.95

0.1

35

9.6

0.93

The curves pore water pressure (u) to number of cycles (N), and effective stress path in p‟-q plane with Critical State Line (CSL, ( )), to Peak Friction Angle (FFA, presented in Figures 3.3, 3.4, 3.5, 3.6, 3.7, and 3.8

(

)), are

Figures 3.3, 3.4, 3.5, 3.6, 3.7, and 3.8 compare typical behavior of undrained isotropic cyclic triaxal tests with different initial density, different mean stress, and different amplitude between model and experimental prediction. The behavioral pattern described previously predicts globally well the basic trends of pore pressure, and stress path. Comparison between Figures 3.3a and 3.4a show significant effect of mean stress on the static stress state existing prior to the application of cyclic loading. With =%25 the pore pressure is positive and it will be stabilized approximately around 200 cycles, on the contrary, with =%75 pore pressure will be generated negatively, and it will be also stabilized approximately around 200 cycles. In Figures 3.3a, 3.4a, 3.6a, and 3.7a, pore pressure changes during the cycles to a constant value, , and in all these cases, positive pore pressure accumulates at a continuously decreasing rate, until it reaches a constant value (stabilization of pore pressure, and axial deformation). In these tests, positive pore pressure accumulates at a continuously decreasing rate, until it reaches a constant value (stabilization of pore pressure, and axial deformation).

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Comparison between Experimental and Finite Element Modeling Data for Triaxial Undrained Cyclic Tests in Compression on HOSTUM Sand Seyed Hassan Golmaei, Marc Boulon

Figures 3.3a and 3.4a show the influence of the mean stress on the evolution of the pore pressure. In fact, if the pore pressure increases from 0.25 to 0.75 , then it falls from a positive to a negative value.

Figure Error! No text of specified style in document..4: Curve fitting undrained monotonic triaxial tests: σ3 = 200 kPa γd=18.3 kN/m3 a) stress path in the p‟-q plane. b) Deviatory stress (σ1- σ3) as a function of strain ε1. c) Pore pressure u as a function of axial strain ε1 DC Line: Critical State Line, RC Line: Peak Friction Angle

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Comparison between Experimental and Finite Element Modeling Data for Triaxial Undrained Cyclic Tests in Compression on HOSTUM Sand Seyed Hassan Golmaei, Marc Boulon

Figure Error! No text of specified style in document..5: Curve fitting for undrained monotonic triaxial tests:σ3 = 200 kPa γd=16.3 kN/m3: a) stress path in the p‟- q plane, b) deviatory stress (σ1 – σ3) as a function of strain ε1 , c) pore pressure u as a function of axial strain ε1

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Comparison between Experimental and Finite Element Modeling Data for Triaxial Undrained Cyclic Tests in Compression on HOSTUM Sand Seyed Hassan Golmaei, Marc Boulon

3.2 Isotropically Consolidated Undrained Cyclic Tests Mean value

At the bottom of cycle

, Critical State Line , Peak Friction Angle

Figure Error! No text of specified style in document..6: Curve Fitting Between Experimental Data and Model Predicted Data for Undrained cyclic tests, amplitude (25% 25%)drained peak ,γd = 18.2 kN/m3 , σ3=200kPa : a) Pore Water Pressure as a Function of Number of Cycle N[], b)Stress Pass in the p‟- q plane.

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Comparison between Experimental and Finite Element Modeling Data for Triaxial Undrained Cyclic Tests in Compression on HOSTUM Sand Seyed Hassan Golmaei, Marc Boulon

Mean value

At the bottom of cycle

Figure Error! No text of specified style in document..7: Curve Fitting Between Experimental Data and Model Predicted Data for Undrained cyclic tests, amplitude(75% 25%)drained peak , γd = 18.0 kN/m3 , σ3=200kPa: a) Pore Water Pressure as a Function of Number of Cycle N[-], b) Stress Pass in the p‟- q plane.

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Comparison between Experimental and Finite Element Modeling Data for Triaxial Undrained Cyclic Tests in Compression on HOSTUM Sand Seyed Hassan Golmaei, Marc Boulon At the bottom of cycle

Mean value

Figure Error! No text of specified style in document..8: Curve Fitting Between Experimental Data and Model Predicted Data for Undrained cyclic tests, amplitude (25% 25%)drained peak , γd = 16.4 kN/m3 , σ3=200kPa: a) Pore Water Pressure as a Function of Number of Cycle N[-], b) Stress Pass in the p‟- q plane.

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Comparison between Experimental and Finite Element Modeling Data for Triaxial Undrained Cyclic Tests in Compression on HOSTUM Sand Seyed Hassan Golmaei, Marc Boulon

Mean value

At the bottom of cycle

Figure Error! No text of specified style in document..9: Curve Fitting Between Experimental Data and Model Predicted Data for Undrained cyclic tests, amplitude(50% 25%)drained peak , γd = 16 kN/m3 , σ3=200kPa: a) Pore Water Pressure as a Function of Number of Cycle N[-], b) Stress Pass in the p‟- q plane.

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Comparison between Experimental and Finite Element Modeling Data for Triaxial Undrained Cyclic Tests in Compression on HOSTUM Sand Seyed Hassan Golmaei, Marc Boulon

Mean value

At the bottom of cycle

Figure Error! No text of specified style in document..10: Curve Fitting Between Experimental Data and Model Predicted Data for Undrained cyclic tests, amplitude (75% 25%)drained peak , γd = 16.3 kN/m3 , σ3=200kPa: a) Pore Water Pressure as a Function of Number of Cycle N[-], b) Stress Pass in the p‟- q plane.

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Comparison between Experimental and Finite Element Modeling Data for Triaxial Undrained Cyclic Tests in Compression on HOSTUM Sand Seyed Hassan Golmaei, Marc Boulon At the bottom of cycle

Mean value

Figure Error! No text of specified style in document..11: Curve Fitting Between Experimental Data and Model Predicted Data for Undrained cyclic tests, amplitude (50% 50%)drained peak , γd = 16 kN/m3 , σ3=200kPa: a) Pore Water Pressure as a Function of Number of Cycle N[-], b) Stress Pass in the p‟- q plane. Acknowledgments We are grateful to Mohammad Mahdi Jalali, Mohammad Reza Jalali, Bahram Farokhzad and Mir Khalegh Ziatabar Ahmadi for their insightful comments and guidelines. We also express our gratitude to GRENOBLE University laboratory under Marc Boulon management since 2010 till 2011. International Journal of Civil and Structural Engineering Volume 3 Issue 2 2012

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Comparison between Experimental and Finite Element Modeling Data for Triaxial Undrained Cyclic Tests in Compression on HOSTUM Sand Seyed Hassan Golmaei, Marc Boulon

References 1.

Bouckovolas, G. Whitman, R. V. and Marr, W. A. “Permanentdisplacement of sand with cyclic loading”. Journal of the geotechnical engineering.vol.110, N 11, pp. 1606-1623.

2.

Ching, S. Chang, Member, ASCE, and Robert, V. Whitman, Fellow, ASCE “Drained Permanent Deformation Of Sand Due To Cyclic Loading.” Journal of Geotechnical Engineering, Vol. 114, No. 10, October, 1988, ASCE.

3.

Messast, S. “Modelisation constitutive du comportementcyclique des sables en coditiondrainee.” Rapport de Recherche, 2eme semester 2006, Dirige par: Boulon, M. Prof. Emerite, Laboratoire Sols SolidesStructures(3S), Universite Joseph Fourier, Laboratoire de Mathematique et de CaculScientifique (LARMACS), Universite de Skikda.

4.

Messast, S. Boulon, M. Flavigny, E. “Constitutive Modeling ofthe Cyclic Behavior of the Sands in Drained Condition – Application toDense Sand.” 14eme CRA MSG. Yaounde, 26-28 Novembre 2007.

5.

Owen &Hinton “Elasto-Viscoplastic Problems in two dimensions.” Pp 271-281, Pineridge press, Swansea, UK, 1986.

6.

Plaxis, essential for geotechnical professionals, “Material Models Manual.” 2010.

7.

Poblete, Mauro. Wichtmann, T.Niemunis, Andrez. Triantafyllidis, Thcodor. “Accumulation of residual deformations due to cyclic loading with multidimensional strain loops”. 5thinternational conference on earthquake Geotechnical Engineering, January 2011, 10-13, Santiago, Chili.

8.

Thanopoulos, I. “contribution a l‟etude du comportementcyclique des milieuxpulverulent.” These Docteur-ingenieur, UniversiteScientifique et medical &L‟institut national polytechnique de Grenoble, 1981.

9.

Wichtmann, T. “Explicit accumulation model for non-cohesive soils under cyclic loading”. PhD thesis, Bochum University, 2005.

10.

Wichtmann, T. Niemunis, A. and Triandtafyllidis, Th. “Strain accumulation in sand due to cyclic loading: drained triaxial tests.” Soil Dynamics and Engineering (Vol. 25, No. 12, pp.967-979, 2005)

11.

Wichtmann, T. Niemunis, A. and Triandtafyllidis, Th. “Strain accumulation in sand due to cyclic loading: drained cyclic with triaxial extension.” Soil Dynamics and Engineering, 2007, vol .27 No. 1, pp. 42-48.

12.

PLAXIS version 8.5: a Finite Element code for soil.

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