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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 Received on September 2012 Published on November 2012 429 Comparison between Experimental and Finite Element Modeling Data for Triaxial Undrained Cyclic Tests in Compression on HOSTUM Sand Seyed Hassan Golmaei 1 , Marc Boulon 2 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 high- cyclic 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
Transcript

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

Received on September 2012 Published on November 2012 429

Comparison between Experimental and Finite Element Modeling Data for

Triaxial Undrained Cyclic Tests in Compression on HOSTUM Sand Seyed Hassan Golmaei

1, Marc Boulon

2

1Sari Agriculture Sciences and Natural Resources University, Sari, Iran

2GRENOBLE 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 high-

cyclic 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

Comparison between Experimental and Finite Element Modeling Data for Triaxial Undrained Cyclic Tests

in Compression on HOSTUM Sand

Seyed Hassan Golmaei, Marc Boulon

International Journal of Civil and Structural Engineering 430

Volume 3 Issue 2 2012

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.

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

Own

weight

of soil

Averag

e load

Recording cycle Explicit creep

Comparison between Experimental and Finite Element Modeling Data for Triaxial Undrained Cyclic Tests

in Compression on HOSTUM Sand

Seyed Hassan Golmaei, Marc Boulon

International Journal of Civil and Structural Engineering 431

Volume 3 Issue 2 2012

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.

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

peak

Comparison between Experimental and Finite Element Modeling Data for Triaxial Undrained Cyclic Tests

in Compression on HOSTUM Sand

Seyed Hassan Golmaei, Marc Boulon

International Journal of Civil and Structural Engineering 432

Volume 3 Issue 2 2012

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

( ) ESSAI ω

18.0 to18.3

Monotone

75% 25%

25% 25%

0.75

0.25

0.25

0.25

16 to 16.4

Monotone

25% 25%

50% 25%

75% 25%

50% 50%

0.25

0.50

0.75

0.50

0.25

0.25

0.25

0.50

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.

Comparison between Experimental and Finite Element Modeling Data for Triaxial Undrained Cyclic Tests

in Compression on HOSTUM Sand

Seyed Hassan Golmaei, Marc Boulon

International Journal of Civil and Structural Engineering 433

Volume 3 Issue 2 2012

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 C[kPa] Φ[Degree] Ψ[Degree] 45000 45000 135000 0.5 0.1 42 23.5 0.95

= 200 kPa = 16.3 e = 0.5

23000 23000 69000 0.5 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, ( )), are

presented in Figures 3.3, 3.4, 3.5, 3.6, 3.7, and 3.8

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).

Comparison between Experimental and Finite Element Modeling Data for Triaxial Undrained Cyclic Tests

in Compression on HOSTUM Sand

Seyed Hassan Golmaei, Marc Boulon

International Journal of Civil and Structural Engineering 434

Volume 3 Issue 2 2012

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

Comparison between Experimental and Finite Element Modeling Data for Triaxial Undrained Cyclic Tests

in Compression on HOSTUM Sand

Seyed Hassan Golmaei, Marc Boulon

International Journal of Civil and Structural Engineering 435

Volume 3 Issue 2 2012

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

Comparison between Experimental and Finite Element Modeling Data for Triaxial Undrained Cyclic Tests

in Compression on HOSTUM Sand

Seyed Hassan Golmaei, Marc Boulon

International Journal of Civil and Structural Engineering 436

Volume 3 Issue 2 2012

3.2 Isotropically Consolidated Undrained Cyclic Tests

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.

At the bottom of

cycle

, Critical State Line

, Peak Friction Angle

Mean value

Comparison between Experimental and Finite Element Modeling Data for Triaxial Undrained Cyclic Tests

in Compression on HOSTUM Sand

Seyed Hassan Golmaei, Marc Boulon

International Journal of Civil and Structural Engineering 437

Volume 3 Issue 2 2012

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.

At the bottom

of cycle

Mean value

Comparison between Experimental and Finite Element Modeling Data for Triaxial Undrained Cyclic Tests

in Compression on HOSTUM Sand

Seyed Hassan Golmaei, Marc Boulon

International Journal of Civil and Structural Engineering 438

Volume 3 Issue 2 2012

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.

At the bottom of

cycle

Mean value

Comparison between Experimental and Finite Element Modeling Data for Triaxial Undrained Cyclic Tests

in Compression on HOSTUM Sand

Seyed Hassan Golmaei, Marc Boulon

International Journal of Civil and Structural Engineering 439

Volume 3 Issue 2 2012

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.

Mean value

At the bottom of

cycle

Comparison between Experimental and Finite Element Modeling Data for Triaxial Undrained Cyclic Tests

in Compression on HOSTUM Sand

Seyed Hassan Golmaei, Marc Boulon

International Journal of Civil and Structural Engineering 440

Volume 3 Issue 2 2012

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.

Mean value

At the bottom of cycle

Comparison between Experimental and Finite Element Modeling Data for Triaxial Undrained Cyclic Tests

in Compression on HOSTUM Sand

Seyed Hassan Golmaei, Marc Boulon

International Journal of Civil and Structural Engineering 441

Volume 3 Issue 2 2012

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.

Mean value

At the bottom of

cycle

Comparison between Experimental and Finite Element Modeling Data for Triaxial Undrained Cyclic Tests

in Compression on HOSTUM Sand

Seyed Hassan Golmaei, Marc Boulon

International Journal of Civil and Structural Engineering 442

Volume 3 Issue 2 2012

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