Triaxial Test - Consolidated Drained

Table of contents

1. Finite Element (FE) representation
2. Validation of simulation approach
3. Sample numgeo input file
4. References

Finite Element (FE) representation

For the simulation of consolidated drained (CD) monotonic triaxial tests we perform a so-called ‘‘single-element-simulation’’ with the FE program numgeo and by doing so enforce element test assumptions, i.e. a homogeneous distribution of stress/strain within the test sample. A schematic of the FE representation of the CD test is given below.

• An axisymmetric solid element with four nodes and linear shape functions for the displacement field is used
• In a first initial step, the initial conditions are applied, i.e. initial stress ($\sigma_1^0, \sigma_2^0$), initial void ratio $e_0$ or any other initial state variable required by the constitutive model to be calibrated
• In the second loading step, the loading is applied by prescribing the vertikal displacements $u_2$ of the top nodes and thus controlling the axial (vertical) strain in the soil. $u_2$ is increased linearly starting from $u_2=0$ until $u_2^{max} = h \cdot \varepsilon_{lab}^{max}$ is reached. Therein, $h$ is the soil sample and $\varepsilon_{lab}^{max}$ is the maximum axial strain measured in the laboratory experiment.

Validation of simulation approach

For the validation of the simulation approach, a comparison with the simulation results on Toyoura Sand with the SANISAND constitutive model reported in the original paper [1] is made. Mahdi Taiebat and Sheng Teng furthermore contributed simulation results of the same tests as in [1] such that a total of three implementations and simulation strategies could be used to benchmark the approach used in numgeo-ACT. The simulation results from Taiebat & Sheng were performed using either the finite element code OpenSees or their in-house constitutive model driver ConModel.

Sample numgeo input file

An example input file for the simulation of a CD triaxial test using the Sanisand with numgeo is shown below.

**=~~=~~=~~=~~=~~=~~=~~=~~=~~=~~=~~=~~=~~=~~=~~=~~=~~=~~=~~=~~=~~=~~=~~=~~=~~=
**                                  numgeo                                    
**             Copyright (C) 2022 Jan Machacek, Patrick Staubach              
**=~~=~~=~~=~~=~~=~~=~~=~~=~~=~~=~~=~~=~~=~~=~~=~~=~~=~~=~~=~~=~~=~~=~~=~~=~~=

*Node
1, 0.0 , 0.00
2, 0.05, 0.00
3, 0.05, 0.1
4, 0.00, 0.10

*Nset, Nset=nall
1, 2, 3, 4, 5
*Nset, Nset=nleft
1, 4
*Nset, Nset=nright
2 , 3
*Nset, Nset=nbottom
1 , 2
*Nset, Nset=ntop
3 , 4

*Element, Type = U4-solid-ax
1, 1, 2, 3, 4

*Elset, Elset=eall
1

** ----------------------------------------

*Solid Section, elset = eall, material=soil

** ----------------------------------------

*Material, name = soil, phases = 1

*Mechanical = Sanisand-2
100,0.934,0.019,0.7,1.25,0.89,0.01,125
0.05,7.05,0.968,1.1,0.704,3.5,4,600

*Density
2.65

** ----------------------------------------

*Initial conditions, type=stress, geostatic
eall, 0.0, -500, 0.1, -500, 1., 1.

*Initial conditions, type=state variables
eall, void_ratio, 0.960

** ----------------------------------------

*Amplitude, name=LoadingRamp, type=ramp
0.0, 0.0, 1.0, 1.0

** ----------------------------------------

*Step, name=Geostatic, inc=1
*Geostatic

*Body force, instant
eall, grav, 0.0, 0., -1, 0.
*Dload, instant
eall, p3, -500
*Dload, instant
eall, p2, -500

*Boundary
nleft, u1, 0.
nbottom, u2, 0.

*Output, print
*Element output, elset=eall
S, E, void_ratio, fyield, flag-integration, stress-p, stress-q

*End Step

** ----------------------------------------

*Step, name=Loading, inc=10000
*Static
0.001, 1, 0.001, 0.001

*Body force, instant
eall, grav, 0.0, 0., -1, 0.
*Dload, instant
eall, p3, -500
*Dload, instant
eall, p2, -500

*Boundary, amplitude = LoadingRamp
ntop, u2, -0.02
*Boundary
nleft, u1, 0.
nbottom, u2, 0.

*Output, print
*Element output, elset=eall
S, E, void_ratio, fyield, flag-integration, stress-p, stress-q

*End Step

** ----------------------------------------

*End Input

References

[1] Y. F. Dafalias and M. T. Manzari, ‘Simple plasticity sand model accounting for fabric change effects’, Journal of Engineering mechanics, vol. 130, no. 6, pp. 622–634, 2004.