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BI-AXIAL TEST WITH MOHR-COULOMB MODEL
BI-AXIAL TEST WITH MOHR-COULOMB MODEL
This document describes an example that has been used to verify
the elasto-plastic
deformation capabilities according to the linear-elastic
perfectly-plastic Mohr-Coulomb
model of PLAXIS. The problem involves axial loading under
biaxial test conditions.
Used version:
PLAXIS 2D - Version 2011
PLAXIS 3D - Version 2012
Input: A bi-axial test is conducted on a geometry displayed in
Figure1for PLAXIS 2D
and PLAXIS 3D.
1 1
2
2
x
xy
y
z
PLAXIS 2D PLAXIS 3D
Figure 1 Bi-axial test - loading conditions
Material: The material behaviour is modelled by means of the
Mohr-Coulomb model.
The lateral pressure 2 is represented by a distributed load on
the right boundary. The
density is set to zero. The model parameters are:
Mohr-Coulomb model E' = 1000 kN/m2 = 0.25
c'ref= 1 kN/m2
' = 30
Meshing: The Coarseoption is used for the Element distributionto
generate the mesh.
Calculations: The active prescribed displacements and loads for
each phase of the test
are given in Table1and Table2. The axial load 1is represented by
a distributed load on
the top of the geometry.
Bi-axial loading of1 = 2 = -1 kPa
Axial loading of 1 = -10 kPa
Output: The soil fails at an axial stress1 =6.4640kN/m2 and 1
=6.4651kN/m
2
in PLAXIS 2D and PLAXIS 3D respectively. The plot of the
principal effective stress 1versus strain 1 is shown in
Figure2.
Verification: The theoretical solution to the failure of the
sample is given by the Mohr -
Coulomb criterion:
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VALIDATION & VERIFICATION
Table 1 Boundary and loading conditions (Phase 1)
Location Points Dispx Dispy Dispz Loadx Loady Loadz
Front (0; 0; 0) (1; 0; 0)
(1; 0; 1) (0; 0; 1)
Free Fixed Free - - -
Rear (0; 1; 0) (1; 1; 0)
(1; 1; 1) (0; 1; 1)
Free Fixed Free - - -
Left (0; 0; 0) (0; 1; 0)(0; 1; 1) (0; 0; 1)
Fixed Fixed Free - - -
Right (1; 0; 0) (1; 1; 0)
(1; 1; 1) (1; 0; 1)
Free Free Free -1.0 - -
Bottom (0; 0; 0) (1; 0; 0)
(1; 1; 0) (0; 1; 0)
Free Free Fixed - - -
Top (0; 0; 1) (1; 0; 1)
(1; 1; 1) (0; 1; 1)
- - - - - -1.0
Table 2 Boundary and loading conditions (Phase 2)
Location Points Dispx Dispy Dispz Loadx Loady Loadz
Front (0; 0; 0) (1; 0; 0)
(1; 0; 1) (0; 0; 1)
Free Fixed Free - - -
Rear (0; 1; 0) (1; 1; 0)
(1; 1; 1) (0; 1; 1)
Free Fixed Free - - -
Left (0; 0; 0) (0; 1; 0)
(0; 1; 1) (0; 0; 1)
Fixed Fixed Free - - -
Right (1; 0; 0) (1; 1; 0)
(1; 1; 1) (1; 0; 1)
Free Free Free -1.0 - -
Bottom (0; 0; 0) (1; 0; 0)
(1; 1; 0) (0; 1; 0)
Free Free Fixed - - -
Top (0; 0; 1) (1; 0; 1)
(1; 1; 1) (0; 1; 1)
- - - - - -10.0
0
0
0.01 0.02 0.03 0.04 0.05 0.06 0.07
1
2
3
4
5
6
7
PLAXIS 2D solution
PLAXIS 3D solution
1
[kN/m
2 ]
1 [ ]
Figure 2 Results of the bi-axial loading test with the
Mohr-Coulomb model
f = |1 2|
2+1 + 2
2 sin c cos = 0
Failure occurs in compression at:
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BI-AXIAL TEST WITH MOHR-COULOMB MODEL
1 = 2 1 + sin
1 sin 2c
cos
1 sin =6.4641 kN/m2
The error in the numerical solutions is therefore 0.001% and
0.015% for PLAXIS 2D and
PLAXIS 3D respectively.
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VALIDATION & VERIFICATION
4 Validation & Verification | PLAXIS 2012
