FLAC3D Theory and Background • Constitutive Models
Triaxial Compression Test with Hoek-Brown-PAC Model
Note
The project file for this example is available to be viewed/run in FLAC3D. The project’s main data file is shown at the end of this example.
Triaxial compression tests are performed on models composed of Hoek-Brown-PAC material in FLAC3D to verify the stress and strain paths that develop.
A single-zone model to simulate the triaxial loading tests is constructed in FLAC3D. The triaxial load conditions are illustrated in Figure 1. Compression loading tests are performed under two loading conditions: \(\sigma_{3}/\sigma_{ci}\) = 0 and 1.0 (\(\sigma_{3}\) = 0 and 1.0 MPa).
The triaxial tests are performed on a sample of Hoek-Brown material with the following properties:
\(m_b\) |
5 |
\(s\) |
0.5 |
\(\sigma_{ci}\) |
1.0 MPa |
\(\sigma^{cv}_3\) |
1.5 MPa |
\(E\) |
100 MPa |
\(\nu\) |
0.35 |
The analytical solutions for stress and strain during compression loading are presented by the plots shown in Figure 2 and Figure 3.
The FLAC3D results are compared to the analytical solutions in Figure 4 through Figure 7. The solutions compare within 1%.
![../../../../../_images/modelhoek-11.png](../../../../../_images/modelhoek-11.png)
Figure 1: Triaxial compression tests—loading conditions.
![../../../../../_images/modelhoek-2.png](../../../../../_images/modelhoek-2.png)
Figure 2: Triaxial compression tests: a) Hoek-Brown failure envelope; b) stress-strain plots.
![../../../../../_images/modelhoek-3.png](../../../../../_images/modelhoek-3.png)
Figure 3: Triaxial compression tests: a) confining (lateral) strain versus axial strain; b) volumetric strain versus axial strain.
![../../../../../_images/modelhoek-test0-stress.png](../../../../../_images/modelhoek-test0-stress.png)
Figure 4: Triaxial compression test—stress versus axial strain (\({\sigma_3}/{\sigma_{ci}}\) = 0).
![../../../../../_images/modelhoek-test0-strain.png](../../../../../_images/modelhoek-test0-strain.png)
Figure 5: Triaxial compression test—lateral strain versus axial strain (\({\sigma_3}/{\sigma_{ci}}\) = 0).
![../../../../../_images/modelhoek-test1-stress.png](../../../../../_images/modelhoek-test1-stress.png)
Figure 6: Triaxial compression test—stress versus axial strain (\({\sigma_3}/{\sigma_{ci}}\) = 1.0).
![../../../../../_images/modelhoek-test1-strain.png](../../../../../_images/modelhoek-test1-strain.png)
Figure 7: Triaxial compression test—lateral strain versus axial strain (\({\sigma_3}/{\sigma_{ci}}\) = 1.0).
Data File
TriaxialCompressionHoekBrownPAC.dat
; Triaxial tests on a Hoek-Brown material
model new
model large-strain off
fish automatic-create off
model title "Triaxial Test on a Hoek-Brown material"
program call 'input_record'
[input]
zone create brick size 1 1 1
zone cmodel assign hoek-brown-pac
zone property density=1.0 young=[young] poisson=[poiss]
zone property constant-sci=[sig_ci] constant-mb=[mb] ...
constant-s=[s] constant-a=[a]
zone property stress-confining-prescribed=[sig3_cv]
[locptrs]
zone face apply velocity-y [y_vel] range position-y 1
zone face apply velocity-y [-y_vel] range position-y 0
fish history record_variables ;; 1
history interval 1000
fish history eps_xx
fish history eps_yy
fish history eps_yy
fish history sig_xx
fish history sig_yy
fish history sig_zz
model save 'ini'
; unconfined
[global sig_conf = 0.0]
zone face apply stress-xx = [sig_conf]
zone face apply stress-zz = [sig_conf]
zone initialize stress xx = [sig_conf] yy = [sig_conf] zz = [sig_conf]
model step [cyc]
model save 'conf0'
; confined
model restore 'ini'
[global sig_conf = -1.0] ; negative is compression
zone face apply stress-xx = [sig_conf]
zone face apply stress-zz = [sig_conf]
zone initialize stress xx = [sig_conf] yy = [sig_conf] zz = [sig_conf]
model step [cyc]
model save 'conf1'
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