FLAC3D Theory and Background • Constitutive Models

# Triaxial Compression Test with Hoek-Brown 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.

The triaxial compression tests performed using the Hoek-Brown-PAC model are repeated for the Hoek-Brown model, with the same material properties:

\(m_b\) |
5 |

\(s\) |
0.5 |

\(\sigma_{ci}\) |
1.0 MPa |

\(\sigma^{cv}_3\) |
1.5 MPa |

\(E\) |
100 MPa |

\(\nu\) |
0.35 |

Two compression loading tests are performed:

at zero confining stress, \(\sigma_{3}/\sigma_{ci}\) = 0, and

at high confining stress, \(\sigma_{3}/\sigma_{ci}\) = 1.

For the zero confining stress case, we specify an associated flow rule; this is done with the command:

```
zone property flag-dilation = -1
```

For the higher confining stress case, we need to specify a dilation angle that is consistent with the limiting constant-volume stress, \(\sigma^{cv}_3\) = 1.5, chosen for the triaxial compression test for the Hoek-Brow-PAC model. We linearly interpolate a value for dilation corresponding to the current confining stress level of \(\sigma_{3}\) = 1, relative to a nonassociated zero dilation at \(\sigma^{cv}_3\) = 1.5. The current dilation, \(\psi_c\), is then taken to be a fraction of the current friction angle, \(\phi_c\), using the linear interpolation:

The following commands are used to apply the modified Hoek-Brown model for this case:

```
zone property flag-dilation = 0.333
```

The FLAC3D results for the zero confining stress case are compared to the analytical solution (see Triaxial Compression Test with Hoek-Brown-PAC Model) in Figure 1 and Figure 2, and the results for the high confining stress case are compared in Figure 3 and Figure 4.

break

Data File

**TriaxialCompressionHoekBrown.dat**

```
; Triaxial tests on a Modified 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
zone property density = 1.0 shear=[shear] bulk=[bulk]
zone property constant-sci = [sig_ci]
;; Method #1
zone property geological-strength-index=100 constant-mi=[mb]
;; Method #2
;zone property constant-s=[a] constant-a=[s] constant-mb=[mb]
;
[locptrs]
zone face apply velocity-y [y_vel] range position-y 1.0
zone face apply velocity-y [-y_vel] range position-y 0.0
fish history record_variables
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
zone property flag-dilation = -1
[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'
zone property flag-dilation = 0.333
[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'
```

⇐ Isotropic Consolidation Test with Modified Cam-Clay Model | Triaxial Compression Test with Hoek-Brown-PAC Model ⇒

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