FLAC3D Theory and Background • Constitutive Models

Triaxial Compression Test with Hoek-Brown Model

Note

To view this project in FLAC3D, use the menu command Help ? Examples…. Choose “ConstitutiveModels/TriaxialCompressionHoekBrown” and select “TriaxialCompressionHoekBrown.f3dprj” to load. 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:

\[{\psi_c \over \phi_c} = 1 - {\sigma_3 \over \sigma^{cv}_3} = 0.333\]

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.

Figure 1: Triaxial compression test—stress versus axial strain (\({\sigma_3}/{\sigma_{ci}}\) = 0).

Figure 2: Triaxial compression test—lateral strain versus axial strain (\({\sigma_3}/{\sigma_{ci}}\) = 0).

Figure 3: Triaxial compression test—stress versus axial strain (\({\sigma_3}/{\sigma_{ci}}\) = 1.0).

Figure 4: Triaxial compression test—lateral strain versus axial strain (\({\sigma_3}/{\sigma_{ci}}\) = 1.0).

Data File

; Triaxial tests on a Modified Hoek-Brown material,
model new
model largestrain off
fish automatic-create off
model title "Triaxial Test on a Hoek-Brown material"
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 constant-mb=@mb   constant-s=@s constant-a=@a
@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
fish set @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
fish set @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'