FLAC3D Theory and Background • Constitutive Models

Triaxial Compression Test with Hoek-Brown-PAC Model

Note

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

Figure 1: Triaxial compression tests—loading conditions.

Figure 2: Triaxial compression tests: a) Hoek-Brown failure envelope; b) stress-strain plots.

Figure 3: Triaxial compression tests: a) confining (lateral) strain versus axial strain; b) volumetric strain versus axial strain.

Figure 4: Triaxial compression test—stress versus axial strain (\({\sigma_3}/{\sigma_{ci}}\) = 0).

Figure 5: Triaxial compression test—lateral strain versus axial strain (\({\sigma_3}/{\sigma_{ci}}\) = 0).

Figure 6: Triaxial compression test—stress versus axial strain (\({\sigma_3}/{\sigma_{ci}}\) = 1.0).

Figure 7: Triaxial compression test—lateral strain versus axial strain (\({\sigma_3}/{\sigma_{ci}}\) = 1.0).

Data File

; Triaxial tests on a 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-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
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'
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'