FLAC3D Theory and Background • Constitutive Models

Drained Triaxial Test with CYSoil Model — Constant Dilation

Note

To view this project in FLAC3D, use the menu command Help ► Examples…. The project’s main data file is shown at the end of this example.

Triaxial tests on dense, medium, and loose sand are simulated using the CYSoil model. The model properties are listed in Table 1. This example does not consider yielding on the cap; therefore, flag_cap is set to 0 (default value). In this case, initial pressure, \(p_{ini}\), is required; it is used by the code to calculate for bulk and shear moduli. The dilation is constant; therefore, flag_dilation is set to 1, and a value is assigned to the dilation property. The initial stress state is isotropic, with mean pressure equal to 100 kPa. The cell pressure is kept constant during the test, the base of the model is fixed in the axial (\(y-\)) direction, and an axial velocity of 10^-6 m/step is applied at the top of the model. In addition, three unloading/reloading excursions are performed.

Table 1: CYSoil Model Properties

Parameter	Dense	Medium	Loose
\(G_{ref}\)	300	225	150
\(\phi_f\)	40	35 30
\(\psi_f\)	10	5	0
\(c\)		0 or 100 kPa
\(p_{ref}\) (kPa)		100
\(p_c\) (kPa)		100
\(\nu\)		0.2
\(m\)		0.5
\(R_f\)		0.9
\(\beta\)		0.35

break

Figure 1: \(\mid \sigma_1 - \sigma_3 \mid\) (in kPa) versus axial strain for dense, medium, and loose sand—constant dilation.

Figure 2: Volumetric strain versus axial strain for dense, medium, and loose sand—constant dilation.

Figure 3: \(\mid \sigma_1 - \sigma_3 \mid\) (in kPa) versus axial strain for dense, medium, and loose sand—constant dilation (dilation = 100 kPa).

Figure 4: Volumetric strain versus axial strain for dense, medium, and loose sand—constant dilation (dilation = 100 kPa).

Data File

DrainedTriaxialConstantDilationCYSoil.dat

; Drained Triaxial Tests - Constant Dilation
model large-strain off
model configure axisymmetry
model title "Drained triaxial test - cap-yield-soil"
;
zone create quadrilateral size 1 1
zone face skin
zone cmodel assign cap-yield
;
zone initialize stress xx -100. yy -100. zz -100.
zone face apply stress-normal -100. range group 'East'
zone face apply velocity-y     0. range group 'Bottom'
zone face apply velocity-y -1e-6  range group 'Top'
;
zone property density 1000 pressure-reference=100. exponent=1.0 ...
              beta=0.35 poisson 0.2
zone property flag-dilation=1 friction-mobilized=0 
zone property shear-reference=[_Gref] friction=[_friu] ...
              cohesion=[_coh] dilation=[_dilu] 
zone property flag-cap=0 pressure-initial=100. 
;
fish define _cy_q
    local _z = zone.head
    global _cy_q = zone.prop(_z, 'stress-deviatoric')
    global _vsi  = zone.strain.vol.inc(_z)
end
;
history interval 1
zone history displacement-y position (1,1)
fish history _cy_q
fish history _vsi
;
fish define trip
    loop local i (1,3)
        command
            zone face apply velocity-y -1e-6 range group 'Top'
            model step 8000
            zone face apply velocity-y  1e-7 range group 'Top'
            model step 6000
            zone face apply velocity-y -1e-7 range group 'Top'
            model step 6000
        end_command
    end_loop
end
;
model step 3000
[trip]
zone face apply velocity-y -1e-6  range group 'Top'
model step 23000
;
history export '2' vs '1' reverse table 'devStress'
history export '3' vs '1' reverse table 'volStrain'
table 'devStress' ...
      export [string.build('devStress%1', _IChoice)] truncate 
table 'volStrain' ...
      export [string.build('volStrain%1', _iChoice)] truncate 
;