FLAC3D Theory and Background • Constitutive Models

Isotropic Compression Test with Plastic-Hardening Model

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.

This example presents the simulation of the isotropic compression test for dense, medium, and loose sands using the Plastic-Hardening (PH) model. The initial stress state is isotropic; the magnitude of the confining stress is 100 kPa. The sands are normally consolidated with \(OCR\) = 1. Material properties for this example are summarized in Table 1. Material parameters not listed in the table are default values.

The resulting plots of mean stress (represented by stress in \(y-\) direction) versus axial strain are presented in Figure 1 and show the nonlinear behavior (corresponding to the power law) of the cap hardening surface.

Table 1: CYSoil Model Properties

Parameter	Dense	Medium	Loose
\(E^{ref}_{50}\) (kPa)	4.0e4	3.0e4	2.0e4
\(E^{ref}_{oed}\) (kPa)	3.2e4	2.4e4	1.6e4
\(\phi\)	40	35	30
\(\psi\)	10	5	0
\(K_{nc}\)	0.36	0.43	0.50
\(p_{ref}\) (kPa)	100	100	100
\(m\)	0.5	0.5	0.5
\(\sigma^{ini}_{1 \sim 3}\) (kPa)	-100	-100	-100
\(OCR\)	1.0	1.0	1.0

Figure 1: Axial stress (in kPa) versus axial strain for dense, medium, and loose sand.

Data File

IsotropicCompressionPlasticHardening.dat

model new
model title "Isotropic Compression Test"
model large-strain off
;
zone create brick size 1 5 1
zone cmodel assign plastic-hardening
zone property density 1000 pressure-reference=100. exponent=0.5 ...
              failure-ratio=0.9 poisson=0.2 over-consolidation-ratio = 1.0
zone property stress-1-effective=-100. stress-2-effective=-100. ...
              stress-3-effective=-100.
zone cmodel assign null range id-list=2, 4
; --- dense ---
zone property stiffness-50-reference=4e4 stiffness-oedometer-reference=3.2e4 ...
              friction=40 dilation=10 ...
              coefficient-normally-consolidation=0.36 range id 5
; --- medium ---
zone property stiffness-50-reference=3e4 stiffness-oedometer-reference=2.4e4 ...
              friction=35 dilation= 5 ...
              coefficient-normally-consolidation=0.43 range id 3
; --- loose ---
zone property stiffness-50-reference=2e4 stiffness-oedometer-reference=1.6e4 ...
              friction=30 dilation= 0 ...
              coefficient-normally-consolidation=0.50 range id 1
;
zone initialize stress xx -100. yy -100. zz -100.
zone gridpoint fix velocity
zone gridpoint fix velocity-x -1e-6 range position-x 1.0
zone gridpoint fix velocity-z -1e-6 range position-z 1.0
zone gridpoint fix velocity-y -1e-6 ...
                   range union position-y 1.0 position-y 3.0 position-y 5.0
;
history interval 50
zone history stress-yy zoneid 5            
zone history displacement-y position (0 5 0)
zone history stress-yy zoneid 3 
zone history displacement-y position (0 3 0)
zone history stress-yy zoneid 1
zone history displacement-y position (0 1 0)
;
fish define trip
    loop i (1,5)
        command
            zone gridpoint fix velocity-x -2e-6 range position-x 1.0
            zone gridpoint fix velocity-z -2e-6 range position-z 1.0
            zone gridpoint fix velocity-y -2e-6 ...
                 range union position-y 1.0 position-y 3.0 position-y 5.0
            model step  500
            zone gridpoint initialize velocity -.15 -.15 -.15 multiply
            model step 3000
            zone gridpoint initialize velocity -1.0 -1.0 -1.0 multiply
            model step 3000
        end_command
    end_loop
end
model step 1000
[trip]
model save 'ph-iso'