FLAC3D Theory and Background • Constitutive Models

Isotropic Compression Test with CYSoil Model

Note

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Isotropic compression tests on dense, medium, and loose sand are simulated using the CYSoil model. The initial stress state is isotropic in each zone; the magnitude of the confining stress is \(\sigma_{xx}\) = \(\sigma_{yy}\) = \(\sigma_{zz}\) = 10 kN/m². The sand is normally consolidated for the tests (the initial cap pressure is equal to 10 kN/m²). The CYSoil model properties for the tests are listed in Table 1. Any property that is not listed in the table is taken as the default value of the CYSoil model (see the complete properties). The base of the zones is fixed in the axial (\(y\)-) direction, confining velocities of magnitude 10^-6 m/step are applied at the top and lateral sides of the zone for a total of 2500 steps. Five unloading/reloading excursions are also included.

Table 1: CYSoil Model Properties

Parameter	Dense	Medium	Loose
\(G_{ref}\)	300	225	150
\(\phi_f\)	45	45	45
\(p_{ref}\) (kPa)	100	100	100
\(p_c\) (kPa)	10	10	10
\(\nu\)	0.2	0.2	0.2
\(m\)	0.5	0.5	0.5
\(R\)	0.667	0.667	0.667

A plot of vertical (axial) stress versus axial strain for the test is shown for dense, medium, and loose soil cases in Figure 1. The plot shows the power law and stiffer behavior achieved by the denser soil, as expected from the model. A plot of elastic bulk modulus versus axial strain for the test is shown in Figure 2. The bulk modulus is seen to remain constant during unloading/reloading; also, the value is higher for higher strain levels, consistent with the dependency of the property on plastic deformation.

Figure 1: Axial stress (in kN/m²) versus axial strain for dense, medium, and loose sand.

Figure 2: Bulk modulus (in kN/m²) versus axial strain for dense, medium, and loose sand.

Data File

IsotropicCompressionCYSoil.dat

model new
model title "Isotropic Compression Test using CYSoil Model"
model large-strain off
[global _pc0  = 10.]
zone create brick size 1 5 1
zone cmodel assign cap-yield
zone property density=1000 pressure-reference=100 ...
              poisson=0.2 multiplier=0.667
zone property friction=45.0 pressure-initial=[_pc0] ...
              flag-cap=1 pressure-cap=[_pc0] 
zone null range id-list 2,4
zone property shear-reference 300 range id 5
zone property shear-reference 225 range id 3
zone property shear-reference 150 range id 1
zone gridpoint fix velocity
zone initialize stress xx [-_pc0] yy [-_pc0] zz [-_pc0]
zone gridpoint initialize velocity-x -1e-6 range position-x 1
zone gridpoint initialize velocity-z -1e-6 range position-z 1
zone gridpoint initialize velocity-y -1e-6 ...
               range union position-y 1 position-y 3 position-y 5
[global _z5 = zone.find(5)]
[global _z3 = zone.find(3)]
[global _z1 = zone.find(1)]
fish define _bulk_current1
    global _bulk_current5  = zone.prop(_z5, 'bulk')
    global _bulk_current3  = zone.prop(_z3, 'bulk')
    global _bulk_current1  = zone.prop(_z1, 'bulk')
end
history interval 10
zone history stress-yy zoneid 5
zone history displacement-y position (0,5,0)
fish history _bulk_current5
zone history stress-yy zoneid 3
zone history displacement-y position (0,3,0)
fish history _bulk_current3
zone history stress-yy zoneid 1
zone history displacement-y position (0,1,0)
fish history _bulk_current1
fish define trip
    loop local i (1,5)
        command
            zone gridpoint initialize velocity-x -1e-6 range position-x=1.0
            zone gridpoint initialize velocity-z -1e-6 range position-z=1.0
            zone gridpoint initialize velocity-y -1e-6 ...
                           range union position-y=1 position-y=3 position-y=5
            model step 300
            zone gridpoint initialize velocity (-0.1,-0.1,-0.1) 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]