Some questions about simulating consolidated undrained triaxial test

>>the confining pressure is changing during shearing.

Could you be more specific? Are you simulating fluid? Is effective stress considered? A minimal working example would be helpful.

Hi Robert,

Thanks for your reply!

>>Are you simulating fluid?

No. Instead, to carry out the undrained test during triaxial shear, the volume of the sample was maintained constant. this is a method to simulate undrained condition in triaxial test without fluid.

We can check confining stress in file 'results_triax_base_' after running the MWE, then you will find that the confining stress is changing.

the MWE:

from yade import pack
nRead=readParamsFromTable(
 num_spheres=10000,
 compFricDegree = 30 ,
 key='_triax_base_',
 unknownOk=True
)
from yade.params import table

num_spheres=table.num_spheres
key=table.key
targetPorosity = 0.43
compFricDegree = table.compFricDegree
finalFricDegree = 22
rate=-0.02
damp=0.2
stabilityThreshold=0.01
young=5e6
mn,mx=Vector3(0,0,0),Vector3(10,10,10)
confiningS=400e3

O.materials.append(FrictMat(young=young,poisson=0.5,frictionAngle=radians(compFricDegree),density=2600,label='spheres'))
O.materials.append(FrictMat(young=young,poisson=0.5,frictionAngle=0,density=0,label='walls'))

walls=aabbWalls([mn,mx],thickness=0,material='walls')
wallIds=O.bodies.append(walls)
sp=pack.SpherePack()

sp.makeCloud(mn,mx,-1,0.3333,num_spheres,False, 0.95,seed=1)
O.bodies.append([sphere(center,rad,material='spheres') for center,rad in sp])

triax=TriaxialStressController(
 maxMultiplier=1.+2e4/young,
 finalMaxMultiplier=1.+2e3/young,
 thickness = 0,
 stressMask = 7,
 internalCompaction=False,
)

newton=NewtonIntegrator(damping=damp)

O.engines=[
 ForceResetter(),
 InsertionSortCollider([Bo1_Sphere_Aabb(),Bo1_Box_Aabb()]),
 InteractionLoop(
  [Ig2_Sphere_Sphere_ScGeom(),Ig2_Box_Sphere_ScGeom()],
  [Ip2_FrictMat_FrictMat_FrictPhys()],
  [Law2_ScGeom_FrictPhys_CundallStrack()]
 ),
 GlobalStiffnessTimeStepper(active=1,timeStepUpdateInterval=100,timestepSafetyCoefficient=0.8),
 triax,
 TriaxialStateRecorder(iterPeriod=100,file='WallStresses'+table.key,truncate=1),
 newton
]

Gl1_Sphere.stripes=0
if nRead==0: yade.qt.Controller(), yade.qt.View()

triax.goal1=triax.goal2=triax.goal3=-confiningS

while 1:
 O.run(1000, True)
 unb=unbalancedForce()
 print 'unbalanced force:',unb,' mean stress: ',triax.meanStress
 if unb<stabilityThreshold and abs(-confiningS-triax.meanStress)/confiningS<0.001:
    break

O.save('confinedState'+key+'.yade.gz')
print "### Isotropic state saved ###"

triax.internalCompaction=False
triax.width0=triax.width
triax.depth0=triax.depth
triax.height0=triax.height

setContactFriction(radians(finalFricDegree))

triax.stressMask=0
triax.goal2= rate
triax.goal1=triax.goal3=-rate/2
newton.damping=0.1

O.saveTmp()

from yade import plot

def history():
  plot.addData(
            e22=-triax.strain[1], # axial strain
            e11=-triax.strain[0],
            e33=-triax.strain[2],
       ev=triax.volumetricStrain,
      s11=-triax.stress(triax.wall_right_id)[0],
      s22=-triax.stress(triax.wall_top_id)[1],
      s33=-triax.stress(triax.wall_front_id)[2],
            args=(-triax.stress(triax.wall_right_id)[0]-triax.stress(triax.wall_top_id)[1]-triax.stress(triax.wall_front_id)[2])/3,
            eta = 3*(-triax.stress(triax.wall_top_id)[1]+triax.stress(triax.wall_right_id)[0])/(-triax.stress(triax.wall_right_id)[0]-triax.stress(triax.wall_top_id)[1]-triax.stress(triax.wall_front_id)[2]),
            devi = -triax.stress(triax.wall_top_id)[1]+triax.stress(triax.wall_right_id)[0],
            i=O.iter,
            )

def stoploading():
    axial_strain = abs(triax.strain[1])
    if axial_strain > 0.3:
        print 'axial strain reach Limitation, stop loading!'
        O.pause()

if 1:
 O.engines=O.engines[0:5]+[PyRunner(iterPeriod=20,command='history()',label='recorder')]+O.engines[5:7]
 O.engines=O.engines+[PyRunner(command='stoploading()',iterPeriod=100)]
else:
 O.engines[4]=PyRunner(iterPeriod=20,command='history()',label='recorder')

while 1:
 O.run(1000,True)
 if O.iter%100 == 0:
    print "iter = ", O.iter
         print "Syy = ",abs(triax.strain[1])
        if abs(triax.strain[1]) > 0.3:
  break

plot.plots={'e22':('devi',),' args ':('devi')}
plot.plot()
plot.saveDataTxt('results'+key)
plot.saveGnuplot('plotScript'+key)

Cloud

Hi Robert,

Thanks for your reply!

>>Are you simulating fluid?

No. Instead, to carry out the undrained test during triaxial shear, the volume of the sample was maintained constant. this is a method to simulate undrained condition in triaxial test without fluid.

We can check confining stress in file 'results_triax_base_' after running the MWE, then you will find that the confining stress is changing.

the MWE:

from yade import pack
nRead=readParamsFromTable(
 num_spheres=10000,
 compFricDegree = 30 ,
 key='_triax_base_',
 unknownOk=True
)
from yade.params import table

num_spheres=table.num_spheres
key=table.key
targetPorosity = 0.43
compFricDegree = table.compFricDegree
finalFricDegree = 22
rate=-0.02
damp=0.2
stabilityThreshold=0.01
young=5e6
mn,mx=Vector3(0,0,0),Vector3(10,10,10)
confiningS=400e3

O.materials.append(FrictMat(young=young,poisson=0.5,frictionAngle=radians(compFricDegree),density=2600,label='spheres'))
O.materials.append(FrictMat(young=young,poisson=0.5,frictionAngle=0,density=0,label='walls'))

walls=aabbWalls([mn,mx],thickness=0,material='walls')
wallIds=O.bodies.append(walls)
sp=pack.SpherePack()

sp.makeCloud(mn,mx,-1,0.3333,num_spheres,False, 0.95,seed=1)
O.bodies.append([sphere(center,rad,material='spheres') for center,rad in sp])

triax=TriaxialStressController(
 maxMultiplier=1.+2e4/young,
 finalMaxMultiplier=1.+2e3/young,
 thickness = 0,
 stressMask = 7,
 internalCompaction=False,
)

newton=NewtonIntegrator(damping=damp)

O.engines=[
 ForceResetter(),
 InsertionSortCollider([Bo1_Sphere_Aabb(),Bo1_Box_Aabb()]),
 InteractionLoop(
  [Ig2_Sphere_Sphere_ScGeom(),Ig2_Box_Sphere_ScGeom()],
  [Ip2_FrictMat_FrictMat_FrictPhys()],
  [Law2_ScGeom_FrictPhys_CundallStrack()]
 ),
 GlobalStiffnessTimeStepper(active=1,timeStepUpdateInterval=100,timestepSafetyCoefficient=0.8),
 triax,
 TriaxialStateRecorder(iterPeriod=100,file='WallStresses'+table.key,truncate=1),
 newton
]

Gl1_Sphere.stripes=0
if nRead==0: yade.qt.Controller(), yade.qt.View()

triax.goal1=triax.goal2=triax.goal3=-confiningS

while 1:
 O.run(1000, True)
 unb=unbalancedForce()
 print 'unbalanced force:',unb,' mean stress: ',triax.meanStress
 if unb<stabilityThreshold and abs(-confiningS-triax.meanStress)/confiningS<0.001:
    break

O.save('confinedState'+key+'.yade.gz')
print "### Isotropic state saved ###"

triax.internalCompaction=False
triax.width0=triax.width
triax.depth0=triax.depth
triax.height0=triax.height

setContactFriction(radians(finalFricDegree))

triax.stressMask=0
triax.goal2= rate
triax.goal1=triax.goal3=-rate/2
newton.damping=0.1

O.saveTmp()

from yade import plot

def history():
  plot.addData(
            e22=-triax.strain[1], # axial strain
            e11=-triax.strain[0],
            e33=-triax.strain[2],
       ev=triax.volumetricStrain,
      s11=-triax.stress(triax.wall_right_id)[0],
      s22=-triax.stress(triax.wall_top_id)[1],
      s33=-triax.stress(triax.wall_front_id)[2],
            args=(-triax.stress(triax.wall_right_id)[0]-triax.stress(triax.wall_top_id)[1]-triax.stress(triax.wall_front_id)[2])/3,
            eta = 3*(-triax.stress(triax.wall_top_id)[1]+triax.stress(triax.wall_right_id)[0])/(-triax.stress(triax.wall_right_id)[0]-triax.stress(triax.wall_top_id)[1]-triax.stress(triax.wall_front_id)[2]),
            devi = -triax.stress(triax.wall_top_id)[1]+triax.stress(triax.wall_right_id)[0],
            i=O.iter,
            )

def stoploading():
    axial_strain = abs(triax.strain[1])
    if axial_strain > 0.3:
        print 'axial strain reach Limitation, stop loading!'
        O.pause()

if 1:
 O.engines=O.engines[0:5]+[PyRunner(iterPeriod=20,command='history()',label='recorder')]+O.engines[5:7]
 O.engines=O.engines+[PyRunner(command='stoploading()',iterPeriod=100)]
else:
 O.engines[4]=PyRunner(iterPeriod=20,command='history()',label='recorder')

while 1:
 O.run(1000,True)
 if O.iter%100 == 0:
    print "iter = ", O.iter
         print "Syy = ",abs(triax.strain[1])
        if abs(triax.strain[1]) > 0.3:
  break

plot.plots={'e22':('devi',),' args ':('devi')}
plot.plot()
plot.saveDataTxt('results'+key)
plot.saveGnuplot('plotScript'+key)

Cloud

Thanks Chareyre, that solved my question.

Thank you for the MWE

>> this is a method to simulate undrained condition in triaxial test without fluid.

Do you have a reference for this?

>>This is a purely conceptual problem. In lab you can impose total confining
stress, yes, but the effective confining stress is changing nevertheless.
In DEM you don't simulate the fluid, so which one do you record? Effective
or total?

Am I mistaken or should strain rate technically depend on maintaining pore pressure equilibrium for a consolidated undrained test? In that case the effective confining stress should remain constant. Right?

Correct me if I am wrong, but the assumption that your volume will not change by simply applying an axial strainRate and lateral -strainRate/2 is incorrect for a dry cubical packing of frictionally interacting spheres. Consider the role of the fluid pressure in an undrained triaxial test, it does not allow the force due to friction between sand grains to increase. In your case, the particles continue to "consolidate" (overlap) since the pore pressure is not modeled. If they are consolidating, the volume is changing and the packing is not expanding outwards with your walls, resulting in a decrease of confining pressure. I don't see how this model could represent the consolidated undrained shear strength.

> should strain rate technically depend on maintaining pore pressure equilibrium for a consolidated undrained test?

No. In undrained tests pore pressure is a result, it is not maintained.

> In your case, the particles continue to "consolidate" (overlap)

I don't think so. If you impose a constant volume there is no consolidation.

It is partly correct to replace fluid by a condition of shear at constant volume, in the sense that it's indeed the only effect of the fluid at the macroscale (if we admit water compressibility can be neglected... not true for rock materials).
What is missed by this approach is the internal circulations of fluid due to heterogeneities of local strain, but in terms of boundary conditions it makes sense.