problem in uniaxial test of rocks

Asked by Chen Lifan on 2020-10-14

Hello:
  I have some questions while using Yade to simulate the uniaxial test of rock material. I do the simulation in 2 steps. In the first step, the packing is formulated and the packing was sheared in the second step, where the problem appears. With the increase of the vertical strain, the horizontal stress (the third column in [3]) can not be well controlled to zero. I wonder what causes the phenomenon.

Here are the scripts and output results:

[1] scripts for generating the packing:

from yade import pack

O.materials.append(CohFrictMat(young=88.e9,alphaKr=2.0,alphaKtw=0.,poisson=.7,frictionAngle=.0,isCohesive=True,normalCohesion=3.e9,shearCohesion=3.e9,momentRotationLaw=True))

sp = pack.SpherePack()
size = .3
sp.makeCloud(minCorner=(0,0,.05),maxCorner=(size,size,.05),rMean=.005,rRelFuzz=0.2,num=400,periodic=True,seed=1)
sp.toSimulation()
O.cell.hSize = Matrix3(size,0,0, 0,size,0, 0,0,.1)
print len(O.bodies)
for p in O.bodies:
   p.state.blockedDOFs = 'zXY'
   p.state.mass = 2650 * 0.1 * pi * p.shape.radius**2 # 0.1 = thickness of cylindrical particle
   inertia = 0.5 * p.state.mass * p.shape.radius**2
   p.state.inertia = (.5*inertia,.5*inertia,inertia)

O.dt = .5*utils.PWaveTimeStep()
print O.dt

O.engines = [
   ForceResetter(),
   InsertionSortCollider([Bo1_Sphere_Aabb()]),
   InteractionLoop(
      [Ig2_Sphere_Sphere_ScGeom6D()],
      [Ip2_CohFrictMat_CohFrictMat_CohFrictPhys(
          label='cohesiveIp',
          setCohesionNow=False)],
      [Law2_ScGeom6D_CohFrictPhys_CohesionMoment( # contact law
          useIncrementalForm=False,
          always_use_moment_law=False,
          label='cohesiveLaw')]
   ),
   PeriTriaxController(
      dynCell=True,
      goal=(-1.e7,-1.e7,0),
      stressMask=3,
      relStressTol=.001,
      maxUnbalanced=.001,
      maxStrainRate=(.5,.5,.0),
      doneHook='term()',
      label='biax'
   ),
   NewtonIntegrator(damping=.2)
]

def term():
   #O.engines = O.engines[:3]+O.engines[4:]
   print getStress()
   print O.cell.hSize
   cohesiveIp.setCohesionNow = True
   cohesiveIp.setCohesionOnNewContacts = False # if False, only existing contacts can be cohesive and new contacts are only frictional
   cohesiveLaw.always_use_moment_law = False # if True, use bending/twisting moments at all contacts. If False, compute moments only for cohesive contacts
   cohesiveLaw.useIncrementalForm = True # use the incremental formulation to compute bending and twisting moments
   setContactFriction(0.5)
   O.cell.trsf=Matrix3.Identity
   O.cell.velGrad=Matrix3.Zero
   area=0.
   for p in O.bodies:
      p.state.vel = Vector3.Zero
      p.state.angVel = Vector3.Zero
      p.state.refPos = p.state.pos
      p.state.refOri = p.state.ori
      area += pi*p.shape.radius**2
   areatol=O.cell.volume/O.cell.hSize[2,2]
   void=areatol-area
   voidratio=void/area
   print voidratio
   O.save('5mm_88_2_3g_3g.yade.gz')
   O.pause()

O.run();O.wait()

[2] scripts to shear

from minieigen import *
from yade import plot
import numpy as np
import math, random

O.load('5mm_88_2_3g_3g.yade.gz')
biax.doneHook='unaxshear()'

fout = file('5mm_88_2_3g_3g.dat','w')
fout.close()

def output():
   fout = open('5mm_88_2_3g_3g.dat','a')
   ss = -biax.stress/1.e6
   st = -biax.strain
   print>>fout,st[0],st[1],ss[0],ss[1]
   fout.close()

def unaxshear():
   print 'Stress:',utils.getStress()
   #print 'Void ratio',getVoidRatio2D()
   print 'Press start to shear............\n'
   O.pause()
   biax.goal=(0.,-8.e-2,0.)
   biax.stressMask=1
   biax.doneHook=''
   biax.relStressTol=.001
   biax.maxUnbalanced=.001
   biax.maxStrainRate=(.5,.5,0)
   O.engines += [PyRunner(command='output()',iterPeriod=1000,label='outdata',dead = False)]

[3] the output results (the first to fourth columns correspond to strainx, strainy, stressx, stressy)

-7.52121482369e-07 7.52121482369e-07 9.99913851027 10.0008273603
-0.000752873321006 0.000752873886694 7.15926320142 12.837817399
-0.00150499452053 0.00150499565191 4.31219709936 15.6755667321
-0.00225711572006 0.00225711741712 1.45740355263 18.526142961
-0.00266968416804 0.00300923918233 0.0115157171184 21.5155486273
-0.00273771945847 0.00376136094755 0.00979896515048 24.6663406295
-0.00280666855613 0.00451348271276 0.0033719341489 27.8333521173
-0.00287633923431 0.00526560447797 -0.00654850390782 31.0103413953
-0.00294295053548 0.00601772624319 -0.00336711696265 34.1881098127
-0.00300797298852 0.0067698480084 0.00707226349218 37.3636314747
-0.00307533520998 0.00752196977361 0.00802915923236 40.5352437554
-0.00314524703698 0.00827409153882 -0.00183744269654 43.7050569085
-0.00321386989005 0.00902621330404 -0.00668459677995 46.8844730087
-0.00327917456332 0.00977833506925 0.00270472319407 50.0643941793
-0.00334556010797 0.0105304568345 0.00899177960859 53.2491342812
-0.00341557991373 0.0112825785997 0.001491789509 56.4419088315
-0.00348589116285 0.0120347003649 -0.00683417129809 59.637067393
-0.00355237104969 0.0127868221301 0.00138416467255 62.833414565
-0.00361950886519 0.0135389438953 0.00835815027534 66.0305029192
-0.00368992686267 0.0142910656605 0.00153102236039 69.2354282407
-0.00376058115813 0.0150431874257 -0.00601641201464 72.4468613355
-0.00382787148795 0.0157953091909 0.00141481127862 75.6640992206
-0.0038956638207 0.0165474309562 0.00729536364911 78.8781351916
-0.00396634183342 0.0172995527214 0.000620098168055 82.0904244441
-0.00403672349961 0.0180516744866 -0.00513130547371 85.3025223036
-0.00410402983545 0.0188037962518 0.0024190577325 88.5164822465
-0.0041723923492 0.019555918017 0.005938186112 91.7269718138
-0.00424382385702 0.0203080397822 -0.00123917245468 94.9584116236
-0.00431425475368 0.0210601615474 -0.00340917988606 98.212898297
-0.00438251060053 0.0218122833126 0.00421155127197 101.470874866
-0.004452769389 0.0225644050779 0.00352830490427 104.728750511
-0.00452453384907 0.0233165268431 -0.00356810593394 107.983760207
-0.00459412394445 0.0240686486083 1.93019513359e-05 111.242540021
-0.00466401389849 0.0248207703735 0.00477487331071 114.510693424
-0.00473665023935 0.0255728921387 -0.000641824585913 117.787600111
-0.0048348254151 0.0263250139039 0.0211661011673 120.723693565
-0.00490868875121 0.0270771356691 0.00664538459604 123.992250803
-0.00498312325481 0.0278292574344 -0.00790247498873 127.256856279
-0.00505196671445 0.0285813791996 0.00411065464488 130.519872755
-0.00512365880878 0.0293335009648 0.00839089900055 133.780466006
-0.00519979868462 0.03008562273 -0.00606149638027 137.036347832
-0.00527114200725 0.0308377444952 0.000305379777266 140.294929032
-0.00534218695276 0.0315898662604 0.00916865624516 143.55567992
-0.00541862882023 0.0323419880256 -0.00360265760326 146.81592264
-0.00566569894716 0.0330941097908 -0.0246143269626 148.925977894
-0.00584178772401 0.0338462315561 0.0236152687876 151.877383128
-0.00633977810145 0.0345983533213 -0.0495288510539 152.217843765
-0.00639921310511 0.0353504750865 -0.00126788619004 155.547312775
-0.00646927311133 0.0361025968517 0.0104959551159 158.869881643
-0.00684201506735 0.0368547186169 4.2969554748 156.872591655
-0.00759413626688 0.0376068403821 1.58273867563 159.83077484
-0.0083462574664 0.0383589621473 2.74802640434 159.347864253
-0.00909837866593 0.0391110839125 0.542720837254 161.736442891
-0.00964824728962 0.0398632056777 0.00273550397618 163.803329122
-0.00995527583587 0.040615327443 -0.0310705052742 166.395416723
-0.0102679683673 0.0413674492082 0.505555470789 167.805500907
-0.0106280371669 0.0421195709734 4.70088903487 164.09076882
-0.0113801583665 0.0428716927386 2.25946919304 166.965152018
-0.012132279566 0.0436238145038 6.11181364871 163.764318811
-0.0128844007655 0.044375936269 3.73136905236 166.756361717
-0.013636521965 0.0451280580342 2.40929789669 169.265274829
-0.0143886431646 0.0458801797994 0.583941788261 171.79578491
-0.0151407643641 0.0466323015647 4.84472420631 170.080127627
-0.0158928855636 0.0473844233299 3.09696572491 172.656590343
-0.0166450067631 0.0481365450951 9.10046282332 171.358481817
-0.0173971279627 0.0488886668603 7.95927798089 173.864594874
-0.0181492491622 0.0496407886255 6.51602834478 176.607464951
-0.0189013703617 0.0503929103907 6.68008631826 178.83249036
-0.0196534915612 0.0511450321559 6.99244412096 178.570644045
-0.0204056127608 0.0518971539211 5.64864727713 181.327652355
-0.0211577339603 0.0526492756864 4.47632442234 183.859413417
-0.0219098551598 0.0534013974516 10.9096384735 182.395929129
-0.0226619763593 0.0541535192168 9.51314230693 185.1828976
-0.0234140975589 0.054905640982 9.51234259049 186.771439188
-0.0241662187584 0.0556577627472 8.3998710985 189.324602613
-0.0249183399579 0.0564098845124 7.47697482727 191.750256267
-0.0256704611574 0.0571620062776 17.0891061413 183.280519954
-0.026422582357 0.0579141280428 15.709808234 186.1038043
-0.0271747035565 0.058666249808 14.6275247213 188.725186947
-0.027926824756 0.0594183715733 14.5355465024 190.511188707
-0.0286789459555 0.0601704933385 13.0690723747 192.92069573
-0.0294310671551 0.0609226151037 13.6144290521 194.867577537
-0.0301831883546 0.0616747368689 14.3592122689 196.018347936
-0.0309353095541 0.0624268586341 14.3735780373 197.873000205
-0.0316874307536 0.0631789803993 15.6655569559 199.639856174
-0.0324395519532 0.0639311021645 15.068025659 202.071814251
-0.0331916731527 0.0646832239297 17.4234982419 201.440055984
-0.0339437943522 0.065435345695 16.43549317 204.011520325
-0.0346959155517 0.0661874674602 15.8724096326 206.270262038
-0.0354480367513 0.0669395892254 16.2344178667 207.623268504
-0.0362001579508 0.0676917109906 21.6553255852 206.253207709
-0.0369522791503 0.0684438327558 20.8618602916 208.846295138
-0.0377044003498 0.069195954521 20.7051411008 211.047833248
-0.0384565215494 0.0699480762862 20.7585700441 212.814848032
-0.0392086427489 0.0707001980514 20.7270096894 214.833722693
-0.0399607639484 0.0714523198167 20.720034288 216.422960685
-0.0407128851479 0.0722044415819 20.7068544646 218.337830941
-0.0414650063475 0.0729565633471 20.8015507292 220.145034936
-0.042217127547 0.0737086851123 20.6900012273 222.091077447
-0.0429692487465 0.0744608068775 20.7132416393 223.815313122
-0.0437213699461 0.0752129286427 28.9666326062 214.336642948
-0.0444734911456 0.0759650504079 27.6675837778 216.883271509
-0.0452256123451 0.0767171721731 26.85215763 219.292386347
-0.0459777335446 0.0774692939384 26.4256876521 221.250059127
-0.0467298547441 0.0782214157036 26.1183281054 223.007427464
-0.0474819759437 0.0789735374688 25.6993997003 224.860692695
-0.0482340971432 0.079725659234 25.2904696203 226.692818382
-0.0489862183427 0.08 24.6288131145 226.580113217

Any kind of help is appreciated. Thanks!

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2020-10-14
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