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Simulate Geo-technical Problem (2 nd part)

Simulate Geo-technical Problem (2 nd part). Zhou Yongfa Project manager. Elastic-Plastic Problem. 1. Analysis of Elastic-Plastic Problem and Yield Function 2. Simulating method of anchor 3. User Practice: Underground Digging in Mohr-Coulomb Rock Field. E-Plastic stress analysis.

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Simulate Geo-technical Problem (2 nd part)

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  1. Simulate Geo-technical Problem(2nd part) Zhou Yongfa Project manager

  2. Elastic-Plastic Problem 1. Analysis of Elastic-Plastic Problem and Yield Function 2. Simulating method of anchor 3. User Practice: Underground Digging in Mohr-Coulomb Rock Field

  3. E-Plastic stress analysis • Calculation of the elastic-plastic stress around pinhole • Use yield function of Mohr-Coulomb

  4. Problem Description A hole in the middle of the elastic plate R0: the radius of the hole P: the pressure around the plate R0＝1.0 m P ＝1600 Pa c ＝1000 Pa f ＝0.2

  5. Problem description With Mohr-Coulomb yield function, we have the theory result around the pinhole Stress in elastic zone

  6. Problem description Stress in plastic zone

  7. Theoretical solution Radius of plastic zone Input R0＝1.0 m，p＝1600 Pa，c＝1000 Pa，f＝0.2 to above express The theory radius of plastic zone is 0.1293 m。

  8. Mohr-Coulomb Mohr－Coulomb yield function

  9. Solving step • 1.Using solid mechanics formula library generate 2D elastic-plastic program • 2.Modify the PRE parameter • 3.Add Mohr-Coulomb yield function • 4.Modeling and meshing • 5.Calculating and analysis

  10. Using formula lib  FEPG  Appwizard  Solid  E_Plastic  2DXY  AWZ  sdispe  q4, ll2, ilu, outcore  OK

  11. Solving step • 1.Using solid mechanics formula library generate 2D elastic-plastic program • 2.Modify the PRE parameter • 3.Add Mohr-Coulomb yield function • 4.Modeling and meshing • 5.Calculating and analysis

  12. Modify PRE file matedata nespa aeq4 1.0e10;0.3;0;0;0.2;1.0e3;1.0;3000;0.6; nespa all2 0;100; nespb beq4 1.0e10;0.3;0;0;0.2;1.0e3;1.0;3000;0.6; matedata nespa aeq4 1.0e10;0.3;0;0;0.2;1.0e3;0.0; nespa all2 0;1600; nespb beq4 1.0e10;0.3;0;0;0.2;1.0e3;0.0;

  13. Solving step • 1.Using solid mechanics formula library generate 2D elastic-plastic program • 2.Modify the PRE parameter • 3.Add Mohr-Coulomb yield function • 4.Modeling and meshing • 5.Calculating and analysis

  14. nespa.pde defi disp u v coor x y coef un,vn func exx eyy exy shap %1 %2 gaus %3 $c6 dimension de(3),e(2,2),d(3,3),dv(3),dg(2,2) $c6 dimension dp(3,3),p(4) $c6 external prager Drucker-Prager function $c6 logical filestr $c6 common /gpstr/ gpstr(6,100000),str(6)

  15. nespa.pde … … $cv de(1) = e(1,1) $cv de(2) = e(2,2) $c6 de(3) = e(1,2)+e(2,1) $c6 call getstr(p,str,de,dv,d,dp,1,prag,prager) $c6 if (prag.gt.-p(2)*0.0001) then $c6 do i=1,3 $c6 do j=1,3 $c6 d(i,j)=d(i,j)-dp(i,j) … … Drucker-Prager function

  16. Drucker-Prager

  17. Plastic matrix Calculation Stres.for & plas.for Calculate plastic matrix Dp Calculate plastic stress Codes of yield function lies in plas.for

  18. Plas.for Drucker-Prager function real*8 FUNCTION PRAGER(X,U) implicit real*8 (a-h,o-z) DIMENSION U(4),S(3),x(4) tgo=x(1) q0=x(4) c=x(2)+q0*U(4) PV= X(3) D = (U(1)+U(2))*(1+pv)/3. S(1) = U(1) - D S(2) = U(2) - D S(3) = U(3) Source codes of Drucker-Prager function In plas.for

  19. nespa.pde UK = (u(1)+u(2))*pv-D SJ = (S(1)**2+S(2)**2+UK**2)/2.+S(3)**2 alpha=tgo/dsqrt(9+12*tgo**2) ck=3*c/dsqrt(9+12*tgo**2) PRAGER = DSQRT(SJ) + ALPHA*D*3 - CK RETURN END Source codes of Drucker-Prager function In plas.for

  20. Add M-C function in plas.for Mohr－Coulomb yield function

  21. Add M-C function in plas.for Mohr-Coulomb function real*8 FUNCTION MohrC(X,U) implicit real*8 (a-h,o-z) DIMENSION U(4),X(4),EMSTR(3) emstr(1)=U(1)+U(2) coefb=-U(1)-U(2) coefc=U(1)*U(2)-U(3)**2 emstr(2)=((-coefb)+dsqrt(coefb**2-4*coefc))/2 emstr(3)=((-coefb)-dsqrt(coefb**2-4*coefc))/2 if (emstr(1).lt.emstr(2)) then etemp=emstr(2) emstr(2)=emstr(1) emstr(1)=etemp end if Source codes of Mohr-Coulomb function In plas.for

  22. Add M-C function in plas.for if (emstr(1).lt.emstr(3)) then etemp=emstr(3) emstr(3)=emstr(1) emstr(1)=etemp end if if (emstr(2).lt.emstr(3)) then etemp=emstr(2) emstr(2)=emstr(3) emstr(3)=etemp end if tgo=x(1) c=x(2) cosf=1./dsqrt(1.+tgo*tgo) Source codes of Mohr-Coulomb function In plas.for

  23. Add M-C function in plas.for MohrC=emstr(1)-emstr(3)-2.0*c*cosf MohrC=MohrC+(emstr(1)+emstr(3))*(dsqrt(1-cosf*cosf)) RETURN END Source codes of Mohr-Coulomb function In plas.for

  24. Compile plas.for Right click mouse button on plas.for in FEPG interface Then run fl32.exe /W0 /nologo /c plas.FOR

  25. Modify nespa.pde defi disp u v coor x y coef un,vn func exx eyy exy shap q 4 gaus q $c6 dimension de(3),e(2,2),d(3,3),dv(3),dg(2,2) $c6 dimension dp(3,3),p(4) $c6 external MohrC $c6 logical filestr $c6 common /gpstr/ gpstr(6,100000),str(6) Modify prager to MohrC

  26. Modify nespa.pde … … $cv de(1) = e(1,1) $cv de(2) = e(2,2) $c6 de(3) = e(1,2)+e(2,1) $c6 call getstr(p,str,de,dv,d,dp,1,prag, MohrC) $c6 if (prag.gt.-p(2)*0.0001) then $c6 do i=1,3 $c6 do j=1,3 $c6 d(i,j)=d(i,j)-dp(i,j) … … Modify prager to MohrC

  27. Compile nespa.pde Click run command button in FEPG interface

  28. Compile nespa.pde In command line run pde nespa aeq4

  29. Compile nespa.pde Right click mouse button on nespa in FEPG interface Then run Let.bat nespa

  30. Modify nespb.pde disp sxx,syy,sxy,wp,vep,vyp,did coor x y coef un,vn shap q 4 gaus q mass q vol $c6 dimension de(3),e(2,2),dv(3),dg(2,2) $c6 dimension dp(3,3),d(3,3),p(4) $c6 external MohrC $c6 logical filestr $c6 common /gpstr/ gpstr(6,100000),str(6) Modify prager to MohrC

  31. Modify nespb.pde … … $cv de(1) = e(1,1) $cv de(2) = e(2,2) $c6 de(3) = e(1,2)+e(2,1) $c6 call getstr(p,str,de,dv,d,dp,1,prag, MohrC) $c6 if (prag.gt.-p(2)*0.0001) then $c6 eid=0.0d0 $c6 else $c6 eid=1.0d0 $c6 endif … … Modify prager to MohrC

  32. Compile nespb.pde Click run command button in FEPG interface

  33. Compile nespb.pde In command line run pde nespb beq4

  34. Compile nespb.pde Right click mouse button on nespb in FEPG interface Then run Let.bat nespb

  35. Summarize 1.Modify PRE file modify parameters 2.Modify plas.for add Mohr-Coulomb function 3.Modifynespa.pde modify yield function to M-C for displacement calculation 4.Modify nespb.pde modify yield function to M-C for stress calculation

  36. Summarize 5.Compile plas.for fl32.exe /W0 /nologo /c plas.FOR 6.Compilenespa.pde pde nespa aeq4 7.Compile nespb.pde pde nespb beq4 8.Link to nespa.exe let.bat nespa 9.Link to nespb.exe let.bat nespb

  37. Solving step • 1.Using solid mechanics formula library generate 2D elastic-plastic program • 2.Modify the PRE parameter • 3.Add Mohr-Coulomb yield function • 4.Modeling and meshing • 5.Calculating and analysis

  38. Assign material One kind of material for the plate

  39. Assign boundary conditions Displacement boundary conditions

  40. Meshing Quadrilateral

  41. Solving step • 1.Using solid mechanics formula library generate 2D elastic-plastic program • 2.Modify the PRE parameter • 3.Add Mohr-Coulomb yield function • 4.Modeling and meshing • 5.Calculating and analysis

  42. Result 1st Principal stress 3rd Principal stress

  43. Compare Theory solution and calculate solution

  44. Compare elastic zone plastic zone The calculate Radius of plastic zone D＝0.130 m The theory radius of plastic zone is 0.1293 m。

  45. Simulating anchor 2. Simulating method of anchor global coor. o’x’y’ & local coor. x

  46. Equations of anchor Equilibrium equations of anchor in local coordinate system Recast to weak form

  47. GES & GLT Prepare 2 files GES file Descript PDE in local coordinate system GLT file Transform local coordinate system to global coordinate system

  48. GES & GLT GES PDE in local coor. GLT Transform to global Coor. automatic Assembling in global Coor.

  49. GES file trull2 defi disp u,v var u1,v1,u2,v2, refc rx, coor x, func = ex, dord 1,1 node 2 $c6 pe=prmt(1) $c6 pa=prmt(2) $c6 fu=prmt(3) $c6 time=prmt(4) Trull2.ges

  50. GES file $c6 dt=prmt(5) $c6 imate=prmt(6)+0.5 $c6 ielem=prmt(7)+0.5 $c6 nelem=prmt(8)+0.5 shap u= u1=(1.-rx)/2 u2=(1.+rx)/2 v= v1=(1.-rx)/2 v2=(1.+rx)/2 Trull2.ges

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