Civil Engineering Reference
In-Depth Information
the deviator stress reaches a peak of 121 kN/m
2
, which is in close agreement with the
closed form solution of 120.8 kN/m
2
(Griffiths, 1985) given by (6.84) for this problem
with
20.
The deviator stress at failure in case (a) is significantly smaller than the drained value
of 200 kN/m
2
due to the compressive pore pressures generated during elastic compression.
Case (b), which includes an associated flow rule (
β
t
=
30
◦
), shows no sign of failure
due to the tendency for dilation. In this case, the pore pressures continue to fall and
the deviator stress continues to rise. This trend would continue indefinitely unless some
additional criterion (e.g. cavitation or particle crushing) was introduced. It may also be
noted from Figure 6.44, that the undrained response is slightly stiffer than the drained
response at small strains.
While the presence of dilation has a very significant influence on undrained behaviour,
it has little influence on the deviator stress at failure in the drained case.
ψ
=
φ
=
Program 6.10 Three-dimensional strain analysis of an elastic-plastic (Mohr-Cou-
lomb) slope using 20-node hexahedra. Viscoplastic strain method.
PROGRAM p610
!-------------------------------------------------------------------------
! Program 6.10 Three-dimensional strain analysis of an elastic-plastic
! (Mohr-Coulomb) slope using 20-node hexahedra. Viscoplastic
! strain method.
!-------------------------------------------------------------------------
USE main; USE geom; IMPLICIT NONE
INTEGER,PARAMETER::iwp=SELECTED_REAL_KIND(15)
INTEGER::i,iel,ifix,iters,iy,limit,ndim=3,ndof=60,nels,neq,nip=8,nn,
&
nod=20,nodof=3,nprops=6,np_types,nsrf,nst=6,nx1,nx2,ny1,ny2,nze
REAL(iwp)::cf,ddt,det,dq1,dq2,dq3,dsbar,dt=1.0e15_iwp,d1,d4=4.0_iwp, &
d180=180.0_iwp,e,f,fmax,h1,h2,lode_theta,one=1.0_iwp,phi,phif,pi,psi, &
psif,sigm,snph,start_dt=1.e15_iwp,s1,tnph,tnps,tol,two=2.0_iwp,v,w1,w2,&
zero=0.0_iwp
CHARACTER(LEN=80)::element='hexahedron'; LOGICAL::converged
!-----------------------dynamic arrays------------------------------------
INTEGER,ALLOCATABLE::etype(:),g(:),g_g(:,:),g_num(:,:),kdiag(:),nf(:,:), &
num(:)
REAL(iwp),ALLOCATABLE::bdylds(:),bee(:,:),bload(:),coord(:,:),dee(:,:), &
der(:,:),deriv(:,:),devp(:),eld(:),eload(:),eps(:),erate(:),evp(:), &
evpt(:,:,:),flow(:,:),fun(:),gravlo(:),g_coord(:,:),jac(:,:),km(:,:), &
kv(:),loads(:),m1(:,:),m2(:,:),m3(:,:),oldis(:),points(:,:),prop(:,:), &
sigma(:),srf(:),weights(:)
!-----------------------input and initialisation--------------------------
OPEN(10,FILE='fe95.dat'); OPEN(11,FILE='fe95.res');
!---(ifix=1) smooth-smooth; (ifix=2) rough-smooth; (ifix=3) rough-rough---
READ(10,*)w1,s1,w2,h1,h2,d1,nx1,nx2,ny1,ny2,nze,ifix,np_types
nels=(nx1*ny1+ny2*(nx1+nx2))*nze
nn=((3*(ny1+ny2)+2)*nx1+2*(ny1+ny2)+1+(3*ny2+2)*nx2)*(1+nze)+
&
((ny1+ny2+1)*(nx1+1)+(ny2+1)*nx2)*nze
ALLOCATE(nf(nodof,nn),points(nip,ndim),weights(nip),g_coord(ndim,nn), &
num(nod),dee(nst,nst),evpt(nst,nip,nels),coord(nod,ndim),fun(nod), &
g_g(ndof,nels),jac(ndim,ndim),der(ndim,nod),etype(nels), &
deriv(ndim,nod),g_num(nod,nels),bee(nst,ndof),km(ndof,ndof),eld(ndof), &
eps(nst),sigma(nst),bload(ndof),eload(ndof),erate(nst),evp(nst),
&
devp(nst),g(ndof),m1(nst,nst),m2(nst,nst),m3(nst,nst),flow(nst,nst),
&
prop(nprops,np_types))
