Geomechanics — Drucker–Prager / Mohr–Coulomb Triaxial Compression & Dilatancy

Verification of pressure-dependent Drucker–Prager / Mohr–Coulomb plasticity with non-associated dilatancy, smooth cone return, apex return, and consistent 6x6 tangent.

Tolerance:

5%

Problem statement

Geometry

Triaxial specimen under confining pressure Pc=5 MPa: E=30 GPa, nu=0.25, cohesion c=2 MPa, friction angle phi=30 deg, non-associated dilatancy angle psi=10 deg.

Material

Constitutive or analytical definition: f(sigma)=q+alpha*p-k<=0 with alpha=6*sin(phi)/(3-sin(phi))=1.2, k=6*c*cos(phi)/(3-sin(phi))=4.156922 MPa, beta=6*sin(psi)/(3-sin(psi))=0.368634.

Boundary conditions

Required solver capability: drucker_prager_nonassociated_return_mapping. Apply lateral confinement sigma_xx=sigma_yy=-5 MPa and axial compression eps_zz=-0.003; also verify hydrostatic tension apex return at p_apex=c*cot(phi).

Measured quantity

Peak axial compressive stress sigma_1c = Pc*(1+sin(phi))/(1-sin(phi)) + 2*c*cos(phi)/(1-sin(phi)) = 21.92820323 MPa; plastic dilatancy ratio tr(eps_p)/eps_p_bar = 0.36863389; apex hydrostatic limit p_apex = 3.46410162 MPa.

WebCAE Terminal

units mm
material E=30000 nu=0.25
primitive box dx=50 dy=50 dz=100
mesh hex size=25
fix surface number 1 component=x
fix surface number 3 component=y
fix surface number 5 component=z
load surface number 2 pressure=5
load surface number 4 pressure=5
load surface number 6 pressure=21.928203
solve
probe stress_zz id="szz"
probe von_mises_max id="vm"

Results comparison

Updated: 2026-10-28 · version not recorded