Excavation of galleries in deep clay formations: An analytical tool for the control of finite element results

Bruyn, Didier De; Ramaeckers, C; Huergo, P J

doi:10.1016/0266-352x(94)90004-3

Cited by 1 publication

(1 citation statement)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Non-associated Mohr-Coulomb (MC) model is commonly used for dense sand and stiff clay in geotechnical engineering. This simple model is able to produce reasonably close results to both experimental data and field data for geotechnical problems like piles [1][2][3], deep excavation [4][5][6][7][8], and tunneling [9,10]. For the MC model, the non-associated flow rule implies that the dilation angle, which controls the volumetric strain of the soil, is different from the friction angle of the soil.…”

Section: Introductionmentioning

confidence: 92%

Preconditioned IDR(s) iterative solver for non‐symmetric linear system associated with FEM analysis of shallow foundation

Tran

Toh

Phoon

2013

Num Anal Meth Geomechanics

View full text Add to dashboard Cite

SUMMARYNon-associated flow rule is essential when the popular Mohr-Coulomb model is used to model nonlinear behavior of soil. The global tangent stiffness matrix in nonlinear finite element analysis becomes nonsymmetric when this non-associated flow rule is applied. Efficient solution of this large-scale nonsymmetric linear system is of practical importance. The standard Krylov solver for a non-symmetric solver is Bi-CGSTAB. The Induced Dimension Reduction [IDR(s)] solver was proposed in the scientific computing literature relatively recently. Numerical studies of a drained strip footing problem on homogenous soil layer show that IDR(s = 6) is more efficient than Bi-CGSTAB when the preconditioner is the incomplete factorization with zero fill-in of global stiffness matrix K ep (ILU(0)-K ep ). Iteration time is reduced by 40% by using IDR(s = 6) with ILU(0)-K ep . To further reduce computational cost, the global stiffness matrix K ep is divided into two parts. The first part is the linear elastic stiffness matrix K e , which is formed only once at the beginning of solution step. The second part is a low-rank matrix Δ, which is re-formed at each Newton-Raphson iteration. Numerical studies show that IDR(s = 6) with this ILU(0)-K e preconditioner is more time effective than IDR(s = 6) with ILU(0)-K ep when the percentage of yielded Gauss points in the mesh is less than 15%. The total computation time is reduced by 60% when all the recommended optimizing methods are used.

show abstract