Abstract
The hyperbolic function proposed by Abbo–Sloan was employed not only to approach the Mohr–Coulomb criterion but also to express the plastic potential function. A better approximation to the Mohr–Coulomb yield and potential surfaces was achieved by increasing the transition angle and proven to be highly efficient in numerical convergence. When a Gaussian integral point goes into plastic state, two cases on yield stress adjustments were introduced. They may avoid solving the second derivative of the plastic potential function and the inverse matrix compared with the existing subroutine. Based on the above approaches, a fully implicit backward Euler integral regression algorithm was adopted. The two- and three-dimensional user subroutines which can consider the associated or non-associated flow rule were developed on the platform of the finite element program—ABAQUS. To verify the reliability of these two subroutines, firstly, the numerical simulations of the indoor conventional triaxial compression and uniaxial tensile tests were performed, and their results were compared with those of the embedded Mohr–Coulomb model and the analytical approach. Then the main influential factors including the associated or non-associated flow rule, the judgment criteria of slope failure, and the tensile strength of soil were analyzed, and the application of the two-dimensional subroutine in the stability analysis of a typical soil slope was discussed in detail through comparisons with the embedded model and the limit analysis method, which shows that this subroutine is more applicable and reliable than the latter two.
Highlights
It is well known that the M–C yield criterion expresses a hexagonal pyramid surface in principal stress space, which has a flaw in numerical computation, i.e., the gradient discontinuities which occur at both the edges and the tip of the hexagonal pyramid surface
In order to sufficiently approach the original M–C yield surface, Abbo–Sloan [8] proposed a simple hyperbolic yield surface to eliminate the singularity of the M–C yield surface and presented two efficient FORTRAN 77 subroutines to illustrate how this yield surface is implemented in practice
In the embedded M–C model the true M–C yield surface is used but the plastic potential function proposed by Menetrey– William [16] is employed, which presents a hyperbola in meridional plane and a closed smooth curve combined by three elliptic arcs in deviatoric plane, and it is the very inconsistency between the yield and potential functions so that the plastic flow rule of the model is always non-associated
Summary
In 1773, Coulomb proposed a soil pressure theory of soil or rock failure, which is expressed by s 1⁄4 c À r tan /; ð1Þ where s and r are respectively the shear strength and the normal stress (tensile stress is positive) in the shearing surface; c and / are the cohesion and the angle of internal friction of soil or rock, respectively. In order to sufficiently approach the original M–C yield surface, Abbo–Sloan [8] proposed a simple hyperbolic yield surface to eliminate the singularity of the M–C yield surface and presented two efficient FORTRAN 77 subroutines to illustrate how this yield surface is implemented in practice They did not build an entire numerical constitutive model. In the embedded M–C model the true M–C yield surface is used but the plastic potential function proposed by Menetrey– William [16] is employed, which presents a hyperbola in meridional plane and a closed smooth curve combined by three elliptic arcs in deviatoric plane, and it is the very inconsistency between the yield and potential functions so that the plastic flow rule of the model is always non-associated. A typical two-dimensional homogeneous soil slope [17] was simulated with the UMAT and compared in detail with the results of the embedded M–C model
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