Kamal C. Das

Bolt-Grout Interactions in Elastoplastic Rock Mass Using Coupled FEM-FDM Techniques

Numerical procedure based on finite element method (FEM) and finite difference method (FDM) for the analysis of bolt-grout interactions are introduced in this paper. The finite element procedure incorporates elasto-plastic concepts with Hoek and Brown yield criterion and has been applied for rock mass. Bolt-grout interactions are evaluated based on finite difference method and are embedded in the elasto-plastic procedures of FEM. The experimental validation of the proposed FEM-FDM procedures and numerical examples of a bolted tunnel are provided to demonstrate the efficacy of the proposed method for practical applications.

An enhanced numerical procedure for modelling fully grouted bolts intersected by rock joint

The stability of underground structure made especially in jointed rock mass is of the utmost important to designer, engineers and operators. Rock bolting is generally being practised to reinforced excavation walls and roofs by minimizing the movement of rock joints. In this study, a numerical procedure has been developed in extended finite element framework (XFEM) to analyze the behaviour of grouted bolt intersected by a joint. A solid finite element intersected by a bolt and a joint along any arbitrary direction is termed as ‘doubly enriched’ element. Nodes of an doubly enriched element have additional degrees of freedom for determining displacements, stresses developed in the bolt rod as well as the displacements jump and traction along the joint. The paper also provides verifications of this procedure by solving two known examples (i) direct shear test performed on a bolted joint sample-experimental verification and (ii) reinforcement of a joint located in the vicinity of a circular tunnel-analytical verification.

A generalized XFEM procedure for analyzing intersecting joints in rock masses with excavation

Purpose – The purpose of this paper is to analyse of structures made in rock mass with multiple intersecting discrete discontinuities such as joint, fault, shear plane. Design/methodology/approach – In this study, a numerical method is proposed for analyzing multiple intersecting joints with varying dip angles, spacing and roughness in eXtended Finite Element Method platform. A procedure is also outlined to treat excavated enhanced (jointed) elements for analysing the effect of excavation sequences. Findings – The proposed method is compared with the existing interface element methods (Phase-2 model) by considering the stress and displacement distributions of a multiple intersecting jointed rock sample under uniaxial loading conditions. A circular tunnel in rock mass having intersecting joints is also analyzed for the distribution of mobilised friction angle of joints and results are compared with a derived analytical solution. Research limitations/implications – Nucleation and propagation of cracks shoul...

Generalized Symmetric Formulation of Tangential Stiffness for Nonassociative Plasticity

AbstractThe behavior of material nonlinearity with nonassociative plastic flow is frequently analyzed for structures made of soil and rock. It is known that for nonassociated plasticity, the elastoplastic tangential stiffness tensor (matrix) is nonsymmetric. In the FEM, this causes inconvenience for solving a system of equations using the Newton-Raphson solution procedure. In this paper, a mathematical transformation was derived for converting the nonsymmetric tangential stiffness tensor (matrix) into a symmetric tensor such that the global system of equations become unconditionally symmetric. A detailed step-by-step procedure of a stress update algorithm using the tangential stiffness method is elaborated in this paper. The paper also compares the results of the tangential stiffness method with those of the initial stiffness method using an illustrative tunnel problem for associative and nonassociative flow conditions and shows the efficacy of the proposed transformation in elastoplastic problems.