A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering

Numerical methods in rock mechanics

SUMMARY A solution procedure for the analysis of planar and axisymmetric contact problems involving sticking, frictional sliding and separation under large deformations is presented. The contact conditions are imposed using the total potential of the contact forces with the geometric compatibility conditions, which leads to contact system matrices and force vectors. Some key aspects of the procedure arc the contact matrices, the use of distributed tractions on the contact segments for deciding whether a node is sticking, sliding or releasing and the evaluation of the nodal point contact forces. The solutions to various sample problems are presented to demonstrate the applicability of the algorithm. Much progress has been made during recent years in the development of computational capabilities for general analysis of certain nonlinear effects in solids and structures. In each of these developments, quite naturally, the first step was the demonstration of some ideas and possibilities for the analyses under consideration, and then the research and development for reliable and general techniques was undertaken. The second step proved in many cases much more difficult, and in the case of capabilities for analysis of contact problems has yielded few general results. Although some of the first complex contact problems have been solved using the finite element method quite some time ago,'- and much interest exists in the research and solution of contact problems (see, for example, References 4-1 5), there is still a great deaiwf effort necessary for the development of a reliable, general and cost-effective algorithm for the practical analysis of such problems. This is largely due to the fact that the analysis of contact problems is computationally extremely difficult, even for the simplest constitutive relations used. Much of the difficulty lies in that the boundary conditions of the bodies under consideration are not known prior to the analysis, but they depend on the solution variables. The aim in our research is the development of a solution algorithm for analysis of general contact conditions which shall include the possibilities to analyse: contact between flexible-flexible and rigid--flexible bodies; sticking or sliding conditions (with or without friction); large relative motions between bodies; repeated contact and separation between the bodies. Since the large deformation motion of the individual bodies can in many cases be analysed already quite effectively,'6 an algorithm of the above nature will certainly enlarge, very

/pdf/a-solution-method-for-planar-and-axisymmetric-contact-3c5bwr6s45.pdf

A solution method for planar and axisymmetric contact problems

It is 100 years since the well-know Mohr-Coulomb strength theory was established in 1900. A considerable amount of theoretical and experimental research on strength theory of materials under complex stress state was done in the 20th Century. This review article presents a survey of the advances in strength theory (yield criteria, failure criterion, etc) of materials (including matellic materials, rock, soil, concrete, ice, iron, polymers, energetic material, etc) under complex stress, discusses the relationship among various criteria, and gives a method of choosing a reasonable failure criterion for applications in research and engineering. Three series of strength theories, the unified yield criterion, the unified strength theory, and others are summarized. This review article contains 1163 references regarding the strength theories. This review also includes a biref discussion of the computational implementation of the strength theories and multi-axial fatigue.

Advances in strength theories for materials under complex stress state in the 20th Century

A physically motivated constitutive law for the behaviour of geologic discontinuities with dilatancy and contact surface degradation (damage) is presented. In the formulation of the law, the paper distinguishes between macroscopic and microscopic features of the contact surface. Through macroscope considerations. an incremental constitutive law is derived which is applicable to a large class of contact-friction problems. By idealizing the microstructure to consist of interlocking asperity surfaces, the constitutive equations are specialized for the description of rock joints including effects such as dilatancy, asperity surface degradation and bulking. Several examples are considered demonstrating the law's behaviour and agreement with experimental data. The incremental form of the equations that are derived are amenable to implementation in numerical procedures such as finite element and discrete element (rigid block) computer programs.

Constitutive models for rock discontinuities with dilatancy and surface degradation

The idea of using a thin solid element, called a thin-layer element, in soil-structure interaction and rock joints is proposed. A special constitutive model is used and various deformation modes such as no slip, slip, debonding and rebonding are incorporated. The shear stiffness is found from special laboratory tests and the normal stiffness is assumed to be composed of participation of the thin-layer element and the adjoining solid elements. A parametric study shows that the thickness of the thin-layer element can be such that the ratio of thickness to (mean) dimension of the adjacent element is in the range of 0.01 to 0.1. A number of simple and practical problems are solved to illustrate the success of the thin-layer element for soil-structure interaction problems.

H. J. Siriwardane

Papers

Thin‐layer element for interfaces and joints