This paper investigates the expected benefits of the implicit time integration scheme in the solution of jointed rock problems. Discontinuous Deformation Analyses (DDA) exploits the unconditional stability of the implicit time integration scheme, and allows the time step size of the solution to be much larger than the critical time step size dictated by the stability requirement of the explicit time integration schemes. This paper discusses the effects of large time step size on the DDA solution of engineering scale jointed rock problems. The findings are numerically verified by comparing the DDA solution to that of the Distinct Element Method (DEM).

1. Introduction

Heterogeneities in materials take various forms such as fractures, joints, bedding planes, voids, and material boundaries. Such features pose great challenges to understanding and predicting the complex range of behaviour of geomaterials. As a result, in recent years, much attention has been focused on efficient numerical techniques for analyzing jointed rock problems. Three approaches are commonly used to model jointed rock masses. These are:

  1. Discrete element techniques, and their combined discrete-continuum derivatives,

  2. Combined continuum-interface methods, which are continuum methods with special joint/interface elements that model discontinuous displacement behaviour, and

  3. Cosserat continuum.

In this paper we focus on the first category of methods. We will compare the computational efficiency of two widely-used discrete-based methods, the Discontinuous Deformation Analysis (DDA) and the Distinct Element Method (DEM), when applied to the analysis of jointed rock problems. The fundamental difference between the two methods arises from their time discretization method. DDA uses an implicit time-integration scheme to solve the governing equations of a discrete problem. DEM is defined as a general term referring to discrete element methods that apply explicit time integration. Depending on the space discretization used, various DEM-based techniques have been developed. Due to its implicit time integration, DDA is unconditionally stable and can accommodate considerably larger time steps than those of DEM. Explicit time integration, on the other hand, requires the time step to be smaller than a critical value to maintain stability of the solution. It has been argued in the literature that due to its larger time steps, DDA can be expected to solve jointed rock problems more efficiently than DEM. This paper intends to investigate the expected benefits of DDA. It will study the effects of time-step size on the solution times of DDA and DEM when applied to the analysis of engineering scale jointed rock problems. The examples examine the stability of slopes in jointed rock masses. To make it possible to directly compare the influence of time step size on the solution time of DDA and DEM, other factors that affect solution time were measured and factored out. This paper uses UDEC numerical package [1], as the DEM representative application. Similar to DDA, UDEC discretizes the space domain into a number of polygonal blocks. Also, Shi's implementation of DDA [2] (which will be referred to as DDA-Shi throughout this text) is used as representative application of DDA.

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