Although a number of numerical simulation models were developed and improved in the theory and programs for jointed rock mass, there are many drawbacks to the simulation techniques, such as discontinuity modeling and free expansion. Instead of the spring model of discontinuity, a new numerical model is developed based on the essences of deformability and mechanical characteristics of discontinuity. Discontinuity is considered as a nonrenewable and volumechangeable plastic medium. In addition, Numerical errors between the linear displacement functions and the exact solutions can accumulate when the block rotates continuously. This cause a change in block size called the free expansion phenomenon. Here, the finite rotation theory is adopted to address the drawback of free expansion. Finally, jointed rock mass is considered as a two-media model. The coupling effects between blocks and discontinuities are established. These developments of simulation techniques can reveal the essences of rock mass and improve analysis accuracy for simulation.


The rock mass is essentially a discontinuous medium due to the presence of various discontinuities at different scales and orientations, such as faults, bedding and joints. Its stability is significantly affected by the geometrical distribution and geological properties of the discontinuities. There are almost no closed-form solutions to solve the complicated problem for jointed rock mass. Therefore, in recent decades, a number of numerical simulation models based on a prior assumption of discontinuity were developed, such as DEM (Cundall 1971; Itasca 1999), DDA (Shi 1989) and BSM (Wang 1993). And there are much improvement in the theory and programs. However, there are still many drawbacks to the numerical simulations for jointed rock masses. In this paper, the authors address two major drawbacks regarding discontinuity model and free expansion.

2.1 Previous discontinuity model

Rock blocks are of static equilibrium state in nature stress field. But some rock block may slide, rotate, fall or simultaneously slide and rotate when it is disturbed. Rock block is subject to not only gravity and outside force but also frictional constraint. It is difficult to determine failure mode for block by reason of three dimension distribution of outside force and friction. Many researchers simplify the calculation based on the theory of concurrent forces. However, one cannot calculate the normal force on each discontinuity when contact occurs on more than three non-parallel discontinuities, or on two or more parallel discontinuities.

In order to overcome the reaction force indeterminacy, one needs to introduce the deformability of the discontinuities. For example, DEM, DDA and BSM use normal and tangential springs at the intersection point between a discontinuity face and a block's vertex. And they consider the thickness of discontinuity as 0. The interactive forces between discontinuity and block are based on the ‘invasion’. Although this discontinuity model can address the problem of discontinuity simulation, it does not reveal the essences of discontinuity, such as discontinuity deformability, mechanical characteristics.

2.2 Discontinuity description

In practical rock engineering, the discontinuities have various geometrical shape and different thickness as shown in Figure 1.

This content is only available via PDF.
You can access this article if you purchase or spend a download.