In this paper, a numerical approach to modeling progressive failure leading to collapse in rock and associated seismicity is reported. In the first part, a newly developed numerical code, RFPA2D (Rock Failure Process Analysis), is introduced. The program allows modeling of the observed evolution of damage and associated seismic events due to progressive failure leading to collapse in brittle rock. There are three features distinguishing the approach from conventional numerical methods such as FEM: (1) by introducing heterogeneity of rock parameters into the model, RFPA2D can simulate non-linear behavior in rock using a linear method; (2) by introducing elastic modulus reduction for failed elements, RFPA2D can process discontinuum mechanics problems by a continuum mechanics method; and (3) by recording the event-rate of failed elements, the seismicities associated with the progressive failure in rock can be simulated. In the second part of the paper, the applications of RFPA2D in simulating geological process and in solving mining design problems are illustrated. Numerical simulation of a fault initiation process indicates that some of the important phenomena, such as coalescence of microfracture, the nucleation and growth of crack clusters, fault initiation and development, elastic rebound, dilatation, uplift and seismic behavior, etc. can be simulated with this numerical code. The simulation of progressive failure leading to collapse in underground openings demonstrates the capacity of this code in solving mining design problems.

A numerical approach to particle breakage is applied using the Rock Failure Process Analysis code, RFPA2D. The numerical tool is validated by simulating the Brazilian test with a two-dimensional disk sample. Then two irregularly shaped particles with an exact geometry and exact mechanical properties are numerically modelled to investigate their breakage behaviour under unconfined and confined loading conditions. The numerical results indicate that the dominant mode of failure is catastrophic splitting and progressive crushing, which mainly depends on the loading conditions with respect to confinement. The analysis of the load-displacement curves obtained from the simulations suggests a brittle-ductile transition between the two cases. The lateral constraint increases the initial stiffness and the maximum breakage strength of the particle. Most of the energy released during the failure process comes from the crushing of highly stressed areas, particularly, in the vicinity of the contact points where a crushed zone forms. It is also found that the particle shape governs the breakage strength in addition to the material properties themselves, and that the heterogeneity of the particles governs the fracture propagation paths.

This paper presents an application of the numerical model presented in the companion paper (Part I) in which, by using a newly developed numerical code, RFPA2D (Rock Failure Process Analysis), a fundamental approach for the simulation of damage initiation and propagation causing seismic energy release during an unstable failure of brittle rock was presented. The in-uence of material and loading system properties including sti

运用新近开发的岩石破坏过程分析RFPA2D（Rock Failure Process Analysis） 系统，以含瓦斯煤岩的破坏过程分析为例，通过对含瓦斯煤岩突出孕育机制及其声发射的数值模拟，说明了数值模拟方法给含瓦斯煤岩突出机制及其预测理论的发展所带来的新契机。数值模拟再现了含瓦斯煤岩突出的发生、发展过程，模拟结果表明，复杂的瓦斯煤岩断裂、突出现象可能是一些简单机理的演化结果。

以东北老工业基地矿产资源型城市为基础，通过大量的实例和数据介绍了矿产资源开采诱发的工程灾害与环境损伤的内容和特点，并指出矿产资源开采诱发的工程灾害与环境损伤中的几个关键科学问题和所应当采用的分析研究方法。