Abstract

In many engineering applications, such as tribology and rock mechanics, it is very important to understand the deformation of rough fractures to evaluate the safety and profitability of the project. Since a lot of materials can be characterized as visco-elastic materials, it is very significant to simulate the visco-elastic deformation of rough fractures. This chapter focuses on using the boundary element method to simulate visco-elastic deformations of rough fractures. First, the principles and procedures of the above-mentioned method will be introduced. Then, one example will be given in detail. This example investigates the effect of surface geometry on visco-elastic deformations of rough rock fractures under normal compressive stresses. The rock fracture surfaces are assumed to be self-affine, and synthetic rough surfaces are generated by systematically changing three surface roughness parameters: the Hurst exponent, root mean square roughness, and mismatch length. The results indicate that by decreasing the Hurst exponent or increasing the root mean square roughness or increasing the mismatch length, the fracture mean aperture increases, and the contact ratio (the number of contacting cells/total number of cells) increases slower with time. Finally, the limitations and possible future research directions will be briefly discussed.

Highlights

  • A lot of natural and engineering materials can be categorized as visco-elastic materials, such as rock, elastomers, and rubbers

  • As root mean square (RMS) increases, the mean aperture increases, and the contact ratio increases slower with time; 3

  • One example, which investigates the effect of surface geometry on visco-elastic deformations of rough rock fractures, is given

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Summary

Introduction

A lot of natural and engineering materials can be categorized as visco-elastic materials, such as rock, elastomers, and rubbers. The boundary element method (BEM) has been extensively used in solving rough surface contacting problems for distinct advantages compared with the traditional finite element method (FEM) It only requires discretization and Recent Developments in the Solution of Nonlinear Differential Equations calculation on the boundaries of the calculation domain, which is two-dimensional. The CG and FFT methods have been applied to simulate plastic and visco-elastic deformations of rough fractures. Spinu and Cerlinca [8] applied different cut-off values for contact pressure to account for the plastic deformation of contacting asperities It appears that there is not much work that systematically simulates the visco-elastic deformation of rock fracture surfaces. The numerical method proposed by Chen et al [7] will be used to simulate the visco-elastic deformation of synthetic fracture surfaces.

Method for calculating fracture elastic deformation
Method for calculating fracture visco-elastic deformation
Model validation
Brief introduction of Brown’s (1995) model
Generated synthetic surface pairs
Creep simulation results for the Maxwell model
Creep simulation results for the SLS model
Limitations of the method
Findings
Conclusions

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