Micro-crack propagation and coalescence during time-dependent deformation of granite based on numerical manifold method

Xian-Yang Yu,Tao Xu,Zhen Heng,Michael J Heap,Patrick Baud

doi:10.1088/1755-1315/570/2/022064

Abstract

An understanding of influence of micro-cracks on time-dependent deformation in granite is of fundamental importance in many situations, such as nuclear waste storage facilities or the exploitation of geothermal resources. Time-dependent cracking is considered to be the main mechanism of brittle creep in granite. Creep strain rates are strongly influenced by the density of pre-existing defects that also exert a significant influence on rock physical properties. We introduce a new model that combines the subcritical crack growth (SCG) theory and the numerical manifold method (NMM) to link the local damage (using an exponential material softening law) caused by micro-crack propagation and the macroscopic creep deformation typically observed in granite specimens. In this model, each element contains a virtual micro-crack that can propagate sub-critically following Charles’ law. Once the virtual micro-crack length reaches a given value, it will convert to a real micro-crack, which can cut through adjacent elements, open, and slide according to the principle of NMM. We also investigated the influence of virtual micro-crack length, confining pressure and differential stress on creep behaviour. The fact that numerical simulations are in good agreement with experimental results shows that the NMM combined with the SCG theory is a suitable method for modelling the creep behaviour of rocks.

Highlights

The long-term stability of engineering rock mass structures have been of practical concern for many years[1]
In this research, when the stress intensity factors (SIFs) of crack tips are smaller than Kc, both virtual and real cracks propagate according to the subcritical crack growth (SCG) theory
We propose that SCG theory can combine with numerical manifold method (NMM) to simulate time-dependent brittle deformation under different loading conditions and different confining pressures

Summary

Introduction

The long-term stability of engineering rock mass structures have been of practical concern for many years[1]. Many researchers have found that micro-crack propagation in a rock mass is one of main parameters that influences the creep strain rate[4]. The SCG theory was initially attributed to stress corrosion. SCG theory in rock masses has been used to explain the growth and development of joints, volcanic eruptions, and underground excavations[7]. Konietzky[9] used FLAC to simulate the time-dependent crack growth of granite. These authors used the SCG theory of a virtual crack within an element to describe rock damage. Using the time step–initial strain method, the creep equation was coupled with the NMM to simulate the time-dependent deformation of rocks[15]. Wu[16] used the NMM to analyze viscoelastic material creep crack problems by incorporating a generalized Kelvin-Voigt model into the NMM

Crack Initiation and Growth Criteria

Simulation

Results

Conclusions