Abstract
Prediction of rock fracture is essential to understand the rock failure mechanism. The three‐point bending test has been one of the most popular experiments for the determination of rock fracture parameters. However, the crack initiation and propagation of rock beam with the center notch and offset notch have not been fully understood. This paper develops a numerical method for modelling the notched beam cracking based on nonlocal extended finite element method (i.e., XFEM) and mixed mode rock fracture model. An example is worked out to demonstrate the application of the numerical method and verified with experimental results. The crack length development, crack pattern, crack opening and slipping displacements, and the load‐crack mouth of displacement (P‐CMOD) curve are obtained. The effects of offset notch location and mechanical properties on the crack length development, P‐CMOD curve, and crack pattern are investigated and discussed. It has been found that the peak load of the notched beam nearly linearly increases with the increase of the notch offset ratio. The cracking of rock beam with offset notch is dominated by mode I fracture, but mode II fracture contributes more when crack deflection occurs. The fracture energy significantly affects the peak load, while it has little effect on the prepeak and postpeak slopes in the P‐CMOD curve.
Highlights
E extended finite element method (XFEM) provided a very helpful tool for modelling rock arbitrary cracking without the requirement for remeshing [31]
The nonlocal stress averaging for cracking can make the prediction of materials cracking more accurate [32]. erefore, it is worth modelling the cracking of notched rock beam under the three-point bending load by the nonlocal XFEM and mixed mode fracture model
The slipping displacement is much smaller than the opening displacement. erefore, the cracking of rock beam with offset notch is dominated by mode I fracture but mode II fracture contributes more when crack deflection occurs
Summary
Rock exhibits the tensile strain-softening behaviour due to an inelastic zone being developed ahead of the crack tip, often referred to as fracture process zone (FPZ) [7, 25]. e cohesive crack model first proposed by Jia and Zhang [26] has been employed to simulate discrete cracking in the fracture process zone of rock and concrete. The stress of rock linearly develops as a linear function: σn Knδn,. When the maximum principal stress reaches the criterion value (i.e., cohesive strength), crack initiation will occur and a damage value is introduced to reduce the stiffness for stress softening, i.e., σn (1 − D)Knδn,. The damage evolution between initiation of damage and final failure can follow a linear or exponential function [33, 34]. Where δm, max is the maximum effective relative displacement during the loading history; δm,0 is the critical effective relative displacement when the damage starts; δm,f is the effective relative displacement when complete failure occurs; δm,f can be calculated by the mixed mode fracture energy as follows: δm,f. The stressstrain relationship of rock under mixed mode fracture is established
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