Modelling the crack initiation and propagation of notched rock beam under the three-point bending load

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.