Bending-damaged fracture criterion and numerical implementation of limestone beam under three-point bending test

Abstract

To study the characteristics of tensile cracking by rock-bending damage, the bending stress–strain curves and the cumulative ringing counts were obtained by a three-point bending test and acoustic emission (AE) monitoring of limestone beams. Based on the Lemaitre strain equivalent principle and the continuous damage theory, the bending damage variable D was defined by the AE cumulative ringing counts, and the bending crack damage evolution equation was established according to the Weibull distribution of the rock element strength. To realize the numerical test of the bending deformation, the damage variable D was used as the intermediate variable, and the specific process of damage bending stress transformation and the realization of the tensile crack criterion were secondary developed by FISH language in FLAC3D. According to the results, the central part of rock beam deforms downward under the action of bending stress, and both ends tilt up. Therefore, the bending failure begins with the tensile crack at the bottom of the rock beam and gradually extends to the compression zone. The maximum damage value is about 0.402 before the peak stress. The compressive stress in the x direction increases from the neutral layer to the top of the rock beam, and the tensile stress in the x direction increases from the neutral layer to the bottom of the rock beam. The maximum tensile stress is distributed in the center of the bottom of the specimen, where the bending effect is obvious. The stress–time curve was divided into the (Ⅰ) compaction stage, (Ⅱ) expansion stage, and (Ⅲ) penetration stage, accordingly, and the evolution of damage equation was divided into three stages: initial damage stage, slow damage stage, and accelerated damage stage. The curves of the experimental result, theoretical model prediction result, and numerical simulation result were in good agreement with each other, which indicates that the numerical simulation based on the criterion of rock damaged fracture can better reflect the bending process of rock beams under three-point bending stress.