Experimental and numerical study on crack propagation in pre-cracked beam specimens under three-point bending

A simultaneous experimental and numerical study on crack propagation in the pre-cracked beams specimens(concrete-like materials) is carried out using three-point bending flexural test. The crack propagation and coalescence paths of internal cracks in side beam specimens are experimentally studied by inserting double internal cracks. The effects of crack positions on the fracturing path in the bridge areas of the double cracked beam specimens are also studied. It has been observed that the breaking of concrete-like cracked beams specimens occurs mainly by the propagation of wing cracks emanating from the tips of the pre-existing cracks in the numerical and experimental analyses, respectively. The same specimens are numerically simulated by an indirect boundary element method(IBEM) known as displacement discontinuity method(DDM) using higher displacement discontinuity. These numerical results are compared with the existing experimental results. This comparison illustrates the higher accuracy of the results obtained by the indirect boundary element method by using only a small number of elements compared with the discrete element method(PFC2D code).

Propagation simulation and dilatancy analysis of rock joint using displacement discontinuity method

A revised displacement discontinuity method(DDM) program is developed for the simulation of rock joint propagation and dilatancy analysis. The non-linear joint model used in the program adopts Barton-Bandis normal deformation model, Kulhaway shear deformation model and Mohr-Coulomb criterion. The joint propagation criterion is based on the equivalent stress intensity factor which can be obtained by regression analysis. The simulated rock joint propagation accords well with the existing knowledge. The closure and opening of joint is investigated by DDM, and it is shown that if the opening volume of propagated joint is larger than closure volume of the old joint, the joint dilatancy occurs. The dilatancy condition is mainly controlled by the normal stiffness of the rock joint. When the normal stiffness is larger than the critical value, joint dilatancy occurs. The critical normal stiffness of rock joint changes with the joint-load angle, and joint dilatancy is most possible to occur at 30°.

Simulation of crack coalescence mechanism underneath single and double disc cutters by higher order displacement discontinuity method

The present research is focused on the numerical crack coalescence analysis of the micro-cracks and cracks produced during the cutting action of TBM disc cutters. The linear elastic fracture mechanics(LEFM) concepts and the maximum tangential stress criterion are used to investigate the micro crack propagation and its direction underneath the excavating discs. A higher order displacement discontinuity method with quadratic displacement discontinuity elements is used to estimate the stress intensity factors near the crack tips. Rock cutting mechanisms under single and double type discs are simulated by the proposed numerical method.The main purposes of the present modeling are to simulate the chip formation process of indented rocks by single and double discs.The effects of specific disc parameters(except speed) on the thrust force Ft, the rolling force Fr, and the specific energy ES are investigated. It has been shown that the specific energy(energy required to cut through a unit volume of rock) of the double disc is less than that of the single disc. Crack propagation in rocks under disc cutters is numerically modeled and the optimum ratio of disc spacing S to penetration depth Pd(i.e. S/Pd ratio) of about 10 is obtained, which is in good agreement with the theoretical and experimental results cited in the literature.

3D-FSM·DDM IBEM numerical system of multi-medium

Based on the idea of the developed 3D-FSM.DDM boundary element method, the field with muti-medium was formulized firstly, then connected at the interface of two fields according to the continuous conditions of stress and displacement, after that, a boundary value problem with unified model was formed and solved. Ultimately, an applied numerical simulation system was developed. It was compared with the model having analytical solution for verifying the applicability and the calculating precision.

Stability analyses of bleeder pillars in longwall mines by displacement-discontinuity method

Caving in coal mines releases significant amounts of dust and gas. This is exhausted from the mine by forcing the air to travel through the caved zones into a set of roadways known as bleeders. These bleeder entries are operated for the life of the mine, and therefore, they have to be kept in stable condition. Caving operations in coal mines are associated with Iongwall mines and complete pillar extraction. The pillars adjoining the caved zone sometimes show rib failures, posing a hazard for mine personnel travelling through the entry. In this paper, we present the results from analyses of bleeder pillars that are near the caved zones and are susceptible to damage because of the transfer of load during the caving process. In this study, bleeder pillars were simulated in a displacement discontinuity program. Results showed that the vertical stresses on bleeder pillars increased while the safety factor of bleeder pillar decreased during the caving process; however, when the caved zone completely consolidated, both the stresses and safety factor did not change for the remaining extraction. When similar extraction was performed at deeoer denths, vertical stress on pillars increased significantly_

Numerical modeling of simultaneous hydraulic fracturing in the mode of multi-well pads

In order to investigate propagation regularity of hydraulic fractures in the mode of multi-well pads, numerical modeling of simultaneous hydraulic fracturing of multiple wells was conducted. The mathematical model was established coupling rock deformation with fluid flow in the fractures and wellbores. And then the model was solved by displacement discontinuity method coupling with implicit level set method. The implicit method was based on fracture tip asymptotical solution and used to determine fracture growth length. Simulation results showed that when multiple wells were fractured simultaneously, adjacent fractures might propagate towards each other, showing an effect of attraction other than repulsion. Fracture spacing and well spacing had significant influence on the propagation path and geometry of multiple fractures. Furthermore, when multiple wells were fractured simultaneously, stress reversal regions had a large area, and stress reversal regions were distributed not only in the area between fractures but also on the outside of them. The area of stress reversal regions was related to fracture spacing and well spacing. Results indicated that multi-well fracturing induced larger area of stress reversal regions than one-well fracturing, which was beneficial to generating complex fracture network in unconventional reservoirs.

Discontinuous deformation and displacement analysis: From continuous to discontinuous

A discontinuous deformation and displacement(DDD) analysis method is proposed for modelling the rock failure process. This method combines the rock failure process analysis(RFPA) method(based on finite element method) and discontinuous deformation analysis(DDA) method. RFPA is used to simulate crack initiation, propagation and coalescence processes of rock during the small deformation state. The DDA method is used to simulate the movement of blocks created by the multiple cracks modelled by the RFPA. The newly developed DDD method is particularly suitable for modelling both crack propagation and block movement during the rock failure process because of the natural and convenient coupling of continuous and discontinuous deformation analyses. The proposed method has been used to simulate crack initiation, propagation and coalescence within a slope as well as the block movement during the landslide process. Numerical modelling results indicate that the proposed DDD method can automatically simulate crack propagation and block movement during the rock failure process without degrading accuracy.