Application of Stress Compensation-Displacement Discontinuity Method (SC-DDM) to The Crack Propagation Analysis of Multi-crack Problem

Abstract

The rock mass properties such as deformability and strength are highly dependent on the existence of cracks. The crack propagation directly influences the decrease of effective Young's modulus and rock mass failure, and the analysis of crack propagation is indispensable for the evaluation of mass properties.In this study, crack propagation analysis was conducted by applying SC-DDM (stress compensation-displacement discontinuity method) to the two-dimensional multi-crack model. Since it is difficult to consider mechanical interaction between all cracks which has arbitrary arrangements, the homogenization method was introduced in the analysis. The model, crack homogenization model, consists of infinite numbers of unit cells and each unit cell has the same crack distribution. Consequently, all cracks behave the same and the mechanical properties of the entire model can be estimated from the analysis of representative unit cell. Here, the alternative model of a single crack set is assumed. The procedure of crack propagation analysis was introduced and the optimization method of crack propagation angle was discussed. In this study, the accuracy of the analyses was verified through the evaluation crack propagation angle and crack profiles, then the characteristics of the crack propagation analysis was discussed. It was proved that the results have enough accuracy and that this method is suitable for the crack propagation analysis. It was also found that this model has a peak strength during crack propagation process, and the relation between loading angle and crack propagation stress was discussed. KEY WORDS : Crack Propagation, Multi-Crack Set, Rock, SC-DDM, Fracture Mechanics

Stability of Dynamic Growth of Two Anti-Symmetric Cracks Using PDS-Fem

“…2 shows snapshots of growing crack foṙ U /V r = 1. As is seen, the anti-symmetry is lost during the crack growth process, which is in contrast with the quasi-static state simulation made by Sato et al 13) . The crack growth process changes when the loading rate is different; see Fig.…”

“…Unlike the crack growth process, we can observe some patterns. For the lowest loading rate (U /V r = 1), regions where probability density of crack passing is concentrated form an anti-symmetric pattern, which seems similar to the anti-symmetric crack configuration computed by Sato et al 13) . For the highest loading rate (U /V r = 27), regions of high probability density appear a branch from the anti-symmetric pattern.…”

“…Sato et al 13) solved a 2D plane strain problem of anti-symmetric cracks which grow in an ideally homogeneous body, assuming quasi-static state. Following his numerical study, we study a thin plate of 5×24.5×140 mm, which includes two anti-symmetric parallel cracks of length 0.6 mm; see Fig.…”

Instable Crack Propagation Analysis with PDS-FEM

“…Problem setting. Sato et al [6] solved a 2D plane strain problem of anti-symmetric cracks which grow in an ideally homogeneous body, assuming quasi-static state. Following his numerical study, we study a thin plate of 5×24.5×140 mm, which includes two anti-symmetric parallel notches of height 0.6 mm, 5mm apart in vertical direction, located in the centre of the model, see Fig.…”