A semi-infinite higher-order displacement discontinuity method and its application to the quasistatic analysis of radial cracks produced by blasting

Abstract

We introduce a higher-order indirect boundary element method in a traction-free half-plane known as semi-infinite displacement discontinuity method. The method is modified to use the linear elastic fracture mechanics principles for radial crack analysis in brittle materials like rocks. In this numerical method there is no need to discretize the traction-free boundary of the half-plane into higher-order elements thus decreasing the number of elements without affecting the accuracy of the solution to the desired problems. The use of higher-order elements increases the accuracy so that it is possible to discretize both the boundary of the body and radial cracks by the same higher-order elements, therefore there may be no need to use the more complicated hybrid methods. A special crack tip element is added for each crack tip to increase the accuracy of displacement discontinuities near the crack ends due to their singularities. Based on the brittle behavior of most rocks, linear elastic fracture mechanics principles have been used to find the fracture mechanics parameters (mode-I and mode-II mixed mode stress intensity factors) of radial cracks occurring in common blasting operations. Arbitrary fracture criteria can be implemented in this code, but here a simple maximum tangential stress criterion is used to predict the angle of deviation (initiation) of radial cracks. Although this code is specially designed to include the traction-free halfplane problems, it is somewhat comprehensive so that any number of radial cracks with any length in the finite, infinite and semi-infinite planes can be treated easily. The validity of the method is proved by solving simple examples and some previously solved problems in the literature.

Numerical Crack Analysis of Blunt Rock Indenters by an Indirect Boundary Element Method

“…If distribution of displacement discontinuity along the length of an element is not constant and changes in linear, quadratic or cubic form then it is called a higher order element which has been used to calculate displacement discontinuities along that element [18,19]. Figure 3 shows the displacement discontinuity along the elements and also the positive direction of displacements discontinuity for each element along the length of it.…”

“…Results showed that discontinuum-based DEM has the potential in simulating rock indentation and fragmentation by TBM cutters when rock joints are taken into consideration [14]. The use of boundary element method for analysis and simulation of cracks can be traced in some studies [15][16][17][18][19][20][21]. Displacement discontinuity method is an indirect boundary element method which has been used for the analysis of crack problems.…”

Stress fields induced by a non-uniform displacement discontinuity in an elastic half plane

“…The Riemann-Hilbert method can be adopted to solve 2D crack problems in an infinite, homogeneous, anisotropic plate [8]. A general higher-order DD method coupled with an indirect BEM has been applied to the quasi-static analyses of radial cracks produced by blasting [9]. Complex crack problems such as multiple branched and intersecting cracks also have been investigated using the numerical manifold method [10], which also has been applied to 2D http://dx.doi.org/10.1016/j.engfracmech.2014.…”

Kinked crack analysis by a hybridized boundary element/boundary collocation method

“…Although the constant displacement discontinuity elements are simple and widely used for analyzing engineering problems, they cannot predict the stresses and displacements for field points closer than approximately one element length from the boundary and also for the crack analysis a higher accuracy of the results near the crack tips is needed. Therefore, the higher order variation of the displacement discontinuities together with special crack tip elements are usually used for the treatment of crack problems (Scavia, 1995;Shou and Crouch, 1995;Tan et al, 1996;Marji et al, 2006;Fatehi Marji et al, 2007;Hosseini Nasab and Fatehi Marji, 2007;Fatehi Marji et al, 2009). Kinked cracks in brittle rocks under compressive loading are studied by Bobet (2000), Kishen and Sing (2001); Sagong and Bobet (2002), Wong et al (2001Wong et al ( , 2002 and Tang et al (2005).…”