Extended Finite Element Method for the Analysis of Discontinuities in Rock Masses

Abstract

The strength and deformability of rock mass primarily depend on the condition of joints and their spacing and partially on the engineering properties of rock matrix. Till today, numerical analysis of discontinuities e.g. joint, fault, shear plane and others is conducted placing an interface element in between two adjacent rock matrix elements. However, the applicability of interface elements is limited in rock mechanics problems having multiple discontinuities due to its inherent numerical difficulties often leading to non-convergent solution. Recent developments in extended finite element method (XFEM) having strong discontinuity imbedded within a regular element provide an opportunity to analyze discrete discontinuities in rock masses without any numerical difficulties. This concept is based on partition of unity principle and can be used for cohesive rock joints. This paper summarizes the mathematical frameworks for the implementation of strong discontinuities in 3 and 6 nodded triangular elements and also provides numerical examples of the application of XFEM in one and two dimensional problems with single and multiple discontinuities.

Influence of the geometry of partially-spanning joints on mechanical properties of rock in uniaxial compression

“…Zhang and Sanderson (2001) evaluated the effects of fracture geometry and loading direction on the instability of fractured rock masses using a distinct element method, while Giacomini et al (2008) investigated the flow anisotropy within a natural joint subjected to mechanical shear. Deb and Das (2009) provided a numerical example of the application of the extended finite element method (XFEM) in jointed rock samples with varying joint inclination angles. More recently, Wong (2012, 2013) studied the cracking and coalescence behavior in a rectangular rock-like specimen containing two parallel pre-existing open flaws under uniaxial compression load using a parallel bonded-particle model.…”

Enriched finite element procedures for analyzing decoupled bolts installed in rock mass

“…Additional degrees of freedom are absent in regular elements and hence the compatibility in displacement fields between neighboring enriched and regular elements satisfies according to Lemma A2 given in the Appendix. The integration procedure of an enriched element (shown in Figure 4(a)) is adopted based on the work proposed by Deb and Das [25,26] for cohesive rock joint analysis. It is found that the procedure is also well suited for the grouted rock bolt.…”

Extended digital image correlation method for analysis of discrete discontinuity

“…However, determination of displacement jump remains a challenge in DIC. In this context, Deb and Das [22] have successfully implemented X-FEM for analysis of displacements and strains in a jointed rock sample. Based on this approach, the multilevel X-DIC method is implemented in this paper to analyze displacement jump in deformed images due to existence of a discrete discontinuity.…”