A new doubly enriched finite element for modelling grouted bolt crossed by rock joint

• A new finite element is developed considering strong displacement discontinuity and reinforcement effect.
• Discontinuity plane intersects with rock bolt at an element in any arbitrary direction.
• A numerical procedure is developed within the framework of XFEM considering “Dowel action” of rock bolt.
• Decoupling at bolt-grout interface and stick-slip characteristics of joint is implemented with material non-linearity.

A doubly enriched finite element (DEFE) procedure has been developed by introducing strong displacement discontinuities in the form of rock joints and reinforcement affect in the form of rock bolts. The proposed procedure extends the concept of extended finite element method (XFEM) and enriches the nodes of an element for determining displacements and stresses of bolt rod as well as displacement jumps and tractions of rock joint. The paper elaborates on the theoretical development of this procedure and derives stiffness matrix of a DEFE using variational approach. The stick-slip behaviour of joint, yielding of rock mass as well as grout material have also been implemented in the DEFE procedure. The paper also provides verifications of this procedure by solving two known examples, (i) direct shear test performed on a bolted joint sample-experimental verification, and (ii) reinforcement of a joint located in the vicinity of a circular tunnel-analytical verification.