Rock bolts as construction elements are often used in underground civil engineering projects. We used Aydan finite elements for numerical description of rock bolt reinforcement and isoparametric bilinear finite elements for description of rock massif. We derived corresponding stiffness matrices and right hand sides and developed a finite element code for the calculation of rock deformations and stresses. The code was tested on several numerical examples. We computed in detail deformations and stresses in a round tunnel, first without any rock bolts and then with rock bolts placed in the tunnel arch. We compared deformations and stresses obtained by our calculations to approximate analytical solution.

1 Introduction

Rock bolts as reinforcing construction elements are often used in underground civil engineering projects. Today it is common to use numerical modelling for designing and verification of various types of constructions and rock bolts are no exception. Several special rock bolt elements were created for this purpose. The most widely used elements was presented in the work of Ömer Aydan (1988). The so-called Aydan element is represented by four nodes in its simplest 2D form. Two nodes create a rod sub-element, which is a simple model of a steel bar. Remaining nodes represent the connection of this bar with surrounding rock massif by cement grout. This paper deals with composition of the stiffness matrix of Aydan element and its application to a simple two-dimensional numerical model of a circular excavation reinforced by rock bolts that are fastened by cement grout along their full length.

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