Comparison of tunnel support requirements assessed by DEM and the Q system

There are several approaches for the design of support systems for tunnels excavated in rock. These approaches can be classified as analytical, numerical and empirical methods. Empirical methods are based on the experience obtained from past tunnelling projects. The Q system is one of the empirical methods used for classification of the rock mass and evaluation of support requirements. In this paper, the effect of rockbolt length, diameter and spacing on the stresses developed in the rockbolts and the deformations developed in the rock mass are evaluated using the distinct element method. Also, the effects of the distance of supporting system from the tunnel face, tunnel depth and diameter on the stresses and deformations are investigated. The results of this numerical analysis are compared with the results obtained using the Q system. It is shown that the design of supporting system using the Q system is more conservative than the numerical method. For the stability analysis of underground excavations and design of support systems three approaches comprising empirical, analytical and numerical methods can be used. Each of these methods has limitations and advantages. To obtain more reliable results, all of these three methods can be used simultaneously in the various phases of analysis and design. Empirical approaches, such as the Q system, are based on the experience obtained from the past projects. Rock mass classification procedures constitute the base for the empirical approaches. In these methods, the values of stresses and displacements developed in the support system and the surrounding ground can not be evaluated. In the analytical approaches, the design of support system is based on the theoretical models and relationships developed for certain conditions. In most of these formulations it is assumed that a circular cross section is excavated in a homogenous and isotropic media with hydrostatic in-situ stresses. In a jointed rock, equivalent continuum media is used in the analysis. Also, in the case of grouted rockbolts, this approach only observes the analysis from a qualitative point of view and takes into account the effect of rockbolts by improving the characteristics of the existing rock mass. Numerical methods for the stress analysis can be classified into two main categories (Brady 1992): • Integral or boundary methods represented by the several versions of the boundary element methods, construct solutions to the field equations using fundamental solutions to these equations and by applying formal solutions from solid mechanics. In these methods only the surface of an excavation is used in the solution, and the interior of the problem domain is not represented explicitly. • Domain or differential methods represented by the finite element, finite difference and distinct element methods. These methods solve the field equations by dividing the rock mass into elements or zones within which the governing equations are formally satisfied. The finite difference and the distinct element methods have the same basis in the solid mechanics. In the finite difference method, attention is focused on the continuum, although several discontinuity surfaces (slip lines) can also be modelled. Alternatively, in the block-jointed medium, the interaction between blocks is of primary concern, and the state of stress in the interior of the blocks is conveniently determined using the distinct elements. The finite element method is