Estimation of Rock Mass Deformation Modulus Based on Analytical and Numerical Methods

Determination of rock mass deformation modulus is one of the main requirements of any civil engineering project. Deformation modulus can be determined by in situ tests such as dilatometer, plate loading and flat jack tests. However, these methods are time consuming and expensive. Analytical methods can be also used to estimate the deformation modulus. These methods can easily evaluate factors affecting the deformation modulus. Analytical methods are based on summing of all displacements of intact rock and joints, which finally predict the deformation modulus of rock mass. In this paper, the effect of lateral stresses on the deformation modulus of jointed rock mass is taken into account. This parameter has not been considered in the previous analytical methods. In order to control and evaluate the analytical equations and to estimate the reliability of these methods, the results of laboratory tests carried out by Pinto on three schist samples were used. Moreover, the results of analytical methods were compared with the numerical methods using 3DEC software. Based on this comparison, it can be stated that:
-          The shear force of the lateral pressure increases the deformation modulus whereas its normal force decreases the deformation modulus of jointed rock mass. Totally, an increase of the lateral pressure will increase the total modulus of the rock mass.
-          Increasing of the joint normal angle, with σ₁, joint spacing, joint normal stiffness (k_n), joint shear stiffness (k_s) and the ratio of in situ principal stresses and confining stresses results in increasing of the deformation modulus of the jointed rock mass. by increasing of these parameters from certain values, the rate of modulus increasing significantly decreases so that the rock mass modulus equals to intact rock modulus.
-          In the blocks containing one and three joint sets, a good correlation was obtained between the modulus calculated from the mathematical equations and the numerical modeling in the absence of the confining pressure. Their maximum error obtained as 2.5% and 2.2%, respectively.
-          Having applied the lateral pressure in a block containing one and three joint sets, the analytical approach and the numerical modeling estimated an error around 7% and 14%, respectively.
-          The results obtained from the suggested analytical method, the numerical modeling and the laboratory tests showed that there is a good agreement among them, which reveals the high accuracy of the analytical model.