A new estimation method and an anisotropy index for the deformation modulus of jointed rock masses

The deformation modulus of a rock mass is an important parameter to describe its mechanical behavior.In this study, an analytical method is developed to determine the deformation modulus of jointed rock masses, which considers the mechanical properties of intact rocks and joints based on the superposition principle. Due to incorporating the variations in the orientations and sizes of joint sets, the proposed method is applicable to the rock mass with persistent and parallel joints as well as that with nonpersistent and nonparallel joints. In addition, an anisotropy index AIdmfor the deformation modulus is defined to quantitatively describe the anisotropy of rock masses. The range of AIdmis from 0 to 1, and the more anisotropic the rock mass is, the larger the value of AIdmwill be. To evaluate the proposed method,20 groups of numerical experiments are conducted with the universal distinct element code(UDEC). For each experimental group, the deformation modulus in 24 directions are obtained by UDEC(numerical value) and the proposed method(predicted value), and then the mean error rates are calculated. Note that the mean error rate is the mean value of the error rates of the deformation modulus in 24 directions,where for each direction, the error rate is equal to the ratio of numerical value minus predicted value to the numerical value. The results show that(i) for different experimental groups, the mean error rates vary between 5.06% and 22.03%;(ii) the error rates for the discrete fracture networks(DFNs) with two sets of joints are at the same level as those with one set of joints; and(iii) therefore, the proposed method for estimating the deformation modulus of jointed rock masses is valid.