Estimation of fracture normal stiffness using a transmissivity-depth correlation

A new method for determination of fracture normal stiffness is developed in this paper. From the point of hydro-mechanical coupling, the relationship between transmissivity and depth is utilized to calculate fracture normal stiffness of large-scale rock masses, which is an important but difficult-to-obtain parameter. The basic idea is that flow in fractured media is very sensitive to aperture of discontinuity, and the aperture of the discontinuity is mainly determined by the normal stress and normal stiffness. A decrease in transmissivity of fractured rock masses with increasing depth, as indicated in hydraulic tests, is due to closure of the joints caused by an increase in the normal stress that is nearly proportional to depth. Consequently, it is possible to estimate in-situ fracture normal stiffness by using information of depth-dependent transmissivity. An equation is derived to achieve the purpose. In our preliminary case study at the fractured sandstone on the left bank of the Xiaolangdi Reservoir in China, the variable fracture normal stiffness is estimated. It satisfies the fact that normal stiffness will increase with increasing stress, i.e. with increasing depth. The value obtained by our method is of the same order of magnitude as the normal stiffness values obtained from laboratory tests reported in the literature. Furthermore, the estimated deformation modulus of the rock mass is close enough to that obtained from in-situ tests or inverse analysis.