Calculation of Elastic Modulus for Fractured Rock Mass Using Dimensional Analysis Coupled with Numerical Simulation

Underground mining activities make the fractures in the natural rock mass develop randomly. The elastic modulus of the fractured rock mass E m is changed with the redistribution and development of the fractures. An equivalent model of fractured rock mass is structured to represent the hydraulic conductivity and the rock mass strain because of the continuum theory. Dimensional analysis is very useful to build relationship of the parameters in complex physical phenomena. Based on the engineering phenomenon of groundwater flowing into the goaf along the fracture in the rock mass, a fuzzy expression among parameters such as the parameter E m , the seepage flow Q , and the exposed area of the goaf A is obtained using dimensionless analysis. To calculate the parameter E m , the fuzzy relationship is then characterized by Darcy’s law and numerical simulation. Under the scripting environment of Python, an automated program to realize the numerical simulation of all scenarios is established, which also provides convenience for drawing the dimensionless flux charts. The results show that the parameter E m can be calculated by the dimensional analysis coupled with numerical simulation. In addition, the parameter E m decreases with the increase of the parameter Q , and the integrity of rock mass is also worse. Finally, a mine example is used to verify the feasibility of the method.