Application of numerical modeling and genetic programming to estimate rock mass modulus of deformation

Estimation of the rock mass modulus of deformation (Em) is one of the most important design parameters in designing many structures in and on rock. This parameter can be obtained by in situ tests, empirical relations between deformation modulus and rock mass classification, and estimating from laboratory tests results. In this paper, a back analysis calculation is performed to present an equation for estimation of the rock mass modulus of deformation using genetic programming (GP) and numerical modeling. A database of 40,960 datasets, including vertical stress (σz), horizontal to vertical stresses ratio (k), Poisson’s ratio (ν), radius of circular tunnel (r) and wall displacement of circular tunnel on the horizontal diameter (d) for input parameters and modulus of deformation for output, was established. The selected parameters are easy to determine and rock mass modulus of deformation can be obtained from instrumentation data of any size circular galleries. The resulting RMSE of 0.86 and correlation coefficient of 97% of the proposed equation demonstrated the capability of the computer program (CP) generated by GP.