An integrated SRM-multi-gene genetic programming approach for prediction of factor of safety of 3-D soil nailed slopes

• An integrated SRM-MGGP method for FOS prediction of nailed slope is proposed.
• Proposed SRM-MGGP is compared to those of MGGP, SVR and ANN.
• Out of four methods, SRM-MGGP evolves a model with better generalisation ability.
• SRM-MGGP method also represents explicit formulation of FOS of nailed slope.

Soil nailing is one of the slope stabilisation techniques useful for the strengthening of existing slopes. It helps to reinforce the soil with passive inclusions that increase the overall shear strength of the soil slope and also restrains its displacements. The limit equilibrium method is usually employed to estimate factor of safety (FOS) of nailed slopes through either finite element or finite difference methods. Alternatively, soft computing methods such as multi-gene genetic programming (MGGP), support vector regression (SVR) and artificial neural network (ANN) can also be used to predict the FOS for different soil properties. Among these methods, MGGP possesses the ability to evolve the model structure and its coefficients automatically. Although widely used, the MGGP method has the limitation of producing models that perform poorly on testing data. Therefore, in this study, an integrated structural risk minimisation-multi-gene genetic programming (SRM-MGGP) method is proposed to formulate the mathematical relationship between FOS and the six input variables of cohesion, frictional angle, nail inclination angle, nail length, slope height and slope angle of 3-D nailed slope. The results indicate that the SRM-MGGP model outperforms the other three models (MGGP, SVR and ANN) and is able to generalise the FOS satisfactorily for any given input variables conditions. This would be useful for engineers in their design calculations of slopes with different soil, slope and nail conditions based on certain limitations such as ignorance of effect of pore water pressure or overburden pressure.