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Ground Reaction Curve (GRC) is one of the most important elements of convergence-confinement method generally used to design tunnels. Realistic presentation of GRC is usually assessed based on the advanced rock strength criteria, also, rock mass behavior (including plasticity and softening treatments). Since taking these parameters into ac­count is not simply possible for practitioners and needs complicated coupled theoretical-numerical solutions, this paper presents a simple novel approach based on Evolutionary Polynomial Regression to determine GRC of rock masses obeying both Mohr-Coulomb and Hoek-Brown criteria and strain softening behaviors. The proposed models accurately present support pressures based on radial displacement, rock mass strength and softening parameter (determination coefficient of 97.98% and 94.2% respectively for Mohr-Coulomb and Hoek-Brown strain softening materials). The ac­curacy of the proposed equations are approved through comparing the EPR developed GRCs with the ground reaction curves available in the literature. Besides, the sensitivity analysis is carried out and in-situ stress, residual Hoek-Brown’s m constant and residual dilation angle are introduced as parameters with the most influence on the support pressure in Hoek-Brown and peak and residual geological strength index are the most affective parameters on the support pressure of tunnels in the strain softening Mohr-Coulomb rock mass.

Rock bolting is one of the most important support systems used for rock structures. Rock bolts are widely used in underground excavations as they are suitable for a wide range of geological conditions and allow using progressive design methods; besides, they help economising in the use of materials and manpower. Thus, to provide the most effective support at minimum cost by means of rock bolting, it is essential to optimise the elements contributing to bolt design, including their length, as well as bolt density and tension during installation. This paper considers the length of bolts for optimisation of the design phase, which is one of the most important parameters impacting the entire design procedure. Presenting and comparing results of some statistical models, neural network modeling is introduced as powerful means in prediction of the optimal length of rock bolts. Subsequent to training and testing of a large number of 1-layer and 2-layer backpropagation neural networks, it was reported that the optimal model was the network with the architecture of 6-18-3-1 as it demonstrated the minimum RMSE and MAE as well as the maximum R 2 . In comparison to statistical models (0.7182 for the value of R 2 in the multiple linear regression model, 0.68 in the polynomial model and 0.7 in the dimensionless model), the results obtained by the neural network modeling − i.e. the coefficient of determination R 2 of 0.9259, the value of mean absolute error MAE of 0.068, and the root mean squared error RMSE of 0.078 − not only proved their superiority but also introduced the neural network modelling as a highly capable prediction tool in forecasting the optimal length of rock bolts. Furthermore, sensitivity analysis was used to obtain parameters that have the greatest and the least impact on the optimal bolt length: the effect of the overburden thickness, tensile strength, cohesion and Poisson's ratio on the optimal bolt length was almost the same while the friction angle had the least influence.Keywords: optimal length of rock bolts, artificial neural networks, statistical methods, sensitivity analysis.

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Featured Application: This work can be conjunctly used with the support characteristic curve of circular tunnels to find the optimum time of the installation of the support system in a way to restrict the displacements to a specific value. The approach described in this manuscript facilitates the design of circular tunnels for elasto-plastic, strain-softening rock masses obeying both Mohr-Coulomb and Hoek-Brown strength criteria. Abstract:The prediction of the support pressure (P i ) and the development of the ground reaction curve (GRC) are crucial elements of the convergence-confinement procedure used to design underground structures. In this paper, two different types of artificial neural networks (ANNs) are used to predict the P i of circular tunnels in elasto-plastic, strain-softening rock mass. The developed ANNs consider the stress state, the radial displacement of tunnel and the material softening behavior. Among these parameters, strain softening is the parameter of the deterioration of the material's strength in the plastic zone. The analysis also presents separate solutions for the Mohr-Coulomb and Hoek-Brown strength criteria. In this regard, multi-layer perceptron (MLP) and radial basis function (RBF) ANNs were successfully applied. MLP with the architectures of 15-5-10-1 for the Mohr-Coulomb criteria and 17-5-15-1 for the Hoek-Brown criteria appeared optimum for the prediction of the P i . On the other hand, the RBF networks with the architectures of 15-5-1 for the Mohr-Coulomb criterion and 17-3-12-1 for the Hoek-Brown criterion were found to be the optimum for the prediction of the P i .