The scheme for accurate and reliable predictions of tunnel stability based on an artificial aeural network (ANN) is presented in this study. Plastic solutions of the stability of unlined elliptical tunnels in sands are first derived by using numerical upper-bound (UB) and lower-bound (LB) finite element limit analysis (FELA). These numerical solutions are later used as the training dataset for an ANN model. Note that there are four input dimensionless parameters, including the dimensionless overburden factor γD/c′, the cover–depth ratio C/D, the width–depth ratio B/D, and the soil friction angle ϕ. The impacts of these input dimensionless parameters on the stability factor σs/c′ of the stability of shallow elliptical tunnels in sands are comprehensively examined. Some failure mechanisms are carried out to demonstrate the effects of all input parameters. The solutions will reliably and accurately provide a safety assessment of shallow elliptical tunnels.

In this study, the Multivariate Adaptive Regression Splines (MARS) model is employed to create a data-driven prediction for the bearing capacity of a strip footing on rock mass subjected to an inclined and eccentric load. The strengths of rock masses are based on the Hoek-Brown failure criterion. To develop the set of training data in MARS, the lower and upper bound finite element limit analysis (FELA) is carried out to obtain the numerical results of the bearing capacity of a strip footing with the width of B. There are six considered dimensionless variables, including the geological strength index (GSI), the rock constant/yield parameter (mi), the dimensionless strength (γB/σci), the adhesion factor (α), load inclined angle from the vertical axis (β), and the eccentricity of load (e/B). A total of 5,120 FELA solutions of the bearing capacity factor (P/σciB) are obtained and used as a training data set. The influences of all dimensionless variables on the bearing capacity factors and the failure mechanisms are investigated and discussed in detail. The sensitivity analysis of these dimensionless variables is also examined.

In this paper, Artificial Neural Networks (ANN) have been utilized to predict the stability of a planar tunnel heading in rock mass based on the well-defined Hoek–Brown (HB) yield criterion. The HB model was developed to capture the failure criterion of rock masses. To provide the datasets for an ANN model, the numerical upper bound (UB) and lower bound (LB) solutions obtained from the finite element limit analysis (FELA) with the HB failure criterion for the problem of tunnel headings are derived. The sensitivity analysis of all influencing parameters on the stability of rock tunnel heading is then performed on the developed ANN model. The proposed solutions will enhance the dependability and preciseness of predicting the stability of rock tunnel heading. Note that the effect of the unlined length ratio has not been explored previously but has been found to be of critical importance and significantly contributes to the failure of rock tunnel heading. By utilizing the machine learning-aided prediction capability of the ANN approach, the numerical solutions of the stability of tunnel heading can be accurately predicted, which is better than the use of the classic linear regression approach. Thus, providing a better and much safer assessment of mining or relatively long-wall tunnels in rock masses.

In this study, various machine learning algorithms, including the minimax probability machine regression (MPMR), functional network (FN), convolutional neural network (CNN), recurrent neural network (RNN), and group method of data handling (GMDH) models, are proposed for the estimation of the seismic bearing capacity factor (Nc) of strip footings on sloping ground under seismic events. To train and test the proposed machine learning model, a total of 1296 samples were numerically obtained by performing a lower-bound (LB) and upper-bound (UB) finite element limit analysis (FELA) to evaluate the seismic bearing capacity factor (Nc) of strip footings. Sensitivity analysis was performed on all dimensionless input parameters (i.e., slope inclination (β); normalized depth (D/B); normalized distance (L/B); normalized slope height (H/B); the strength ratio (cu/γB); and the horizontal seismic acceleration (kh)) to determine the influence on the dimensionless output parameters (i.e., the seismic bearing capacity factor (Nc)). To assess the performance of the proposed models, various performance parameters—namely the coefficient of determination (R2), variance account factor (VAF), performance index (PI), Willmott’s index of agreement (WI), the mean absolute error (MAE), the weighted mean absolute percentage error (WMAPE), the mean bias error (MBE), and the root-mean-square error (RMSE)—were calculated. The predictive performance of all proposed models for a bearing capacity factor (Nc) prediction was compared by using the testing dataset, and it was found that the MPMR model achieved the highest R2 values of 1.000 and 0.957 and the lowest RMSE values of 0.000 and 0.038 in both the training and testing phases, respectively. The parametric analyses, rank analyses, REC curves, and the AIC showed that the proposed models were quite effective and reliable for the estimation of the bearing capacity factor (Nc).

This paper presents an Artificial Neural Network (ANN)-based approach for predicting tunnel stability that is both dependable and accurate. Numerical solutions to the instability of unlined horseshoe tunnels in cohesive-frictional soils are established, primarily by employing numerical upper bound (UB) and lower bound (LB) finite element limit analysis (FELA). The training dataset for an ANN model is made up of these numerical solutions. Four dimensionless parameters are required in the parametric analyses, namely the dimensionless overburden factor γD/c′, the cover-depth ratio C/D, the width-depth ratio B/D, and the soil friction angle ϕ. The influence of these dimensionless parameters on the stability factor is explored and illustrated in terms of a design chart. Moreover, the failure mechanisms of a shallow horseshoe tunnel in cohesive-frictional soil that is influenced by the four dimensionless parameters are also provided. Therefore, the current stability solution, based on FELA and ANN models, is presented in this paper, allowing for the efficient and accurate establishment and evaluation of an optimum surcharge loading of shallow horseshoe tunnels in practice.