Improved radial movement optimization (IRMO) is adopted to investigate the critical slip surface and ultimate bearing capacity of a rough embedded strip footing on sands under inclined loading using the upper-bound limit analysis. Based on the Mohr–Coulomb yield criterion, a planar kinematically admissible multi-block failure mechanism of strip footing under inclined loading is formulated. The soil is assumed to be elastic–perfectly plastic material with an associated flow rule, and a solution procedure for the ultimate bearing capacity is established based on the virtual work principle. The results show that IRMO can calculate the ultimate bearing capacities efficiently, accurately and stably. The size and shape of normalized failure envelopes and inclination factors depend on the friction angle and embedment ratio. Moreover, the errors of the joint and individual influences of soil unit weight and surcharge for the bearing capacity of strip footing decrease with increasing load inclination angle α.

The development height of the water-conducting fracture zone (WCFZ) is crucial for the safe production of coal mines. The back-propagation neural network (BP-NN) can be utilized to forecast the WCFZ height, aiding coal mines in water hazard prevention and control efforts. However, the stochastic generation of initial weights and thresholds in BP-NN usually leads to local optima, which might reduce the prediction accuracy. This study thus invokes the excellent global optimization capability of the Improved Radial Movement Optimization (IRMO) algorithm to optimize BP-NN. The influences of mining thickness, coal seam depth, working width, and hard rock lithology proportion coefficient on the height of WCFZ are investigated through 75 groups of in situ data of WCFZ heights measured in the Jurassic coalfield of the Ordos Basin. Consequently, an IRMO-BP-NN model for predicting WCFZ height in the Jurassic coalfield of the Ordos Basin was constructed. The proposed IRMO-BP-NN model was validated through monitoring data from the 4⁻²216 working faces of Jianbei Coal Mine, followed by a comparative analysis with empirical formulas and conventional BP-NN models. The relative error of the IRMO-BP-NN prediction model is 4.93%, outperforming both the BP-NN prediction model, the SVR prediction model, and empirical formulas. The results demonstrate that the IRMO-BP-NN model enhances the accuracy of predicting WCFZ height, providing an application foundation for predicting such heights in the Jurassic coalfield of the Ordos Basin and protecting the ecological environment of Ordos Basin mining areas.

The stability of abandoned open-pit mine slopes and their ecological environment are threatened owing to their fragile, complicated, and uncertain characteristics. This study establishes a novel evaluation indicator system for enhancing mine design and environmental protection insight. The weights in the system are assigned using a combined method, which consists of the game theory, the interval analytic hierarchy process (IAHP), and the entropy weight method (EWM). The IAHP is optimized by the improved radial movement optimal (IRMO) algorithm and the simulated annealing (SA) algorithm to ensure calculation stability and efficiency. Meanwhile, a two-dimensional cloud model (TDCM) is developed to obtain the slope resilience level and visualize the result. This comprehensive evaluation method is applied to three abandoned mine slopes in the Yellow River Basin, and the results demonstrate that the method can provide crucial insights for rational mine slope stabilization and ecological restoration.

The ultimate axial bearing capacity (UABC) of a single pile is an important parameter in pile design. BP neural network (BPNN) has a strong nonlinear mapping ability and can effectively predict the UABC of a single pile. However, frequent immersion in unstable search results with local vibration leads BPNN to a less usable solution. The weights and biases of the BPNN model are optimized using the improved radial movement optimization (IRMO) algorithm in this study, and a new method named the IRMO-BP neural network (IRMO-BPNN) is proposed to predict the UABC of a single pile. The IRMO-BPNN model was developed from a database of 196 static load test (SLT) samples, and model hyper-parameter analysis was carried out to determine the optimal number of hidden nodes, population size, and the number of iterations. The prediction accuracy and stability of the IRMO-BPNN model are verified by comparing it with the GA-based ANN model, ANFIS-GMDH-PSO model, and RBFANN model. The results show that the IRMO-BPNN model can accurately predict the UABC of a single pile and improves the situation that the BPNN model is easy to fall into local optimal values and its search results are unstable. The IRMO-BPNN model has significant advantages over other models.