Unconfined compressive strength (UCS) is the most significant mechanical index for cemented backfill, and it is mainly determined by traditional mechanical tests. This study optimized the extreme gradient boosting (XGBoost) model by utilizing the whale optimization algorithm (WOA) to construct a hybrid model for the UCS prediction of cemented backfill. The PT proportion, the OPC proportion, the FA proportion, the solid concentration, and the curing age were selected as input variables, and the UCS of the cemented PT backfill was selected as the output variable. The original XGBoost model, the XGBoost model optimized by particle swarm optimization (PSO-XGBoost), and the decision tree (DT) model were also constructed for comparison with the WOA-XGBoost model. The results showed that the values of the root mean square error (RMSE), coefficient of determination (R²), and mean absolute error (MAE) obtained from the WOA-XGBoost model, XGBoost model, PSO-XGBoost model, and DT model were equal to (0.241, 0.967, 0.184), (0.426, 0.917, 0.336), (0.316, 0.943, 0.258), and (0.464, 0.852, 0.357), respectively. The results show that the proposed WOA-XGBoost has better prediction accuracy than the other machine learning models, confirming the ability of the WOA to enhance XGBoost in cemented PT backfill strength prediction. The WOA-XGBoost model could be a fast and accurate method for the UCS prediction of cemented PT backfill.

The problem of backfilling pipeline invalidation has become a bottleneck restricting the application and development of backfilling technology. This study applied the whale optimization algorithm and random forest (WOA–RF) to predict the invalidation risk of backfilling pipelines based on 59 datasets from actual mines. Eight influencing factors of backfilling pipeline invalidation risk were chosen as the input parameters of the WOA–RF model, and the risk level was selected as the output parameters of the WOA–RF model. Furthermore, random forest, decision tree, artificial neural network, k-nearest neighbor, and support vector machine models were also established according to the collected datasets. The prediction performance of the six classification models was compared. The evaluated results showed that the established WOA–RF hybrid model has the best prediction performance and the highest accuracy (0.917) compared to other models, with the highest kappa value (0.8846) and MCC value (0.8932). In addition, the performed sensitivity analysis showed that the deviation rate is the most important influencing factor, followed by the internal diameter of the pipeline. Eventually, the WOA–RF hybrid model was used to predict the failure risk level of the backfilling pipelines of nine actual mines in Sichuan, China. The field datasets were collected through field investigation, and engineering verification was carried out. The research results show that the WOA–RF hybrid model is reasonable and effective for backfilling pipeline invalidation risk, and it can provide a novel solution for backfilling pipeline invalidation, with good engineering practicability.

To address the challenges associated with deep ground pressure control at the Sanshandao Gold Mine, a pre-controlled top-to-middle and deep-hole upper and lower-wall goaf subsequent filling mining method was proposed. Three distinct downward mining schemes were designed, the excavation procedure is systematically designed with 18 steps, and the temporal and spatial evolution characteristics of stress and displacement were analyzed using FLAC3D. The results revealed that stress concentration occurred during excavation steps 1–3. As excavation progressed to steps 4–9, the stress concentration area shifted primarily to the filling zones of partially excavated and filled sections. By steps 10–12, the stress concentration in these areas was alleviated. Upon completion of all excavation and filling steps, a small plastic zone was observed, accompanied by an alternating distribution of high and low stress within the backfill. Throughout the excavation process, vertical displacement ranged from 4.42 to 22.73 mm, while horizontal displacement ranged from 1.72 to 3.69 mm, indicating that vertical displacement had a more significant impact on stope stability than horizontal displacement. Furthermore, the fuzzy comprehensive evaluation method was applied to optimize the selection among the three schemes, with Scheme 2 identified as the optimal. Field industrial trials subsequently confirmed the technical rationality and practical applicability of Scheme 2 under actual mining conditions.

In this paper, we consider a g-circulant matrixA 1(T), whose the first row entries are generalized Tribonacci numbers T(a)i. We give an explicit formula of the spectral norm of this matrix. When g = 1, we also present upper and lower bounds for the spread of the 1-circulant matrix A1(T).