By incorporating the fabric effect and Lode’s angle dependence into the Mohr–Coulomb failure criterion, a strength criterion for cross-anisotropic sand under general stress conditions was proposed. The obtained criterion has only three material parameters which can be specified by conventional triaxial tests. The formula to calculate the friction angle under any loading direction and intermediate principal stress ratio condition was deduced, and the influence of the degree of the cross-anisotropy was quantified. The friction angles of sand in triaxial, true triaxial, and hollow cylinder torsional shear tests were obtained, and a parametric analysis was used to detect the varying characteristics. The friction angle becomes smaller when the major principal stress changes from perpendicular to parallel to the bedding plane. The loading direction and intermediate principal stress ratio are unrelated in true triaxial tests, and their influences on the friction angle can be well captured by the proposed criterion. In hollow cylinder torsional shear tests with the same internal and external pressures, the loading direction and intermediate principal stress ratio are related. This property results in a lower friction angle in the hollow cylinder torsional shear test than that in the true triaxial test under the same intermediate principal stress ratio condition. By comparing the calculated friction angle with the experimental results under various loading conditions (e.g., triaxial, true triaxial, and hollow cylinder torsional shear test), the proposed criterion was verified to be able to characterize the shear strength of cross-anisotropic sand under general stress conditions. 相似文献
Rockburst is a common dynamic geological hazard, severely restricting the development and utilization of underground space and resources. As the depth of excavation and mining increases, rockburst tends to occur frequently. Hence, it is necessary to carry out a study on rockburst prediction. Due to the nonlinear relationship between rockburst and its influencing factors, artificial intelligence was introduced. However, the collected data were typically imbalanced. Single algorithms trained by such data have low recognition for minority classes. In order to handle the problem, this paper employed stacking technique of ensemble learning to establish rockburst prediction models. In total, 246 sets of data were collected. In the preprocessing stage, three data mining techniques including principal component analysis, local outlier factor and expectation maximization algorithm were used for dimension reduction, outlier detection and outlier substitution, respectively. Then, the pre-processed data were split into a training set (75%) and a test set (25%) with stratified sampling. Based on the four classical single intelligent algorithms, namely k-nearest neighbors (KNN), support vector machine (SVM), deep neural network (DNN) and recurrent neural network (RNN), four ensemble models (KNN–RNN, SVM–RNN, DNN–RNN and KNN–SVM–DNN–RNN) were built by stacking technique of ensemble learning. The prediction performance of eight models was evaluated, and the differences between single models and ensemble models were analyzed. Additionally, a sensitivity analysis was conducted, revealing the importance of input variables on the models. Finally, the impact of class imbalance on the prediction accuracy and fitting effect of models was quantitatively discussed. The results showed that stacking technique of ensemble learning provides a new and promising way for rockburst prediction, which exhibits unique advantages especially when using imbalanced data.
