基于集成树算法的岩石黏聚力和内摩擦角预测方法

Prediction Method of Rock Cohesion and Internal Friction Angle Based on Ensemble Tree Algorithm

岩石的黏聚力(c)和内摩擦角(φ)是岩石工程设计及稳定性评价的重要参数,其直接测量需通过多组三轴或剪切试验,耗时多且成本高。基于4个易获取的岩石物理力学参数(纵波波速VP、密度ρ、单轴抗压强度UCS和巴西抗拉强度BTS),构建了用于预测c和φ值的智能模型。共收集了199组含不同岩石类型的数据,采用5种集成树算法开发预测模型,使用贝叶斯优化算法对模型的超参数进行优化。模型评估结果表明:构建的模型均具有较好的预测性能,其中极端随机树模型表现最佳(测试R^(2)>0.97)。敏感性分析表明:VP、UCS和BTS对c值的预测结果影响较大,ρ对φ值的预测结果影响较大。研究成果已成功应用于金川矿区,验证了模型的实用性,开发的图形用户界面便于工程技术人员使用。

The cohesion(c)and internal friction angle(φ)of rock are critical parameters in the design and stability assessment of rock engineering projects.Direct measurement of these parameters necessitates condu-cting numerous rock triaxial or shear tests,which are both time-intensive and expensive.This study proposes the development of intelligent models to predict the values of c andφbased on four readily obtainable parameters:P-wave velocity(VP),density(ρ),uniaxial compressive strength(UCS),and Brazilian tensile strength(BTS).A total of 199 datasets containing various rock types were collected and randomly partitioned into a training set(80%)and a test set(2%).The distribution characteristics and correlations among the data were analyzed using scatter plots for data distribution and correlation plots for variables.To address discrepancies in characteristic attributes,such as magnitude and order of magnitude across different input variables,a normalization function was applied.Subsequently,five ensemble trees were utilized to develop predictive models for rock shear strength parameters.Bayesian optimization was employed to optimize the hyperparameters of the models.Concurrently,five-fold cross-validation was implemented during model training.To evaluate the performance of the models,four widely recognized regression metrics were utilized:The coefficient of determination(R^(2)),root mean square error(RMSE),mean absolute error(MAE),and variance accounted for(VAF).Additionally,a ranking system was introduced to provide a comprehensive assessment of the five models.The model evaluation demonstrated that the constructed models exhibited robust predictive performance,with the extremely randomized tree model outperforming others.Specifically,for predicting the value of c,the R2 was 0.993,the RMSE was 0.45,the MAE was 0.309,and the VAF was 99.306%.For predicting the value ofφ,the R2 was 0.97,the RMSE was 0.823,the MAE was 0.612,and the VAF was 97.058%.Furthermore,the application of the SHAP interpretation method for sensitivity analysis indicated that VP,UCS,and BTS significantly influenced on the prediction of c,whereasρhad a substantial impact on the prediction ofφ.Finally,rock blocks were collected and processed into samples for physical-mechanical testing to determine the VP,ρ,UCS,BTS,c,andφvalues of rocks at various locations within the JinchuanⅡandⅣmining areas in China.The model was effectively utilized to predict the c andφvalues for rocks in the Jinchuan mining area,thereby validating its practicability.Furthermore,a graphical user interface was developed to facilitate ease of use for engineers and technicians in the field.