基于对数函数的岩石三轴强度回归预测模型

Regression Prediction Model of Rock Triaxial Strength Based on Logarithmic Function

岩石的破坏强度对于采矿的安全性和经济性有重要的影响,为了更精确地预测岩石在不同围压条件下的三轴压缩破坏强度,根据其非线性特征,建立了基于对数函数的三轴强度回归预测模型。首先,以砂岩常规三轴试验数据为基本信息,运用回归预测方法推导出该预测模型的数学表达式,再通过4个指标对该模型进行检验,初步证明该模型预测结果具有合理性;然后,将该预测模型与Hoek-Brown准则和Mohr-Coulomb准则进行比较,发现该模型预测的岩石三轴强度平均相对误差MMRE仅为5.01%,明显低于另外两种准则(12.72%和9.10%),具备更高的预测精度;最后,通过既有文献中4种不同类型岩石的三轴试验数据对该预测模型进行适用性验证,验证结果表明,该模型对这4种岩石三轴强度预测的平均相对误差MMRE为6.93%~9.48%,均低于10%,适用性较好。该预测模型可为采矿工程中安全经济的结构设计提供参考。

The failure strength of rock has an important influence on the safety and economy of mining.In order to predict the triaxial compression failure strength of rock under different confining pressures more accurately,a regression prediction model of triaxial strength based on logarithmic function was established according to its nonlinear characteristics.Firstly,taking the conventional triaxial test data of sandstone as the basic information,the mathematical expression of the prediction model was derived by regression prediction method,and the model was tested by four indexes,which preliminarily proven that the prediction results of the model were reasonable.Then,comparing the prediction model with Hoek-Brown criterion and Mohr-Coulomb criterion,it was found that the average relative error of rock triaxial strength predicted by the model was only 5.01%,significantly lower than that of the other two criteria(12.72%and 9.10%),with a higher prediction accuracy.Finally,the applicability of the prediction model was verified through triaxial test data of four different types of rocks in existing literature.The validation results show that the average relative error of the model for predicting the triaxial strength of these four types of rocks is 6.93%to 9.48%,all lower than 10%,and the applicability is good.The prediction model can provide a reference for safe and economic structural design in mining engineering.