三轴试验抗剪强度参数值回归分析法的区别与修正

对岩土三轴试验数据采用两种线性回归法计算所得的抗剪强度参数c、φ值会有差别。为了揭示这两种回归方法差别的根本原因，深入最小二乘法线性回归的基本原理指出，按大小主应力回归的结果是最佳估值，而按p-q曲线回归的计算结果不可靠，为了得到统一的结果，对后者所基于的最小二乘法进行了修正；推导了修正后的回归系数计算公式，证明了修正后两种方法得到的结果相同，并用一组千枚岩三轴试验数据进行了验证。结果表明，修正后用这两种方法确定三轴试验抗剪强度参数值都将得到同样的最佳无偏估值。

Difference and modification of regression analysis methods to estimate shear strength parameters obtained by triaxial test

The values of shear strength parameters,c and φ,estimated by two linear regression methods from data of rock or soil triaxial test are different.To reveal the basic cause of differences between the two regression methods,the principle of linear regression based on the least square method is analyzed thoroughly.The results estimated by regressing maximum principal stress with minor principal stress are the best values,while the results obtained by regressing maximum shear stress with average normal stress are not reliable.Modification for least square method of the latter regression method is done to obtain uniform results.Formulas for calculating modified regression coefficients are deduced.It is proved that results by the two methods after modification are the same;and they are applied to calculate the shear strength parameters in triaxial tests of phyllite.The results show that to rock or soil triaxial test,the values of shear strength parameters calculated by the two methods after modification are also the same best and unbiased estimations.