脆性各向同性材料的强度准则数学形式研究

Study on Mathematical Form of Strength Criterion for Brittle Isotropic Materials

针对质量比为水泥∶河砂∶水∶减水剂=1∶0.5∶0.4∶0.002的脆性各向同性材料,探究了胡克-布朗(H-B)准则、Power Curve准则与单参数Bieniawski准则等3类岩石经典非线性强度准则与Singh抛物线型强度准则的适用性,并对Singh抛物线型强度准则数学形式进行了修正。研究结果表明,单参数Bienianski准则能较好地反映脆性各向同性材料非线性强度特征,数学形式拟合值与试验值的残差平方和(RSS)最小;H-B准则与Power Curve准则均能反映抗压强度指标的非线性特征,但两者均过高估计抗拉强度值;将Singh抛物线型强度准则数学形式等效为因变量(σ_(1)-σ_(3))与自变量σ_(3)的二次多项式,试验数据拟合效果良好,并通过引入参数n表征试样进入临界状态时的围压σ_(crt)=nσ_(c),得到了修正的Singh抛物线型强度准则数学形式。

Based on a brittle isotropic material with a mass ratio of cement∶river sand∶water∶water reducer=1∶0.5∶0.4∶0.002,the applicability of three types rock classical nonlinear strength criterion,including the Hoek-Brown(H-B)criterion,the Power Curve criterion and the single-parameter Bienianski criterion,and the Singh parabolic strength criterion are investigated,and the mathematical form of the Singh parabolic strength criterion is modified.The research results show that the single-parameter Bienianski criterion can well reflect the nonlinear strength characteristics of brittle isotropic material,and the residual sum of squares(RSS)between the mathematical form fitting value and the test value is the smallest;the H-B criterion and the Power Curve criterion can reflect the nonlinear characteristics of compressive strength index,but both of them overestimate the tensile strength value;and when the mathematical form of the Singh parabolic strength criterion is equivalent to the quadratic polynomial of the dependent variable(σ_(1)-σ_(3))and the independent variableσ_(3),the test data will have a good fitting effect,and the improved mathematical form of the Singh parabolic strength criterion can be obtained by introducing parameter n to characterize the critical confining pressure σ_(crt)=nσ_(c) of the sample when it enters the critical state.