Mathematical and physical significances and applicability of tangent and secant strength indices of total stress of consolidated undrained triaxial tests based on Coulomb’s law
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摘要: 以土体抗剪强度规律在破坏面上归结为库仑定律，并同种各向同性土的三轴试验有效应力强度指标唯一存在为立论基础展开分析，通过建立不排水条件的库仑强度定律与三轴固结不排水剪切（CU）试验破坏时超静孔压的联系，对CU试验总应力强度指标线性存在的数学基础和物理意义进行了解析。结果表明：由排水和不排水条件下库仑强度规律的线性特征，可证明破坏面上与法向应力相关的孔压系数Df为常数；而CU总应力强度包线之所以线性存在是由于斯开普敦孔压系数Af能与Df 、黏聚力及破坏时的偏应力建立起特定的数量关系，并明确提出了该关系的数学表达式。同时利用CU试验所得参数，求解了CU总应力割线强度指标φR，cR的值。割线强度指标的确定为已定滑动面的工程问题提供更为合理和可操作的强度计算方法，而若选用切线强度指标，强度值可能会有10%以上的高估，带来极大的安全隐患。Abstract: Most of the strength criteria for soils should satisfy the Coulomb’s law on the failure surface, and the effective stress strengh indices of isotropic soil are unique under different drainage conditions. The mathematical and physical meanings of triaxial total stress strength indices are investigated based on the relationship between the excess pore pressure at failure in Coulomb's law under undrained conditions and that in consolidated undrained (CU) triaxial tests. The results show that, in view of the linear envelope of the Coulomb's law under drained and undrained conditions, the pore pressure coefficient Df is proved to be constant, which is related to the normal stress state on the failure surface. The existence of linear total stress failure envelop of CU is based on the certain relationship among Skempton’s pore pressure coefficients Af , Df , cohesion and deviator stress at failure. The corresponding expression is also obtained. Furthermore through the strength parameters of CU tests, the secant strength indices, φR and cR, are obtained. It provides more reasonable and operational method for engineering problems with known sliding surfaces. However if the total stress tangent strength indices of CU are used, the strength will be overvalued by more than 10%, which will cause great security risk.
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