【摘要】 为了精确地描述岩土材料的Mohr圆包络线，首先，构建了分数阶微积分破坏准则，阐明了其参数含义，推导了其在三轴面和子午面上的表达形式；其次，分析了在Mohr圆应力平面、三轴面和子午面上分数阶微分阶数和分数阶微分值对分数阶微积分破坏准则Mohr圆包络线的影响；最后，基于分数阶微积分破坏准则，研究了超固结黏土剪切强度、干湿循环下砂泥岩混合料的三轴剪切强度及岩石的剪切强度。研究结果表明：分数阶微积分破坏准则认为破坏面上剪应力对正应力的分数阶微分为常数，分数阶微分阶数反映了Mohr圆包络线的非线性演化，其范围为[0.5,1.0]；当阶数等于1时，分数阶微积分破坏准则为线性Mohr-Coulomb准则；当阶数为(0.5,1.0)，它为一种非线性幂函数准则，且阶数越接近0.5,Mohr圆包络线的非线演化越明显。分数阶微积分破坏准则表明了岩土材料破坏面上剪应力与正应力的微分关系，较好地描述了岩土材料Mohr圆包络线的演化。分数阶微积分破坏准则可以表征岩土材料的非线性强度，丰富了岩土材料破坏准则。更多还原

【Abstract】 To accurately describe the Mohr envelope of geomaterials, a novel failure criterion named as fractional calculus failure criterion(FCFC) was firstly proposed based on fractional calculus theory. The parameter meaning of the FCFC was clarified. The expression of the criterion in the triaxial plane and meridian plane was derived.Secondly, the influence of the differential order and differential value on the Mohr envelope on the Mohr stress plane, triaxial plane, and meridian plane was analyzed. Finally, the shear strength of over-consolidated clay, the triaxial shear strength of sandstone-mudstone mixture under dry-wet cycling, and the shear strength of rock were studied based on the FCFC. The results show that the fractional differential of shear stress to normal stress on the failure surface is constant. The order of fractional differentiation reflects the nonlinear Mohr envelope, which ranges in [0.5, 1.0]. When the order is equal to 1, the failure criterion will be the Mohr-Coulomb criterion. When the order ranges in(0.5, 1.0), the FCFC will be a power-type failure criterion. The closer the order is to 0.5, the more obvious the nonlinear evolution of the Mohr envelope is. The FCFC shows the differential relationship between shear stress and normal stress on the failure surface of geomaterials, which accurately describes the evolution of the Mohr envelope of geomaterials. The FCFC can well characterize the nonlinear strength of geotechnical materials, enriching the failure criteria for geomaterials.更多还原