摘要
天然固体材料例如岩石或者土体材料都具有显著的各向异性性质,而各向异性性质对于岩石或者土体材料的破坏规律以及变形性质影响无法忽视。从以下3方面对各向异性性质影响破坏规律给出了数学描述。(1)提出了一种广义非线性破坏准则-RMNLD准则,在偏平面上可描述接近von Mises到SMP准则等一系列破坏曲线的广义准则,在子午面上采用幂函数来描述静水压力的非线性性质。(2)利用组构张量来表述岩石或者土体材料在三维空间中的颗粒排列特性,并将组构张量与普通应力量通过所提出的联合公式表述为联合应力量,将原有普通应力替换为联合应力量,可以用来表达各向异性RMNLD准则。(3)在偏平面上建立由各向异性RMNLD准则到各向同性von Mises准则的映射关系,具体转换过程分为2步,第1步先将各向异性RMNLD准则转换为各向同性RMNLD准则,建立原生各向异性到原生各向同性应力空间的关系,这由普通应力量到联合应力量的映射关系来实现,第2步将各向同性应力空间中的RMNLD准则转换为von Mises法则,这由偏平面上曲边三角形与圆形极半径之比作为对偏应力分量放大系数来实现。通过岩石与黏土,砂土的破坏试验数据以及应力-应变关系测试及所提破坏准则和变换应力方法预测对比,对比结果验证了所提各向异性RMNLD准则以及变换应力方法的正确性以及适用性。
Natural solid materials,including rocks and soils,are characterized with remarkably anisotropic properties,and the effect of anisotropy of rocks or soils on their failure laws and deformation behaviors shall not be ignored.In this work,a mathematical description of the failure laws of rocks or soils affected by their anisotropic behaviors is provided in view of the following three aspects.①A generalized nonlinear failure criterion,RMNLD,is proposed,and the proposed failure criterion can be used to describe a series of failure curves such as von Mises and SMP criteria on the deviatoric plane and describe the nonlinear behavior of hydrostatic pressure on the meridian plane with the power function.②The fabric tensor is applied to describing the particle arrangement characteristics of rocks or soils in three-dimensional space,the fabric tensor and ordinary stress are combined and expressed as a joint stress by applying the proposed joint formula,and the anisotropic RMNLD criterion can be expressed by replacing the native ordinary stress with the joint stress.③The mapping relationship from the anisotropic RMNLD criterion to the isotropic von Mises criterion on the deviatoric plane can be established.The mapping process can be divided into two steps.In the first step,by applying the mapping relationship between the ordinary stress and the joint stress,the anisotropic RMNLD criterion is converted to the isotropic RMNLD criterion,which further establishes the relationship between native anisotropy and native isotropic stress space.In the second step,by taking the ratio of the radius of the curved triangle to the polar radius of circle on the deviatoric plane as the amplification factor of the deviator stress component,the RMNLD criterion in the isotropic stress space is converted to the von Mises criterion.Consequently,the correctness and applicability of the proposed anisotropic RMNLD criterion and the proposed stress transformation method can be verified by comparing the failure test data of rock,clay and sand,and the measured stress-strain relationships with the predicted results from the proposed failure criterion and the stress transformation method.
作者
万征
刘媛媛
江培华
Wan Zheng;Liu Yuanyuan;Jiang Peihua(North China Institute of Science and Technology,Langfang 065201,China)
出处
《土木工程学报》
北大核心
2026年第2期126-144,共19页
China Civil Engineering Journal
基金
国家自然科学基金(42177170,52004090)
河北省自然科学基金(E2021508031)。
关键词
破坏
变形
组构张量
原生各向异性
应力-应变关系
failure
deformation
fabric tensor
native anisotropy
stress strain relationship
