岩土塑性力学的新进展——广义塑性力学

New development of geotechnical plastic mechanics-generalized plastic mechanics

多数岩土工程都处于弹塑性状态 ,因而岩土塑性在岩土工程的设计中至关重要。本文首先简要回顾了岩土塑性的发展过程 ,分析了经典塑性力学用于岩土类材料存在的问题 ,指出其采用的 3个不符合岩土材料变形机制的假设。放弃这 3条假设 ,从固体力学原理直接导出广义塑性位势理论 ,从而将经典塑性力学改造成更一般的塑性力学———广义塑性力学。广义塑性力学采用了塑性力学中的分量理论 ,能反映应力路径转折的影响 ,克服了塑性应变增量方向与应力增量无关的错误 ;要求屈服面与塑性势面对应 ,而不要求相等 ,避免了采用正交流动法则引起过大剪胀等不合理现象 ,也不会产生当前非关联流动法则中任意假定塑性势面引起的误差。文中给出了广义塑性力学的屈服面理论、硬化定律和应力—应变关系 ,并在应力增量分解的基础上 ,建立了考虑应力主轴旋转的广义塑性位势理论 ,从而可求出应力主轴旋转产生的塑性变形。通过分析屈服面的物理意义 ,表明屈服条件是状态参数 ,它与应力状态、应力历史及材性等状态量有关 ;同时也是试验参数 ,只能由试验给出。通过实际应用 ,表明广义塑性力学不仅可以作为岩土材料的建模理论 ,而且还可以应用于诸如极限分析等土力学的诸多领域 ,具有广阔的应用前景。

Geotechnical plasticity plays an important role in the design of geotechnical engineering because most of them are in an elasto plastic state. In this paper, the development of geotechnical plasticity is reviewed and some problems of applying the classic plastic mechanics to geomaterials are analyzed, and then its three hypotheses unfitting to the deformation mechanism of geomaterials are pointed out. By giving up these three hypotheses, a generalized plastic potential theory can be obtained from solid mechanics directly, and then the traditional plastic mechanics can be changed to a more generalized plastic mechanics, namely generalized plastic mechanics (GPM). The GPM adopts the component theory as theoretical base, so it can reflect the influence of transition of stress path, and eliminate the mistake that the direction of plastic strain increments is independent of the stress increment; it requires that the yield surface must correspond to but not coincide with the plastic potential surfaces,then the unreasonable phenomena such as excessive dilatancy caused by the normality of flow rule,and the error caused by the arbitrarily assumed plastic potential surfaces can be avoided. The yield surface theory, hardening rules and stress-strain relations of GPM are given. Based on the decomposition of stress increments, a GPM including the rotation of principal stress axes can be established, and the plastic deformation caused by the rotation of principal stress axes can also be calculated. It is pointed out that the yield condition is a state parameter, which is relevant to stress state and stress history as well as the properties of material. On the other hand, the yield condition is also a test parameter, and it can only be given by test. After the practical application, it is shown that the GPM can not only be applied to the modeling theory of geomaterials but also to other fields of geomechanics such as limit analysis.