This paper presents a framework of the closest point projection method (CPPM) based on the unified hardening (UH) model. The UH model based on the Cam-clay model and the concept of the subloading yield surface was rewrote as a concise form of classical elasto-plastic model. Then the CPPM algorithm combining the exact elastic property and the spatially mobilized plane (SMP) strength criterion by the transformed stress method could be conveniently derived for the numerical implementation of the UH model. According to this algorithm, the consistent tangent operator corresponding to the final stress state of the integration increment was deduced formally. And the mean stress probed by the elastic predictor was avoided to be negative or zero for the usage of exact elastic property. Eventually, the accuracy, robustness and efficiency of the proposed integration scheme were demonstrated by the numerical examples including the boundary value problems of the single integral point and multi-elements of geotechnical engineerings, which was respectively compiled as the single integral point program and the user defined subroutine (UMAT) of the commercial finite element program ABAQUS.

本文提出了一种基于统一硬化（UH）模型的最近点投影方法（CPPM）的框架。改写了基于凸轮粘土模型和超载屈服面概念的UH模型，将其作为经典弹塑性模型的简明形式。然后，可以方便地导出通过转换应力法将精确的弹性特性与空间动员平面强度准则相结合的CPPM算法，以用于UH模型的数值实现。根据该算法，正式推导了与积分增量的最终应力状态相对应的一致切线算子。而且，对于使用精确的弹性属性，避免了由弹性预测器探测到的平均应力为负或零。最终，准确性