This paper presents numerical treatments of elastoplasticity relations for a previously developed critical state two-surface plasticity model and its implementation into a bespoke finite element code as well as the commercial software Abaqus via the user defined subroutine, UMAT. The model is implemented with an efficient integration scheme based on the explicit modified Euler scheme with automatic substepping and error control. Validation of the implemented model is assessed through simulation of several laboratory tests comprising a variety of initial states and loading conditions followed by a study on the accuracy and efficiency of the integration scheme. Subsequently, the model is employed to analyse some sophisticated boundary value problems involving finite deformations, inertia effects, soil-structure interactions and saturated porous media. The constitutive model captures particular features of clay behaviour, such as the prediction of strain rate dependence, small-strain stiffness degradation, the development of residual strength at very large shear strains and stress anisotropy. The effects of these features on the behaviour of two important geotechnical problems – including pipe-seabed interaction under lateral motion and dynamically installed anchors – are specifically investigated using two advanced finite deformation schemes: one based on the Arbitrary Lagrangian Eulerian (ALE) method and another on the Particle Finite Element Method (PFEM). The study illustrates the robustness of the proposed integration scheme and successful application of the soil model, indicating that the use of such complex soil models may be useful for realistic analyses of geotechnical problems.

本文介绍了对先前开发的临界状态双表面塑性模型的弹塑性关系的数值处理，以及通过用户定义的子程序 UMAT 在定制的有限元代码和商业软件 Abaqus 中的实现。该模型采用基于显式修改欧拉方案的高效集成方案实现，具有自动子步进和误差控制。通过模拟包括各种初始状态和负载条件的几个实验室测试来评估实施模型的验证，然后研究集成方案的准确性和效率。随后，该模型用于分析一些复杂的边界值问题，包括有限变形、惯性效应、土-结构相互作用和饱和多孔介质。本构模型捕捉粘土行为的特定特征，例如应变率相关性的预测、小应变刚度退化、在非常大的剪切应变和应力各向异性下残余强度的发展。这些特征对两个重要岩土工程问题的影响——包括横向运动和动态安装锚下的管道-海床相互作用- 使用两种先进的有限变形方案进行专门研究：一种基于任意拉格朗日欧拉 (ALE) 方法，另一种基于粒子有限元方法 (PFEM)。该研究说明了所提出的集成方案的稳健性和土壤模型的成功应用，表明使用这种复杂的土壤模型可能有助于岩土工程问题的实际分析。