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Numerical integration of an elasto-plastic critical state model for soils under unsaturated conditions

机译：不饱和条件下土壤弹塑性临界状态模型的数值集成

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This paper presents the complete set of incremental equations for the numerical integration of the Glasgow Coupled Model (GCM) and a comprehensive algorithm for its numerical integration. The incremental formulation proposed is expressed in terms of strain and suction increments (i.e. strain-driven) and defines an initial value problem (IVP) that can be solved once the initial state and the pair of increments of the driven variables are known. The numerical integration of this IVP is carried out by extending to unsaturated condition, the wellknown explicit substepping formulation with automatic error control widely used for saturated soils. A notable feature of the substepping integration scheme presented is that it integrates simultaneously the model equations for both mechanical and water retention responses. Hence, the estimate of the local truncation error to automatically adjust the size of the integration step is not only affected by the local error in stresses and mechanical hardening parameter (as in a saturated soil model) but, additionally, by the local error incurred in the integration of the water retention relations (i.e. degree of saturation and water retention hardening parameter). The correctness of the integration scheme is then verified by comparison of computational outcomes against analytical/reference solutions.
机译：本文介绍了Glasgow耦合模型（GCM）的数值集成的完整增量方程，以及一种综合算法的数值集成。提出的增量制剂以应变和吸入增量（即应变驱动）表示，并定义一旦初始状态和驱动变量的一对增量可以解决的初始值问题（IVP）是已知的。该IVP的数值集成通过延伸到不饱和条件，是具有自动误差控制的众所周知的显式代入配方，广泛用于饱和土壤。所呈现的子电平积分方案的一个值得注意的特征是它同时集成了机械和水保留响应的模型方程。因此，局部截断误差自动调整集成步骤的尺寸的估计不仅受到应力和机械硬化参数（如饱和土壤模型中的局部误差的影响，而且通过局部误差水保留关系的整合（即饱和度和水保留硬化参数）。然后通过对分析/参考解决方案的计算结果进行比较来验证积分方案的正确性。

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