Reformulation and Extension of an Elastoplastic Constitutive Model for Sandy Soils accounting for Cycling Loading and Large Deformations

现代岩土工程问题的精确和有效的数值模拟需要复杂的土体本构模型，其中包括有限应变理论和复杂的循环加载机理。为此，过去已经开发了很多模型。特别是对于沙子，现有的模型都不能被认为是一个彻底的解决方案。提供最大潜力的模型之一是CSSA模型(临界状态沙子模型)。本课题的研究解决了其不足之处。该研究项目旨在将关于任意曲线坐标系的有限应变理论纳入到模型中。此外，还增强了模型对平均有效应力变化的加载机制(帽机制)，以考虑循环加载。进一步发展的结果是ECSSA-Model(扩展的CSSA-Model)。在该项目已经完成的第一阶段期间，已经从数学和机械的角度制定了ECSSA模型。此外，还给出了它在大变形问题数值方法中的实现方法。此外，还为ECSSA-Model的验证和测试做了准备工作。在本申请将考虑的项目第二阶段，对再造砂样进行了实验室测试。通过一系列排水循环三轴压缩试验，研究了恒应力比循环压缩条件下砂土的特性。这是完成对ECSSA-Model封顶机制的增强所必需的。此外，还进行了单调和循环三轴试验，以确定ECSSA模型的试验砂的模型常数。由于ECSSA模型是在有限变形理论的基础上发展而来的，所以在实验室进行了与有限变形理论相一致的试验，并在实验工作的基础上完成了ECSSA模型循环盖机构的开发。随后，确定了试验砂的模型常数，并利用室内试验结果对模型进行了验证。在研究项目的最后一步，通过将ECSSA-Model应用于具有循环荷载和大土体挠度的边值问题，进一步验证和测试了ECSSA-Model。对于这里要研究的问题，存在来自模型试验或其他模拟方法的参考解决方案。

Precise and efficient numerical simulation of contemporary geotechnical problems requires elaborate constitutive models for the soil which incorporate the finite strain theory as well as sophisticated mechanisms for cyclic loading. To this end, a lot of models have been developed in the past. Particularly for sands none of the existing models can be considered an exhaustive solution. One of the models which offer the greatest potential is the CSSA-Model (Critical State Sand Model). Its shortcomings are resolved by this research project. The research project aims at incorporating the finite strain theory with regard to arbitrary curvilinear coordinate systems into the Model. Furthermore, the model's loading mechanism for changes of the mean effective stress (cap mechanism) is enhanced to account for cyclic loading. The outcome of the further development is the ECSSA-Model (Extended CSSA-Model). During the already finished first phase of the project the ECSSA-Models has been formulated mathematically and mechanically. Moreover, its implementation in the context of numerical methods for large deformation problems has been worked out. In addition, preparations for the validation and testing of the ECSSA-Model have been done.During the second phase of the project, which is to be considered in the present application, laboratory tests on reconstituted sand samples are conducted. By a comprehensive series of drained cyclic triaxial compression tests the behavior of sand under cyclic compression at constant stress ratio is investigated. This is necessary to finish the enhancement of the cap mechanism of the ECSSA-Model. Furthermore, monotonic and cyclic triaxial tests are conducted to determine the model constants of the test sand for the ECSSA-Model. Since the ECSSA-Model evolves out of the finite deformation theory, the laboratory tests are carried out and evaluated in a manner consistent with that theory.On the basis of the experimental work the development of the ECSSA-Model's cyclic cap mechanism is finalized. Subsequently the model constants of the test sand are determined and the model is validated by means of laboratory test results. In the last step of the research project, the ECSSA-Model is further validated and tested by applying it to boundary value problems that feature cyclic loading and large soil deflections. For the problems that are to be investigated here reference solutions from model tests or other simulation approaches exist.