Polymorphic uncertainty modeling, evaluation and quantification for fluid saturated soil and earth structures

在土体结构的尺寸确定和评估中，主要的困难不在于提供合适的确定性物理计算模型，而在于如何处理关于材料参数、初始条件和边界条件的模糊数据。为此，需要有效的数值和概率工具。在土结构中，土的非线性行为和时变的微结构，例如在侵蚀过程中，额外地增加了可靠的设计。其后果是不可预见的损害或不经济的规模。因此，该项目的目标是发展数值和概率方法，以改进具有不确定土和土结构特性的结构的设计。由于材料参数的离散性或不完备性、初始条件和边界条件以及建模和数值计算的不准确性，导致了多态不确定性(PU)。作为第一个资助期的延伸，该模型被扩展到描述典型的土体破坏机理，包括非线性膨胀、塑性和侵蚀过程。基于SPP1886第一个资助期的结果，对TPM的变分敏感性分析(VSA)及其通过局部和全球影响分析进行的可解释性评价将被用作概率方法的先验知识。因此，可以实现贝叶斯灵敏度分析的改进。此外，在蒙特卡罗(MC)分析中，VSA将大大缩减要研究的参数空间，此外，还使用模糊算法对认知不确定性进行充分建模。所有方法的结合应结合各自的优势，为PU的量化提供一个整体模型。计算效率可以通过克立格方法来提高，这是一种元模型，可以减少分析所需的评估数量。采用离散经验插值法(DEIM)的模型约简法(MOR)加速单项评价，最终形成统一的数字化工具，可灵活、高效地用于土体结构数值设计中不确定数据的决策。为此，必须解决不同程序和编程语言之间的接口问题。

In the dimensioning and assessment of earth structures, the main difficulties lie less in providing a suitable deterministic physical calculation model, but in dealing with fuzzy data on material parameters, initial and boundary conditions. For this purpose efficient numerical and probabilistic tools are needed. In earth structures the coupled non-linear behavior of the soil and the time-varying microstructure, e. g. in erosion processes, additionally aggravate a reliable design. The consequences are unforeseen damage or uneconomic dimensions. The aim of the project is therefore the development of numerical and probabilistic methods for the improved design of structures with uncertain properties of soil and earth structures. The polymorphic uncertainties (PU) result from the scatter or incompleteness in the material parameters, the initial and boundary conditions and inaccuracy of the modeling and numerical calculation.The multi-physical soil response behavior is described in this project by means of the Theory of porous Media (TPM) and numerically evaluated within the framework of the finite element method (FEM) for specific initial boundary value problems. As an extension to the first funding period, the model is extended to describe typical mechanisms of soil failure, including the phenomena of non-linear expansion, plasticity and erosion processes. As representative benchmark studies tectonic disorders as well as the hydraulic ground failure will be investigated.Based on the results of the first funding period of the SPP1886, the variational sensitivity analysis (VSA) for the TPM and its well interpretable evaluation by the local and global impact analysis shall be used as a priori knowledge for probabilistic methods. Thus, an improvement of the Bayesian sensitivity analysis can be achieved. Furthermore, the parameter space to be investigated is to be considerably reduced in advance by the VSA in a Monte Carlo (MC) analysis.In addition, fuzzy arithmetic is used to adequately model epistemic uncertainties. The combination of all approaches should combine their strengths and provide a holistic model for PU quantification. The computational efficiency can be improved by the Kriging approach, a meta-model that reduces the number of evaluations necessary for an analysis. The individual evaluations are accelerated by a model reduction method (MOR) using the discrete empirical interpolation method (DEIM).Finally, a uniform digital tool will be created, which can be flexibly and efficiently used for decision making on uncertain data for the numerical design of soil and earth structures. For this, interface problems between the different programs and programming languages have to be solved.