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

在土方结构的尺寸和评估中，主要的困难不在于提供一个合适的确定性物理计算模型，而在于处理材料参数、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，土的非线性耦合行为和随时间变化的微观结构，例如在侵蚀过程中，也加剧了可靠的设计。其后果是不可预见的损害或不经济的规模。因此，该项目的目的是发展数值和概率方法，以改进具有不确定性质的土壤和土结构的结构设计。多态不确定性是由于材料参数的分散或不完备、初始条件和边界条件以及建模和数值计算的不准确性造成的。本项目利用多孔介质理论（TPM）描述了土体的多物理态响应行为，并在有限元法（FEM）的框架内对具体的初始边值问题进行了数值计算。作为第一个资助期的延伸，该模型被扩展到描述典型的土壤破坏机制，包括非线性膨胀、塑性和侵蚀过程。作为代表性的基准研究，将对构造紊乱和水力地面破坏进行研究。基于SPP1886第一个资助期的结果，将TPM的变分敏感性分析（VSA）及其局部和全局影响分析应使用的可解释性评价作为概率方法的先验知识。从而实现贝叶斯灵敏度分析的改进。此外，在蒙特卡罗（MC）分析中，要研究的参数空间要提前被VSA大大减小。此外，还利用模糊算法对认知不确定性进行了充分的建模。所有方法的结合应结合其优势，为PU量化提供一个整体模型。Kriging方法可以提高计算效率，这是一种元模型，可以减少分析所需的评估次数。采用离散经验插值法（DEIM），采用模型约简法（MOR）加速个体评价。最后，将创建一个统一的数字工具，该工具可以灵活有效地用于土壤和土壤结构数值设计的不确定数据决策。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.