Polymorphic uncertainty modeling of heterogeneous thermo-hydro-mechanical coupled systems under vague assumptions of parameter correlations

由于新型轻质建筑概念的发展，具有异质材料特性的新型混合材料和建筑变得越来越重要。此外，在现有的工程建设中，许多自然材料和技术材料表现出不均匀的材料分布，例如典型的地学材料或骨料-基质材料，在多尺度下对其进行细观和微观处理。在预测模拟期间，材料行为的建模可以通过估计上界和下界或通过应用多维随机场来完成。在多场情况下，例如耦合的热-水-机械系统，如水坝、堤坝或底土沉积物，存在一系列可以通过随机场建模的敏感材料参数。通常，这些场表现出一定的相关性，例如，在劣化材料的区域中，透水性可能增加，而机械刚度和强度降低。由此产生的问题是，如果这也对其他材料性能产生影响，以及在这种情况下如何有效地考虑相互依赖性。在给定的建议中，应推导出一种通用方法，该方法允许基于多态不确定性模型生成多个应用程序的随机场，但是，不同场及其模型参数的相互依赖程度并不完全清楚。因此，该提案包括多态不确定性模型的开发，分析和应用，该模型捕获了材料特性的随机变化性，并提供了有关其相关性和相关长度的模糊信息。该方法计划应用于以多物理现象为主的土木和岩土工程结构的可靠性评估。定性增益应用多态不确定性模型相比，经典的单态模型将进行分析。作为第二个供资期的展望，可能会处理相关的逆问题，例如如何确定多态不确定性模型中的系统参数，以及如何评估已确定参数中的不确定性。 因此，我们的方法满足SPP 1886公告的复合体B和C。

New hybrid materials and constructions with heterogeneous material properties gain increasing importance due to the development of new light-weight building concepts. Furthermore, many natural and technical materials applied show a heterogeneous material distribution in the existing engineering constructions.Examples are typical geoscience materials or aggregate-matrix materials w.r.t their meso- and microscopic treatment in a multi-scale approach. The modeling of the material behavior during forecast simulations can either be done by the estimation of upper and lower bounds or by the application of multi-dimensional random fields. In multi-field situations, e.g. coupled thermal-hydro-mechanical systems like dams, dikes or subsoil deposits, there are a series of sensitive material parameters which can be modeled via random fields. Often, these fields exhibit a certain correlation, e.g. in regions of deteriorated material the hydraulic permeability might be increased while the mechanical stiffness and strength are reduced. The question arising is, if this has also effects on other material properties and how the interdependency can be taken effectively into consideration in this case. In the given proposal, a general methodology shall be derived which allows, based on a polymorphic uncertainty model, the generation of random fields for multi-physic applications, where however, the degree of interdependence of the different fields and their model parameters is not fully known. Therefore, the proposal comprises the development, analysis and application of a polymorphic uncertainty model, which captures the random variability of the material properties with vague information concerning their correlations and correlation lengths. The methodology is planned to be applied for the assessment of the reliability of structures in civil and geotechnical engineering which are dominated by multi-physical phenomena. The qualitative gain applying polymorphic uncertainty models compared to classical uni-morphic models will be analyzed. As outlook for a second funding term, the related inverse problems might be tackled, e.g. how to determine parameters of the systems in a polymorphic uncertainty model and how to asses uncertainties in the identified parameters. Therefore, our approach meets the complexes B and C of the announcement of the SPP 1886.