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

由于新型轻量化建筑概念的发展，具有异质材料特性的新型混合材料和结构变得越来越重要。此外，许多天然材料和技术材料在现有的工程结构中表现出非均匀的材料分布。例如典型的地球科学材料或聚集体基质材料及其多尺度的细观和微观处理。在预测模拟中，材料行为的建模可以通过估计上界和下界来完成，也可以通过应用多维随机场来完成。在多场情况下，如热-水-力学耦合系统，如大坝、堤防或底土沉积物，存在一系列敏感的材料参数，可以通过随机场建模。通常，这些场表现出一定的相关性，例如在材料变质的区域，水力渗透率可能会增加，而机械刚度和强度则会降低。由此产生的问题是，这是否也对其他材料特性产生影响，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，应推导出一种通用的方法，该方法允许基于多态不确定性模型，为多物理场应用生成随机场，然而，不同领域及其模型参数的相互依赖程度尚不完全清楚。因此，该提案包括开发，分析和应用一个多态不确定性模型，该模型可以捕获材料特性的随机变异性，并提供有关其相关性和相关长度的模糊信息。该方法计划应用于土木和岩土工程中多物理现象主导的结构可靠度评估。将分析应用多态不确定性模型与经典单态模型的定性增益。作为第二个资助期的展望，相关的逆问题可能会得到解决，例如如何在多态不确定性模型中确定系统的参数以及如何评估所识别参数中的不确定性。因此，我们的方法符合SPP 1886公告的配合物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.