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

由于新的轻质建筑概念的发展，具有不同材料性能的新型混合材料和结构越来越受到重视。此外，许多自然和技术材料在现有的工程结构中表现出不均匀的材料分布，例如典型的地学材料或集料基质材料，它们的细观和微观处理是多尺度的。在预测模拟过程中，材料行为的建模可以通过上下限的估计或通过应用多维随机场来完成。在多场情况下，如大坝、堤坝或地基沉积物等热-水-力耦合系统，存在一系列敏感的材料参数，可以通过随机场进行建模。通常，这些场表现出一定的相关性，例如，在劣化材料的区域，水力渗透性可能增加，而机械刚度和强度降低。出现的问题是，这是否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到这种相互依存关系。在给定的提案中，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用于多物理应用的随机场，然而，其中不同场及其模型参数的相互依赖程度并不完全已知。因此，该提案包括开发、分析和应用多态不确定性模型，该模型利用关于材料属性的相关性和关联长度的模糊信息来捕捉材料属性的随机变异性。该方法计划应用于土木工程和岩土工程中以多物理现象为主的结构的可靠性评估。分析了应用多态不确定性模型与经典单态模型相比的定性收益。作为对第二个供资期限的展望，可能会解决相关的反问题，例如如何在多态不确定性模型中确定系统的参数，以及如何评估已确定参数中的不确定性。因此，我们的方法符合宣布SPP 1886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.