Computational Simulation of Stochastic Soils

本研究涉及一种方法的发展，将概率论纳入弹塑性计算地质力学。特别令人感兴趣的是不确定的土壤性质和土壤的非均匀性对（平均）力学响应的影响。目前最先进的固体和结构（由岩土材料、混凝土或钢材制成）的非弹性模拟只考虑了荷载（地震和风）的概率方法，但非常重要的（在许多情况下，主要的）不确定性来源是材料特性。对于土壤材料来说尤其如此。提出发展的动机有以下几个原因：-现代建筑法规越来越多地基于可靠性方法。基于负载和阻力系数的代码就是一个很好的例子。法律方面的考虑要求使用概率框架（可靠性分析，如在核工业和海上工业中发现的那样）对岩土工程对象的行为进行评估。不幸的是，岩土工程对象行为的高级评估（数值模拟）仍然几乎完全是确定性的；-对象所有者越来越多地使用概率理论来决定开发新，升级或修复现有对象的最佳行动方案。关于工作范围、资金和日程安排的关键决策是使用概率理论做出的。在决策过程中使用的实际业绩评估仍然几乎完全是确定的；-岩土模拟概率框架的持续发展将提供一种合理的方式来解决我们对模拟行为的信心（或缺乏信心）。例如，拟议的开发将使工程师能够证明需要更多（统一的）材料特性数据，开发新的场地特征技术，并设计（可能）达到最佳性能的基础和堤防系统；建议的发展将基于最先进的概率框架，以Fokker-Planck方程的数值解为中心，它在弹塑性理论中的一致使用，以及在有限元公式中使用Karhunen-Loeve展开和Galerkin方法的多项式混沌展开。该项目的智力优势在于首次应用了弹塑性建模和模拟的概率发展。特别重要的是将已开发的方法应用于表现出高度非均匀性和材料性质高度不确定的土壤。岩土工程问题的建模和模拟（例如岩土地震工程，边坡的静态和动态稳定性，水坝和堤坝，浅基础和深基础的静态和动态行为）是计算力学中最复杂的问题之一。将概率方法应用于非均匀土和不确定土参数，将在适当的概率框架下重新定义这些问题。它还可以减少认知不确定性的数量，减小认知不确定性域的大小。预计拟议研究的更广泛影响将比岩土工程广泛得多。材料性质的空间变异性和不确定性现象在所有材料中都存在。将上述现象纳入高级数值模拟的适当制定和实施（在拟议项目期间开发，实施，验证和验证）将对机械，生物医学，材料，航空航天以及土木工程的其他领域产生影响。

This research deals with the development of a methodology to incorporate probabilistic theory into elastic-plastic computational geomechanics. Of special interest are the influence of uncertain soil properties and the non-uniformity of soil on the (average) mechanical response. Current state-of-the-art in inelastic simulations of solids and structures (made of geomaterials, concrete or steel)take into account probabilistic approach to loads only (earthquake and wind) but the very important (and in many cases, the main) source of uncertainty is in material properties. This is particularly true for soil materials. The proposed development is motivated by several reasons: - Modern building regulations are increasingly being based on reliability methods. Load and Resistance Factor based codes are a good example. Legal concerns require that assessment of geotechnical object behavior be made using probabilistic framework (reliability analysis, as found in nuclear and offshore industry). Unfortunately, advanced assessment of behavior of geotechnical objects (numerical simulations) are still almost exclusively done deterministically; - Object owners increasingly use probabilistic theories to decide on best course of action for developing new, upgrading or repairing existing objects. Crucial decisions on the extent of work, financing and scheduling are made using probabilistic theories. The actual performance assessment used in that decisions process is still almost exclusively deterministic; - Consistent development of probabilistic framework for geotechnical simulations will provide a rational way to address our confidence (or lack of one) in simulated behavior. For example, proposed development will empower engineers to demonstrate the need for more (uniform) data on material properties, development of novel site characterization techniques and to design the foundation and levee systems that (probably) achieve best performance; Proposed development will be based on state-of-the-art probabilistic framework, centered on numerical solutions to Fokker-Planck equation and it's consistent use in theory of elasto-plasticity and to the use of Karhunen-Loeve expansion and Galerkin method with polynomial chaos expansion for the Finite Element Formulation. The intellectual merit of proposed project is in first application of state of the art probabilistic developments for elastic-plastic modeling and simulations. Of particular importance is the application of developed methodology to soils, which exhibit high degree of non-uniformity and where material properties are highly uncertain. Modeling and simulations of geotechnical problems (for example geotechnical earthquake engineering, static and dynamic stability of slopes, dams and levees, static and dynamic behavior of shallow and deep foundations) are some of the most complex problems in computational mechanics. Application of probabilistic methodology to non-uniform soils and uncertain soil parameters will recast these problems in appropriate probabilistic framework. It will also reduce the amount of epistemic uncertainty and decrease the size of aleatory uncertainty domain. The broader impact of proposed research is expected to be much wider than in geotechnical engineering. The phenomena of spatial variability and uncertainty of material properties is present in all materials. The appropriate formulation and implementation (developed, implemented, verified and validated during proposed project) that incorporate above phenomena into advanced numerical simulations will have impact in mechanical, biomedical, materials, aerospace, as well as other areas of civil engineering.