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.
