Non-Coaxial Multi-laminate model for anisotropic granular material and its numerical implementation

Non-coaxiality plays a key role in modelling of problems with significant stress rotation in soil mechanics. This will be more crucial in types of soils or granular materials with anisotropy. Many of the constituent rocks of oil and gas reservoirs are of the anisotropic type, so considering anisotropy in the study of oil reservoirs will have special significance. Neglecting to account for stress and strain non-coaxiality would result in errors and overestimating soil capacity. A mathematical solution is developed and applied within the framework of multi-laminate model, to deal with this issue. Selecting multi-laminate frame as the base of the model facilitates consideration of anisotropy with less mathematical effort. In addition, tracing fabric evolution may be much easier in this framework. Concept of stress and strain vector fields are introduced for shear components of planes, and in contrast to ancestor multi-laminate models, shear stress is calculated through this concept for each plane in the proposed model. Using this method, non-coaxiality may be considered on planes, and consequently the integrated result of plane stresses will be non-coaxial as well. Finally, to apply the model for greater problems, a code is developed to introduce the new model to FE program, Opensees. The program is implemented for analyzing an experimental plane-strain loading test of an anisotropic dense specimen of Toyoura sand. The results show a good agreement between theory and experiment.