The paper deals with formulation and numerical implementation of anisotropic strength condition for micro layered rock. Periodically layered two–constituent microstructure is considered. The failure criterion of the constituents is assumed to be governed by Drucker-Prager strength condition. The macroscopic criterion is derived based on the micro-mechanics approach. It appears that a microstructure failure function can be satisfactory described by the conjunction of Jaeger critical plane condition and Pariseau anisotropic criterion. The formulation derived is then implemented into the commercial codes FLAC and FLAC3D. Numerical integration scheme, i.e. an elastic predictor and a plastic corrector of the failure function proposed are discussed in details, in the paper. Efficiency and numerical stability of the model proposed are verified against a series of numerical examples. The proposed model is also compared with "Ubiquitous Joints": a classical Jaeger critical plane approach available in FLAC environment. The presented results show that the model in some cases provides more precise description of micro-layered rock then Jaeger criterion.
In many rocks one can recognize a characteristic pattern: two or more constituents appear in a form of thin, periodically repeating layers. These rocks are sometimes referred as "micro layered". The microstructure especially often occurs in sedimentary rocks: sandstone, claystone and schist are the most typical examples. The main consequence of the presence of micro layers in the material is its strong anisotropy in both elastic and inelastic range.
The micro layered rocks are usually considered in civil engineering practice as a problematic case for foundations. From the other hand necessity of structures foundation in such condition continues to grow. New structures are usually designed based on numerical calculations performed with some commercial codes. Identification and implementation of adequate, numerically efficient model of micro layered rock to one of these codes is an important and complex task.
A number of researchers focused on formulating a macroscopic anisotropic strength criterion for micro layered rocks based, mainly, on a phenomenological approach. Brief review of some of these criteria is presented in a work of Duveau et al. (1997). Two of these criteria are especially worth noting, i.e. Pariseau criterion (Pariseau 1972) which is an extension for the case of anisotropy of Drucker-Prager isotropic criterion, and Jaeger criterion (Jaeger 1960) which can be interpreted as a basis of a so-called critical plane approach.
The above mentioned Jaeger criterion is implemented as yield function for one of the plastic models available in FLAC and FLAC 3D codes. The model referred as "Ubiquitous Joints" is one of the few most popular models of micro layered rock.