Abstract:Recently,localized planar zones of deformation have been discovered in high-porosity rock,which are called compaction bands,shear bands and dilation bands. It is one of the most concerned issues in the research of rock physical and constitutive relations. The research of localized deformations has practical significance in the storage of water,oil,nuclear wastes,the disposal of garbage and environmental pollution. It is also helpful for the research of geological structure,engineering geology,and engineering of soils and rocks. The compaction band and shear band theories,based on localized bifurcation,are introduced. The conditions for band formation and discrimination in porous rocks and the critical hardening modulus for compaction bands,shear bands and dilation bands are also introduced. The compaction bands and shear bands on an elliptic yield cap are introduced based on the cap model. They are close related to the s-e curves. Under low confining pressure,the first zero modulus point,i.e. the shelf,corresponds to the compaction band,or the volumetric yield surface of cap model. When loading continues,the s-e curve keeps ascending until the sample hardens. The second zero modulus point in the s-e curve,i.e. the peak of the s-e curve,corresponds to the shear failure,or the shear yield surface of the cap model. Mass experimental results obtained from axisymmetric compression tests on sandstones with different grain scales and porosities can be described by the same cap model.