Continuity hypothesis of soil mechanics and its application in modeling

In order to make up for the important theoretical defect of its lack in the soil mechanics, the continuity hypothesis is properly put forward on the basis of systematic reviews and studies on the continuity concept in multiple disciplines, and then the concept, category, attribute and modeling idea of the constitutive model for soils are clarified. The results show that the continuity hypotheses in the continuum mechanics and dynamics of fluids in porous media provide useful references for the continuity hypothesis in soil mechanics, but both have certain defects. The viewpoint and method in the theory of mixtures are suitable for describing the continuity of soils, and it can avoid the difficulties encountered in defining the porosity. The continuity is a relative concept. A research object can be regarded as a continuous medium when the external feature size is much larger than the internal feature size of the medium of which the research object is made. The existing constitutive models for soils are all based on the continuum mechanics and generally belong to phenomenological ones. The concept, category and modeling idea of the constitutive relation are clarified, that is, the constitutive relation is a mathematical model for the macro-properties of substances; The constitutive model for soils includes various aspects such as water retention, water permeability, gas permeability, heat transfer, yield, deformation, strength, meso-structure evolution, thermodynamic effects, phase transformation laws, etc., not merely limited to stress-strain relationship. For the studies on the constitutive relation of soils, the specific soil category should be highlighted, the main influencing factors should be grasped, and the mathematical model to solve the main problem should be established.