Abstract: In order to obtain the volumetric constitutive relations of saturated porous media considering the deformation of component matrices, the volume strain of solid phase in saturated porous media was divided into solid volume fraction strain and solid matrix volume strain on the basis of mixture theory. By means of derivation and analysis of the conservation equation of volume deformation work, the deformation rules were revealed under small strain condition that Terzaghi effective stress determines uniquely the solid volume fraction strain and the solid matrix pressure determines uniquely the solid matrix volume strain, respectively. The double-stress principle was accordingly proposed, that was, Terzaghi effective stress and solid matrix pressure determined the volume deformation of solid phase in saturated porous media together. The double-stress principle degenerated into the effective stress principle when the compressibility of the solid matrix was neglected. On the basis of the above theoretical study results and the data of Lade and de Boer model test, the expression of nonlinear volumetric constitutive relations of saturated porous media was achieved in order to verify the feasibility and correctness of the above theory. Finally, based on the double stress variables model, the variation laws of Biot coefficient, pore pressure coefficient and void ratio with Terzaghi effective stress were discussed.

Key words: saturated porous media; constitutive relation; volume fraction strain; matrix volume strain; effective stress; double-stress principle