Abstract:

When solving Biot’s consolidation equations, different researchers used different continuum equations. The methods Biot M.A. used to deduce the consolidation equations are firstly reviewed. It can be seen that some mistakes exist in the strain energy density function. In order to derive the correct form of continuum equation, two methods are used here. Firstly, based on the analysis of the deformation of the representative element volume (REV) of the soil, a fluid continuum equation which can take the compressibility of grain and fluid into account is derived. Secondly, based on the method Biot M.A. used with modified strain energy density, another continuum equation is derived. The continuum equations deduced from the two methods listed above are found to be equivalent. In addition, the equations are compared to the continuum equation derived by other researchers based on mass conservation law, and they are found to be coincident. Then, the right form of fluid continuum equation is proved and the result can provide theoretical support to consolidation calculation.

Key words: Biot consolidation equation, continuum equation, strain energy density, variable mass system