Computational Geomechanics. Manuel Pastor

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2 Equations Governing the Dynamic, Soil–Pore Fluid, Interaction

2.1 General Remarks on the Presentation

      In this chapter, we shall introduce the reader to the equations which govern both the static and dynamic phenomena in soils containing pore fluids. We shall divide the presentation into three sections: Section 2.2 will deal with soil, or indeed any other porous medium, saturated with a single fluid. This most common problem contains all the essential features of soil behavior and the equations embrace and explain the vast majority of problems encountered in practice.

      We shall show here how the dynamic equations, which are essential for the study of earthquakes, reduce to those governing the quasi‐static situations of consolidating soils and indeed to purely static problems without modification. This feature will be used when discretization is introduced and computer codes are derived since a single code will be capable of dealing with most phenomena encountered in soil and rock mechanics.

      The limitations of the approximating simplification are discussed in Section 2.2 by using a simple linearized example and deriving conclusions on the basis of an available analytical solution. The same discussion will show the domain of the validity of the assumptions of undrained and fully drained behavior.

      In the same section, we shall introduce a simplification which is valid for the treatment of most low‐frequency phenomena – and this simplified form will be used in the subsequent Section 2.3 dealing with partially saturated soil in which the air pressure is assumed constant and also, finally, in Section 2.4 dealing with simultaneous water and airflow in the pores.

      The notation used throughout this chapter will generally be of standard, tensorial form. Thus:

       Alternatively,