Manuel Pastor - Computational Geomechanics

and assuming isotropic permeability

(3.19b)

The summation range for the upper‐case indices will depend on the number of nodes with solid displacement and pore water pressure degrees‐of‐freedom (dofs), respectively.

Applying Green’s identity to the internal force term (first term on the left‐hand side)

Rearranging

(3.20)

The definition of the Bmatrix in Equation (3.21)is not needed in tensorial form.

(3.23b)

(3.24b)

(3.25b)

(3.26b)

(3.27b)

Neglecting source term and integrating by part the first part of the first term

Inserting the shape functions

(3.28b)

(3.29b)

(3.30b)

(3.31b)

(3.32b)

Equation (3.33)is scalar.

In this chapter, the governing equations introduced in Chapter 2are discretized in space and time using various implicit and explicit algorithms. They are now ready for implementation into computer codes. In Chapter 5, we shall address some special modeling aspects and in Chapters 6– 8, we shall show some applications for static, quasi‐static, and dynamic examples to illustrate the practical applications of the method and to validate and verify the schemes and constitutive models used.

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