Basic Formulation of Static and Dynamic Behaviour of Soil and other Porous Media

Abstract

Notation: We shall use throughout a ‘vectorial’ tensor notation for convenience in subsequent finite element manipulations. Thus strain and stress increments are written as

$${(d\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{\varepsilon } )^T} = (d{\varepsilon _x},d{\varepsilon _y},d{\varepsilon _z},d{\gamma _{xy}},d{\gamma _{yz}},d{\gamma _{zx}})$$

$${(d\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{\sigma } )^T} = (d{\sigma _x},d{\sigma _y},d{\sigma _z},d{\tau _{xy}},d{\tau _{yz}},d{\tau _{xz}})$$

and the equivalent of Kroneker delta is

$${\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{m} ^T} = (1,1,1,0,0,0)$$

Symbols occuring are defined in text.