Page 53 - Numerical Analysis and Modelling in Geomechanics
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34 A.A.JAVADI
Figure 2.3 Typical tunnel geometry and the boundary conditions.
(2.4)
and Boyle’s law expresses the relationship between the pressure, volume and
temperature of ideal gases. For an isothermal condition, Boyle’s law can be
written as:
(2.5)
In the above equations, ρ is the mass density of air, q is the vector of specific
discharge, ≥ is the gradient operator, K is the permeability tensor, γ is the unit
weight of the fluid, u is the pore air pressure, and Φ is the potential function,
a
defined as:
(2.6)
Combining equations (2.3), (2.4) and (2.6), the governing equation can be
obtained as:
