Map3D Thermal-Fluid Flow can be used to simultaneously solve steady state heat/fluid flow coupled to the stress analysis. The program is set up so that the user need only specify the temperature/head boundary conditions, then the coupled thermal/fluid flow stress problem is solved simultaneously. This feature is useful for the simulation of heating or cooling effects and drained or undrained response of soils.
The steady state thermal/fluid flow problem is solved according to Laplace's equation in three-dimensions. This is directly coupled to the stress analysis through an expansion coefficient A, where the temperature change or fluid pressure change (from the background value) induces the initial stresses
σ° = A ΔT
The stresses can be presented either without or with the initial stresses σ°.
Plot > Stress > Value > Seff Effective Stress
Plot > Stress > Value > Stotal Total Stress
For fluid flow problems the expansion coefficient should be set to unity (positive one) for saturated media
A = 1
For thermal problems the expansion coefficient should be specified as a negative quantity given by
A = -α E /(1-2ν)
where α, E and ν represent the coefficient of thermal expansion (i.e. the linear expansivity), Young's (rock mass scale - deformation) modulus and Poisson's ratio.
It is also necessary to specify the conductivity C. This parameter relates the gradient to the flux qx such that
qx = -C ∂T/∂x
The recommended units for C are J/(m s 8C).
The various flow parameters can be plotted using
