Heat Flow Analysis for Unsaturated Soils - Unsaturated Soil Mechanics in Engineering Practice - page 516

450 m

50 m

5 ° C

−

+4 ° C

Temperature increases
at a rate of 1 ° C per 30 m

450 m

Figure 10.34 Geometry and boundary conditions for warm building placed over frozen soil

problem.

above freezing is placed on frozen soil. Once again the build-
ing is modeled as a heated strip at a temperature of

10.11 ALDRICH (1956) EXAMPLE OF
VERTICAL COLUMN

4 ◦ C.
Only steady-state conditions are considered in the analy-
sis. The ground surface temperature on either side of the
building is maintained at

+

Aldrich (1956) and Li and Koike (2001) published a
closed-form analytical heat flow for the calculation of frost
depth. Only conductive heat flow was modeled. The geometry
consisted of a one-dimensional vertical column 5 m long, as
shown in Fig. 10.37. The soil is assumed to be homogeneous.
The freezing temperature applied at ground surface was

5 ◦ C, as shown in Fig. 10.34.
However, it is assumed that the temperature below ground
surface increases at a rate of 1 ◦ C per 30 m. The thermal con-
ductivity of the soil is 1.0 W/m/K. Only half of the geometry
is modeled due to symmetry.
The finite element mesh should be refined in the vicinity
of the edge of the building to ensure accuracy of the solu-
tion (Fig. 10.35). The refinement of the computer-generated
mesh can be controlled by specifying the desired tolerance
for the final solution. Figure 10.36 shows contours of the
computed constant temperatures below and around the heated
building.

−

5 ◦ C. The
intermittent temperatures were applied in accordance with the
graph shown in Fig. 10.38. The graph shows that the freezing
temperatures were applied for 120 days. It was assumed that
10 days were required to change to freezing conditions and
vice versa. The bottom of the soil column has a unit gradient
imposed and its initial temperature was 5 ◦ C.

5 ◦ C and later the thawing temperature was set at − +