Environmental Engineering Reference
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0.16
180
160
0.14
140
0.12
120
0.10
100
0.08
80
0.06
60
Freezing
Thawing
0.04
40
Drying
Wetting
0.02
20
0
0
0
5
10
15
20
25
30
35
40
45
Gravimetric water content, %
Figure 10.9
Experimental data showing similarity between SFCCs and SWCCs, including hys-
teresis effects (after Koopmans and Miller, 1966).
50
50
45
SWC1
SWC2
SWC3
45
40
40
35
30
35
25
30
20
25
15
10
20
5
15
0
10
6
1
10
100
1000
10,000 100,000
10
Matric suction, kPa
(a)
5
0
1.0E+01
1.0E+00
1.0E-01
1.0E-02
1.0E-03
1.0E-04
1.0E-05
1.0E-06
1.0E-07
0.0
1.0
2.0
3.0
4.0
5.0
6.0
Negative temperature,
°
C
SWC1
SWC2
SWC3
Figure 10.10
SFCC for silica flour (after Jame,1972).
shows the results for the silica flour tested by Jame (1977).
The saturated coefficients of permeability ranged from 2
.
5
×
10
−
6
10
−
7
m/s when the porosity ranged from 0.52
to 0.48, respectively. The SWCCs for the silica flour are
shown in Fig. 10.11a and the relative coefficients of per-
meability versus soil suctions computed using the Fredlund
and Xing (1994) equation are shown in Fig. 10.11b.
to 3
.
0
×
1
10
100
1000
10,000
Matric suction, kPa
(b)
Figure 10.11
Relative coefficient-of-permeability functions com-
puted for three specimens of silica flour using Fredlund and Xing
(1994) SWCC equation: (a) SWCCs for silica flour (Jame, 1972);
(b) relative coefficient-of-permeability curves for silica flour.
10.4 FORMULATION OF PARTIAL
DIFFERENTIAL EQUATIONS FOR CONDUCTIVE
HEAT FLOW
of a REV. The conservation of thermal energy under steady-
state conditions requires that the heat flow into an element
must be equal to the outward heat flow.
Partial differential equations can be written for one-, two-
and three-dimensional geometries. The partial differential
Conductive heat flow differential equations can be derived
satisfying the conservation of thermal energy. The formu-
lations are similar in form to those previously derived for
water flow and air flow. The analysis starts with the selection
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