32
If one side of the cell lies in contact with a rigid structure, e.g., a concrete retaining wall or a
concrete bridge footing, then:
Y = 0.73 PR (1-
ν
2
) x 0.5/E = 0.36 PR (1-
ν
2
)/E
And
P (D/G + 0.36 R (1-
ν
2
)/E) = KD
Where (E) pertains to the soil material.
Since these expressions are only approximate, they can be simplified even further:
For all E < 10 x 10
6
psi the term D/G is negligible, so long as the cell is designed and constructed
properly, i.e., G is large, (no air trapped inside the cell), and D is small. In addition, the term (1-
ν
2
) can be replaced by 0.91 since ν usually lies between 0.25 and 0.35.
The total embedment is given by:
P = 1.5 EKD/R psi /
o
C
Equation 15 - Total Embedment
And for contact pressure cells:
P = 3 EKD/R psi /
o
C
Equation 16 - Total Embedment for Contact Pressure Cells
Some typical values of the various parameters are:
Liquid
K x 10
-6
/ ºC
G x 10
6
psi
Oil
700
0.3
Mercury
180
3.6
Water
170
0.3
Glycol
650
0.26
50/50 Glycol/Water
400
0.28
Embedment Material
E x 10
6
psi
ν
Plastic Clay
0.003
Soil
0.001 to 0.02 [Ref 2]
0.25 to 0.45
Sand
0.02 to 0.06 [Ref 3]
0.28 to 0.35
Compacted Ottawa
Sand
0.2
Weathered Rock
0.04 to 0.11 [Ref 4]
Concrete
5.0
0.25
Table 8 - Typical Values of Various Cell Parameters
