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24 | TEMPERATURE EFFECT ON EARTH PRESSURE AND CONCRETE STRESS CELLS | GEOKON
At the edge of the cell:
2
4PR 1 v
–
Y
=
------------------------------
E
EQUATION 10: Deformation at the Edge
The difference being:
2
2 4/
/E
PR 1 v
–
–
EQUATION 11: Difference in Deformation
The above formulas apply to pressures acting on a free surface. However, in the
confined case, Y, at the edge of the cell, can be assumed to be nearly zero.
Therefore, Y, at the center, is assumed to be the same as shown in Equation 11.
If the average Y across the cell is assumed to be half this value, and if the
deformation of the medium on either side of the cell is assumed to be the same,
then the average total expansion of the cell is given by:
2
Y = 0.73 PR (1 – ν
) x 0.5 x 2/E = 0.73 PR (1 – ν
EQUATION 12: Average Total Expansion of the Cell
Equating Equation 8 and Equation 12 gives:
2
P (D/G + 0.73 R (1– n
)/E) = KD
EQUATION 13: Combined Equations
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:
2
Y = 0.73 PR (1 – ν
) x 0.5/E = 0.36 PR (1 – ν
and
2
P (D/G + 0.36 R (1 – ν
)/E) = KD
Where (E) pertains to the soil material.
Since these expressions are only approximate, they can be simplified even
further:
6
For all E < 10 x 10
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
between 0.25 and 0.35.
The total embedment is given by:
P = 1.5 EKD/R psi / °C
EQUATION 14: Total Embedment
And for contact pressure cells:
P = 3 EKD/R psi / °C
EQUATION 15: Total Embedment for Contact Pressure Cells
2
)/E
2
)/E
2
) can be replaced by 0.91 since ν usually lies
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