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MODEL 4800 SERIES VW EARTH PRESSURE CELLS | TEMPERATURE EFFECT ON EARTH PRESSURE AND CONCRETE STRESS CELLS | 23
APPENDIX C.
TEMPERATURE EFFECT ON EARTH
PRESSURE AND CONCRETE STRESS CELLS
The following theoretical treatment is by no means rigorous — there are some
questionable assumptions and approximations — but it should give some idea
of the magnitude of the thermal effect to be expected on hydraulic earth
pressure cells, buried in soil, or installed at the contact between soil and
structure, and on concrete stress cells embedded in concrete.
FIGURE 20: Radius (R) and Thickness (D)
C.1 FORMULAS
Consider a circular cell of radius (R) containing a liquid film of a thickness (D),
coefficient of thermal expansion Kppm / C, and bulk modulus (G).
For a temperature rise of 1 C the expansion (Y
equation:
Y
= KD
T
EQUATION 6: Expansion of Liquid for a 1
Expansion of the liquid is resisted by the confinement of the surrounding
medium (soil or concrete) and this causes a pressure rise (P) in the liquid, as well
as a compression of the liquid (Y
Y
= PD/G
c
EQUATION 7: Compression of Liquid
The net expansion (Y) of the cell is equal to:
Y = D (K – P/G)
EQUATION 8: Expansion of Liquid
Liquid pressure inside the cell causes deformation of the surrounding medium.
The amount of deformation can be quantified by modification of formula found
in Equation 6, where the deformation (Y), produced by a uniform pressure (P),
acting on a circular area, (R) radius, on the surface of a material with modulus of
elasticity (E) and Poisson's ratio (), is given by:
At the center of the cell:
2
2PR 1 v
–
Y
=
------------------------------
E
EQUATION 9: Deformation at the Center
) of the liquid film is given by the
T
C Temperature Rise
) given by the equation:
c
20:
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