3.6. Temperature Effect on Earth Pressure and Concrete Stress Cells
Some Theoretical Considerations
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. Consider
a circular cell of radius R containing a liquid film of thickness D,
coefficient of thermal expansion Kppm/°C, and bulk modulus G.
YT = KD ……………………………(3.5)
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 and a compression of the liquid, Yc, given by the equation:
Yc = PD/G……………………………(3.6)
So that the net expansion, Y, of the cell is equal to:
Y = D (K- P/G)…………………………..(3.7)
Liquid pressure inside the cell causes deformation of the surrounding medium. The amount of deformation can be quantified by modification of formulas found in [1], 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 Poissons ratio, ν, is given by:
SI NO
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CONDITION
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Y=
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DIFFERENCE
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1
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AT THE CENTER
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2
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AT THE EDGE
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