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 and so Y, at the center, is assumed to be:
(For contact pressure cells, multiply the above values for P by 2.)
References:
[1] Roark, R.J. and Young, W.C. “ Formulas for Stress and Strain,” McGraw Hill, fifth edition, 1982, p 519.
[2] Weiler, W.A. and Kulhawy, F.H. “ Factors Affecting Stress Cell Measurement in Soil” J. Geotech. Eng. Div. ASCE . Vol. 108, No. GT12.
[3] Lazebnik, G.E., “Monitoring of SoilStructure Interaction.” Chapman & Hall.
[4] Fujiyasu, Y. and Orihara, K. “Elastic Modulus of Weathered Rock.” Proc. of the 5th Intl. Symp. on Field Measurements in Geomechanics  Singapore 1999. p 183
[5] Arora, K. R., “Soil Mechanics & Foundation Engineering.” p 218
i.e. the same difference as before.
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:
Y = 0.73 PR (1ν^{2}) x 0.5 x 2/E =
0.73 PR (1ν^{2})/E...........(3.8)
Equating 3.8 & 3.9 gives:
P (D/G + 0.73 R (1 ν^{2})/E) = KD ...........(3.9)
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 (1ν^{2}) x 0.5/E =
0.36 PR (1ν^{2 })/E ...........(3.10)
P (D/G + 0.73 R (1 ν^{2})/E) = KD ...........(3.11)
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. Also, the term }(1ν^{2}) can be replaced by 0.91 since v usually lies between 0.25 and 0.35. Hence, for total embedment:
P
= 1.5 EKD/R psi / ^{o}C
And, for contact pressure cells:
P = 3 EKD/R psi / ^{o}C
Some typical values of the various parameters are:
Liquid

K x 106 / ºC

G x 106 psi

Oil

700

0.3

Mercury

180

3.6

Water

170

0.3

Glycol

650


50/50 Glycol/Water

400

Embedment Material

E x 106 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

Examples.
For an oilfilled cell, 9 inches diameter and D = 0.060 inches, totally embedded in:
SI No

Soil
Type

E(PSI)

ν

P(psi /^{o}C)

1

Plastic Clay

3000

0.3

0.042

2

Soil, medium stiffness

10000

0.3

0.138

3

Coarse Sand

50000

0.3

0.69

(For contact pressure cells, multiply the above values for P by 2.)
For a concrete stress cell, 9 inch diameter and D = 0.020 inches:
4. Concrete, E = 5 x 106 psi, ν = 0.25 ……….P = 22.7 psi /^{o}C
Same cell, embedded in concrete, filled with mercury instead of oil, P = 5.8 psi / ^{o}C
For an oilfilled cell embedded in a completely rigid medium ……… P = 210 psi / ^{o}C
For a mercuryfilled cell embedded in a completely rigid medium …P = 650 psi / ^{o}C
References:
[1] Roark, R.J. and Young, W.C. “ Formulas for Stress and Strain,” McGraw Hill, fifth edition, 1982, p 519.
[2] Weiler, W.A. and Kulhawy, F.H. “ Factors Affecting Stress Cell Measurement in Soil” J. Geotech. Eng. Div. ASCE . Vol. 108, No. GT12.
[3] Lazebnik, G.E., “Monitoring of SoilStructure Interaction.” Chapman & Hall.
[4] Fujiyasu, Y. and Orihara, K. “Elastic Modulus of Weathered Rock.” Proc. of the 5th Intl. Symp. on Field Measurements in Geomechanics  Singapore 1999. p 183
[5] Arora, K. R., “Soil Mechanics & Foundation Engineering.” p 218
No comments:
Post a Comment