Volume Change Testing
Volume Change Testing
Volume Change Testing
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<strong>Volume</strong> <strong>Change</strong> <strong>Testing</strong><br />
• <strong>Volume</strong> <strong>Change</strong> Coefficients or Indices<br />
The parameters required for constitutive equations relating<br />
deformation state variables and stress state variables.<br />
Elasticity<br />
Form<br />
Table 1 - <strong>Volume</strong> <strong>Change</strong> Coefficients or Indices<br />
Compressiblity<br />
Form<br />
<strong>Volume</strong>-mass<br />
Form<br />
Plane I and III<br />
Plane II<br />
Deformation Coefficient Stress<br />
State or State<br />
Variable Index Variable<br />
dεv 3(1-2µ)/E d(σmean-ua)<br />
3/H d(ua - uw)<br />
dVw/Vo 3/Ew d(σmean-ua)<br />
1/Hw d(ua - uw)<br />
dεv 1 d(σmean-ua)<br />
s<br />
m<br />
2 s<br />
m d(ua - uw)<br />
dVw/Vo 1 d(σmean-ua)<br />
w<br />
m<br />
2 d(ua - uw)<br />
w<br />
m<br />
de at d(σmean-ua)<br />
am d(ua - uw)<br />
dw bt d(σmean-ua)<br />
bm d(ua - uw)<br />
de Ct d log(σ - ua)<br />
Cm d log(ua - uw)<br />
dw Dt d log(σ - ua)<br />
Dm d log(ua - uw)<br />
de C't d log(σ - ua)<br />
C'm d log(ua - uw)<br />
UNSAT13 - 1
Constitutive Surface on Log Scale<br />
Ct<br />
or<br />
Dt<br />
log (σ – ua)<br />
e<br />
or<br />
w<br />
I<br />
UNSAT13 - 2<br />
II<br />
III<br />
Cm or<br />
Dm<br />
log (ua – uw)
• <strong>Volume</strong> <strong>Change</strong> Tests<br />
1) Free-swell oedometer test<br />
Procedure<br />
a) Place unsaturated soil in consolidation ring and<br />
allow water to enter soil until soil reaches<br />
equilibrium (volume change stops);<br />
b) Increase loads incrementally as per a consolidation<br />
test.<br />
Measurements and Calculations<br />
Vertical displacement is measured in order to<br />
calculate water content and void ratio.<br />
<strong>Volume</strong> <strong>Change</strong> Indices<br />
e<br />
eo<br />
Cts<br />
Ct<br />
UNSAT13 - 3<br />
Ps = swelling pressure<br />
log (σv – uw)
2) Constant-volume oedometer test<br />
e<br />
Procedure<br />
a) Place unsaturated soil in consolidation ring and<br />
allow water to enter soil until soil stops swelling<br />
while applying vertical load that will maintain the<br />
soil at constant volume;<br />
b) Increase loads incrementally as per a consolidation<br />
test.<br />
Measurements and Calculations<br />
Vertical pressure to maintain constant volume and<br />
displacement is measured in order to calculate water<br />
content and void ratio.<br />
<strong>Volume</strong> <strong>Change</strong> Indices<br />
Cs<br />
Ps Corrected<br />
Swelling<br />
Pressure,<br />
Ct<br />
P’s<br />
Parallel<br />
Adjusted<br />
rebound<br />
curve<br />
eo<br />
a<br />
t<br />
de<br />
d( σ v −u<br />
w)<br />
log (σv – uw) (σv – uw)<br />
UNSAT13 - 4
3) Pressure plate tests<br />
Procedure<br />
a) Place unsaturated soil in pressure plate extractor and<br />
allow water to enter soil until soil comes to<br />
equilibrium;<br />
b) Vary air pressure incrementally (drying or wetting<br />
cycles) and maintain water pressure at<br />
atmospheric pressure until soil comes to<br />
equilibrium (no water flow) and measure water<br />
volume changes to determine water content.<br />
Measurements and Calculations<br />
Air pressure and water volume (content) measurements<br />
to calculate matric suction and water content.<br />
<strong>Volume</strong> <strong>Change</strong> Indices<br />
w<br />
or<br />
θ<br />
b<br />
m,ms<br />
dw<br />
=<br />
d(<br />
u −u<br />
a<br />
w<br />
)<br />
D<br />
m,<br />
ms<br />
dw<br />
=<br />
d log( u −u<br />
(ua – uw) log (ua – uw)<br />
UNSAT13 - 5<br />
a<br />
w<br />
)
4) Shrinkage (swell) tests<br />
Procedure<br />
Allow an initially moist soil to come to equilibrium<br />
at various matric suction pressures (in air or in<br />
pressure plate extractor) and measure total<br />
volume changes and moisture content changes.<br />
Measurements and Calculations<br />
Soil volume measurement and water volume<br />
measurements to calculate void ratio and water<br />
content.<br />
<strong>Volume</strong> <strong>Change</strong> Indices<br />
e<br />
w Gs<br />
de<br />
dw<br />
UNSAT13 - 6<br />
de<br />
dw<br />
de<br />
dw<br />
=<br />
=<br />
a<br />
b<br />
m,<br />
ms<br />
m,<br />
ms<br />
D<br />
C<br />
m,<br />
ms<br />
m,<br />
ms<br />
G<br />
s
Summary<br />
Table 2 Determination of Indices<br />
Index Method<br />
at = de/d(σ - ua) Constant-volume oedometer<br />
am = de/d(ua - uw) am = (am /bm) bm<br />
bt = dw/d(σ - ua) bt = at Gs<br />
bm = dw/d(ua - uw) Pressure plate test<br />
Ct = de/d log(σ - ua) Oedometer test<br />
Cm = de/d log(ua - uw) Cm = (Cm/Dm Gs ) Dm Gs<br />
Dt = dw/d log(σ - ua) Dt = Ct / Gs<br />
Dm = dw/d log(ua - uw) Pressure plate test<br />
am /bm Shrinkage test<br />
Cm/Dm Gs Shrinkage test<br />
Tests required for measurement of volume change indices<br />
for loading (one-dimensional tests)<br />
1) Oedometer Test - compute Ct then ⇒ Dt<br />
2) Pressure Plate Drying Test - compute Dm<br />
3) Shrinkage Test – compute Cm/Dm Gs then ⇒ Cm<br />
Tests required for measurement of volume change indices<br />
for unloading (one-dimensional tests)<br />
1) Oedometer Test (rebound) - compute Cts then⇒ D ts<br />
2) Pressure Plate Wetting Test - compute Dms<br />
3) Free Swell Test – compute Cms/Dms Gs then ⇒ Cms<br />
UNSAT13 - 7
Mechanics of Unsaturated Soils<br />
Homework Assignment<br />
UNSAT13 - 8