Volume Change Testing

Volume Change Testing
• Volume Change Coefficients or Indices
The parameters required for constitutive equations relating
deformation state variables and stress state variables.
Elasticity
Form
Table 1 - Volume Change Coefficients or Indices
Compressiblity
Form
Volume-mass
Form
Plane I and III
Plane II
Deformation Coefficient Stress
State or State
Variable Index Variable
dεv 3(1-2µ)/E d(σmean-ua)
3/H d(ua - uw)
dVw/Vo 3/Ew d(σmean-ua)
1/Hw d(ua - uw)
dεv 1 d(σmean-ua)
s
m
2 s
m d(ua - uw)
dVw/Vo 1 d(σmean-ua)
w
m
2 d(ua - uw)
w
m
de at d(σmean-ua)
am d(ua - uw)
dw bt d(σmean-ua)
bm d(ua - uw)
de Ct d log(σ - ua)
Cm d log(ua - uw)
dw Dt d log(σ - ua)
Dm d log(ua - uw)
de C't d log(σ - ua)
C'm d log(ua - uw)
UNSAT13 - 1

Constitutive Surface on Log Scale
Ct
or
Dt
log (σ – ua)
e
or
w
I
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II
III
Cm or
Dm
log (ua – uw)

• Volume Change Tests
1) Free-swell oedometer test
Procedure
a) Place unsaturated soil in consolidation ring and
allow water to enter soil until soil reaches
equilibrium (volume change stops);
b) Increase loads incrementally as per a consolidation
test.
Measurements and Calculations
Vertical displacement is measured in order to
calculate water content and void ratio.
Volume Change Indices
e
eo
Cts
Ct
UNSAT13 - 3
Ps = swelling pressure
log (σv – uw)

2) Constant-volume oedometer test
e
Procedure
a) Place unsaturated soil in consolidation ring and
allow water to enter soil until soil stops swelling
while applying vertical load that will maintain the
soil at constant volume;
b) Increase loads incrementally as per a consolidation
test.
Measurements and Calculations
Vertical pressure to maintain constant volume and
displacement is measured in order to calculate water
content and void ratio.
Volume Change Indices
Cs
Ps Corrected
Swelling
Pressure,
Ct
P’s
Parallel
Adjusted
rebound
curve
eo
a
t
de
d( σ v −u
w)
log (σv – uw) (σv – uw)
UNSAT13 - 4

3) Pressure plate tests
Procedure
a) Place unsaturated soil in pressure plate extractor and
allow water to enter soil until soil comes to
equilibrium;
b) Vary air pressure incrementally (drying or wetting
cycles) and maintain water pressure at
atmospheric pressure until soil comes to
equilibrium (no water flow) and measure water
volume changes to determine water content.
Measurements and Calculations
Air pressure and water volume (content) measurements
to calculate matric suction and water content.
Volume Change Indices
w
or
θ
b
m,ms
dw
=
d(
u −u
a
w
)
D
m,
ms
dw
=
d log( u −u
(ua – uw) log (ua – uw)
UNSAT13 - 5
a
w
)

4) Shrinkage (swell) tests
Procedure
Allow an initially moist soil to come to equilibrium
at various matric suction pressures (in air or in
pressure plate extractor) and measure total
volume changes and moisture content changes.
Measurements and Calculations
Soil volume measurement and water volume
measurements to calculate void ratio and water
content.
Volume Change Indices
e
w Gs
de
dw
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de
dw
de
dw
=
=
a
b
m,
ms
m,
ms
D
C
m,
ms
m,
ms
G
s

Summary
Table 2 Determination of Indices
Index Method
at = de/d(σ - ua) Constant-volume oedometer
am = de/d(ua - uw) am = (am /bm) bm
bt = dw/d(σ - ua) bt = at Gs
bm = dw/d(ua - uw) Pressure plate test
Ct = de/d log(σ - ua) Oedometer test
Cm = de/d log(ua - uw) Cm = (Cm/Dm Gs ) Dm Gs
Dt = dw/d log(σ - ua) Dt = Ct / Gs
Dm = dw/d log(ua - uw) Pressure plate test
am /bm Shrinkage test
Cm/Dm Gs Shrinkage test
Tests required for measurement of volume change indices
for loading (one-dimensional tests)
1) Oedometer Test - compute Ct then ⇒ Dt
2) Pressure Plate Drying Test - compute Dm
3) Shrinkage Test – compute Cm/Dm Gs then ⇒ Cm
Tests required for measurement of volume change indices
for unloading (one-dimensional tests)
1) Oedometer Test (rebound) - compute Cts then⇒ D ts
2) Pressure Plate Wetting Test - compute Dms
3) Free Swell Test – compute Cms/Dms Gs then ⇒ Cms
UNSAT13 - 7

Mechanics of Unsaturated Soils
Homework Assignment
UNSAT13 - 8