1. Daryl Dagesse Department of Geography St. Catharines, Ontario, Canada
Application of a Thermodynamically Based Shrinkage Equation to Freezing Induced Bulk Soil Volume Changes
Daryl Dagesse
Department of Geography
St. Catharines, Ontario, Canada

2. Soil Freezing What happens when a soil freezes?
soil volume increases
Soil Freezing
What happens when a soil freezes?
~9% volumetric expansion of pore water
pore water redistribution

3. Soil Freezing What happens when a soil freezes?
soil structural change
improvement
degradation
What happens when a soil freezes?
pore water redistribution

4. Freezing shrinkage in compacted clays. Can. Geotech. Journal, 3: 1-17.
Hamilton, A.B
Freezing shrinkage in compacted clays. Can. Geotech. Journal, 3: 1-17.
Fig. 5
Expansion
Shrinkage
Dry end
Wet end
-6.7°C
-30.6°C
Shrinkage Effects
Expansion Effects

5. Objectives
can a similar analysis of soil shrinkage be carried out for frozen soils as for unfrozen soils?
fit a theoretically based constitutive shrinkage equation
elucidate the effects of the freezing process on soil structure that have until now yielded seemingly conflicting results

6. Materials Soil Type Clay (%) Atterberg Constants Proctor Tests LL* PL*
PI*
Opt.
W/C*
Max
Max.
Dry
Den.*
(g/cm3)
Gleyed Luvisol 11
23.59
18.06
5.53
16.73
1.709
Gleysol 33
38.43
22.15
16.28
19.28
1.647
LL: liquid limit
PL: plastic limit
PI: plasticity index
Opt.W/C: optimum water content at maximum dry density
Max. Dry Den.: maximum dry density from compaction tests

7. Methods Cores taken from moulds during Proctor testing
range of water contents

8. 1-D freezing from the top down under closed conditions -15°C for 24 hr

9. Volume change fitted curves
Soil C11
(11% Clay)
Soil C33
(33% Clay)
Volume change fitted curves

10. Volume change fitted curves
Soil C11
(11% Clay)
Soil C33
(33% Clay)
Volume change fitted curves
Soil A2
(23% Clay)
Soil A5
(50% Clay)
-7.54%
66.7%
Soil GH
(55% Clay)
Soil A11
(32% Clay)
Soil TH
(75% Clay)

11. Analysis of volumetric change fitted curves
Soil
Clay Content
(kg kg-1)
Minimum
%VC
(maximum
shrinkage) %
Min %VC
VC = 0%
Maximum
C11
0.11
-1.28
65.91
74.47
3.09 A2
0.23
-3.84
65.03
87.10
15.32z
A11
0.32
-5.87
66.76
81.02
2.74
C33
0.33
-1.70
69.13
79.22
3.50 A5
0.50
-7.77
63.39
82.15
2.83
GHy
0.55
-7.54
66.69
84.96
2.92 TH
0.75
-10.12
68.52
89.76
4.63z
Z Unrealistic value due to curve fitting limitations
Y Interpolated at -15°C

12. Shrinkage Equation Development
Original thermodynamic-based theory of Groenevelt and Bolt (1972)
shrinkage of swelling soils under different load pressures
Unloaded shrinkage curve equation extracted by Groenevelt et al. (2001)
Subsequently used by Groenevelt and Grant (2002, 2004a, 2004b)

13. Idealized shrinkage plot.
void ratio as a function
of the moisture ratio
void ratio at air entry
dimensionless fitting
parameters
moisture ratio
Idealized shrinkage plot.
Groenevelt & Grant (2004) Figure 1

14. Idealized shrinkage plot. ZS: zero shrinkage RS: residual shrinkage
void ratio as a function
of the moisture ratio
void ratio at air entry
dimensionless fitting
parameters
moisture ratio
Idealized shrinkage plot.
ZS: zero shrinkage
RS: residual shrinkage
PS: proportional shrinkage
SS: structural shrinkage

15. First derivative ≡ slope
First derivative ≡ slope
Second derivative ≡ curvature
Idealized shrinkage plot.
ZS: zero shrinkage
RS: residual shrinkage
PS: proportional shrinkage
SS: structural shrinkage
See: Groenevelt & Grant (2002)

16. First derivative ≡ slope
First derivative ≡ slope
Second derivative ≡ curvature
Idealized shrinkage plot.
ZS: zero shrinkage
RS: residual shrinkage
PS: proportional shrinkage
SS: structural shrinkage
Shrinkage limit
Structural limit
Plastic limit
See: Groenevelt & Grant (2002)

17. Frozen Shrinkage Curve: 11% clay soil
Data points: measured shrinkage values.
Line: fitted curve via Eq. 1.

18. Frozen Shrinkage Curve: 11% clay soil
Shrinkage Limit? (0.331)
SL = 0.552
Plastic Limit? (0.857)
PL = 0.487
Slope, σ(ϑ) (magenta dashed line)
Curvature, κ(ϑ), (cyan dashed line)
Fitted curve (red solid line) via Eq. 1.
Data points: measured shrinkage values.

19. Frozen Shrinkage Curve: 33% clay soil
Data points: measured shrinkage values.
Line: fitted curve via Eq. 1.

20. Frozen Shrinkage Curve: 33% clay soil
Slope, σ(ϑ) (magenta dashed line)
Curvature, κ(ϑ), (cyan dashed line)
Fitted curve (red solid line) via Eq. 1.
Data points: measured shrinkage values.

21. Frozen & Air Dried Shrinkage Curves: 33% clay soil
Freezing induced shrinkage (red solid line and data points)
Air drying shrinkage (magenta dashed line and data points)
Curves fitted via Eq. 1.

22. Conclusions
Shrinkage equations were successfully fitted to the freezing induced shrinkage data
experimental data (11% clay & 33% clay soils)
Hamilton’s (1966) data
But…….

23. Conclusions
absence of 'structural' shrinkage at the wet end prevented analysis in the high clay soil
existence of a pre-existing skeletal soil structure in low clay soil?
destroyed natural structure in high clay soil?
variability in data
each data point a separate sample frozen at a particular water content

24. Conclusions
The usefulness of Atterberg constants in the analysis remains uncertain

25. Conclusions
Freezing induced soil shrinkage displays a similar pattern as shrinkage generated by air drying across soils with different clay contents
comparable air entry void ratios
greater shrinkage due to freezing than due to air drying

26. Conclusions
Further study using structured, non-remoulded samples may provide elucidation to these questions