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

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

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

Freezing shrinkage in compacted clays. Can. Geotech. Journal, 3: 1-17. Hamilton, A.B. 1966. 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

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

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

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

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

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

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)

Analysis of volumetric change fitted curves Soil Clay Content (kg kg-1) Minimum %VC (maximum shrinkage) % Sat @ 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

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)

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

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

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)

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)

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

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.

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

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.

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.

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

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

Conclusions The usefulness of Atterberg constants in the analysis remains uncertain

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

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