This research investigates the coupled effect of normal stress and matric suction on shear strength of unsaturated soils. The main contributions include the development of: (i) simplified laboratory protocol for indirect estimation of matric suction from water retention curve to determine shear strength in the conventional direct shear equipment and (ii) new mechanistic approach for prediction of shear strength of unsaturated soils under different normal stresses. Using a well graded silty sand, the water retention curves (measured under 75 kPa, 150 kPa and 300 kPa normal stresses) were used to prepare direct shear test samples at pre-determined values of volumetric water content and matric suction. Results indicate that shear strength parameters vary differently during desaturation. For the investigated soil, c and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\phi $</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϕ</mi> </math></EquationSource> </InlineEquation> were found to be linear (R2 ≥ 0.90) when plotted versus volumetric water content and followed power law (R2 ≥ 0.50) with respect to matric suction. In contrast, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">${\phi }^{b}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi>ϕ</mi> </mrow> <mi>b</mi> </msup> </math></EquationSource> </InlineEquation> depended on normal stress and followed sigmoidal functions (R2 ≥ 0.80) for both volumetric water content and matric suction. This parameter gradually decreased from 38° (approaching <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\phi ^{\prime}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>ϕ</mi> <mo>′</mo> </msup> </math></EquationSource> </InlineEquation>) at saturation to 0.0 under residual conditions. The similarity in <InlineEquation ID="IEq4"> <EquationSource Format="TEX">${\phi }^{b}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi>ϕ</mi> </mrow> <mi>b</mi> </msup> </math></EquationSource> </InlineEquation> versus matric suction (and volumetric water content) plot to the sigmoidal water retention curve (van Genuchten, 1980) was used to determine the non-linear shear strength behavior of the unsaturated soil following a forward marching approach (Fredlund, 2019). Based on statistical indicators, the proposed equations performed well for the investigated soil as well as for other soil types. The method is user-friendly, time-saving, and cost-effective and useful to determine shear strength under field-relevant unsaturated conditions.

Coupled Effect of Normal Stress and Matric Suction on Shear Strength of Unsaturated Soils

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发表日期：

2026年5月4日

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Dinusha Ranasingha,
Shahid Azam

摘要

This research investigates the coupled effect of normal stress and matric suction on shear strength of unsaturated soils. The main contributions include the development of: (i) simplified laboratory protocol for indirect estimation of matric suction from water retention curve to determine shear strength in the conventional direct shear equipment and (ii) new mechanistic approach for prediction of shear strength of unsaturated soils under different normal stresses. Using a well graded silty sand, the water retention curves (measured under 75 kPa, 150 kPa and 300 kPa normal stresses) were used to prepare direct shear test samples at pre-determined values of volumetric water content and matric suction. Results indicate that shear strength parameters vary differently during desaturation. For the investigated soil, c and $\phi $ $ϕ$ were found to be linear (R² ≥ 0.90) when plotted versus volumetric water content and followed power law (R² ≥ 0.50) with respect to matric suction. In contrast, ${\phi }^{b}$ $ϕ^{b}$ depended on normal stress and followed sigmoidal functions (R² ≥ 0.80) for both volumetric water content and matric suction. This parameter gradually decreased from 38° (approaching $\phi ^{\prime}$ $ϕ^{'}$ ) at saturation to 0.0 under residual conditions. The similarity in ${\phi }^{b}$ $ϕ^{b}$ versus matric suction (and volumetric water content) plot to the sigmoidal water retention curve (van Genuchten, 1980) was used to determine the non-linear shear strength behavior of the unsaturated soil following a forward marching approach (Fredlund, 2019). Based on statistical indicators, the proposed equations performed well for the investigated soil as well as for other soil types. The method is user-friendly, time-saving, and cost-effective and useful to determine shear strength under field-relevant unsaturated conditions.