Role of Bimodal Water Retention Curve on the Unsaturated Shear Strength
Abstract
:1. Introduction
2. Investigated Soil and Methodology
2.1. Investigated Soils
2.2. Methodology
3. Mathematical Equation
3.1. Applicable Theory
- θs1 = saturated volumetric water content
- θs2 = volumetric water content related to air-entry value 2
- β1 = 0 when ψ ≤ ψa1; β1 = 1 when ψ > ψa1
- β2 = 0 when ψ ≤ ψa2; β2 = 1 when ψ > ψa2
- Cr = input parameter according to Fredlung and Xing [43] (kPa)
- erfc = the complementary error function,
- ψm1 = parameter related to suction at the inflection point 1 (Figure 1)
- ψm2 = parameter related to suction at the inflection point 2 (Figure 1)
- θr = parameter related to volumetric water content at residual condition (Figure 1)
- s1 = parameter related to standard deviation 1 (Figure 1)
- s2 = parameter related to standard deviation 2 (Figure 1)
- AEV = air-entry value of soil (kPa)
- y and b = fitting parameters.
- Ip = plasticity index.
- n = fitting parameter from Fredlund and Xing [43] equation for fitting WRC
3.2. Proposed Equation
4. Results of Laboratory Testing
5. Discussion
6. Conclusions
- Lower air-entry value and lower inflection point of soil WRC signify larger sizes of dominant macropore and micropore in PSD of soil.
- Dual porosity structure in PSD is more unlikely if there are higher percentages of fine-grained particles inside the soil.
- For matric suctions less than AEV1, the relationship between shear strength and matric suction is linear and ϕb is the same with ϕ′.
- For matric suctions between AEV1 and AEV2, the relationship between shear strength and matric suction is still linear but ϕb is less than ϕ′.
- For matric suctions beyond AEV2, the relationship between shear strength and matric suction is non-linear and ϕb is much smaller than ϕ′.
- A new mathematical equation has been proposed to estimate the unsaturated shear strength of soil with bimodal water retention curve. The proposed equation has been evaluated and it is in agreement with the experimental data of the unsaturated shear strength carried out in this study.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Laboratory Testing | ASTM |
---|---|
Grain-size distribution | ASTM D422-63 [35] |
Atterberg limit | ASTM D4318-00 [36] |
Specific gravity | ASTM D854-02 [37] |
Standard Proctor | ASTM D698-12e1 [38] |
Unified soil classification system (USCS) | ASTM D2487-00 [39] |
Soil Properties | 70S30K | 50S50K |
---|---|---|
Dry Density, γd (Mg/m3) | 1.85 | 1.65 |
Water Content, w (%) | 7.50 | 13.50 |
Saturated Water Content, wsat (%) | 17.7 | 20.5 |
Void Ratio, e | 0.43 | 0.64 |
Liquid Limit, LL (%) | 27.50 | 38.00 |
Plastic Limit, PL (%) | 14.76 | 19.72 |
Plasticity Index, Ip (%) | 12.74 | 18.28 |
Specific Gravity, Gs | 2.61 | 2.59 |
GSD–Sand (%) | 73.3 | 50.0 |
GSD–Silt (%) | 19.2 | 36.0 |
GSD–Clay (%) | 7.5 | 14.0 |
Unified Soil Classification System (USCS) | SC (Clayey Sand) | CL (Sandy Clay with Low Plasticity) |
Parameters | 70S30K | 50S50K |
---|---|---|
θs1 | 0.310 | 0.341 |
θs2 | 0.248 | 0.269 |
ψa1 or AEV1 (kPa) | 6 | 20 |
ψm1 (kPa) | 10 | 25 |
s1 | 1.50 | 1.17 |
θr2 | 0.000 | 0.000 |
ψa2 or AEV2 (kPa) | 50 | 75 |
ψm2 (kPa) | 152 | 225 |
ψr2 (kPa) | 1175 | 1500 |
s2 | 1.92 | 1.00 |
R2 | 0.9989 | 0.9985 |
Parameters | 70S30K | 50S50K |
---|---|---|
AEV (kPa) | 15 | 25 |
Ip (%) | 12.74 | 18.28 |
c′ (kPa) | 8 | 12 |
ϕ′ (°) | 35 | 28 |
n | 2 | 1.59 |
σ–ua (kPa) | 0 | 0 |
y | 0.987 | 1.141 |
b | 0.889 | 0.908 |
Parameters | 70S30K | 50S50K |
---|---|---|
AEV1 (kPa) | 6 | 20 |
AEV2 (kPa) | 50 | 75 |
s1 | 1.5 | 1.172 |
s2 | 1.919 | 1 |
b1 | 0.814 | 0.806 |
b2 | 0.447 | 0.428 |
e | 0.43 | 0.64 |
fines | 0.267 | 0.5 |
Zone | Matric Suction (kPa) | 70S30K | 50S50K |
---|---|---|---|
ϕb (°) | ϕb (°) | ||
1 | <AEV1 | 35 | 28 |
2 | AEV1–AEV2 | 20 | 17 |
3 | AEV2 | <11 | <10 |
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Satyanaga, A.; Bairakhmetov, N.; Kim, J.R.; Moon, S.-W. Role of Bimodal Water Retention Curve on the Unsaturated Shear Strength. Appl. Sci. 2022, 12, 1266. https://doi.org/10.3390/app12031266
Satyanaga A, Bairakhmetov N, Kim JR, Moon S-W. Role of Bimodal Water Retention Curve on the Unsaturated Shear Strength. Applied Sciences. 2022; 12(3):1266. https://doi.org/10.3390/app12031266
Chicago/Turabian StyleSatyanaga, Alfrendo, Nail Bairakhmetov, Jong R. Kim, and Sung-Woo Moon. 2022. "Role of Bimodal Water Retention Curve on the Unsaturated Shear Strength" Applied Sciences 12, no. 3: 1266. https://doi.org/10.3390/app12031266
APA StyleSatyanaga, A., Bairakhmetov, N., Kim, J. R., & Moon, S.-W. (2022). Role of Bimodal Water Retention Curve on the Unsaturated Shear Strength. Applied Sciences, 12(3), 1266. https://doi.org/10.3390/app12031266