Oloo et al. (1997)Oloo, S.Y., Fredlund, D.G., & Gan, J.K.-M. (1997). Bearing capacity of unpaved roads. Canadian Geotechnical Journal, 34(3), 398-407. http://dx.doi.org/10.1139/t96-084. https://doi.org/10.1139/t96-084...
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(5) |
qult: ultimate bearing capacity |
Vanapalli & Mohamed (2007)Vanapalli, S.K., & Mohamed, F.M.O. (2007). Bearing capacity of model footings in unsaturated soils. Springer Proceedings in Physics, 112, 483-493. http://dx.doi.org/10.1007/3-540-69873-6_48. https://doi.org/10.1007/3-540-69873-6_48...
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(6) |
c’: effective cohesion |
Vahedifard & Robinson (2016)Vahedifard, F., & Robinson, J.D. (2016). Unified method for estimating the ultimate bearing capacity of shallow foundations in variably saturated soils under steady flow. Journal of Geotechnical and Geoenvironmental Engineering, 142(4), 04015095. http://dx.doi.org/10.1061/(ASCE)GT.1943-5606.0001445. https://doi.org/10.1061/(ASCE)GT.1943-56...
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(7) |
ct’: unified effective cohesion |
(8) |
Vo & Russel (2016)Vo, T., & Russel, A.R. (2016). Bearing capacity of strip footings on unsaturated soils by the slip line theory. Computers and Geotechnics, 74, 122-131.
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(9) |
of matric suction |
(10) |
Ghasemzadeh & Akbari (2019)Ghasemzadeh, H., & Akbari, F. (2019). Determining the bearing capacity factor due to nonlinear matric suction distribution in the soil. Canadian Journal of Soil Science, 99(4), 434-446. http://dx.doi.org/10.1139/cjss-2019-0071. https://doi.org/10.1139/cjss-2019-0071...
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Constant suction distribution |
(ua – uw)AVE: average matric suction |
Garakani et al. (2020)Garakani, A.A., Sadeghi, H., Saheb, S., & Lamei, A. (2020). Bearing capacity of shallow foundations on unsaturated soils: analytical approach with 3D numerical simulations and experimental validations. International Journal of Geomechanics, 20(3), 04019181. http://dx.doi.org/10.1061/(ASCE)GM.1943-5622.0001589. https://doi.org/10.1061/(ASCE)GM.1943-56...
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(11) |
(ua – uw)b: air-entry value |
Yan et al. (2020)Yan, Q., Zhao, J., Zhang, C., & Wang, J. (2020). Ultimate bearing capacity of strip foundations in unsaturated soils considering the intermediate principal stress effect. Advances in Civil Engineering, 2020, 1-14. http://dx.doi.org/10.1155/2020/8854552. https://doi.org/10.1155/2020/8854552...
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Linear suction distribution |
(ua – uw)s: matric suction at soil surface |
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(12) |
(ua – uw)m: representative matric suction |
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Residual zone of unsaturation |
A1: fitting parameter |
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(13) |
B: width of shallow foundation |
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(14) |
cAEV: cohesion for air-entry value |
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Uniform suction distribution |
cres: constant cohesion due to the residual suction |
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(15) |
ks: saturated hydraulic conductivity |
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Linear suction distribution |
Nc, Nq, Nγ: bearing capacity factors |
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(16) |
Nct, Nqt, Nγt: bearing capacity factors based on the unified strength theory |
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(Ns)cst, (Ns)l: bearing capacity factor in terms of suction for constant and linear suction distribution, respectively |
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q: constant infiltration at the ground surface |
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qs: surface surcharge |
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s: soil suction |
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F, V: dimensionless ratios |
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z’: height above a horizontal ground water table |
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α and n: van Genuchten (1980)van Genuchten, M.T. (1980). A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal, 44, 892-898. http://dx.doi.org/10.2136/sssaj1980.03615995004400050002x. https://doi.org/10.2136/sssaj1980.036159...
fitting parameters |
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λm: rate of decrease of matric suction with depth |
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γ: unit weight of soil |
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γm: modified average unit weight |
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ψ: fitting parameter for bearing capacity |
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ξc, ξq, ξγ: shape factors |
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ξs: shape factor for suction (=ξc) |
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ϕ’: effective internal friction angle |
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ϕt’: unified internal friction angle |
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ϕtb: unified internal friction angle due to the contribution of suction |
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ϕb: internal friction angle due to the contribution of suction |
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ϕr: internal friction angle due to the contribution of suction in residual zone |