Determination of effective stress parameter of unsaturated soils: A Gaussian process regression approach

Abstract

This article examines the capability of Gaussian process regression (GPR) for prediction of effective stress parameter (\chi) of unsaturated soil. GPR method proceeds by parameterising a covariance function, and then infers the parameters given the data set. Input variables of GPR are net confining pressure (σ₃), saturated volumetric water content (θ_s), residual water content (θ_r), bubbling pressure (h_b), suction (s) and fitting parameter (λ). A comparative study has been carried out between the developed GPR and Artificial Neural Network (ANN) models. A sensitivity analysis has been done to determine the effect of each input parameter on \chi. The developed GPR gives the variance of predicted \chi. The results show that the developed GPR is reliable model for prediction of \chi of unsaturated soil.

Keywords

unsaturated soil / effective stress parameter / Gaussian process regression (GPR) / artificial neural network (ANN) / variance

References

[1] Bishop A W. The principle of effective stress. Teknisk Ukeblad, 1959, 106(39): 859–863

[2] Khalili N, Khabbaz M H. A unique relationship for the determination of the shear strength of unsaturated soils. Geotechnique, 1998, 48(5): 681-687

[3] Russell A R, Khalili N A. Unified bounding surface plasticity for unsaturated soils. International Journal for Numerical and Analytical Methods in Geomechanics, 2006, 30(3): 181–212

[4] Garven E N, Vanapalli S K. Evaluation of empirical procedures for predicting the shear strength of unsaturated soils. In: Proceedings of the Unsaturated Soils. ASCE, Sharma and Singhal, 2006, 2570–81

[5] Fazeli A, Habibagahi G. Ghahramani A V. Shear strength characteristics of Shiraz unsaturated silty clay. Iranian Journal of Science Technology, 2010, 33(B4): 327–341

[6] Ajdari M, Habibagahi G, Ghahramani A. Predicting effective stress parameter of unsaturated soils using neural networks. Computers and Geotechnics, 2012, 40: 89–96

[7] Park D, Rilett L R. Forecasting freeway link ravel times with a multi-layer feed forward neural network. Computer-Aided Civil and Infrastructure Engineering, 1999, 14: 357–367

[8] Kecman V. Learning and Soft Computing: Support Vector Machines, Neural Networks, and Fuzzy Logic Models. Cambridge, MA: MIT Press, 2001

[9] Ažman K, Kocijan J. Application of Gaussian processes for black-box modelling of biosystems. ISA Transactions, 2007, 46(4): 443–457

[10] Stegle O, Fallert S V, MacKay D J, Brage S. Gaussian process robust regression for noisy heart rate data. IEEE Transactions on Bio-Medical Engineering, 2008, 55(9): 2143–2151

[11] di Sciascio F, Amicarelli A N. Biomass estimation in batch bio-technological processes by Bayesian Gaussian process regression. Computers & Chemical Engineering, 2008, 32(12): 3264–3273

[12] Yuan J, Wang K, Yu T, Fang M. Reliable multi-objective optimization of highspeed WEDM process based on Gaussian process regression. International Journal of Machine Tools & Manufacture, 2008, 48(1): 47–60

[13] Pal M, Deswal S. Modelling pile capacity using Gaussian process regression. Computers and Geotechnics, 2010, 37(7-8): 942–947

[14] Williams K I, Rasmussen C E. Gaussian Processes for Regression, Cambridge, MA: MIT Press, 1996

[15] Liong S Y, Lim W H, Paudyal G N. River stage forecasting in Bangladesh: Neural network approach. Journal of Computing in Civil Engineering, 2000, 14(1): 1–8

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