Soil-water characteristic curve (SWCC) is significant to estimate the site-specific unsaturated soil properties (such as unsaturated shear strength and coefficient of permeability) for geotechnical analyses involving unsaturated soils. Determining SWCC can be achieved by fitting data points obtained according to the prescribed experimental scheme, which is specified by the number of measuring points and their corresponding values of the control variable. The number of measuring points is limited since direct measurement of SWCC is often costly and time-consuming. Based on the limited number of measuring points, the estimated SWCC is unavoidably associated with uncertainties, which depends on measurement data obtained from the prescribed experimental scheme. Therefore, it is essential to plan the experimental scheme so as to reduce the uncertainty in the estimated SWCC. This study presented a Bayesian approach, called OBEDO, for probabilistic experimental design optimization of measuring SWCC based on the prior knowledge and information of testing apparatus. The uncertainty in estimated SWCC is quantified and the optimal experimental scheme with the maximum expected utility is determined by Subset Simulation optimization (SSO) in candidate experimental scheme space. The proposed approach is illustrated using an experimental design example given prior knowledge and the information of testing apparatus and is verified based on a set of real loess SWCC data, which were used to generate random experimental schemes to mimic the arbitrary arrangement of measuring points during SWCC testing in practice. Results show that the arbitrary arrangement of measuring points of SWCC testing is hardly superior to the optimal scheme obtained from OBEDO in terms of the expected utility. The proposed OBEDO approach provides a rational tool to optimize the arrangement of measuring points of SWCC test so as to obtain SWCC measurement data with relatively high expected utility for uncertainty reduction.
References
[1]
Lu, N. and Likos, W.J. (2004) Unsaturated Soil Mechanics. Wiley.
[2]
Wang, L., Cao, Z., Li, D., Phoon, K. and Au, S. (2018) Determination of Site-Specific Soil-Water Characteristic Curve from a Limited Number of Test Data—A Bayesian Perspective. GeoscienceFrontiers, 9, 1665-1677. https://doi.org/10.1016/j.gsf.2017.10.014
[3]
Huang, W., Wang, Y., Shao, S., Xu, X. and Liu, Y. (2024) An Experimental Study of the Morphological Evolution of Rills on Slopes under Rainfall Action. Sustainability, 16, Article No. 6297. https://doi.org/10.3390/su16156297
[4]
Phoon, K., Santoso, A. and Quek, S. (2010) Probabilistic Analysis of Soil-Water Characteristic Curves. JournalofGeotechnicalandGeoenvironmentalEngineering, 136, 445-455. https://doi.org/10.1061/(asce)gt.1943-5606.0000222
[5]
Sivia, D. and Skilling, J. (2006) Data Analysis: A Bayesian Tutorial. OUP Oxford.
[6]
Zhu, Z. and Gong, D. (2014) Determination of the Experimental Conditions of the Transglutaminase-Mediated Restoration of Thermal Aged Silk by Orthogonal Experiment. JournalofCulturalHeritage, 15, 18-25. https://doi.org/10.1016/j.culher.2012.12.002
[7]
Zhang, J., Zeng, L., Chen, C., Chen, D. and Wu, L. (2015) Efficient Bayesian Experimental Design for Contaminant Source Identification. WaterResourcesResearch, 51, 576-598. https://doi.org/10.1002/2014wr015740
[8]
Ding, S., Li, D., Cao, Z. and Du, W. (2022) Two-Stage Bayesian Experimental Design Optimization for Measuring Soil-Water Characteristic Curve. BulletinofEngineeringGeologyandtheEnvironment, 81, Article No. 142. https://doi.org/10.1007/s10064-022-02598-y
[9]
Li, X.Y., Zhang, L.M., Jiang, S.H., Li, D.Q. and Zhou, C.B. (2016) Assessment of Slope Stability in the Monitoring Parameter Space. JournalofGeotechnicalandGeoenvironmentalEngineering, 142, Article ID: 04016029. https://doi.org/10.1061/(asce)gt.1943-5606.0001490
[10]
Zetterlund, M.S., Norberg, T., Ericsson, L.O., Norrman, J. and Rosén, L. (2015) Value of Information Analysis in Rock Engineering: A Case Study of a Tunnel Project in Äspö Hard Rock Laboratory. Georisk: AssessmentandManagementofRiskforEngineeredSystemsandGeohazards, 9, 9-24. https://doi.org/10.1080/17499518.2014.1001401
[11]
Li, H. and Ma, Y. (2015) Discrete Optimum Design for Truss Structures by Subset Simulation Algorithm. JournalofAerospaceEngineering, 28, Article ID: 04014091. https://doi.org/10.1061/(asce)as.1943-5525.0000411
[12]
Zhai, Q., Rahardjo, H. and Satyanaga, A. (2017) Effects of Residual Suction and Residual Water Content on the Estimation of Permeability Function. Geoderma, 303, 165-177. https://doi.org/10.1016/j.geoderma.2017.05.019
[13]
Huan, X. and Marzouk, Y.M. (2013) Simulation-Based Optimal Bayesian Experimental Design for Nonlinear Systems. JournalofComputationalPhysics, 232, 288-317. https://doi.org/10.1016/j.jcp.2012.08.013
[14]
Li, H. and Au, S. (2010) Design Optimization Using Subset Simulation Algorithm. StructuralSafety, 32, 384-392. https://doi.org/10.1016/j.strusafe.2010.03.001
[15]
Au, S. and Wang, Y. (2014) Engineering Risk Assessment with Subset Simulation. Wiley. https://doi.org/10.1002/9781118398050
[16]
Tao, R., Li, D.Q., Cao, Z.J. and Fu, X.Y. (2021) Experimental Study and Parameter Identification of Soil Water Characteristic Curve of Sandy Loess. Engineering Journal of Wuhan University, 54, 579-587.
[17]
Punrattanasin, P., Subjarassang, A., Kusakabe, O. and Nishimura, T. (2002) Collapse and Erosion of Khon Kaen Loess with Treatment Option. 1stInternationalConferenceonScourofFoundations, College Station, 17-20 November 2002, 1081-1095.
[18]
Huang, M.B., Fredlund, D.G. and Fredlund, M.D. (2009) Estimation of SWCC from Grain Size Distribution Curves for Loess Soils in China. 62ndCanadian Geotechnical Conference, Halifax, September 2009, 19-25.
[19]
Chen, C.L., Chu, F., Dong, Y.Z., Jiang, X., Li, L.L. and Cao, Z.M. (2011) Experimental Study on Influence Factors of Matric Suction State of Undisturbed Unsaturated Loess. JournalofLanzhouUniversity (NaturalSciences), 47, 12-17.
[20]
Jiao, W.G., Zhan, L.T., Lan, J.W. and Chen, Y.M. (2016) Analysis of Capillary Barrier Effect and Design Thickness with Loess-Gravel Cover. JournalofZhejiangUniversity (EngineeringScience), 50, 2128-2134.
