Reliability analysis of soil–water characteristics curve and its application to slope stability analysis C.F. Chiu a, ⁎, W.M. Yan b , Ka-Veng Yuen c a Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, Xikang Road, Nanjing 210098, China b Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China c Department of Civil and Environmental Engineering, University of Macau, Macau, China abstract article info Article history: Received 27 April 2011 Received in revised form 9 March 2012 Accepted 12 March 2012 Available online 21 March 2012 Keywords: Bayesian analysis Unsaturated soils Probability density functions Slope stability Soil–water characteristic curve (SWCC) is a crucial input for modeling the geotechnical problems with unsaturated soil. The accuracy of modeling relies on the assessment of the model parameter uncertainty. In this paper a Bayesian framework is presented to evaluate the updated probability density function (PDF) of the uncertain model parameters for SWCC. The Bayesian analysis is applied to derive the PDF of the model parameters in various forms of van Genuchten equation using the observed data of sand, sandy loam and silty loam. The analysis demonstrates that a 2-parameter model is sufficient for curve-fitting of the SWCC and the two model parameters are approximately statistically independent. Furthermore, the model parameters are influenced by the soil texture. Finally, an engineering example of the probabilistic slope stability analysis is used to illustrate the application of the reliability of SWCC. © 2012 Elsevier B.V. All rights reserved. 1. Introduction Numerous soils encountered in engineering practice are partially saturated, for example, compacted soils and natural soils in the arid regions. The unsaturated soil properties, significantly influenced by a change in the matric suction and the degree of saturation, are important for predicting the performance of geotechnical structures as well as the flow of water and contaminants in the vadose zone. The soil–water characteristic curve (SWCC) represents the water storage capacity of a soil with respect to a change in matric suction, which is important for the transient seepage analysis in the vadose zone. Past studies have shown that the SWCC can also be empirically correlated to some other unsaturated soil properties, such as hydraulic conductivity and shear strength (Childs and Collis-George, 1950; Mualem, 1976; Fredlund et al., 1994, 1996; Vanapalli et al., 1996; Lu and Griffiths, 2004). Many empirical equations have been proposed to curve fit the SWCC (Gardner, 1958; Brooks and Corey, 1964; van Genuchten, 1980; Williams et al., 1983; McKee and Bumb, 1984; Fredlund and Xing, 1994). One of the crucial questions is how precise the existing equations can represent the SWCC. Furthermore, the laboratory mea- surement of SWCC is very time-consuming and alternate methods have been proposed to estimate the SWCC. One of the methods is to use the SWCC of a similar soil. Another approach is to estimate the SWCC from the grain-size distribution curve (Arya and Paris, 1981; Fredlund et al., 1997). It is expected that a better estimation of SWCC would be resulted from a thorough statistical analysis of its distribution within a given soil class. Reliability analysis is an area of growing importance in geotechnical engineering. The success of numerical modeling of geotechnical systems greatly depends on the uncertainty modeling, among which uncertainty in soil properties is a crucial input of the analysis. Baecher and Christian (2008) classified four sources for the uncertainty of soil properties: (i) spatial variability of soil, (ii) random measurement noise, (iii) statistical estimation error, and (iv) model bias. The first two sources are caused by data scatter and the last two are caused by the systematic errors. There are generally two approaches for conducting the statistical estimate from the sample data: frequentist and Bayesian. The frequentist approach is widely used in geotechnical engineering, which has been used recently in analyzing the SWCC data. Sillers and Fredlund (2001) conducted a conventional statistical analysis over 200 data sets and presented the statistics (mean and standard deviation) on the model parameters for different empirical equations of SWCC. Phoon et al. (2010) have demonstrated the suitability of a lognormal random vector in predicting the parameters of van Genuchten (1980) model based on the database UNSODA. Despite the rare applications of the Bayesian approach in modeling the uncertainty of soil properties (Miranda et al., 2009; Yan et al., 2009; Wang et al., 2010), Bayesian estimation is advantageous over frequentist estimation (Yuen, 2010a). For example, it can incorporate the ‘a priori’ knowledge into the analysis of current observation data. Another advantage is that it estimates the Engineering Geology 135-136 (2012) 83–91 ⁎ Corresponding author. E-mail addresses: acfchiu@yahoo.com.cn (C.F. Chiu), ryanyan@hku.hk (W.M. Yan), kvyuen@umac.mo (K.-V. Yuen). 0013-7952/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.enggeo.2012.03.004 Contents lists available at SciVerse ScienceDirect Engineering Geology journal homepage: www.elsevier.com/locate/enggeo