Engineering Geology 184 (2015) 96–103 Contents lists available at ScienceDirect Engineering Geology journal homepage: www.elsevier.com/locate/enggeo Slope stability analysis under unsaturated conditions: Case studies of rainfall-induced failure of cut slopes Seboong Oh a,⁎,NingLub a Department of Civil Engineering, Yeungnam University, Gyeongsan, Republic of Korea b Department of Civil and Environmental Engineering, Colorado School of Mines, Golden, CO 80401, United States article info abstract Article history: We present two case studies of rainfall-induced failure of engineered slopes. The traditional limit equilibrium and Received 18 July 2014 finite element methods are expanded to unsaturated conditions using a generalized effective stress framework. Received in revised form 11 October 2014 Because effective stress is represented by the suction stress characteristic curve (SSCC), and the SSCC and the Accepted 10 November 2014 soil water retention curve (SWRC) have been unified with the same set of hydromechanical parameters, the Available online 17 November 2014 expanded framework requires only three hydromechanical parameters in addition to those used for saturated Keywords: slope stability analysis. Using recorded rainfall, measured shear strength parameters and the SWRC, and site fi Slope stability geology, transient slope stability analyses are conducted to reconstruct the failure events. We nd that, despite Effective stress differences in slope geometry, hydromechanical properties, shear strength, and rainfall history, the actual failure Shear strength occurred when the simulated factor of safety approaches its minimum below 1.0. It is shown that the hydrome- Suction stress chanical framework under the suction stress-based effective stress can reconcile the observed timing of failure. Unsaturated soil © 2014 Elsevier B.V. All rights reserved. Finite elements 1. Introduction been made using either the “gravity increase method”,orthe“strength reduction method” (e.g., Dawson et al., 1999; Griffiths and Lane, 1999; Limit equilibrium (LE) methods are the most widely used for Krahn, 2003), or the field of local factor of safety method (Lu et al., analyzing slope stability and designing engineered slopes. The simplici- 2012). ty and versatility of the LE methodology rest with the concept that the One common assumption made in most of the existing slope geometry of the potential failure surface in a slope is known a-priori stability methods is that along the failure surface pore water pressure and the slope can be discretized into finite vertical slices. Each slice is is positive or zero (e.g., Bishop, 1954; Morgenstern and Price, 1965; then analyzed using principles of force and/or moment equilibrium Duncan, 1996). In reality, under rainfall conditions, the degree of satura- (e.g., Peterson, 1955; Duncan and Wright, 2005) for its contribution to tion within a slope and along a failure surface could be highly variable the stability of the slope. Over the previous century, a variety of LE and pore water pressure could be negative (e.g., Godt et al., 2009; techniques have been developed to determine stability conditions, Borja and White, 2010; Buscarnera and Whittle, 2012). Thus this depending on the equations of equilibrium that are included and what assumption could lead to incorrect treatment of effective stress or assumptions are made to account for inter-slice forces (e.g., Bishop, shear strength, and ultimately, inaccuracy in computing the factor of 1954; Morgenstern and Price, 1965; Spencer, 1967; Duncan, 1996). In safety of a slope. Although some recent studies are specifically focused recent years, to accurately compute inter-slice forces and seepage on infiltration induced landslides, most of them combine analysis of conditions, advanced quantitative methods such as analytical, finite the hydrological behavior with an infinite or analytical slope-stability elements and finite differences have been developed and incorporated analysis or examine rainfall patterns and relate them to slope stability with LE algorithms (e.g., Ugai and Leshchinsky, 1995; Duncan, 1996; over large areas that include multiple landslides (e.g., Iverson, 2000; Dawson et al., 1999). Crosta and Frattini, 2003). However, most of these studies only consider The key indicator in slope stability analysis is the factor of safety slope failure below the groundwater table, overlooking the contribution (FOS), which is commonly defined as the ratio of the resisting shear of effective stress (suction stress) to the strength of the soil under force to the driving shear force along a failure surface. To better calculate transient unsaturated flow conditions. the factor of safety and identify the failure surface, recent advances have In recent years, slope-stability analyses have been expanded to include coupled hydromechanical processes under variably saturated conditions (e.g., Griffiths and Lu, 2005; Lu and Godt, 2008; Borja and ⁎ Corresponding author. White, 2010; Buscarnera and Whittle, 2012; Lu et al., 2013). These E-mail addresses: [email protected] (S. Oh), [email protected] (N. Lu). analyses incorporate the variation of saturation, leading to more http://dx.doi.org/10.1016/j.enggeo.2014.11.007 0013-7952/© 2014 Elsevier B.V. All rights reserved. S. Oh, N. Lu / Engineering Geology 184 (2015) 96–103 97 accurate assessments of stability of slopes under infiltration conditions fields are governed by the following linear momentum equilibrium and demonstrate that a better physical representation of water flow equation: and stress can be attained in unsaturated soils. When water infiltrates γ into hillslopes, the water content of the hillslope materials and the ∇ Á σ þ b ¼ 0 ð4Þ water table level vary accordingly. Changes in the water content of the g soil imply changes in weight, matric suction, effective stress, and stabil- where, σ is stress tensor with 3 independent total stress variables in ity of a slope. Thus, understanding the physical conditions (i.e., if they two-dimensional space; b is vector of body forces with 2 components; are saturated or not) within variably saturated slopes when failures γ is the unit weight of materials and depends on water content; g is occur is needed for accurate assessment and prediction. The study pre- acceleration due to gravity. The effective stress field is computed by sented here presents some of the first documented case studies of failed the suction stress-based equation (Lu and Likos, 2004, 2006): engineered cut slopes analyzed by employing unsaturated soil mechan- ics concept. The main objectives of this work are as follows: (1) to quan- σ′ ¼ σ−u −σ s ð5Þ titatively understand why slopes failed at the studied sites under rainfall a conditions, and (2) to use these case studies to demonstrate that the where the suction stress characteristic curve σ s (or SSCC) can be failure of unsaturated engineered cut slopes under transient rainfall expressed as a function of matric suction (u − u )(Lu and Likos, conditions can be reconciled using the hydromechanical framework a w 2004; Lu et al., 2010): described below. θ−θ 1 1−1=n σ s − r u −u − u −u 6 2. An LE/FE framework for variably saturated slope stability analysis ¼ θ −θ ðÞ¼a w ðÞa w α − n ð Þ s r 1 þ fgðÞua uw fi In comparison with the classical LE and nite element-based slope where parameters α and n are identical to van Genuchten's (1980) stability analysis, the framework employed in this work involves SWRC model (Eq. (2))andMualem's (1976) HCF model (Eq. (3)). two major enhancements: (1) accounting for transient unsaturated Note that using a common set of parameters to define a soil's SWRC, fl fi ow, and (2) implementing a uni ed effective stress for all degrees of HCF, and SSCC minimizes the number of parameters involved in a vari- saturations. The framework involves a one-way hydromechanical ably saturated slope stability analysis; the other remaining parameters coupling in which simulated transient water content and matric suction in the hydromechanical framework are the drained cohesion c′ and fric- fi fi elds are used to compute elds of total and effective stress, and tion angle ϕ′ defined in the Mohr–Coulomb failure criterion. The inter- consequently, the factor of safety. For completeness, the essentials of relations among a soil's SWRC, HCF, and SSCC have been theoretically fl such framework are brie y described below. established and experimentally validated (van Genuchten (1980) and fi Transient elds of water content and pressure head in variably Wayllace and Lu (2011) for the relation between SWRC and HCF; Lu saturated soil slopes are governed by Richards' equation (Richards, and Likos (2006), Lu et al. (2010), Song et al. (2012),andLu and Kaya 1931): (2013) for the relations among SWRC, HCF, and SSCC). Finally, once the fields of total and effective stresses are obtained, the ∂θðÞh ∇ Á khðÞ∇H ¼ ð1Þ classical LE analysis with finite element (FE) solutions is used to deter- ∂t mine the FOS of the slope under transient infiltration conditions where h is the pressure head or suction head; H is the total head being (e.g., Godt et al., 2012). A method of slices is used to compute the FOS the sum of suction head and elevation; k(h) is the hydraulic conductiv- along failure surfaces and to search a critical slip surface (a surface ity function (HCF); and θ(h) is the pressure-head dependent volumetric with the lowest FOS). The FOS is commonly defined as the ratio of the water content (or water content hereafter). The relation between the shear resistance and the mobilized shear force along the entire length pressure head and water content is called the soil water retention of the slip surface as: fi curve (SWRC). To solve Eq. (1) for elds of suction head and water X X ÂÃÀÁ τ l 0 σ 0 φ0 content, two characteristic functions, namely, SWRC and HCF, have to i f base c þ tan lbase FOS ¼ X i ¼ i X i ð7Þ be defined and known.