Veiskarami, M. & Zanj, A. (2014). Ge´otechnique 64, No. 10, 759–775 [http://dx.doi.org/10.1680/geot.14.P.020] 759 Stability of sheet-pile walls subjected to seepage ﬂow by slip lines and ﬁnite elements M. VEISKARAMI  and A. ZANJ† Stability of sheet-pile walls is often very sensitive to seepage ﬂow. In the presence of seepage ﬂow, the reduction in passive pressure on one side and increase in active pressure on the other side of the wall increase the risk of the instability that may precede instabilities due to piping or ground heaving. In this research the earth pressure behind sheet-pile walls in granular soils is studied. The ﬂow ﬁeld is computed by the ﬁnite-element method and the slip lines (stress characteristics) method is utilised to compute the associated stress ﬁeld required to compute the effective passive pressure. The same ﬁnite- element mesh and interpolation functions are used to solve the ﬂow ﬁeld and to interpolate the seepage forces in the stress ﬁeld solved by the stress characteristics method. Comparisons are made to verify the numerical results with those values available in the literature; these show reasonable agreement. The stability of sheet-pile walls is then analysed for a number of different problems with varying geometries and boundary conditions. These different geometries and boundary conditions are expressed in terms of non-dimensional factors and results are plotted. KEYWORDS: earth pressure; failure; ﬁnite-element modelling; groundwater; numerical modelling; sheet piles and cofferdams INTRODUCTION Passive earth pressure is one of the classical problems in soil plasticity which has been well studied in the literature. Dating back to historical works of Coulomb (1776) with the force limiting equilibrium approach and Rankine (1857) based on the stress state at plastic limiting equilibrium, a number of different methods and approaches have been developed (e.g. Terzaghi, 1943; Caquot & Ke´risel, 1948; Brinch-Hansen, 1953; Janbu, 1957 among many). Later on, methods based on the limiting equilibrium (Shields & Tolunay, 1972; Rahardjo & Fredlund, 1984; Kumar & Subba Rao, 1997; Chen & Li, 1998; Subba Rao & Choudhury, 2005; Ghosh, 2008; Ghosh & Sharma, 2012); limit analysis (Collins, 1973; Chen, 1975; Arai & Jinki, 1990; Soubra, 2000; Soubra & Macuh, 2002; Shiau et al., 2008); methods based on the stress characteristics (Sokolovskii, 1965; Graham, 1971; Sabzevari & Ghahramani, 1972, 1973; Houlsby & Wroth, 1982; Kumar, 2001; Kumar & Chitikela, 2002); and those methods based on the zero exten- sion lines (ZEL) concept (James & Bransby, 1970; Habibagahi & Ghahramani, 1979; Ghahramani & Clemence, 1980; Anvar & Ghahramani, 1997) were developed; these covered both active and passive earth pressure problems under either static or seismic loads (Sokolovskii, 1960; Harr, 1966). The inﬂuence of seepage on the stability of earth- supported structures has also been studied; although there are few works known to the present authors that deal with this special topic (Terzaghi, 1943; Kawamura & Watanabe, 1989; Soubra et al., 1999; Benmebarek et al., 2006; Barros, 2006; Wang et al., 2008a, 2008b; Barros & Santos, 2012). Very recently, Barros & Santos (2012) studied the effect of seepage ﬂow on the active earth pressure on a rigid retaining wall under heavy rainfall by the limit equilibrium method. They assumed a failure surface and computed the pore pressure along this surface which had been found numeri- cally by solving the steady-state ﬂow problem in the domain. They concluded that the active pressure increases substan- tially under seepage ﬂow. In both the attempts by Terzaghi (1943) and Soubra et al. (1999), as well as others, a failure surface was assumed and the effect of seepage ﬂow was taken into account by reducing the effective stress along this failure surface; no consideration was given to the decrease in the body forces due to the seepage ﬂow. As stated by Soubra et al. (1999), Benmebarek et al. (2006) and Barros & Santos (2012), the active earth pressure increases and the passive earth pressures decreases with the increase in hydraulic head loss. As a consequence, it seems to be essential to assess the effective active and passive earth pressures in the presence of seepage ﬂow. A rough estimate of both active and passive earth pressures can be made by using an equivalent submerged unit weight of the soil (see Soubra et al., 1999). This formula makes use of an average approximate hydraulic gradient. However, studies have shown that this is still a very rough estimate, in particular for the passive earth pressure problem (Benmebar- ek et al., 2006). In addition, there is no consideration for the groundwater ﬂow pattern and its effect on the resisting soil mass behind the sheet-pile wall. In the present research, the main goal is to compute the passive earth pressure behind a sheet-pile wall, supporting a granular soil, in presence of a groundwater ﬂow. The procedure is based on the general solution of plasticity problems in soil mechanics under body forces resulting from the soil weight and the seepage ﬂow. Unlike the unit weight (or the submerged unit weight, in presence of seepage ﬂow), which is constant through a homogeneous soil medium, the seepage force has both its magnitude and direction change as it passes through the soil. Accordingly, there is no closed- form solution for the problem and a numerical method will be required to compute the effective passive pressure. The ﬁnite-element method is employed to compute the ﬂow ﬁeld and the method of stress characteristics is used for the determination of the effective stress ﬁeld in the soil domain. Manuscript received 1 February 2014; revised manuscript accepted 12 September 2014. Published online ahead of print 28 October 2014. Discussion on this paper closes on 1 March 2015, for further details see p. ii.  University of Guilan, Rasht, Iran; also Shiraz University, Shiraz, Iran. † University of Guilan, Rasht, Iran.