Engineering Geology 241 (2018) 76–85 Contents lists available at ScienceDirect Engineering Geology journal homepage: www.elsevier.com/locate/enggeo Slope stability of landfills considering leachate recirculation using vertical wells T ⁎ Shi-Jin Fenga, Zheng-Wei Chena, Hong-Xin Chena, , Qi-Teng Zhenga, Run Liub a Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China b State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China A R T I C LE I N FO A B S T R A C T Keywords: Bioreactor landfill Municipal solid waste Vertical well Leachate recirculation Slope stability In bioreactor landfills, leachate recirculation system can significantly promote moisture distribution, thereby enhancing the biodegradation of municipal solid waste (MSW). However, it increases pore pressure inside landfills, which can greatly affect slope stability. In this study, a three-dimensional numerical model is established to study the landfill slope stability under leachate recirculation through Vertical Wells (VWs). A leachate flow model is adopted to describe the migration of leachate, and the distribution of pore pressure is then used to calculate the Factor of Safety (FS) using strength reduction method. A large number of simulations are conducted using the proposed model to investigate the influences of injection pressure, hydraulic and mechanical properties, slope gradient, VW location and group-well configuration on slope stability. Large injection pressure or anisotropy of MSW is adverse to the slope stability. FS changes almost linearly with the variation of friction angle and cohesion. The horizontal distance between the VWs and the slope surface (d) and well spacing (D) are two important factors for slope stability. Design charts of the minimum safe distance (ds) and the minimum safe well spacing (Ds) are proposed considering various conditions. Finally, a design method of leachate recirculation system using VWs is proposed considering both recirculation efficiency and slope stability. The proposed model can well accommodate practical landfills with leachate recirculation system using VWs. The method and the results are promising to be used as a reference in engineering practice. 1. Introduction Landfill is the main method for Municipal Solid Waste (MSW) disposal all around the world. In recent decades, bioreactor landfills have been developed by recirculating the leachate collected from Leachate Collection and Removal System (LCRS) back into the landfill, which reduces the amount of leachate needed to be disposed. By leachate recirculation, the moisture content of MSW can be increased, which accelerates MSW degradation and landfill stabilization processes (Allen, 2001; Reinhart et al., 2002). In engineering practice, Vertical Wells (VWs), which consist of spraying pipes and highly permeable filter materials surrounded, are the most widely used facility for leachate recirculation, compared with horizontal trenches and surface spraying (Reinhart and Townsend, 1997). On the other hand, the injection of leachate also increases pore pressure inside landfills, and it may cause slope failure. For example, the slope failure in Payatas landfill was caused by excess pore pressure (Merry et al., 2005). The failure of landfill slopes would pose a threat to the infrastructures and the socio- economic activities nearby (Marcato et al., 2012). Therefore, it is very important to investigate the effect of leachate recirculation on slope stability for rational design of landfills. Numerous researches have studied leachate recirculation in landfills. Jain et al. (2010), Haydar and Khire (2005) and Feng et al. (2014, 2015) investigated leachate migration in bioreactor landfills with VWs, horizontal trenches and surface spraying, respectively. Kadambala et al. (2011) presented the impact of leachate recirculation using VWs on pore pressure at a full-scale landfill. Feng et al. (2017) employed a three-dimensional two-phase flow model based on OpenFOAM to study the leachate recirculation using VWs and the interactions between leachate and gas were evaluated. However, these studies did not consider the impact of recirculated leachate on slope stability in landfills, which is a very important concern when a landfill is designed. Some researches further considered the influence of leachate recirculation on slope stability in landfills. Koerner and Soong (2000) presented a unified approach explaining the influence of leachate on landfill stability in a sequential manner, but the spatial-temporal ⁎ Corresponding author. E-mail addresses: [email protected] (S.-J. Feng), [email protected] (Z.-W. Chen), [email protected] (H.-X. Chen), [email protected] (Q.-T. Zheng), [email protected] (R. Liu). https://doi.org/10.1016/j.enggeo.2018.05.013 Received 8 November 2017; Received in revised form 31 March 2018; Accepted 11 May 2018 Available online 16 May 2018 0013-7952/ © 2018 Elsevier B.V. All rights reserved. Engineering Geology 241 (2018) 76–85 S.-J. Feng et al. characteristics of leachate recirculation were not considered. Thiel and Christie (2005) studied the potential long-term concern of slope stability caused by leachate recirculation, whereas the discussion was qualitative rather than quantitative. Xu et al. (2012) and Giri and Reddy (2014) developed two-dimensional (2D) single-phase (leachate) and two-phase (leachate and gas) flow models, respectively, to investigate the landfill slope stability under leachate recirculation condition using horizontal trenches. However, the geometries of landfills are always complex, which cannot be simulated by these 2D models. Moreover, in a landfill with leachate recirculation system using VWs, the transport of leachate and the distribution of pore pressure are spatially complicated and cannot be simulated with 2D models. To the best of our knowledge, few studies have focused on the slope stability of landfills with leachate recirculation using VWs. This paper presents a three-dimensional (3D) model for analyzing slope stability in landfills when recirculating leachate using VWs. This model can reasonably reflect the landfill conditions and simulate both single-well and group-well recirculation systems. The effects of injection pressure, hydraulic-mechanical properties of MSW, and landfill geometric parameters (i.e., slope gradient, VW location) on slope stability are then investigated using the proposed model. A preliminary design method of VWs considering the slope stability of landfill is also proposed. Two key design parameters, including the minimum safe distance between VWs and landfill slope surface (ds) and the minimum safe well spacing (Ds), are carefully investigated and recommended values are given. The established 3D model can well accommodate landfills with leachate recirculation system using VWs. The method and the results are promising to be used as a reference in engineering practice. 2. Methodology 2.1. Conceptual model There are numerous vertical wells working together in a leachate recirculation system of landfill (Fig. 1). In this section, a 3D bioreactor landfill is established with a cover system on the top and the slope surface, and a Leachate Collection and Removal System (LCRS) at the bottom (Fig. 1). FLAC3D is employed to build the model and both brick and radial cylinder grid types are used. A sensitivity analysis is carried out first to estimate the grid size and it is found that when the grid size is smaller than 0.5 m, the simulation results are almost the same, so a grid size of 0.5 m is chosen. The cover system, including the top and the slope surface, is regarded as impermeable. The bottom LCRS is assumed as a free-drainage boundary to allow the leachate flowing out by fixing the pore pressure of grids at the bottom to zero. In a basic scenario, a VW is set near the slope (Fig. 1a). The height of the landfill is H and the elevation of the injection screen is h (Fig. 1b). d is the horizontal distance between the VW and slope surface at the elevation of the injection screen top. The injection screen at the bottom of the VW has a length of 2 m and a diameter of 0.3 m in this study. Leachate is recirculated into the landfill under controlled pressure. The mechanical boundary conditions are shown in Fig. 1a. The bottom surface is totally constrained and the displacements of two end faces are fixed in the y direction (v = 0), and the back face is constrained in the x direction with a u of 0. Leachate migrates in the landfill, which can increase the water content of MSW. The impact zone in Fig. 1 is defined as area with degree of saturation larger than 0.8, which can provide an optimal environment for biodegradation (ITRC, 2006). During leachate recirculation, leachate flows inside landfill and spreads widely before being collected by the LCRS, and thus the impact zone gets larger with time before reaching a steady state. The effective stress of MSW within the impact zone decreases with the increase of degree of saturation, resulting in a decrease of shear strength (Zhang et al., 2015). With the expansion of the impact zone, slope failure may occur (Fig. 1b). The anisotropic structure of MSW has been reported in both field Fig. 1. Conceptual model of a landfill slope with vertical wells: (a) 3D view of single-well scenario; (b) cross-sectional view of single-well scenario; (c) 3D view of group-well scenario. (Kadambala et al., 2011; Singh et al., 2014) and laboratory tests (Hudson, 2007; Stoltz et al., 2010). The anisotropy is mainly attributed to the anisotropic deposition of MSW (landfilling layer by layer), the high compression stress in the vertical direction, and the nature of some predominant waste components such as plastic and paper. Hence, MSW has different hydraulic conductivities in horizontal and vertical directions, and the anisotropic coefficient (A) is used to evaluate the difference, which can be expressed as A = kh/ k v (1) where kh and kv are the horizontal and vertical hydraulic conductivities, respectively. Reddy et al. (2009) reported that the hydraulic conductivity of MSW has a wide range of 3.7 × 10−8 to 1 × 10−2 cm/s. Landva et al. (1998) also reported that kv could range from 2 × 10−6 to 2 × 10−3 cm/s and A from 4 to 10. An even larger range of A (1 to 100) was reported by Tchobanoglous et al. (1993). Thus, in this study, a range of 1 × 10−6 to 1 × 10−3 cm/s for hydraulic conductivity and a range of 1 to 20 for A are adopted for analysis. The initial saturation of MSW is 0.4 which is within the reported range in landfills and was also adopted in other studies (e.g., Reddy et al., 2014). Under the gravity load, the initial pore pressure can be solved automatically by the 77 Engineering Geology 241 (2018) 76–85 S.-J. Feng et al. FLAC3D. It is noteworthy that this study intends to investigate the slope stability of typical landfills and hence the geometry of the conceptual model in Fig. 1 is simple. Nonetheless, the method is also applicable for more complex landfill as long as the information of landfill geometry and MSW properties are given. 2 aP = σ P = σt As leachate recirculation can saturate the waste, a leachate flow model should be established to simulate the leachate migration under this condition. In this study, the Fast Lagrangian Analysis of Continua in 3 Dimensions (FLAC3D) is used with detailed mathematical formulations provided in FLAC3D manual (ITASCA, 2012). Pore pressure distribution obtained by the leachate flow model can then be used in the slope stability analysis, wherein the Factor of Safety (FS) is calculated by the strength reduction method combined with the Mohr-Coulomb failure criterion. The initial stress field is calculated by solving mechanical equilibrium equations under gravity before leachate recirculation and stability calculation. The transport of leachate is described by Darcy's law: ki k (̂ s ) (p − ρw x j gj ), i μ c trial = Performance of the model in describing leachate flow has been validated by Feng et al. (2016) using both field data and numerical solution. Since published slope stability analysis results of landfill considering leachate recirculation using VW are quite limited, a 2D model with horizontal trenches reported by Xu et al. (2012) is adopted for verification. Xu et al. (2012) used SEEP/W and SLOPE/W (from Geo-Slope International) to analyze the landfill slope stability under leachate recirculation condition. This 2D landfill model has a height of 50 m, a width of 175 m and the slope gradient is 1:3 (vertical/horizontal). A horizontal injection trench (1 m wide and 1 m high), under a continual injection pressure of 49 kPa, is set near the slope at a height of 30 m above the LCRS. MSW inside the landfill is assumed to be homogeneous and anisotropic. In order to compare with the 2D model, a 3D model is built using the present method, which has the same size, material properties and boundary conditions, and the model is one meter thick. Leachate is injected continually for 10 years, and the moisture distribution inside the landfill reaches a steady state. Different values of friction angle (i.e., 20°, 25°, 30° and 35°) are used to calculate FS (Fig. 2). Although different calculation methods for FS are adopted in the two studies (limit equilibrium method in Xu et al., 2012 and strength reduction method in this paper), the obtained results match reasonably well (Fig. 2). The small difference is acceptable because of the difference between the two methods. A similar difference was also observed by Wei et al. (2009), who concluded that the strength reduction method could obtain a slightly higher FS than the limit equilibrium method in 3D slope models. (4) where qi,i is the gradient of qi; qv is the leachate source term; t is the time; θ is the water content. The balance of momentum can be expressed as dvi dt (5) where σij, j is the gradient of normal stress; ρ (=ρd + nsρw) and ρd are the density and dry density of MSW, respectively; vi is the velocity; n is the porosity. The Mohr-Coulomb model in the FLAC3D is employed in the analysis of slope stability. The failure criterion of this model is a composite Mohr-Coulomb failure criterion with tension failure criterion. The Mohr-Coulomb failure criterion can be expressed as σ1 − σ3 1 + sin(φ) 1 + sin(φ) =0 + 2c 1 − sin(φ) 1 − sin(φ) (6) where c is the cohesion; φ is the friction angle; σ1 and σ3 are the principal stresses. The tension failure criterion can be expressed as σ3 ‐σ t = 0 (7) where σ is the tensile strength and The flow rule can be expressed as t σ3 ‐σ t + aP (σ1 t σmax − σ P) = =0 c . tan φ 4. Slope stability analysis and design of VW (8) In this part, slope stability of a typical bioreactor landfill is assessed. The effects of some important influence factors are studied first, the where a and σ are constants defined as P (11) 3. Model verification The fluid mass balance law for leachate flow in porous MSW can be expressed as σij, j + ρgi = ρ (10) Trial values of FS (FS ) are employed to reduce the strength parameters with a bracketing approach. Firstly, stable and unstable bracketing states are found (stable bracketing state corresponds to FStrial values for which solution converges, and unstable bracketing state corresponds to FStrial values for which solution does not converge), and then the intermediate FStrial value is adopted for a new solution. If the new solution converges, the new FStrial value supersedes the stable FStrial, otherwise the unstable FStrial value is updated. The calculation ends when the difference between stable and unstable solutions is less than a specified tolerance, which is named the limiting equilibrium state (ITASCA, 2012; Giri and Reddy, 2013). The above-mentioned equations are numerically solved with FLAC3D using the finite difference method. (3) ∂θ ∂t (9) trial where qi is the flow rate; p is the pore pressure; ki is the saturated permeability; k (̂ s ) is the relative hydraulic conductivity; s is the leachate saturation; μ is the coefficient of dynamic viscosity; ρw is the leachate density; xj is the coordinate; gj is the gravity; i and j take the values of 1, 2, 3 for components that involve spatial dimensions. The relative hydraulic conductivity is adopted to describe the effect of saturation on leachate transport, which is zero for completely dry condition and one for fully saturated condition (ITASCA, 2012): − qi, i + qv = c FS trial tan φ φtrial = arctan ⎛ trial ⎞ ⎝ FS ⎠ (2) k (̂ s ) = s 2 (3 − 2s ) 1 + sin(φ) 1 + sin(φ) − 2c 1 − sin(φ) 1 − sin(φ) The strength reduction method is applied for calculating FS by reducing the shear strength parameters in the Mohr-Coulomb failure criterion (Eq. 6) to bring the slope to a limiting equilibrium state. This method offers a number of significant advantages over traditional limit equilibrium method as it eliminates the need for prior assumptions on failure mechanisms (e.g., the type, shape and location of failure surfaces). FS is defined according to the following equations: 2.2. Leachate flow model and slope stability analysis qi = − 1 + sin(φ) ⎞ 1 + sin(φ) 1 + ⎛⎜ ⎟ + 1 − sin(φ) ⎝ 1 − sin(φ) ⎠ P 78 Engineering Geology 241 (2018) 76–85 S.-J. Feng et al. a larger time to reach the steady state. For P = 200 kPa (250, 300 kPa), Vim reaches a maximum value of approximately 52,000 m3 (62,500, 76,000 m3) at T = 680 days (750, 820 days). On the other hand, FS of the landfill slope decreases with the recirculation time (Fig. 4). All the curves have an initial FS of around 2.4. For P = 200 kPa, FS drops slightly to 2.3 indicating little effect of leachate recirculation on slope stability. However, this effect is significant for P = 300 kPa as FS reduces to 1 at T = 826 days. When P is 250 kPa, both Vim and FS curves lie between those of P = 200 and 300 kPa. The variation of FS with P and T can be explained by the leachate migration. At T = 100 days, the impact zones for different P values are all small and far from the slope surface (Fig. 3a), resulting in large FS. When a steady state is reached, higher pore pressure near the slope can be observed for a larger P, leading to a greater decrease in the effective stress and thus a greater possibility of slope failure. Besides, Fig. 5 shows the effect of leachate recirculation on the slope stability in terms of shear strain increment. Both contours are obtained at a limiting equilibrium state when calculating FS, and much larger shear strain increment can be observed on the slope surface with a P of 300 kPa, compared to no leachate injection scenario. Fig. 2. Comparison of FS values obtained by Xu et al. (2012) and this paper. reference values of two important parameters for group well system (the minimum safe distance between VWs and slope surface, and the minimum safe well spacing) are investigated, and finally a preliminary design method for VW is also proposed. The analyzed landfill has a height of 20 m (H), and the elevation of injection screen (h) is assumed to be 14 m, except for when studying the effect of group-well configuration. Its size along the slope is 200 m. According to the results of field and laboratory tests (Benson and Wang, 1998; Zekkos et al., 2006; Bray et al., 2009; Stoltz et al., 2011; Xu et al., 2012; Giri and Reddy, 2014), the parameters adopted for analysis are determined and summarized in Table 1, which are within the reported ranges in the literature, and detailed parameters in the following simulations are also presented in the corresponding figures. 4.2. Influence of hydraulic and mechanical properties Hydraulic properties of MSW are the most important factors in leachate migration, and mechanical properties can substantially affect the slope stability (Zhan et al., 2008). Thus, a sensitivity analysis for single-well scenario is conducted to evaluate the influence of hydraulic and mechanical properties. In each simulation, d = 10 m and P = 225 kPa. Six values of kv (i.e., 1 × 10−6, 1 × 10−5, 3 × 10−5, 5 × 10−5, 1 × 10−4, 1 × 10−3 cm/s) and six values of A (i.e., 1, 3, 5, 7, 9, 10) are used to describe the variation in hydraulic properties. For mechanical properties, four values of cohesion (i.e., 5, 10, 15, 20 kPa) and five values of friction angle (i.e., 20°, 25°, 30°, 35°, 40°) are adopted. FS is calculated when the steady state is reached. As shown in Fig. 6, the hydraulic conductivity kv slightly affects FS, but the anisotropic coefficient A significantly affects FS. For example, when A is 1, FS for kv = 1 × 10−5 cm/s equals to 2.62 and then decreases to 2.61 for kv = 1 × 10−4 cm/s. On the other hand, when kv is 1 × 10−5 cm/s, FS decreases from 2.62 to 2.02 as A increases from 1 to 10. The reason is that a larger A means easier transport of leachate in the horizontal direction, thus resulting in greater pore pressure near the slope and a lower FS. Therefore, the value of anisotropic coefficient should be cautiously taken into consideration when designing the leachate recirculation system in a landfill. It is not strange that FS increases with increasing friction angle (φ) and cohesion (c) (Fig. 7). An interesting phenomenon is that FS changes almost linearly with the variation of friction angle and cohesion. FS increases by approximately 0.4 when the friction angle increases by 5°. Similarly, FS increases by nearly 0.2 when the cohesion increases by 5 kPa. The increase rates of FS with friction angle and cohesion can be 4.1. Influence of injection pressure To study the influence of injection pressure (P), leachate is injected back into the landfill through a VW under different injection pressures: 200, 250 and 300 kPa. The horizontal distance between the VW and the slope surface (d) is 12 m. Fig. 3 shows the impact zone on the 100th and the 1000th recirculation days. A larger P can dramatically increase the extent of impact zone in both horizontal and vertical directions. Under a P of 300 kPa, the recirculated leachate can even reach the slope surface on the 1000th day (Fig. 3b), which is harmful to the slope stability and environment. The volume of impact zone (Vim) and FS can be monitored during the recirculation process and the variations with the recirculation time (T) are shown in Fig. 4. The results reveal that P plays an important role in leachate migration and slope stability with regard to Vim and FS, respectively. Vim almost linearly increases with T in the initial period until reaching a steady state (Ts). A greater P leads to a greater Vim and Table 1 Properties and variables used in numerical simulations. Property Density (kg/m3) Fluid density (kg/m3) Porosity Initial saturation Bulk modulus (Pa) Shear modulus (Pa) Fluid bulk modulus (Pa) Value 1500 1000 0.45 0.4 1.5 × 105 1.0 × 105 2.0 × 109 Variable Scenario Slope gradient: (1:λ) Hydraulic conductivity: kv (cm/s) Anisotropic coefficient: A Cohesion: c (kPa) Friction angle: φ (°) Distance between slope and VW: d (m) Well spacing: D (m) Landfill height: H (m) Elevation of injection screen: h (m) Injection pressure: P (kPa) 79 Single-well Group-well 1:3, 1:4, 1:5 1 × 10−6–1 × 10−3 1, 3, 5, 7, 9, 10, 20 5, 10, 15, 20 20, 25, 30, 35, 40 1–20 – 20, 50 8, 10, 12, 14 100, 150, 200, 250, 300 1:3 1 × 10−5 10 15 30 6–42 4–22 20 12, 14 100, 150, 200, 250 Engineering Geology 241 (2018) 76–85 S.-J. Feng et al. Fig. 3. Variation of impact contours at (a) T = 100 days; (b) T = 1000 days. Fig. 4. Variations of volume of impact zone and FS with time. Fig. 6. Influences of hydraulic conductivity and anisotropic coefficient on FS. Fig. 5. Shear strain increment in slope at a limiting equilibrium state: (a) no injection; (b) P = 300 kPa. 80 Engineering Geology 241 (2018) 76–85 S.-J. Feng et al. Fig. 7. Influences of cohesion and friction angle on FS. used as a reference for similar scenarios. In fact, for other combinations of hydraulic parameters, similar linear variation of FS is observed and hence not presented here. 4.3. Influence of slope gradient Slope gradient greatly influences the landfill slope stability, and thus it is necessary to investigate it for the design of landfill (Ersoy et al., 2013). Three different values of slope gradient are considered in this paper, including 1:3, 1:4 and 1:5 (vertical/horizontal). A VW is set under the slope corner (Fig. 8) and leachate is recirculated with a series of injection pressure values. The obtained FS is calculated when the steady state is reached. Under the same injection pressure, the landfill slope with a smaller slope gradient has a greater FS. For example, when P = 150 kPa (260 kPa), FS equals to 2.43 (1.50), 3.11 (2.28) and 3.80 (2.86) for slope gradients of 1:3, 1:4 and 1:5, respectively. It is clear that slope gradient has a significant impact on the landfill slope stability and should be rationally designed. It is noteworthy that with the increase of P, FS slightly decreases first and then starts a dramatic drop at approximately 210 kPa for all the three slope gradient values. Thus, there exists a critical injection pressure (e.g., 210 kPa in this case) beyond which FS starts to drop quickly, and the value is almost the same for different slope gradients. Fig. 9. Variation of FS with d: (a) P = 200 kPa; (b) different P values. 4.4. Influence of VW location and design of ds The location of VW may significantly affect the landfill slope stability. For example, the horizontal distance between the injection screen and the slope surface (d) is a key factor for the design of landfill recirculation system. A too small d can increase the pore pressure near the slope and thus endanger the slope stability, so a minimum safe distance (ds) should be guaranteed. Simulations are first carried out with different d values (9, 10, 11 and 12 m) to determine ds for P = 200 kPa as an example. As mentioned above, the hydraulic conductivity slightly affects slope stability and kv of 1 × 10−5 cm/s is chosen in this section. c = 15 kPa and φ = 30° are adopted for analysis here. Fig. 9a shows the distribution of pore pressure along the horizontal axis for the four scenarios, and the origin is located at the slope surface (see Fig. 9a). The leachate is close to the slope surface when d equals to 9 and 10 m, leading to lower FS of 1.60 and 2.29, respectively. When d equals to 11 or 12 m, the increased pore pressure caused by the recirculated leachate does not affect the slope stability since the FS values are almost the same (2.42 and 2.43), indicating that the minimum safe distance (ds) is around 12 m. In order to determine a more accurate value of ds, more simulations are carried out with a series of d values between 9 and 13 m. For P = 200 kPa, FS increases with increasing d, and when d is around 11.3 m, FS achieves a stable value of approximately 2.43 (Fig. 9b). Therefore, 11.3 m is defined as the ds for P = 200 kPa. Another four curves in Fig. 9b show the Fig. 8. Influence of slope gradient on FS. 81 Engineering Geology 241 (2018) 76–85 S.-J. Feng et al. Fig. 10. Reference values of the minimum safe distance between VW and slope surface (at the top of injection screen). same trend and it can be found that a greater P results in a larger ds. Similar simulations are conducted for different elevations of injection screen, such as 8, 10 and 12 m, and similar ds values are obtained, indicating that the influence of h on ds is not significant. As aforementioned, the anisotropy of waste significantly affects the landfill slope stability, and the results in Fig. 9 are based on an A value of 10. Therefore, a wide range of A from 1 to 20 is used in the simulation to better investigate the variation of ds, and a design chart for ds is given in Fig. 10. The three curves describe the relationship between ds and P for three A values (i.e., 1, 10 and 20). With the increase of P, ds remains constant below 100 kPa and then linearly increases. Herein, we suggest using conservative ds value according to the results in Fig. 10. For example, when P = 200 kPa and A = 5, a ds value of 11.3 m is recommended as the minimum safe distance according to the curve of A = 10. In this way, the ds may be slightly larger, but can benefit the landfill slope stability. Fig. 11. Influence of well spacing on FS for different d values: (a) P = 100 kPa; (b) P = 250 kPa. 4.5. Influence of group-well spacing and design of Ds 4.6. Influence of group-well configuration In engineering practice, there are numerous VWs installed along the landfill slope, and the well spacing (D) is another key design factor for a leachate recirculation system. In this study, a landfill slope with three VWs is established to investigate the effect of well spacing (Fig. 1c). A too small D is not economical and may lead to excessive pore pressure between two VWs, thereby causing slope failure. Therefore, simulations are carried out to search for the minimum safe well spacing (Ds). For example, when d = 10 m and P = 100 kPa, FS continuously increases with increasing D, and then reaches a stable value of 2.38 after D = 9 m (Fig. 11a). In this case, 9 m is defined as Ds. Generally, a larger d leads to a smaller Ds. When d increases from 7 to 10 m, Ds decreases from 11.9 to 9 m because of less impact of recirculated leachate on the slope stability when VWs are set far from the landfill slope. Fig. 11b shows a similar trend but higher Ds values for P = 250 kPa. Variations of FS with D for another two injection pressures (P = 150 and 200 kPa) are listed in Table 2, with which Ds can be obtained. A large number of simulations are then conducted in this paper to investigate the variation of Ds with different d and P values, and a design chart of reference values for Ds is shown in Fig. 12, which is helpful for the design of leachate recirculation system near the slope of bioreactor landfills. For example, when d = 23 m and P = 210 kPa, the minimum safe well spacing (Ds) is suggested to be 11.8 m according to the curve of P = 250 kPa for safety sake. Feng et al. (2016) investigated a group-well recirculation system with different configurations and reported that the volume of impact zone would increase if adjacent wells are designed to have different heights. In this section, both equal-height wells and unequal-height wells are simulated (kv = 1 × 10−5 cm/s, A = 10). The equal-height wells are at an elevation of 14 m, while the unequal-height wells are located at staggered heights of 12 and 16 m (the average height is 14 m). All the wells are 18 m away from the slope surface in the horizontal direction and the well spacing is 9 m under an injection pressure of 250 kPa. Fig. 13 shows the saturation contours in the vertical cross sections for both configurations. Vim of the unequal-height recirculation system is 33,158 m3, slightly higher than that of the equal-height scenario (31,597 m3), indicating that unequal-height recirculation system is slightly more effective in saturating MSW. However, it should be noted that FS obtained from the unequal-height recirculation system is much smaller than that of the equal-height recirculation system (1.02 for unequal-height, 2.16 for equal-height). Therefore, it is reasonable to adopt the unequal-height configuration far from slope but it is not suggested when VWs are close to slope. 82 Engineering Geology 241 (2018) 76–85 S.-J. Feng et al. Table 2 Variation of FS with well spacing D for different d and P values. FS P = 150 kPa P = 200 kPa D (m) d = 11 m d = 12 m d = 13 m d = 14 m d = 15 m d = 14 m d = 16 m d = 18 m d = 20 m d = 22 m 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 15 15.5 – – – – 0.67 – – – – 2.27 – – – – 1.52 – – – – 2.31 – – – 0.81 2.24 – – – 1.0 2.31 – – – 1.68 2.31 – – – 2.29 2.31 – – 1.01 2.29 2.31 – – 0.82 2.31 2.31 – 0.95 1.96 2.30 2.31 – – 1.87 2.31 – 1.75 2.30 2.31 1.15 2.26 2.31 2.31 2.04 2.31 2.31 2.30 2.32 2.32 2.32 2.32 2.32 2.32 2.32 2.32 – – 2.28 2.31 – 0.98 2.30 2.31 – 1.91 2.30 – 2.29 2.31 – 2.30 2.31 1.62 2.31 2.15 2.31 2.30 recirculation system, and well spacing (D) is also an important parameter. A too large well spacing (D) value may prevent MSW from being moistened, and a too small D is not economical. Feng et al. (2016) have investigated the optimal well spacing (Dopt) for optimizing the recirculation efficiency (not close to a slope), the method will be adopted in design in the later part. Based on the aforementioned content, the design procedures for leachate recirculation system using VWs can be summarized considering both slope stability and recirculation efficiency (Fig. 14). Firstly, it is essential to investigate the geometry of the landfill slope and MSW properties. Considering the recirculation efficiency, the VW height (h) and the optimal well spacing (Dopt) are determined based on the recirculation pressure (rate) and MSW properties (Feng et al., 2016). In order to ensure the safety of landfill slope, ds should be determined first considering geometry of the landfill (e.g., slope gradient), MSW properties (e.g., hydraulic conductivity, anisotropic coefficient, friction angle, cohesion) and the recirculation pressure (rate), then ds can be used for the design of Ds. Finally, three main design factors are obtained including h, ds and D, and D is chosen from the bigger one of Dopt and Ds. Due to the computational capability, some parameters are not comprehensively considered in this study and the proposed design charts may not be sufficient. Nonetheless, the design method can offer preliminary guideline for landfill design. Fig. 12. Reference values of the minimum safe well spacing for a group-well recirculation system. 4.7. Design of VW considering the slope stability of landfill As revealed by the aforementioned analysis, there are two key parameters in the design of a leachate recirculation system using VWs considering slope stability, including the minimum safe distance between slope surface and VWs (ds) and the minimum safe well spacing (Ds). The recirculation efficiency is another concern when designing the 5. Summary and conclusions This paper establishes a 3D model to study the landfill slope stability under leachate recirculation through VWs. A leachate flow model is adopted to describe the migration of leachate and the distribution of Fig. 13. Variation of saturation contour with recirculation time: (a) equal-height configuration; (b) unequal-height configuration. 83 Engineering Geology 241 (2018) 76–85 S.-J. Feng et al. ki ̂ k (s) kh kv n P p qi qv s T Ts t Vim vi xj θ μ ρ ρd ρw σij,j σt σ1 σ3 φ Fig. 14. Design procedures for leachate recirculation system using VWs in a bioreactor landfill. pore pressure is then used to calculate the factor of safety using strength reduction method. The model is verified against published analysis results. The model can accommodate practical landfill with a leachate recirculation system using VWs. In fact, the model is also applicable for leachate recirculation system using horizontal tranches or surface spraying as long as appropriate boundary conditions are set. Using the proposed model, the effects of leachate injection pressure, hydraulic-mechanical properties (hydraulic conductivity, anisotropic coefficient, cohesion and friction angle) are investigated in terms of impact zone, evolution of pore pressure and FS. The results show that these factors have remarkable influence on FS and should be cautiously considered in design. Large injection pressure or anisotropic coefficient is adverse to the slope stability. FS changes almost linearly with the variation of friction angle and cohesion. In addition, two different group-well configurations are compared, and the results show that the unequal-height recirculation system has a larger volume of impact zone, however it has an adverse impact on slope stability. The horizontal distance between VWs and landfill slope surface (d) is a crucial factor in the design of a leachate recirculation system because a too small d may cause slope failure. A large number of simulations are performed to find the minimum safe distance (ds) for different injection pressures and anisotropic coefficients. Design chart for reference values of ds is proposed and can be used as a guideline for landfill design. The influence of well spacing (D) of a group-well recirculation system on the landfill slope stability is also investigated. A design chart of the minimum safe well spacing (Ds) is proposed considering various injection pressures and ds values. 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