Vertical Expansion Stability of an Existing Landfill: A Case Study of a Landfill in Xi’an, China

The vertical expansion of existing landﬁlls can hold signiﬁcant amounts of domestic waste and solve practical diﬃculties such as local government site selection. This research topic has become increasingly popular in the ﬁeld of environmental geotechnical engineering. This study examined vertical expansion stability of landﬁlls considering high leachate water level. The results showed the following. (1) Four slope instability modes for landﬁll vertical expansion are categorized according to the following slip surface positions: shallow slippage of the existing landﬁll, shallow slippage of the expanding landﬁll, interface slip between the existing landﬁll and expanding landﬁll, and deep slippage passes through the foundation soil. (2) The factor of safety decreases as the height of leachate level increases. When the height of leachate level rises from 2m to 20 m, the factor of safety of the landﬁll is reduced by 13.2–15.4%. (3) As the vertical expansion height increases, the factor of safety of the existing landﬁll decreases, and when the expansion height increases to 30 m, the stability factor of safety of the old waste landﬁll is reduced by 4.83%. A landﬁll in Xi’an is considered as an example for the analysis, which shows that a leachate drainage layer can discharge leachate from the landﬁll body eﬃciently, reduce the leachate level height of the landﬁll body, and improve the stability of vertical expansion of the landﬁll. This study and its ﬁndings can be used as a reference for similar expansion projects.


Introduction
Since the 1980s, with the development of Chinese society and economy and the expansion of urban population, municipal solid waste (MSW) has increased substantially. Some economically developed cities began building China's first sanitary MSW landfills [1]. ese landfill operations generally follow relatively simple methods, and most have been operating for more than ten or 20 years. Some of them have already constructed a second-phase landfill and are nearly occupied with sealed landfills. e 21 st century has witnessed a rapid growth in urban population, with subsequent rapid increase in MSW. ere is an urgent need to build a new landfill to store and manage MSW. However, due to urban land scarcity, especially in densely populated cities, land is extremely limited. It is challenging to construct a new landfill to handle increased MSW. erefore, the expansion of existing landfills is of great significance for protecting land resources [2]. Moreover, vertical expansion necessitates enhanced requirements for landfill stability. Landfill stability is closely related to the engineering behavior of MSW. For example, assessing the stability of landfill slopes requires an understanding of the shear strength of MSW [3][4][5][6]. In addition, the expansion of a landfill may lead to the settlement of the existing landfill and expanded landfill, which may cause problems with the liner system and slope stability [7].
Roche [8] conducted on-site monitoring and finite element analysis on the soft, sensitive silty clay foundation soils, which confirmed the feasibility of vertical expansion on the existing landfill. Tieman et al. [9] considered the bottom liner and existing side slope grades, interface friction angles, type, and orientation of the geosynthetics relative to grade, and depth of leachate in the drainage layer above the piggyback liner system, using the computer program STABL, written at Purdue University, using Modified Bishop's and Simplified Janbu methods to analyze the stability of the vertical expansion landfill. Chen et al. [10] proposed the three-part wedge limit equilibrium method for landfill expansion, considering horizontal seismic force and analyzing the seismic stability of landfill. e results showed that landfill expansion is more likely to occur from seismic loads, and the extended landfill was more likely to slide along the interface between the new landfill and the old landfill under seismic loads. Choudhury and Savoikar [11] used a pseudostatic limit equilibrium method to consider the impact of horizontal and vertical seismic acceleration and analyzed the seismic stability of the vertical expansion landfill. e results showed that the average factor of safety decreased as both horizontal and vertical seismic accelerations increased. Rong et al. [12] used Qizishan landfill expansion project as an example to numerically simulate the stability of the existing landfill.
e results showed that improving the strength of the landfill soil, establishing a good leachate guide exhaust system, controlling the leachate liquid level, and selecting a reasonable landfill elevation and gradient can ensure the stability of the vertical expansion of a landfill. Houlihan et al. [13] used the limit equilibrium method for the expansion of the Cherry Island Landfill to calculate slope stability and used SLIDE software to analyze the stability factor of safety. Ruan et al. [14] used the pseudodynamic method to calculate the factor of safety for the expanded landfill with a trapezoidal shape based on the slope failure conditions and found that the factor of safety decreased with the increase of the amplification factor. is showed that reasonable consideration of the magnitude of the amplification factor would be conducive to the seismic design of the landfill. Khoury et al. [15] evaluated the feasibility of increasing an existing landfill vertical height by 145 feet through geotechnical investigations, engineering analysis, and finite element method analysis to determine the stability of the vertically expanded landfill. Many scholars apply geosynthetics, reinforced soil, and reinforced walls to the vertical expansion of the landfill, which can improve the stability of the landfill. Chen et al. [16] found that when the thickness of the expansion pile is less than 40 m, a two-layer high-strength geogrid can generally meet the design requirements of the vertical expansion landfill. Ke et al. [17] took the Xingfeng Vertical Extension Landfill in China as an example and adopted a geogrid to improve the stability of the eastern slope. Koda et al. [18] discussed a case study of an old MSW landfill in Poland and proposed reinforcing the landfill slope with a geogrid, geocomposite, and berms to improve the stability of the vertical expansion of the landfill; they used the limit equilibrium method to analyze the stability of the landfill. Gupta et al. [19] used the limit equilibrium method to calculate the slope stability of the original waste slope and the waste slope strengthened with reinforced soil and found that factor of safety of the existing landfill could reach 1.5 after the reinforcement of the waste slope with reinforced soil. Munwar Basha et al. [20] proposed applying reinforced soil berm (RSB) to the vertical expansion of an existing MSW landfill; they used the limit equilibrium method and assumed three-wedge failure mechanism to evaluate the stability of the RSB and compute the optimum dimensions of RSB. Mahapatra [21] used reinforced soil wall (RSW) for vertical expansion of MSW landfills and presented a methodology to evaluate the safe seismic design of RSW for a vertical expansion of landfill under six different leachate build-up conditions. Mahapatra et al. [22] proposed that a system reliability framework for the design of mechanically stabilized earth (MSE) walls should be applied to the vertical expansion of the MSW landfill. When the landfill was expanded vertically, the minimum ratio of the length of the geosynthetic reinforcement to the height of the MSE walls should be increased above 0.6 for the MSE walls to perform satisfactorily.
During vertical expansion, an intermediate liner system containing a variety of geosynthetics should be installed at the interface of the new landfill and old landfill as an impermeable barrier for the expansion pile [7]. Although this intermediate liner system provides good impermeability, the shear strength of the clay-geomembrane and geomembranegeotextile interface is low, which can result in sliding along the liner interface and damage to the expanded landfill [23]. Gao et al. [24] proposed that the deformation of the intermediate liner system could be reduced by vibration compaction, lowering the leachate level, setting folds, and laying flexible geomembrane. Zhan et al. [25] improved slope liner configuration systems, established a three-dimensional drainage system to reduce the leachate level, raised the height of the downstream retaining dam, and established a safety monitoring system, which can fill the landfill to a design elevation of 130 m. Tano et al. [26] studied the numerical simulation of nonlinear mechanical behavior of various geosynthetics for vertical expansion intermediate liners in landfills. Qian et al. [27] used a geosynthetic clay liner (GCL) instead of a compacted clay liner (CCL) for the vertical expansion of a landfill. Jiang et al. [28] proposed the design of a geosynthetic reinforced embankment, which can be used as a reference for landfill expansion.
However, limited studies exist which consider the leachate level [6,12]. Due to the high organic waste content and high yield of leachate in Chinese landfills, it is difficult to effectively drain leachate only through the drainage system at the bottom of the reservoir. e leachate that cannot be drained is retained in the body of the landfills, resulting in high leachate levels [29,30]. Vertical expansion of a landfill needs to control the leachate level of the existing landfill. It is difficult to manage leachate drainage only by the guide and drainage system at the bottom of a landfill. It must be ensured that leachate drainage facilities can be continuously drained after the closure of the landfill [31]. Leachate drainage facilities could also be built in the landfill body to reduce the leachate level so that the existing landfill can meet the expansion stability requirements. e most commonly used engineered leachate drainage facilities mainly include vertical wells [32,33] and horizontal trenches [34]. Lan [29] used the Seep/W model to analyze horizontal trenches, which effectively reduced the leachate level and pressure head in the simulation unit. Ye et al. [34] studied the spacing design, established a seepage model of a horizontal trench, and identified the relationship between the design spacing and corresponding warning water level for the landfill stability control requirements. e drainage layer effectively reduced the leachate level of the landfill [35,36].
is study analyzes the problems existing in landfill vertical expansion and examines the instability modes of landfill vertical expansion. Using GeoStudio software, the Morgenstern-Price limit equilibrium method is used to calculate factor of safety of the landfill and analyze the stability of the vertical expansion of the landfill. A landfill site in Xi'an, China, was selected as the case study. Considering its high leachate level, the drainage layer was installed during the vertical expansion of the landfill. e drainage layer was then evaluated based on surface horizontal displacement, deep lateral displacement, and leachate level. e drainage layer applies to the stability control effect of the vertical expansion, evaluates the subsequent filling height, and guides the stability analysis in vertical expansion of the landfill.

MSW Composition.
e MSW used in this study is from a landfill in Xi'an, China. e composition of the waste is detailed in Figure 1, where Figure 1(a) shows the composition of the existing landfill waste [37], and Figure 1(b) shows the composition of the expanding waste [38]. Figure 1 shows that the existing landfill waste contained organic waste (47.8%), plastic (31.1%), paper (3.9%), wood (3.8%), and others (13.4%); and the expanding landfill waste contained organic waste (56.9%), plastic (12.1%), paper (8.9%), textiles (2.5%), wood (1.9%), and others (17.7%). Organic waste is the dominant component; the proportion of plastics in the existing landfill waste is 19% higher than that in the expanding landfill waste, and the proportions of other components such as paper, wood, and textiles are approximately equal.

Shear Strength Parameters of MSW.
Shear strength is the basic parameter in the stability calculation of geotechnical engineering. e shear strength of MSW is usually described by the Mohr-Coulomb failure criterion commonly used in geotechnical engineering [39], and the shear strength calculation is represented as follows: where τ f is the shear strength of MSW, σ is the normal stress, c is the cohesion, and φ is the internal friction angle. e landfill shear strength parameters are key parameters in determining the landfill stability and ensuring its stable operation. Considering the high leachate level in Xi'an landfill, the consolidation undrained shear test is used to determine the shear strength parameters of the waste. e shear strength parameters of the waste [40] are listed in Table 1, which shows that the cohesion of the expanding landfill waste is greater than that of the existing landfill waste, and the angle of internal friction is smaller than that of the existing landing waste.

Analysis Method.
e limit equilibrium method is also known as vertical strip method.
is method divides the landslide body into a series of strips with vertical interfaces and uses soil strips and the whole static balance or the moment equilibrium equation to calculate factor of safety of the slope. e traditional limit equilibrium methods include the Bishop method [41], Spencer method [42], and Morgenstern and Price method [43]. Table 2 lists the different methods used by scholars with increasing research on landfill stability analysis. e methods, on the basis of the traditional limit equilibrium method, included the wedge limit equilibrium method [44], three-part wedge limit equilibrium method [45], simplified Bishop [46], and other methods to meet specific conditions.

Expansion Method.
e common expansion modes include vertical, horizontal, and compound expansion [66]. Vertical expansion is also called "piggyback" [67], which refers to continuing to pile and add waste on top of the existing landfill waste. Examples of this method are observed at a landfill site in Peabody, MA [67], the Cherry Island Landfill in Delaware [13], and the Quarantine Road Landfill in Maryland [15]. A landfill in Xi'an, China, is used for the vertical expansion case study presented in this article. It is a valley-type vertical expansion project with a vertical elevation of 30 m on the existing landfill ( Figure 2).

Problems with Expansion.
Vertical expansion introduces additional problems, such as landfill settlement, the migration and diffusion of leachate, and the stability of the landfill [66].
(1) Under the forces of self-compression, mechanical creep, biodegradation, and vertical expansion of the landfill load, the existing landfill body can experience significant settling. Landfill age, composition, and depth also contribute to settlement in different areas in the old landfill site, resulting in uneven settlement of the existing landfill. e vertical expansion will lead to large settlement and uneven settlement of the old landfill, which will change the slope of the intermediate liner system at the junction of the new landfill and old landfill. (2) Due to the large and uneven settlement of the old landfill, the leachate drainage system slope at the junction of the new landfill and old landfill changes and even produces a reverse slope. is obstructs the drainage, thereby causing an increased leachate head and subsequently increasing the landfill body instability risk. Vertical expansion has increased the lateral deformation of the slope area of the old landfill, causing the intermediate liner system to generate a certain additional tensile strain. is may cause tensile failure of the impermeable material and lead to an impermeability failure and generate continuing secondary pollution to surrounding water and soil [68].

Advances in Civil Engineering
(3) e stability of vertically expanded landfill depends on the stability of the old landfill, new landfill, and the interface between the expanded landfill and existing landfill.
Before performing the stability analysis, it is necessary to study the vertical expansion failure modes [46,54]. According to the position of the slip surface of the vertical expansion landfill, the instability can be divided into the four following modes:   (1) Shallow slippage of the existing landfill (Figure 3(a)).
(2) Shallow slippage of the expanding landfill ( Figure 3(b)). ere are generally four slope instability modes in the vertical expansion of the landfill. Modes (a) and (b) occur in the shallow slope of the landfill. In addition to factors such as the aspect ratio and shear strength parameters of the slope pile, it is also related to the height of the leachate level. e excessively high leachate water level in landfill sites will increase pore water pressure and reduce the shear strength of MSW, which can create instability and slip [69]. e vertical expansion of the existing landfill is a dynamic landfill process. e stress conditions of the existing landfill are constantly changing, causing uneven settlement in the existing landfill, which makes the interface between the expanding landfill and existing landfill an impermeable liner system. e slope change also increases the lateral deformation of the slope area of the existing landfill, causing the interface liner system to generate additional tensile stress, which may cause tensile failure of the liner material [68]. e geomembrane set in the liner interface can isolate the upper and lower garbage piles, but the geomembrane is relatively smooth, and its shear strength is very low. e vertical expansion of the waste piles readily loses stability and slips at the geomembrane interface, resulting in mode (c). For example, the Kettleman Landfill in the United States slips at the interface of the geomembrane [70,71]. e soft foundation has low shear strength, low bearing capacity, and high compressibility. Under the load of the existing and expanded waste dump, a large foundation settlement occurs. erefore, on soft foundations, such as tidal flats and swamp soil, vertical expansion of the waste dump needs to include the consolidation settlement and horizontal slippage of the foundation soil. Mode (d) represents deep slippage, which causes significant harm, such as the Rumpke Landfill in the United States [72] and Meethotamulla Landfill in Sri Lanka [73,74]. is mode includes instability due to insufficient foundation bearing capacity.

Stability Analysis.
e SLOPE/W module in GeoStudio (GEOSLOPE International Ltd, Canada) is used to establish the corresponding geometric model, and the Morgenstern-Price limit equilibrium method is used for stability analysis. e corresponding model is established for the calculation of different soil layers, sliding surface shapes, and various pore water pressure conditions. e minimum factor of safety (Fs) is used to determine the vertical expansion stability. e landfill length is set to 300 m, and the MSW to be landfilled is divided into existing landfill waste and expanding landfill waste. e top surface average gradient of the existing landfill is approximately 5%, landfill slope ratio is 1 : 3, base thickness is 20 m, and vertical expansion is 30 m. e material parameters of the landfill are presented in Table 3. To analyze the influence of different leachate level heights on the stability of the landfill, the leachate level height is set to 2 m, 4 m, 6 m, 8 m, 10 m, 15 m, and 20 m from the liner system to calculate the overall Fs of the existing and the vertically expanded landfills. e calculation results are presented in Table 4. Table 4 shows that Fs decreases with an increase in the leachate level. When the leachate level increases from 2 m to 20 m, the overall factor of safety of the landfill decreases by 13.2 to 15.4%. Fs decreases as the height of the vertical expansion increases. When the vertical expansion height increases from 0 m to 30 m, Fs decreases by 3.5 to 7.7%. e change range of Fs is significantly influenced by the changes in leachate level but is minimally impacted by changes in the vertical expansion height.
When the leachate level increases to 8 m, the vertical expansion of the 30 m landfill is in an unstable state (Figure 4), which is the instability mode of deep slippage passing through the foundation soil.
To analyze the influence of different vertical expansion heights on the stability of the existing landfill, the vertical expansion heights are set to 10 m, 20 m, and 30 m; the leachate level of the existing landfill is 0.3 m. e results are presented in Table 5.   e average daily landfill volume has increased from the initial 1260 t/d to the current 10,000 t/d, and the daily waste collection and transportation volumes have doubled. is far exceeds the designed landfill capacity, and the landfill has been operating in overload conditions for a long time. e landfill mainly receives layered landfill, gradually filling from the south of the landfill to the north. e thickness of each landfill layer is approximately 10 m with a total of 14 layers. Presently, two vertical expansion projects have been completed at the landfill with a maximum elevation difference of 155 m, becoming the highest landfill slope in China. Subsequently, the existing landfill was vertically expanded by 30 m and filled in three times, with a landfill slope ratio of 1 : 4, and a 10 m wide platform was installed for each additional layer.

Stability Analysis.
e model proposed in this paper was based on the topographic profile of the landfill in November 2019 (Figure 2), and the stability analysis parameters are listed in Table 3. To analyze how leachate level reduction affects landfill vertical expansion stability, the leachate level height was set at 3 m, 5 m, 10 m, and 15 m from the top of the slope, and the factors of safety were calculated (Table 6). e       Figure 7 shows the monitoring results of the 12 th platform, where W is the average daily surface displacement rate and the horizontal dotted line is the warning value. As shown in Figure 7, after the leachate drainage layer installation was completed in December 2017, the surface displacement rates of monitoring points at the bottom and top of the 12 th platform were significantly less than those from October to November 2017; neither exceeded the warning value. e maximum displacement rate at the bottom of the slope was 9.0 mm/d, which was 12% of the maximum displacement rate of the monitoring point in November 2017. e maximum displacement rate of the slope top was 9.9 mm/d, which was 26% of the maximum displacement rate of the monitoring point in November 2017.

Deep Lateral Displacement Monitoring.
ree deep lateral displacement monitoring points, CX2-1, CX2-2, and CX2-3, located at the slope bottom and top of the 12 th platform and the slope top of the 13 th platform were selected. Monitoring results in Figure 8 show that CX2-3 experienced significant displacement from the ground to a depth of 17 m above the leachate drainage layer, and the maximum displacement rate reached 1.4 mm/d. is was significantly less than the displacement rate of the monitoring point under the leachate drainage layer. e maximum daily average displacement of 1.4 mm/d at the top of the 13 th platform slope above the leachate drainage layer was 33% of the maximum daily average displacement of 4.3 mm/d at the bottom of the 12 th platform slope below the leachate drainage layer. is was 50% of the maximum daily average displacement of 2.8 mm/d at the top of the 12 th platform slope.

Leachate Level Monitoring.
e buried leachate level monitoring points at the top of the 12 th and 13 th platforms were selected, and results are presented in Figure 9. Figure 9 shows that the leachate depths of CX1-1, CX2-2, and CX3-1 on top of the 12 th platform slope below the leachate drainage layer were −5.1 m, −5.8 m, and −6.0 m, respectively. e buried depths of CX1-2, CX2-3, and CX3-2 on the top of the 13 th platform slope above the leachate drainage layer were −12.8 m, −5.7 m, and −8.8 m, respectively. e existence of the drainage layer effectively reduced the leachate level, indicating that the drainage layer application had an effect on the vertical expansion stability of the landfill. Table 7 lists the vertical expansion indicators for different landfills, combining the expansion projects of a landfill in Xi'an, China, Qizishan landfill in Suzhou, China [12,74], Tianziling landfill in Hangzhou, China [25], and Quarantine  Road landfill in the United States [15]. To analyze landfill vertical expansion, the vertical expansion height, gradient, shear strength parameters, leachate level height, and Fs of the vertical expansion stability were compared. Table 7 shows that the landfill height of the Xi'an landfill in China is 155 m, which has become the tallest landfill in China. Increased   Advances in Civil Engineering waste loading causes increased instability; therefore, its vertical expansion height is smaller than those of the other three landfills. e buried depth of leachate in the Xi'an landfill is the same as that in the Qizishan landfill. Fs of the vertical expansion of 40 m at the Qizishan landfill is greater than Fs of the Xi'an landfill expansion of 30 m, which may be related to the shear strength parameters of waste. Fs of the vertical expansion of 44.2 m at the Quarantine Road landfill is greater than Fs of the Xi'an landfill, which may be related to the landfill and leachate level heights.

Discussion
e Tianziling landfill is equipped with vertical drainage wells in its expansion to reduce the leachate level and meet the stability requirements, whereas Xi'an landfill meets stability requirements using a drainage layer.

Conclusions
is case study considers leachate level and vertical expansion heights in investigating the stability of vertical expansion of an existing landfill in Xi'an, China. Combined with monitoring projects, the application of a drainage layer in the vertical expansion landfill is evaluated based on surface horizontal displacement, deep lateral displacement, and leachate levels. e following conclusions are obtained: (1) Four slope instability modes in the vertical expansion of the landfill are categorized according to the position of the slip surface: shallow slippage of the existing landfill, shallow slippage of the expanding landfill, the interface slip between the existing landfill and the expanding landfill, and deep slippage passes through the foundation soil. (2) e factor of safety decreases as the leachate water height increases. When the leachate level rises from 2 m to 20 m, the overall factor of safety of the landfill decreases by 13.2-15.4%. e overall factor of safety of the landfill decreases as the vertical expansion height increases. When the vertical expansion height increases from 0 m to 30 m, the overall factor of safety of the landfill decreases by 3.5-7.7%. e change range of the overall landfill factor of safety is significantly influenced by the change in the leachate level but is minimally influenced by the changes in vertical expansion height.
(3) With an increase in vertical expansion height, the stability factor of safety of the existing landfill decreases. When the height is increased by 30 m, the stability factor of safety of the existing landfill is reduced by 4.83%. (4) After vertical expansion of the landfill was completed, the surface displacement rate did not exceed the warning value. e maximum daily displacement was 33-50% of the nonconductive layer, and the leachate level was effectively reduced.

Data Availability
e data used to support the findings of this study are included within the article.

Conflicts of Interest
e authors declare no conflicts of interest.