Introduction

Increasing population and rapid urbanisation have consequently led to an increase in the output of municipal solid waste (MSW) (Guerrero et al. 2013; Eskandari et al. 2016). However, improper disposal of waste will not only pollute the environment but also increase the risk of cancer for humans (Chaudhary et al. 2021). Therefore, pre-treatment technology for solid waste has gradually attracted attention. In April 1999, the European Union Landfill Directive (99/31/EC) defined the design and operation standards of landfills and mandatory requirements to reduce the biodegradable materials in MSW entering landfills. Under this directive, member states adopt different strategies to transfer organic matter in domestic waste from landfills, such as converting the biodegradable component into fertiliser, incinerating MSW, and then proceeding with landfilling or recycling the residue from incineration. Member states have also increased their focus on pre-treatment technologies for MSW, with mechanically and biologically treated (MBT) waste demonstrating the most favourable characteristics.

MBT technology is primarily divided into two parts: first, mechanical processing (crushing, sieving, centrifugation, or selection) is used for separation of biodegradable and non-biodegradable materials, and large-size materials are sieved or shredded. Next, biological treatment (anaerobic digestion and leaching hydrolysis, etc.) accelerates the degradation of biomass in MSW. Compared with MSW that is directly landfilled, the MBT process reduces the amount of biodegradable materials and their biodegradability, thereby reducing environmental pollution caused by the discharge of leachate and greenhouse gases. Therefore, this technology is applied in many European cities (Kuehle-Weidemeier and Doedens 2004). In several cases, the residue produced by the MBT process does not have a high enough economic value, making it unsuitable for use or a disposal method other than landfill (Archer et al. 2005). However, because the MBT process converts MSW into another material, the product from this pre-treatment varies from its parent material in terms of characteristics. Thus, the physical properties of MSW (particle size, composition, moisture content, density, and void ratio) to be discarded in landfills are fundamentally changed (Zhang et al. 2018), consequently changing its mechanical properties, such as shear strength, compression, and consolidation. This greatly affects the strength, stiffness, and stability of the landfill (Jones and Dixon 2015). The design of the slope and pile stability calculation of the MBT landfill site should be based on its mechanical characteristics to ensure the safety of the project.

Many researchers performed a shear strength test study on MSW and conducted an instability failure simulation model analysis on an existing landfill. For example, the values of cohesion (c) and internal friction angle (φ) reported by Landva and Clark (1990), Kavazanjian et al. (1995), Bray et al. (2009), Reddy et al. (2009), Zhang et al. (2014), Abreu and Vilar (2017), Falamaki et al. (2019), and Keramati et al. (2020) were 19–22 kPa and 24–39°; 24 kPa and 33°; 15 kPa and 36°; 31–64 kPa and 31–35°; 11.1–34.2 kPa and 11.2–30.6°; 4.4–13.7 kPa and 22–30°; 13.1–19.9 kPa and 17–21°; and 1.17–2.22 kPa and 21.5–31.5°, respectively, based on direct shear (DS) tests. In addition, some researchers (Singh and Murphy 1990; Stark et al. 2009) have conducted theoretical analysis on the stability of landfills. Furthermore, Zekkos and Fei (2016) studied the influence of different test methods on the shear strength of MSW. However, unlike MSW, research on the shear strength of MBT waste appears to be more limited. Fucale (2005) and Mahler and Neto (2006) used DS equipment to analyse the influence of fibre on the strength of MBT waste. Fucale (2005) mixed MSW and MBT waste with different percentages of fibres to study the effect of randomly distributed plastic fibres on the mechanical properties of the material, and to verify the possible similarities between these properties. Mahler and Neto (2006) observed that the fibre composition of MBT waste has a substantial influence on the shear strength of MBT waste. This is because, although MBT waste is characterised by a coarse material with non-sticky particle behaviour, the tensile strength of the fibre is high, and it may still show a high false viscosity value. Frenando et al. (2009) and Fernando and Sudarshana (2011) conducted DS experiments on MBT waste with different reinforcement contents and compared the strength of MSW. Experimental results show that MBT waste is stronger than MSW. Petrović and Bauer (2011) conducted experimental research and numerical simulations on the mechanical behaviour of MBT waste with different moisture contents. Bhandari and Powrie (2013) conducted triaxial experiments on MBT waste with different particle sizes and shapes to study the stress-strain-strength characteristics of MBT waste. Pimolthai and Wagner (2014) used DS equipment to test the shear strength of MBT waste with a particle size of less than 10 mm. Babu et al. (2015) used the DS test, and small-scale triaxial text and large-scale triaxial text apparatus were used for experiments to comprehensively test the shear strength characteristics of MBT waste. Fucale et al. (2015) experimentally found that the reinforcement phases (plastics, textiles, fibres, etc.) present in landfills have a great influence on the various characteristics (including strength) of MBT waste. Relevant literature on the shear strength characteristics of MBT waste is presented in Table 1.

Table 1 Reference summary
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The MBT landfill is constructed using a layer-by-layer accumulation method, and the landfill rate changes based on the daily amount of MBT waste that needs to be landfilled. The landfill rate is high when MBT waste production is high. The waste piles up rapidly, and the slope becomes steep. All landfill piles are affected by the lateral earth pressure exerted by subsequent piles, which causes lateral sliding damage to the piles. Moreover, the rapidly piled-up waste can easily cause slippage and instability damage to the bottom of the pile. The landfill rate has a decisive influence on the shear strength parameters (c, φ) of the MBT waste. Shear strength parameters are also key influencers in the stability analysis of MBT waste landfills. To simulate the impact of the MBT landfill rate on the shear strength parameters of the landfill, we conducted laboratory shear tests under different shearing rates and established a correlation between the shear strength parameters (c, φ) and the shearing rate. A theoretical model of shear strength prediction is established, and the variation range of the shear strength parameters is obtained. The findings of this work provide basic data and strength models for the design and instability and destruction prediction of MBT landfills.

Materials, device, and process

Materials

Hangzhou is the largest city in Zhejiang province with a population of approximately 10.36 million. At least 12,000 t of domestic waste is generated daily, and part of the waste is transported to the Hangzhou Tianziling (HT) Landfill. The HT-MSW treatment plant is divided into two landfills: the first (closed) and second (in operation). The second landfill is expanded vertically and horizontally on a one-field basis. Its total storage capacity is 22.02 million m3, which can absorb 24.05 million t of MSW and treat 1940–4000 t of waste daily. The geographical location of the HT Landfill is shown in Fig. 1.

Fig. 1
figure 1

Floor plan of HT Landfill, China

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The China Hangzhou Environment Group introduced MBT technology from Germany and produced MBT waste through several processes. First, the fresh MSW is crushed and sieved in a rotating drum screen with an aperture of 120 mm. Through the screen, large-sized materials (mainly cardboard, plastic, and textiles) are manually screened for recycling. The metal and material passing through the screen are separated by a magnetic separation method, and the remaining small-sized materials enter the reactor for hydrolysis treatment. Subsequently, the solid-phase hydrolysate with a moisture content of more than 40% is usually transferred to a drying chamber for biological drying. Finally, after biological drying for ⁓9 days, it becomes MBT waste.

The initial unit weight of the MBT waste can be determined based on the volume and weight of the materials acquired from the MBT plant. In this study, the MBT waste was collected as the test material, placed in a 20-L sealed plastic bucket, and transported to the Environmental Geotechnical Laboratory at Zhejiang Sci-Tech University for experimentation. The samples used for the laboratory tests were reconstituted. The average unit weight of the MBT waste was measured to be 4 kN/m3. Therefore, we selected the initial unit weight of the MBT waste to be 4 kN/m3. The original appearance of the MBT materials is shown in Online Resource 1. The MBT waste composition, specific gravity, and water content were determined as follows.

First, a combination of a mechanical vibrating screening and manual sorting was used to study the composition of the MBT waste. The MBT waste (6 kg) was weighed, and its various components were distinguished. The samples were dried in an oven for at least 24 h at 65 °C. after which the dry mass was determined. The dry mass percentage of each component, Mdi, can be calculated as

$$ {M}_{di}\left(\%\right)=\left({m}_{di}/\sum {m}_{di}\right)\times 100 $$
(1)

where mdi (g) is the dry mass of the components.

Second, specific gravity was determined as follows. First, the dried sample (50 g) was crushed into particles smaller than 5 mm. A volumetric flask was used to weigh out 500 mL of pumped kerosene. Then, the kerosene was removed. The sample was placed in the volumetric flask, and kerosene was poured into the flask until the sample was completely immersed. Subsequently, the volumetric flask was placed inside a vacuum dryer, where it was vacuum-pumped for more than 1 h (the vacuum degree should be approximately the local negative pressure value of 1 atmosphere). Finally, the volumetric flask was taken out, the kerosene after pumping was poured into the volumetric flask scale, the total mass of the volumetric flask, kerosene, and sample was measured, and the temperature in the flask was measured. The specific gravity of the MBT waste, Gs, can be calculated as

$$ {G}_s={m}_s\times {G}_{0T}/\left({m}_{bo}+{m}_s-{m}_{bo s}\right) $$
(2)

where G0T is the specific gravity of pure water at 4 °C under standard atmospheric pressure; ms (g) is the mass of the dry sample; mbo (g) is the total mass of the volumetric flask and kerosene; and mbos (g) is the total mass of the volumetric flask, kerosene, and sample.

Finally, the quartering method was used to prepare a 6 kg sample. The wet material was weighed before being placed in the oven. After being dried at 65 °C for 24 h, the sample was removed, and its dry mass was measured. The moisture content, ω, can be calculated as

$$ \omega \left(\%\right)=\left({m}_w/{m}_s-1\right)\times 100 $$
(3)

where mw (g) and ms (g) are the masses of the wet and dry MBT waste samples, respectively.

The components and physical characteristics of HT-MBT waste are presented in Table 2, which shows that MBT waste includes paper, plastic, rubber, textiles, wood, stone, ceramics, glass, metal, fine-grained soil, and other visually indistinguishable materials. Judging from the MBT waste, the most important components are plastic and rubber, and their combined mass is 1216.5 g, accounting for 23.3% of the total dry mass. This is because they are not easily biodegradable and there is poor national recycling awareness. The quantity of the paper is 0 g, mainly because the paper is broken during the MBT process. After degradation, it is not the correct size of paper or easy to identify. The residue is classified into an undefined particle size. The moisture content of general waste is 60–80% (Gao et al. 2015), and the moisture content of MBT waste is 20%, which is significantly lower than that of general waste.

Table 2 Composition and physical properties of MBT waste sample
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Direct shear test device

In this study, a DS apparatus (Online Resource 2) was used. This device uses a stepper motor, continuous variable, and can input any speed within the range of the test protocol for shearing. Furthermore, the device has a relatively large shear box with a diameter of 185 mm (upper and lower shear box heights of 40 and 20 mm, respectively). The instrument loading device includes horizontal and vertical loading. The maximum horizontal load is 50 kN. The mass of the suspension plate of the apparatus is 2.856 kg, and a vertical load of 12.5 kPa is applied to the sample. The maximum mass can be increased to 88.536 kg, which would generate a vertical load of 400 kPa on the sample. The shear displacement and vertical deformation of the sample were measured using two displacement meters.

Test process

The horizontal displacement applied by the motor generates shear stress at a constant rate, and the shearing rate adjustment range is between 0.01 and 99.99 mm/min. Researchers (Fard et al. 2015; Abreu and Vilar 2017) have conducted experiments on MSW or MBT waste and set a shearing displacement rate ranging from 0.2 to 19 mm/min; however, these studies did not consider the effect of shearing displacement rate on the material. Therefore, this study covers the above-mentioned rates and selects five shearing rates for comparison experiments: 0.25, 1, 5, 10, and 20 mm/min. The waste in the landfill is gradually piled up in layers during the landfill process, because of which, the landfill body will undergo compression and deformation accompanied by slipping instability, allowing it to be simulated and studied. There were changes in the shear strength parameters of MBT waste with buried depth (10–100 m). The preparation of MBT waste samples included chopping it into particles <23 mm to ensure that the ratio of the maximum material particle size to the diameter of the shear box did not exceed 1:8 (CJJ/T 2013) (Online Resource 3). To ensure that the moisture content of each sample was consistent, the MBT waste sample with a moisture content of 20% was prepared before the DS test. The specific steps were as follows: a 700-g MBT waste sample was placed into an oven at 65 °C, and the sample was dried for 24 ± 1 h, to a constant weight. Then, 140 g of purified water was sprayed evenly on the MBT waste soil with a watering can, and the sample was turned continuously. Finally, the sample was kept for 24 ± 1 h.

The sample was placed in the shear box in 10-mm layers, and then a simple tamping hammer was used to evenly compact the sample to ensure the same vertical settlement in the same plane to reach an initial unit weight of 4 kN/m3. Table 3 lists all the samples and test parameters used in this study. In total, 50 samples were tested. The vertical stresses were 40, 80, 120, 160, 200, 240, 280, 320, 360, and 400 kPa. After compressing the sample for 1440 ± 60 min under continuous vertical pressure, a shearing test was performed. Finally, the specimens were sheared at constant and slow (0.25, 1, and 5 mm/min) or fast (10 and 20 mm/min) shearing rates. The horizontal load was recorded every time the specimen produced 1% shear horizontal displacement. The test ended when the ratio of the shear horizontal displacement to the sample diameter reached 20%.

Table 3 Specimen and test parameters
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Results and analysis

Consolidation phase

During the consolidation and compression stages, the specimen underwent compression deformation. However, due to the low organic content and low moisture content of MBT waste, no drainage occurred during consolidation. The relationship between the void ratio of the sample and logarithm of the vertical pressure in the consolidation and compression stages shows that as the vertical pressure increases, the void ratio gradually decreases (Fig. 2). The relationship can be fitted into a straight line, the slope of the straight line (compression index) is 1.14, and the sample has high compressibility. Because the initial unit weight of the sample is 4 kN/m3, when the vertical pressure increases from 40 to 400 kPa, it can simulate the self-weight stress of MBT waste from 10 to 100 m. The weight of the MBT waste material is comparable to the simulated landfill depth; the relationship is shown in Online Resource 4, which shows that as the self-weight stress increased, the unit weight of the material increased from 4.00 to 7.84 kN/m3. The relationship between the void ratio of MBT waste materials and simulated landfill depth is shown in Fig. 3. Figure 3 shows that the void ratio of MBT waste is generally larger than that of MSW, and the void ratio of deep MBT waste is close to that of shallow MSW.

Fig. 2
figure 2

Relationship between the void ratio (e) and the logarithm of vertical stress (lgσ)

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Fig. 3
figure 3

Void ratios of MSW and MBT waste vary with depth

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Shear stress–displacement behaviour

In this study, the DS stress–horizontal displacement graphs of all specimens show strain hardening, which is illustrated with a shearing rate of 5 mm/min (Fig. 4). In all tests, the shear stress continued to increase until the horizontal displacement reached 37 mm (the ratio of horizontal displacement to sample diameter reached 20%). This is because the maximum displacement of the test equipment is 40 mm; therefore, the test must be interrupted when the horizontal displacement of the sample reaches 37.5 ± 0.5 mm. The value range of the horizontal displacement is the same as that performed by Zhan et al. (2008) and that of Feng et al. (2016) was 20% of the range. The test settings are similar, and the maximum ratios of horizontal displacement to sample diameter are all less than 35%. Therefore, even under relatively large displacements, displacement hardening is a common phenomenon in MBT waste.

Fig. 4
figure 4

Shear stress–horizontal displacement graph (shearing rate is 5 mm/min)

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The shear stress–horizontal displacement curve of the sample shows an upward convex trend. As the horizontal displacement increases, the shear stress increases rapidly. When the horizontal displacement of the specimen reached 9.25 mm (the ratio of horizontal displacement to sample diameter reached 5%), the growth rate of the shear stress changed from high speed to stable. The shear stress–horizontal displacement relationship of MBT waste is similar to that of general MSW (Zhang 2018). The main reason for this phenomenon is that initially, the shear strength of the material is borne by the fine-grained aggregate, and as the horizontal displacement increases, it quickly rises to the ultimate shear strength of the aggregate. Subsequently, reinforced materials such as plastics are used as the main shear resistance components, and fibrous materials such as plastics will be stretched and deformed under the action of shear load. However, these materials are not easily broken by instantaneous breakage during the stretching process owing to their good toughness; nevertheless, like elastic materials, there is still a process of yielding before failure, showing reinforcement characteristics.

In this study, 10 different vertical pressures were applied to the sample to simulate the landfill depth of MBT waste of 10–100 m. It can be clearly observed in Fig. 4 that the shear strength obtained by the shear test of MBT waste increases with the increase in vertical pressure (landfill depth), which is similar to the increase in MSW shear strength with increasing depth (Cho et al. 2011; Feng et al. 2016). However, the reasons for the increase in the two quantities are different. After mechanical and biological treatment, as the depth of the landfill increases, the material and moisture content do not change significantly. However, the void ratio decreases, and the components become denser; thus, the shear strength increases with depth. The reason for the shear strength increase in MSW as depth increases is that the content of organic material (such as food waste) decreases with depth and age, whereas that of the plastic components increases, leading to an increase in the φ value of the material. Nonetheless, some studies have shown that the shear strength of MSW samples decreases with depth. This is because increasing the amount of foil-like parts, with increased depth, causes the DS plane to be aligned parallel to the fibre, which reduces the shear strength (Karimpour-Fard 2018).

Since MBT waste does not have a distinct shear strength peak, the shear stresses when the shear strain reached 5, 10, 15, and 20% under each vertical pressure were taken as the shear strength under this pressure. Taking the 5 mm/min result as an example, the relationship between shear strength and vertical pressure is plotted (Fig. 5). It can be seen from Fig. 5 that with the increase in vertical pressure, the shear stress of the sample also increases, indicating that the larger the pressure, the denser the sample and the larger its shear strength. Moreover, as the value of shear horizontal displacement increases, the shear strength of MBT waste increases; therefore, the value of horizontal displacement also affects the determination of material shear strength.

Fig. 5
figure 5

MBT waste shear strength envelope (shearing rate is 5 mm/min)

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Shear strength parameters in different shearing rate of MBT waste

When the ratio of the shear horizontal displacement to the sample diameter under each vertical pressure reaches 10 and 20%, the corresponding shear stress is taken as the shear strength under the pressure. As can be seen in Fig. 6, as the shearing rate (logarithm) increases, the shear strength of the sample increases accordingly. This is similar to applying a rapid impact load to MBT waste. It takes a certain amount of energy to destroy MBT waste in a short period of time; therefore, the shear strength of MBT waste was improved. Additionally, owing to the high ratio of plastic to textile in the material, there were more large-sized strip-shaped plastics and textiles participating in the force. In addition, in the case of larger shearing displacement rates (10 and 20 mm/min), it can be observed that the shear strength of the ratio of different shear horizontal displacements to the sample diameter (10% and 20%) was not substantially different. However, as the vertical pressure increased, the slope of the shear strength line increased. This shows that choosing different shearing displacement rates and shear displacements affects the shear strength. In addition, with a higher rate, although the value of the shear displacement slightly affects the shear strength, different vertical pressures have obvious changes in the shear strength of the material.

Fig. 6
figure 6

Relationship between shear strength and the logarithm of the shearing rate

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In order to better describe the correlation between shear strength and shearing rate, a shearing rate sensitivity coefficient β is introduced, as shown in Eq. 4.

$$ \beta =\frac{S_i/{S}_0}{\log \left({V}_i/{V}_0\right)} $$
(4)

where S0 is the given initial shear stress (kPa), Si is the shear stress (kPa) corresponding to the shearing rate, V0 is the given initial shearing rate (mm/min), and Vi is the corresponding final shearing rate (mm/min).

The shearing rate sensitivity coefficient can be fitted to a straight line as shown in the figure (Online Resource 5). The absolute value of the slope of the straight line is 1.61, and the shearing rate sensitivity coefficient is between 0.64 and 2.66. The absolute value of the slope of the line fitted by Zekkos et al. (2010) (test shearing rates are 0.1, 1, and 5) is 0.71, and the rate sensitivity coefficient is between 0.5 and 1.0. The absolute value of the slope of the line fitted by Karimpour-Fard et al. (2013) (test shearing rates are 0.8, 8, and 19) is 0.55, and the shearing rate sensitivity coefficient is between 0.8 and 1.2. As the increment between shearing rates increases, the sensitivity between shear strength and shearing rate decreases. The linear slope of the MBT waste sample in this test is greater than that of the MSW sample, and the shear strength and shearing rate sensitivity of MBT waste are strong.

The shear strength parameters of MSW are calculated based on the Mohr–Coulomb theory. The shear strength parameters of the MBT waste were obtained. The relationship between the shear strength parameters c and φ of MBT waste with different shearing rates and ratio of shear displacement to sample diameter is shown in Fig. 7. It can be seen from Fig. 7a that the value of c increases with the increase in the ratio of shear displacement to the sample diameter and with the increase in the shearing rate. When the ratio of shear displacement to sample diameter was 20%, the shearing rate increased from 0.25 to 20 mm/min, and the cohesive force increased from 22.32 to 39.51 kPa. In particular, in the slow shearing rate (0.25 mm/min) test at a low ratio of shear displacement to sample diameter (5%), the shear strength of MBT waste is mainly caused by the friction angle, whereas c is negligible. Figure 7b shows that φ increases with the increase in shearing rate but has a minimal relationship with the ratio of shear displacement to sample diameter. When the ratio of shear displacement to sample diameter was 20%, the shearing rate increased from 0.25 to 20 mm/min, and φ increased from 64.24° to 68.52°, which is consistent with the results of Gao et al. (2010). The reason for the increase in c and φ is that MBT waste becomes denser after consolidation and compression. The faster shearing rate makes the MBT waste material swell and produces negative pressure. Furthermore, band-shaped plastics and textiles are drawn to generate greater tensile stress, thereby increasing the shear strength parameters.

Fig. 7
figure 7

Relationship between shear strength parameters and ratio of horizontal displacement to sample diameter: (a) cohesion; (b) internal friction angle

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Shear strength prediction theoretical model

The relationship among the shear strength, shearing rate, and vertical pressure of MBT waste is shown in Fig. 8. Figure 8 shows that the shear strength of MBT waste increases with the increase in the shearing rate and vertical pressure. The relationship between the shear strength of MBT waste and the shearing rate and vertical pressure can be fitted to a nonlinear surface. The fitting equation is shown in Eq. 5, and the fitting correlation coefficient R2 is 0.98, which shows a high degree of fit.

Fig. 8
figure 8

Shear strength fitting model

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$$ {\tau}_f={Z}_0+ B\sigma + Cv+{Dv}^2 $$
(5)

where τf is the shear strength of the material (kPa), σ is the normal stress (kPa), v is the shearing rate (mm/min), and Z0, B, C, and D are the fitting correlation coefficients (Table 4).

Table 4 Fitted correlation coefficient
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As shown in Fig. 9a, the relationship between c and the logarithm of the shearing rate can be fitted to a straight line. The fitting correlation coefficients R2 of the two lines are 0.89 and 0.93. The degree of fit is relatively high, and the fitted straight-line equation is shown in Eq. 6. As can be seen in Fig. 9b, the relationship between φ and the logarithm of the shearing rate can be fitted to a straight line. The fitting correlation coefficients R2 of the two lines are 0.97 and 0.85. The degree of fit is relatively high, and the fitted straight-line equation is shown in Eq. 7.

$$ \left\{\begin{array}{cc}c=8.790\log v+25.274& \left(\varepsilon =10\%\right)\\ {}c=4.562\log v+16.495& \left(\varepsilon =20\%\right)\end{array}\right. $$
(6)
$$ \left\{\begin{array}{cc}\varphi =2.294\log v+65.492& \left(\varepsilon =10\%\right)\\ {}\varphi =3.478\log v+63.962& \left(\varepsilon =20\%\right)\end{array}\right. $$
(7)
Fig. 9
figure 9

Relationship between shear strength parameters and logarithm of shearing rate: (a) cohesion; (b) internal friction angle

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where c is the cohesion (kPa) of the sample, v is the shearing rate (mm/min), ε is the ratio of the horizontal displacement to the sample diameter, and φ is the internal friction angle of the sample (°).

Discussion

Sample moisture content

We selected 18 references to compare the moisture content of HT landfill MBT waste (Online Resource 6). It can be seen from Online Resource 6 that the moisture content is generally distributed between 20 and 60%, among which the moisture content of MBT waste is between 18 and 40%, and the moisture content of MSW is between 20 and 100%. The moisture content of MBT waste is generally lower than that of MSW, and the range of variation is small. The main reason is that MBT technology removes most of the organic matter in MSW and greatly reduces the moisture content of the material through air drying.

Sample unit weight

The unit weight of the sample is shown in Online Resource 7. The unit weights of MBT waste, MSW, and HT-MBT waste are between 5.3 and 12.4 kN/m3, 3.5 and 14.1 kN/m3, and 4 and 8 kN/m3, respectively. Between them, the HT-MBT waste is generally smaller than the heavy range of other MSW and MBT waste. By comparing the composition of these wastes, it is observed that the percentage of plastic content in the MBT waste materials in the HT landfill is higher than that of the above materials. On one hand, considering that most of the organic materials are eliminated, the unit weight of MBT waste is lower. On the other hand, due to poor recycling awareness and different consumption patterns, the increase in the percentage of low-weight and large-volume plastics may also be why the unit weight of MBT waste is relatively low.

Test parameters

Table 5 lists the experimental parameters used in the references. Many scholars have provided results of on-site (Miyamoto et al. 2014; Keramati et al. 2020) or laboratory direct shearing of MSW or MBT waste. The largest sample size for laboratory research reaches 860 × 860 × 620 mm, the smallest is 60 × 60 × 30 mm, and the size of in situ test samples can reach 1220 × 1220 × 750 mm. Further, the DS test device is divided into square and round shapes; the test shear box used in this study was a relatively large round shear box. The range of vertical pressure applied was 2–774 kPa, and the vertical pressure range for most of the tests was 50–200 kPa. The duration of the pressure application is generally ⁓1440 min. Most of the literature research content includes sample composition, moisture content, buried depth, severity, age, fibre orientation, void ratio, particle size, top overburden pressure, upper earth pressure, and self-weight stress on MSW/MBT waste shear impact of intensity. Only Zekkos et al. (2010) and Karimpour-Fard et al. (2013) studied the effect of multiple shearing rates on shear strength. Zekkos et al. (2010) studied the effects of different components, unit weights, and shearing rates on the shear strength of MSW. The shearing rates were 0.1, 1, and 5 mm/min, and the vertical pressures were 2, 50, 150, 370, and 700 kPa maintained for 1440 min. The test results show that the greater the depth in the landfill, the greater the reduction of φ, and that the shear strength is likely to correspond to the weakest direction of the shear plane. Karimpour-Fard et al. (2013) studied the influence of fibre content, fibre orientation, age, and shearing rate on MSW, applying 20, 50, 100, and 200-kPa vertical pressures and maintaining them for 1440 min. The shearing rate was set to 0.8, 8, and 19 mm/min. The results show that as the shearing rate increased, so did the shear strength of MSW. When the horizontal displacement was 1.5, 3, and 4.5 cm, the shear strength of MSW increased to 27%, 22%, and 16%, respectively. The sensitivity coefficient was up to 0.33. This study investigates the effect of shearing rate on the strength of MBT waste samples, and the set rate covers the above-mentioned rates. A vertical pressure of 40–400 kPa was applied to simulate the self-weight stress at a landfill depth of 10–100 m.

Table 5 Reference test parameters
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Shear strength parameters

We collected references with a time span of up to 30 years (1990–2020) and extracted shear strength parameters (data with similar strain values) obtained at various shearing rates in the literature. The influence of shearing rate on the shear strength parameters of samples was compared (Fig. 10).

Fig. 10
figure 10figure 10

Comparison of shear strength parameters: (a) MBT waste cohesion, (b) MSW cohesion, (c) MBT waste internal friction angle, (d) MSW internal friction angle

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Figure 10 shows that as the shearing rate increases, the shear strength parameters c and φ of MSW and MBT waste also increase. Compared with MSW, MBT waste is significantly affected by the shearing rate. The shearing rate reflects the change in the landfill rate of a body subjected to lateral earth pressure loading. When the moisture-rich MSW is subjected to lateral earth pressure, the water pressure reaches its limit. Therefore, the shear strength of MSW does not change significantly when the MSW is subjected to different shearing rates. The variation in range of the MSW c is generally between 0 and 46 kPa, and the c range of MBT waste is concentrated between 5.4 and 39.5 kPa (some data points with larger increases are excluded); the range of MSW c is larger than that of MBT waste. The MSW φ range was 7–50.6°, and the MBT waste φ range was 17.2–48.1°; most fluctuate around 30°. The ranges of the shear strength parameters of MSW are wider than those of the MBT waste. The main reasons for the differences in c and φ between MSW and MBT waste are the composition, moisture content, density, test parameters, and shearing rate. After the MBT waste is mechanically sorted and biologically treated, its composition, moisture content, and density are all changed, and the particle sizes of its constituents become relatively uniform. Thus, the shear strength parameters of the MBT waste vary less than those of the MSW.

The φ range of this study was 59.92–68.52°, which is generally greater than the those reported by other publications in the literature. The main reason for this phenomenon is that on one hand, HT-MBT waste contains a large amount (23.3%) of plastic and rubber materials, and the rubber material has suitable friction properties; on the other hand, the moisture content of HT-MBT waste is relatively low, and relatively dry MBT waste materials have suitable friction properties.

Conclusion

Considering the influence of shearing rate and vertical pressure (in simulating landfill depth), the shear strength characteristics and variation laws of MBT waste were studied using a DS test apparatus after collecting MBT waste materials from HT landfills. Research shows that MBT waste is mainly composed of plastic, rubber, textiles, wood, stone, ceramics, glass, metal, fine-grained soil, and other visually indistinguishable materials. Among them, plastic and rubber are the most common components, accounting for 23.3% of the total. The natural moisture content of MBT waste is 20%, and its unit weight is 4 kN/m3; these values are significantly lower than the corresponding values for general MSW.

The shear strength of MBT waste increases with an increase in shear displacement. Moreover, no shear strength peak is observed during the test process, which would indicate displacement hardening, as in the case of MSW. The shear strength of MBT waste also increases with an increase of the shearing rate. The sensitivity coefficient between the shear strength and shearing rate of MBT waste is 0.64–2.66 and that of MSW is 0.5–1.1. A theoretical model for predicting the shear strength of the MBT waste considering the effects of shearing rate and vertical normal stress was established. The model was fitted to a nonlinear smooth surface in a rectangular coordinate system, with a fitting coefficient of 0.98. A linear expression relating the shear strength parameters (c, φ) to the logarithm of the shearing rate was established, and the ranges of the shear strength parameters were determined. The c value of MBT waste was 22.32–39.51 kPa, and φ was 64.24–68.52°. The shear strength parameters of the MBT waste and untreated MSW were compared. The ranges of c and φ for the MSW were wider than those for the MBT waste. The c ranges of the MSW and MBT waste were 0–46 and 5.4–39.5 kPa, respectively. The φ ranges of the MSW and MBT waste were 7–50.6° and 17.2–48.1°, respectively. The findings of this paper can provide basic data and be used to establish strength models for the design, instability, and damage prediction of MBT landfills.