Keywords

1 Introduction

In karst regions, road surface collapses frequently occur during engineering construction, often characterized by their hidden nature and sudden occurrence, posing significant risks to both human life and property safety [1, 2]. To address this issue, Huckert et al. [3] conducted full-scale model tests on the deformation behavior of reinforced materials and subgrade surfaces under circular collapse. Wittekoek et al. [4] conducted a two-dimensional numerical study, identifying the length and quantity of geogrid anchor rods as critical factors in determining load-bearing capacity. From the analysis, When single-layer geotextile reinforcement treatment of karst collapse. If the buried width of the reinforcement material is too wide, it will cause the excavation surface of the soil to become larger, thereby increasing the engineering cost, and if the buried width is insufficient, anchoring length of the tendon will be insufficient, the stability of the project will be affected. In order to save the project cost, improve the management effect of tendons, and when the highway grade is low, multi-layer reinforced bedding technology can be used to deal with [5]. He et al. [6] examined the loads and deformation experienced by single-layer and multi-layer geogrid-reinforced cushion layers during collapse processes through large-scale indoor model testing. They further analyzed the distribution patterns of subgrade loads across various reinforcement layers and the deformation characteristics of cushion layers. In this study, three numerical models were employed to investigate the impact of different numbers of reinforced geotextile layers on top vertical settlement of the soil, and geotextile tensile force.

2 Methods and Materials

2.1 Discrete Element Model

To investigate the influence of different numbers of reinforced geotextile layers on the management of collapses in karst areas, the subsidence treatment project of the Xihuan Road embankment in Hechi City, Guangxi, China, was taken as a case study. A discrete element numerical model was established for this purpose. Figure 1 illustrates the numerical model of the discrete element, measuring 15 m in length and 10 m in height. The subsidence area includes an active baseplate with a width (B) of 3 m, flanked by stable areas on both sides, each with a width of 6 m. The center of the subsidence area’s bottom plate is designated as the coordinate origin (0,0). The model boundary employs wall elements integrated within the Particle Flow Code (PFC) software to simulate the underlying bedrock.

Fig. 1
A diagram of the numerical model. It includes vertical settlement mark the point, sand particle, origin of coordinates, active baseplate, stable area, and substable area. An enlarged view on the right presents the geotextile, sand particle, and tensile force mark the point.

Numerical model

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2.2 Discrete Element Simulation Material

In this study, the simulated soil is composed of sandy material, and therefore, a linear contact model is employed for particle interactions. To ensure computational efficiency, the particle radii are appropriately scaled up, and the soil samples are generated using a stepwise expansion method. The model encompasses approximately 24,000 soil particles with particle sizes ranging from 3 to 5 cm. Microscopic parameters for discrete elements corresponding to different particle types are detailed in Table 1.

Table 1 Particle–particle and particle–wall microscopic parameters
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To confirm the correspondence of the microscopic parameters of the soil used in this study to the macroscopic parameters, flexible biaxial tests were conducted under three different confining pressures: 50, 150, and 300 kPa. When the model’s friction coefficient was set to 0.2, our calculations yielded an internal friction angle of 14.48° and cohesion of 0 kPa. Figure 2 illustrates the deviational stress–strain curves and schematic representations of the flexible biaxial tests conducted under these three confining pressures, with an interparticle friction coefficient of 0.2.

Fig. 2
A multiline graph of the deviational stress versus strain illustrates 3 lines for 300, 150, and 50 kilopascals, along with corresponding contour plots. The lines have ascending trends, where 300 kilopascals has the highest peak among others.

Deviational stress–strain curve and schematic diagram of flexible biaxia

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In this study, the simulation experiments were conducted using a geotextile material that is relatively soft but capable of withstanding a certain shear strength and tensile strength. The selected geotextile particles were modeled using a linear contact bonding model. To ensure computational accuracy and the precise calculation of inter-particle forces within the geotextile, the dimensions of the geotextile particles were appropriately scaled up. A particle generation method based on specific rules was employed to create the specimens, with a total of 188 geotextile particles per layer and a particle diameter of 3 cm.

To confirm the correspondence of the microscopic parameters of the geotextile material used in this study with real-world macroscopic parameters, a tensile test on the geotextile material in ambient conditions was conducted. During the simulation, the left end's first particle was fixed, and a constant velocity of 0.004 m/s was applied to the right end’s first particle. The relationship between geotextile tensile force and elongation was recorded. When the elongation reached 32.85%, the tensile force was 200 kN. The microscopic parameters utilized for simulating the geotextile material in this study are presented in Table 2, and schematic diagrams of the tensile test as well as the tensile force–elongation relationship are depicted in Fig. 3.

Table 2 Microscopic parameters of geotextile
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Fig. 3
A line graph of tensile force in kilonewtons versus elongation in percentage presents V = 0.004 meters per second. It illustrates an ascending line between 0 and 200 on the y-axis and 0 and 35 on the x-axis. There is a horizontal line with arrows at the end representing fix.

Tensile force–elongation curve and drawing diagram of tensile test of geotextile

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2.3 Discrete Element Simulation Scheme

This study comprised a total of three simulation groups, and the test schemes are detailed in Table 3. In Group T1, the geotextile was buried at a height of H1 = 0 m. In Group T2, the first layer (bottom layer) of geotextile was buried at a height of H1 = 0 m, while the second layer was buried at a height of H2 = 1 m. Group T3 involved the burial of the first layer of geotextile at H1 = 0 m, the second layer at H2 = 1 m, and the third layer at H3 = 2 m.

Table 3 Experiment plan
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2.4 Discrete Element Simulation Method

The active baseplate was controlled using the FISH language to move in the negative y-direction at a velocity of vy = 0.01 m/s. The movement was stopped when the active baseplate had a displacement of 0.9 m. The center of the subsidence area of the baseplate was taken as the origin of coordinates(0,0), and the location of the tensile force test points of geotextile are indicated in Fig. 4 and Table 4. In order to get the top vertical settlement of the soil,150 soil particles were marked at the top of the soil, the model was recorded the change of the soil particles in position at the beginning and end, thereby providing data on the settlement of the soil surface.

Fig. 4
A line graph, presenting the location of the tensile force test points of geotextile, illustrates 2 lines. The lines follow a horizontal trends at 0.0 and 2.0 on the y-axis and from negative 4.5 to 4.5 on the x-axis. Values are estimated.

Schematic diagram of the location of the tensile force test points of geotextile

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Table 4 The tensile force test points for each layer of geotextile
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3 Results and Discussion

3.1 Top Vertical Settlement of the Soil

Figure 5 displays the subsidence trends of the top layer in the T1-T3 soil profiles. Notably, all the curves exhibit their peaks within the subsidence area, and as one moves away from this region, an overall reduction in subsidence is observed. With an increase in the number of reinforced geotextile layers, there is a noticeable decrease in the overall subsidence of the top layer. This observation indicates that the augmentation of reinforced geotextile layers effectively mitigates the soil’s propensity for subsidence.

Fig. 5
A muliline graph of vertical settlement versus horizontal distance from the center of subsidence area in meters. It has 3 vertical sections for stable areas and subsidence area. It plots 3 descending to ascending lines for T 1, T 2, and T 3. T 1 has the lowest peak among others.

The trend diagram of top verticle settlement of group T1-T3 soil

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3.2 Tensile Force of Geotextile

Figure 6 depicts the trend of geotextile tensile force at test points K0 to K5 in Group T1 as a function of the displacement of the subsidence plate. Notably, within the subsidence area, test points K4 and K5, as well as test point K3 at the boundary between the subsidence and stable regions, exhibit a pattern of initial rapid increase followed by stabilization throughout the subsidence phase. K3, in particular, shows the highest tensile force values, possibly due to stress concentration resulting from the contact between the geotextile and the underlying bedrock. At K2, tensile forces remain relatively constant during the initial 0.2 m of subsidence plate displacement, after which they exhibit a trend of initial rapid increase followed by stabilization after 0.2 m. This behavior is attributed to the incomplete manifestation of the membrane tensile force effect in the early stage and its full manifestation in the later stage. For test point K1, tensile forces are nearly negligible during the first 0.35 m of subsidence plate displacement, gradually increasing to 8.11 kN after 0.35 m, and then stabilizing. Tensile forces at test point K0 consistently remain close to 0 kN. The trends in tensile force variation at various test points in the bottom layer of Groups T2-T3 are similar and, therefore, are not further elaborated.

Fig. 6
A multiline graph of tensile force in kilonewtons versus active baseplate displacement in meters. It illustrates 6 lines. K 2, K 3, K 4, and K 5 have ascending trends, while K 0 and K 1 have nearly horizontal trends. K 3 has the highest peak among others.

The trend diagram of test points K0-K5 tensile force with the displacement of the active plate in group T1

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The final tensile force values at all test points for each layer in Groups T1-T3 were sequentially connected from K0 to K10, resulting in the tensile force distribution diagrams at different horizontal positions for the reinforced geotextile layers in T1-T3. Figure 7 illustrates the tensile force distribution at different horizontal positions for the reinforced geotextile layers in T1-T3. From the graph, it can be observed that with an increase in the number of geotextile layers, the tensile force in the first layer (bottom layer) of geotextile decreases overall. The tensile force in the first layer (bottom layer) of geotextile generally increases from the stable region to the subsidence area, with the maximum tensile force occurring at the edges of the stable and subsidence areas. The maximum tensile force in the non-bottom layer geotextile appears on both sides of the subsidence area in the stable region, and it extends into the stable region. This could be due to the formation of a soil arch in the soil as the height increases, similar to an expansion of the subsidence area, causing test points at the edges of the stable and subsidence areas to move towards the stable region. When multiple layers of geotextile are arranged, the first layer (bottom layer) experiences the highest tensile force.

Fig. 7
A line graph of tensile force versus horizontal distance from the center of subsidence area plots 6 lines. It has 3 vertical sections for stable areas and subsidence area. First layers of T 1, T 2, and T 3, and second layers of T 2 and T 3, and T 3 third layer have ascending to descending trends.

The tensile force distribution of all geotextiles in groups T1-T3 at different horizontal positions

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4 Conclusions

The use of multi-layer reinforced geotextile to treat karst collapse can save the project cost, improve the effect of reinforcing material to treat karst collapse, and the optimal number of layers of reinforced geotextile can be explored in depth in the future. Discrete element numerical simulations were conducted for varying reinforced numbers of geotextile layers, analyzing top verticle settlement of the soil, and geotextile tensile force. The objective was to investigate the influence of different numbers of reinforced geotextile layers on the collapse of karst subgrades. The primary conclusions are as follows:

  • (1) As the number of reinforced geotextile layers increases, there is a general reduction in the overall settlement of the soil. This indicates that the addition of more reinforced geotextile layers can effectively diminish the tendency for soil collapse.

  • (2) With an increasing number of reinforced geotextile layers, the tensile force within the bottom layer of the geotextile consistently decreases. Conversely, from the stable area to the collapse area, the tensile force exhibits a general trend of increase. The bottom layer experiences the highest tensile force, followed by the second layer, while the third layer experiences the least tensile force. As the number of reinforced geotextile layers increases, the overall tensile force within the first layer (bottom layer) decreases, while the non-bottom layers of the geotextile share a portion of the tensile force.