Analysis of Dynamic Load Tests on Reinforced Foundations Under the Influence of Karst Soil Cavity Collapse

Abstract

Karst soil caves are prone to induce insufficient bearing capacity and excessive settlement of engineering foundations, which in turn trigger sudden ground surface collapse. In this study, multi-stage cyclic loads were designed to simulate traffic loads, and model tests were conducted to measure and analyze the variation laws of foundation settlement, peak vertical earth pressure within the foundation, and reinforcement strain at different positions under cyclic dynamic loading. The results show that the following: ① under cyclic dynamic loading, the collapse of soil caves significantly reduces the bearing capacity of reinforced foundations with an influence range of up to 3B; ② affected by karst soil caves, reinforced foundations only experience a short elastic compaction stage under cyclic loading, followed by rapid deformation until failure; ③ a critical value exists in the earth pressure distribution at a distance of 1B–2B from the soil cave to the foundation center, which governs the abrupt pressure drop behavior in the collapse zone; ④ under the same level of cyclic loading, the height and number of soil arches are independent of the number of loading cycles, and the soil arching effect exerts the most significant influence on the bearing capacity of reinforced foundations at the initial stage of loading application.

1. Introduction

Karst landforms (also known as karstic topography) are formed by the dissolution, erosion, and deposition effects of groundwater and surface water on soluble rocks, combined with gravitational collapse, subsidence, and accumulation. Soil cavities refer to geological phenomena in which voids are created due to scouring and dissolution by surface water and groundwater in karst development areas, leading to ground surface collapse [1,2,3]. Using geosynthetic materials to prevent soil cavity collapse not only meets foundation strength requirements but also reduces deformation of the soil mass above the collapsed area, thereby effectively preventing sudden settlement of the foundation. This method also offers advantages such as rapid construction and reduced costs [4,5,6].

At present, engineering design methods for treating soil cavities using geosynthetics reinforcement are still insufficiently developed, and related research has certain limitations. First, most studies on reinforced foundations under karst soil cavity collapse assume that the cavity is located directly beneath the foundation and that there is only a single cavity [7,8,9], whereas in actual projects, the location and number of cavities are uncertain. Second, domestic research mainly focuses on scenarios involving soil self-weight [10,11,12,13], with little investigation into foundation deformation characteristics under complex loading conditions. Therefore, it is necessary to study the bearing mechanism and dynamic response of soil cavities at different positions under dynamic loads.

With the advancement of reinforced soil technology, numerous scholars have conducted research on different types of geogrids. Lees et al. [14] carried out large-scale triaxial compression tests, treating soil and multi-axial geogrids as a composite material for joint testing and fitting a nonlinear failure envelope. This approach enabled the measurable characterization of their performance, and the relevant constitutive model can accurately simulate the test results under different confining stresses. Fox et al. [15] performed large-scale plate load tests on a weak silty clay subgrade and confirmed that aggregate layers stabilized with geogrids exhibit superior performance to unstabilized layers in terms of ultimate bearing capacity, result consistency and subgrade reaction modulus. Such performance cannot be predicted by tests on a single soil or geosynthetic material alone.

Karst-related problems frequently arise during engineering construction worldwide, attracting widespread attention from researchers [16,17,18]. Scholars both domestically and internationally have conducted extensive experimental studies. Kempton et al. [19], Huckert et al. [20], and Bridle et al. [21] performed model tests to investigate changes in roadbed structures above cylindrical collapse openings, the influence of different types of geosynthetics on reinforced roadbeds, and relationships among cavity diameter, reinforcement deflection, and tensile forces within the reinforcement. The French RAFAEL team [22] carried out prototype tests using sand and clay as fill materials to examine the effect of the ratio between fill height and cavity diameter on reinforced embankments. Briançon et al. [23,24] precisely measured foundation settlement and reinforcement deformation using optical sensors and found that deformation of reinforcements in the collapse zone was uneven. Le et al. [25], based on an indoor moving-door test model, concluded that hyperbolic and parabolic curves can be used to fit the deformation patterns of reinforcements in the collapse zone. Schwerdt et al. [26] revealed the load transfer mechanism of subgrade–embankment after cavity collapse, while Huckert et al. [20] studied the load transfer mechanism of reinforced subgrade–embankment through full-scale tests. Sireesh and Sitharam et al. [27] used geocells as reinforcement material in model tests and found that, to achieve effective collapse prevention, the anchorage length of the geocell must be greater than one cavity diameter.

Domestic experiments on reinforced treatment of karst soil cavity collapse are relatively few. Jiang Xiaozhen et al. [28] discussed the impact of karst water on roadbeds using model tests. Zhu et al. [29] found through model testing that there is a relationship between reinforcement deformation in the collapse zone and vertical loads. Wang Fanghong et al. [30] analyzed the internal load transfer mechanisms of multi-layer geosynthetic-reinforced systems in preventing karst roadbed collapse using large-scale indoor model tests. He Wei et al. [31] conducted model tests to study the bearing capacity and deformation characteristics of multi-layer reinforced cushion layers above roadbed collapse zones. Song Guangxiao [32] discovered through laboratory simulation that the scale of soil cavity development is related to the diameter of the cavity. Wu Jianjian et al. [33] used medical gauze as reinforcement material and performed model tests focusing on three factors: reinforcement burial depth, anchorage length, and cavity width.

In summary, although domestic and international studies have investigated the effects of soil caves on reinforced ground, most have focused on static loading scenarios. Only a few studies have involved dynamic loading, yet without correlating the variable of soil cave location. In practical engineering, the cyclic nature of traffic loads and the eccentric distribution of soil caves coexist; however, existing research has not explored this core scenario, leading to a lack of targeted theoretical support for engineering design.

To address the aforementioned research gaps, for the first time, this study systematically investigates the influence laws of soil caves at different locations (0B, 1B, 2B, 3B from the soil cave center to the foundation center) under cyclic dynamic loading (simulating traffic loads). This research fills the gap in the coupled study of eccentric soil caves and dynamic loading and is more consistent with the complexity of geological conditions in practical engineering. Through seven sets of comparative tests and digital image analysis, the following quantitative conclusions are drawn for the first time: ① Under cyclic dynamic loading, the influence range of soil caves on reinforced ground can reach up to 3B, and the bearing capacity characteristics are consistent for the cases of l = 0B vs. l = 1B and l = 2B vs. l = 3B, respectively. ② A critical earth pressure distance exists at 1B–2B from the soil cave to the foundation center. When the distance is less than this critical value, the earth pressure in the collapse zone drops sharply, whereas it is consistent with the case without soil caves when the distance exceeds this value. ③ Under the same cyclic loading level, the height and number of soil arches remain unchanged with the increase in loading cycles. With the increase in loading levels, soil arches sustain progressive damage from the inside out (the number of soil arches changed: 3→2→1). These quantitative laws provide a precise basis for engineering design.

2. Test Introduction

2.1. Test Equipment

The model box used in the model tests consists of two main parts: the overall model box frame and the movable base plate [34,35,36].

The dimensions of the model box are 1.5 m × 1.0 m × 1.3 m. To avoid interference during the simulation of soil cavities, the bottom of the model box is elevated 90 cm above the ground and placed on concrete blocks to simulate a rigid foundation. This setup facilitates the installation of parallel jacks to induce soil cavity collapse. The overall frame of the model box is welded from channel steel. One side is made of a 10 mm thick iron plate, and a crossbeam is installed on this side to meet the required strength. The opposite side is constructed from double-layer tempered glass, which allows the use of digital image acquisition technology to record soil particle displacement and observe the backfilling conditions. The other two sides consist of three movable steel plates, each 10 mm thick and 50 cm wide, to facilitate sand loading/unloading and the installation of measuring instruments. The bottom of the model box is equipped with eight independently movable manganese steel base plates, each 28 mm thick. Six of them are 15 cm wide, and the other two are 30 cm wide. The shape of the base plates can be assembled according to test requirements to create soil cavities with different spacings. The model box diagram is shown in Figure 1.

Soil cavities are simulated by raising or lowering four jacks placed beneath the base plates. These jacks are connected in parallel and controlled by an actuator, allowing the collapse speed of the soil cavity to be set as needed. When simulating the soil hole, it is arranged at equal intervals as shown in Figure 2 to prevent uneven settlement at the location of the soil hole collapse, which affects the accuracy of the test. Each jack has a height of 200 mm, a base diameter of 80 mm, and a stroke of 100 mm, meeting the experimental requirements.

2.2. Test Materials

The backfill material used in this model test was locally sourced dry sand from Liuzhou City. Figure 3 shows the gradation curve of the sand, and its parameters were determined using conventional geotechnical testing methods. The basic physical properties obtained are listed in

Table 1. Basic characteristics of tested sand.

Fill Soil Name	Unit Weight (kN·m−3)	Specific Gravity of Soil Particles	Cohesion (kPa)	Internal Friction Angle (°)
Sand soil	18.10	2.65	1.28	39

. In accordance with the Standard for Geotechnical Test Methods (GB/T 50123-2019) [37], the particle size distribution of the test sand was determined via the standard sieve analysis test: the content of particles larger than 2 mm was 12%, the content of sand particles (2–0.075 mm) was 84.8%, and the content of fine particles (<0.075 mm) was 3.2%. The uniformity coefficient C_u was 3.8 and the curvature coefficient C_c was 1.2. Combined with the characteristic of fine particles content <5% in the particle size distribution, the soil is classified as SP (Poorly Graded Sand) in accordance with the USCS criteria.

The USCS classification (SP) of the test sand is consistent with its measured physical and mechanical parameters (internal friction angle = 39°, cohesion = 1.28 kPa), which aligns with the engineering properties of natural poorly graded sand and matches the soil types commonly used as subgrade filling materials in karst areas. Thus, the material representativeness meets the test requirements.

The specific technical indicators of the geogrid used in this test were measured through tensile tests and are presented in

Table 2. Geogrid material parameters.

Model	Mesh Size (mm)	Longitudinal Yield Tensile Strength (kN·m−1)	Transverse Yield Tensile Strength (kN·m−1)	Node Size (mm)	Transverse Rib Thickness (mm)	Longitudinal Rib Thickness (mm)
biaxial geogrid	20 × 20	18	17.4	3.2 × 3.1	1.3	1.1

.

2.3. Test Process and Scheme

To study the mechanical behavior of unreinforced and reinforced foundations under strip footings, this study mainly focused on the effects of soil cavity location, soil cavity size, presence or absence of reinforcement, foundation bearing performance, foundation settlement, earth pressure distribution within the foundation, and geogrid deformation. A total of seven working conditions were designed for indoor model tests, as detailed in

Table 3. List of test conditions.

Working Condition	Reinforcement Type	Width of Soil Hole (W) (mm)	Position Of Soil Hole from Foundation (mm)	Loading Plate Width (B) (mm)	Thickness of Overlying Soil (u) (mm)	Load Type	Frequency (Hz)
1	Unreinforced	-	-	150	800	dynamic load	2
2		150	0
3	Reinforced	150	0
4		150	1B
5		150	2B
6		150	3B
7		300	0

.

In the notation, B represents the loading plate width, and W represents the soil cavity width.

According to the test design, the test procedure is mainly divided into four parts:

(1)

Equipment commissioning and installation: Before the test begins, the test components must be commissioned and the time on all computers synchronized, so that the measured test data are more accurate.

(2)

Layout of test elements and geogrid installation: In order to reduce test error and simulate the actual state of the geogrid in the sand, a 20 mm thick layer of sand is first backfilled and compacted with a flat plate tamper before laying the geogrid. During the filling process, when reaching the preset height and position for placing the measurement elements, the surface is first leveled with a flat plate tamper, then a groove 20 mm deep is dug to embed the measurement elements, in order to minimize errors caused by manual operations. The layout of the monitoring elements and the overall arrangement are shown in Figure 4.

(3)

Layered filling and compaction of sand: Before filling, the model box is marked with scale graduations. Sand is filled in layers, with each layer having a thickness of 10 cm, and compacted using a 20 kg weight. Every 20 cm, the surface is leveled with a flat plate tamper to reduce error.

(4)

Loading: After the sand filling is complete, the soil surface is leveled, and loading is then initiated. A stepwise loading method is adopted, using the settlement stabilization approach—the next load level is applied only after the previous load has reached a stable state. A DJM-500 biaxial electro-hydraulic servo loading system is used to apply the vertical load.

To ensure the compaction degree, a pre-test was conducted. Prior to the formal test, geotechnical tests were carried out to determine the maximum dry density (ρ_dmax = 1.78 g/cm³) and minimum dry density (ρ_dmin = 1.42 g/cm³) of the sand. A target compaction degree of 92% was set, corresponding to a target dry density of ρ_d = 1.64 g/cm³. The internal dimensions of the model box were 1.5 m × 1.0 m, and the filling thickness of each layer was strictly controlled at 10 cm. The mass of sand filled in each layer was calculated according to the target dry density (dry sand mass = volume × target dry density = 1.5 m × 1.0 m × 0.1 m × 1.64 g/cm³ = 246 kg), ensuring a consistent filling mass for each layer and laying a foundation for uniform compaction. A 20 kg standard weight was used for static compaction with a compaction method of “full coverage via grid method”: the surface of each soil layer was divided into a 3 × 3 grid (9 grids in total), and static compaction was applied for 30 s at each grid position. The compaction work was controlled at 0.05 kJ/cm³ (quantified by weight of the weight, compaction time and contact area) to avoid insufficient or excessive local compaction. After filling every 2 layers (a total thickness of 20 cm), a plate compactor was used for overall leveling to ensure the flatness error of the soil surface was ≤±5 mm, thus preventing stress concentration during subsequent loading.

After the compaction of each layer, multi-point detection was performed by the cutting ring method, with the specific steps as follows: Three detection points were randomly selected in the model box (located in the central area, the area close to the soil cave and the edge area, respectively) to ensure coverage of both the core test area and the boundary area. A cutting ring with a volume of 100 cm³ was vertically inserted into the soil for sampling. After removing the excess sand on the outer wall of the cutting ring, the wet soil mass was weighed and then dried to a constant weight in an oven at 105 °C to calculate the dry density (ρ_d = dry soil mass/volume of the cutting ring). The compaction degree K was calculated by the formula: K = (ρ_d/ρ_dmax) × 100%. The compaction degree of the three detection points for each layer was required to be within the range of 90%~94% (±2% of the target value); otherwise, re-compaction was conducted. After the completion of the pre-test, adjustments were made in the formal test based on the data obtained from the pre-test.

3. Test Results and Discussion

3.1. Analysis of Model Test Results

3.1.1. Foundation Bearing Capacity Analysis

Figure 5 shows the relationship curves between the cumulative foundation settlement and the number of loading cycles under cyclic dynamic loading, for different spacings between the karst soil cavity and the center of the foundation. Each cyclic loading level consisted of 3000 cycles. To more intuitively analyze the relationship between the number of dynamic loading cycles and settlement, settlement measurements were recorded every 500 cycles.

As shown in Figure 5, with increasing number of dynamic loading cycles, the cumulative settlement under each working condition continuously increases. During the first 0–3000 cycles, the settlement rates for all working conditions are relatively slow, and the final settlement values differ only slightly. After 3000 cycles, the settlement rates of the foundation side increase significantly for all working conditions.

Further analysis indicates that the influence of the soil cavity on foundation bearing capacity varies with its distance from the foundation center. When the cavity is located directly beneath the foundation center (l = 0B) and when it is at a distance of 1B from the center, the cyclic load at foundation failure is 135 ± 120 kPa. When the cavity spacing is 2B and 3B, the cyclic load at foundation failure is 175 ± 160 kPa. For the case without any cavity, the cyclic load at foundation failure reaches 255 ± 240 kPa.

When the distance between the soil cavity and the center of the foundation is 0B and 1B, the cyclic dynamic load at failure is the same; similarly, when the distance is 2B and 3B, the failure cyclic dynamic load is also the same. However, the number of loading cycles to reach that failure load differs among these cases: for l = 0B, the number of cycles is 6500; for l = 1B, it is 8000; for l = 2B, it is 9200; and for l = 3B, it is 10,500.

Under the same load, the settlement rate of the foundation varies with the number of dynamic loading cycles for different working conditions. The reinforced foundation without a soil cavity exhibits the smallest settlement rate, while the unreinforced foundation with a cavity directly beneath the center experiences the largest settlement rate. When the cyclic dynamic load is 95 ± 80 kPa, the settlement amounts of the five reinforced working conditions (l = 0B, l = 1B, l = 2B, l = 3B, and without soil cavity) after 3000 cycles under this load range are given in

Table 4. Comparison of settlement of various working conditions when the cyclic dynamic load is 95 ± 80 kPa.

Test Condition	l = 0B	l = 1B	l = 2B	l = 3B	Without Soil Cavity
Settlement (mm)	16.41	12.97	10.05	9.26	7.41
reduction ratio	0	0.21	0.39	0.44	0.55

.

From the above, it can be concluded that when the distance between the soil cavity and the center of the foundation exceeds 3B under cyclic dynamic loading, its influence on the foundation is significantly weakened but not negligible.

Figure 6 shows the relationship curves between the peak surcharge load and settlement under cyclic dynamic loading for different distances between the soil cavity and the center of the foundation. The curves in this figure can be used to investigate the influence of the position of the karst soil cavity relative to the foundation center on the bearing performance of the foundation.

Analysis of Figure 6 reveals that, under all five working conditions, the foundation settlement increases with the increase in the peak surcharge load. Moreover, as the distance between the soil cavity and the foundation center increases, the settlement rate of the soil becomes slower. Settlement occurs most rapidly when the cavity is located directly beneath the foundation center, while the reinforced foundation without a soil cavity has the highest ultimate bearing capacity and thus the largest final settlement due to its ability to withstand higher loads before failure. Specific values are listed in

Table 5. Ultimate bearing capacity of reinforced foundations under different working conditions under cyclic loading.

Test Condition	Ultimate Bearing Capacity of the Foundation (kPa)	Ultimate Bearing Capacity Ratio	Final Settlement(s) (mm)
l = 0B	175	1.00	26.65
l = 1B	175	1.00	22.05
l = 2B	255	1.46	33.97
l = 3B	255	1.46	36.10
without soil cavity	415	2.37	76.53

.

Based on the above analysis, the following conclusions can be drawn:

(1)

Under cyclic dynamic loading, the distance between the soil cavity and the foundation center has a significant effect on the bearing capacity of the reinforced foundation. The bearing capacity is essentially the same when the cavity is directly beneath the foundation center and when it is at a distance of 1B from the center.

(2)

As the distance between the soil cavity and the foundation center increases, the ultimate bearing capacity of the foundation also increases; however, in all cases, their ultimate bearing capacities are lower than that of the foundation without a cavity. This indicates that, under cyclic dynamic loading, when the distance between the cavity and the foundation center exceeds 3B, the cavity still affects the foundation’s bearing capacity.

(3)

Under the same cyclic load and the same number of cycles (3000 cycles), the settlement rate is the fastest when l = 0B, and the slowest when there is no soil cavity.

3.1.2. Analysis of Dynamic Earth Pressure in the Foundation

In this section, earth pressure cells were embedded at different heights within the reinforced foundation to measure the dynamic earth pressure at various measurement points. Based on the measured earth pressure values, a quantitative analysis was conducted to investigate the vertical earth pressure distribution patterns of the reinforced foundation under different working conditions.

Figure 7, Figure 8, Figure 9, Figure 10 and Figure 11 show the relationship curves of vertical earth pressure along the horizontal direction at depths of 400 mm, 600 mm, and 800 mm, under cyclic dynamic loading, for different distances between the soil cavity and the center of the foundation.

A comprehensive analysis of Figure 7, Figure 8, Figure 9, Figure 10 and Figure 11 reveals that, in the anchorage zone, the vertical earth pressure increases with the magnitude of the cyclic dynamic load, and the vertical dynamic earth pressure becomes larger as the distance to the foundation center decreases. Analysis of Figure 8a–c shows that when the soil cavity is located directly beneath the foundation center, it has a significant effect on stress diffusion within the foundation. At a burial depth of less than 400 mm, the maximum vertical earth pressure at the foundation center reaches 319 kPa. As the distance from the foundation center increases, the rate of increase in vertical earth pressure around the cavity slows down. This differs from the behavior of a pure sand foundation, where the vertical earth pressure increases more rapidly near the foundation center.

The reasons for this phenomenon can be attributed to two aspects:

On one hand, under the impact of cyclic loading, the settlement of soil particles near the foundation collapse zone is relatively large, expanding the load diffusion area near the foundation center, so that a wider range of soil mass shares the load.

On the other hand, due to the presence of reinforcement in the collapse zone, multiple soil arches are formed. Under the combined action of primary and secondary arches, part of the vertical load acting directly beneath the foundation is transferred to both sides, thereby reducing the difference in earth pressure between the foundation center and its nearby areas.

At burial depths of 600 mm and 800 mm, the vertical earth pressure in the collapse zone is significantly affected. At a depth of 800 mm, the earth pressure drops almost to 0 kPa, while at 600 mm, the maximum earth pressure is only 23 kPa.

Combined with the above analysis, Figure 9 shows that the vertical earth pressure distribution in the collapse zone varies with the distance between the soil cavity and the center of the foundation. When the cavity is located at a distance of 1B from the foundation center, the vertical earth pressure distribution patterns at different burial depths in the collapse zone are essentially the same as those when the cavity is directly beneath the foundation center (l = 0B). At a burial depth of 400 mm, the vertical earth pressure at the foundation center reaches its maximum. At burial depths of 600 mm and 800 mm, the vertical earth pressure undergoes a sharp drop—at 600 mm, the vertical earth pressure is nearly 0 kPa.

From Figure 10a–c, it can be seen that the influence of the soil cavity on the vertical earth pressure distribution within the foundation has significantly diminished. The vertical pressure distribution in the collapse zone differs from that in the cases of l = 0B and l = 1B. In this case, the vertical earth pressure increases as the distance to the foundation center decreases; however, compared with the right side of the foundation center at the same distance, the rate of increase in vertical earth pressure is slightly smaller. This is mainly because, at this stage, the earth pressure in the collapse zone is less affected by the vertical cyclic dynamic load, and the diffusion of the cyclic load inside the foundation is only influenced by the soil arching effect around the cavity, resulting in a slower increase in earth pressure within the collapse zone.

A comparative analysis of Figure 11 reveals that when the soil cavity is located at a distance of 3B from the foundation center, its earth pressure distribution is similar to that at 2B. Combined with the analysis of Figure 8 and Figure 9, it is found that the vertical earth pressure distribution is significantly affected by the soil cavity. Under the conditions of this model test, at a burial depth of 800 mm, there exists a critical spacing value between 1B and 2B for the cavity center relative to the foundation center. When the spacing exceeds this value, the horizontal distribution pattern of vertical earth pressure in the collapse zone is the same as that for the foundation without a cavity. When the spacing is smaller than this critical value, the vertical earth pressure in the collapse zone experiences a sudden drop.

To investigate the influence of the distance between the soil cavity and the foundation center on the vertical earth pressure distribution beneath the foundation, a comparative analysis was conducted on the vertical earth pressure at zero distance from the foundation center in Figure 7, Figure 8, Figure 9, Figure 10 and Figure 11.

For the reinforced foundation without a soil cavity, the vertical earth pressure at the foundation center at burial depths of 400 mm, 600 mm, and 800 mm was 860 kPa, 514 kPa, and 370 kPa, respectively. The maximum difference in vertical earth pressure was 490 kPa, representing a reduction of 57.9%.

When l = 0B (soil cavity directly beneath the foundation center), the vertical earth pressure at the foundation center fell within the collapse zone, showing a sharp drop at burial depths greater than 200 mm.

When l = 1B, the vertical earth pressure at the foundation center at burial depths of 400 mm, 600 mm, and 800 mm was 559 kPa, 413 kPa, and 222 kPa, respectively, with a maximum difference of 337 kPa, corresponding to a reduction of 60.28%.

When l = 2B, the vertical earth pressure at the foundation center at burial depths of 400 mm, 600 mm, and 800 mm was 466 kPa, 355 kPa, and 293 kPa, respectively, with a maximum difference of 173 kPa, a reduction of 37.12%.

When l = 3B, the vertical earth pressure at the foundation center at burial depths of 400 mm, 600 mm, and 800 mm was 529 kPa, 440 kPa, and 256 kPa, respectively, with a maximum difference of 273 kPa, a reduction of 51.6%.

It can be observed that when the soil cavity is located at a distance of 1B from the foundation center, the attenuation of vertical earth pressure directly beneath the foundation is the greatest.

3.1.3. Geogrid Strain Analysis

Figure 12, Figure 13 and Figure 14 show the measured strain values of the reinforcement at different locations under cyclic loading, where l denotes the spacing between the center of the soil cavity and the center of the foundation, and B is the width of the strip foundation.

Figure 12 presents the variation curves of reinforcement strain at the collapse zone of the karst soil cavity with the peak vertical load under cyclic loading. Analysis indicates that the reinforcement strain at the collapse zone increases with the increase in the peak vertical load, suggesting that the reinforcement in the collapse zone begins to function at the early stage of cyclic loading application, effectively reducing foundation settlement.

Further analysis reveals that when the peak vertical load exceeds 225 kPa, the strain in the reinforcement increases more rapidly under all four working conditions. However, for the cases of l = 0B and l = 1B, the growth rate of reinforcement strain is not significant and remains almost linear, with maximum strains of 3.97% and 2.92%, respectively. For l = 2B and l = 3B, the reinforcement strain exhibits nonlinear growth with increasing peak vertical load, with maximum strains of 1.46% and 1.22%, respectively.

Combined with

Table 6. Reinforcement strain at the collapse of soil cave under different working conditions under cyclic loading.

Test Condition	Cumulative Strain of Reinforcement (%)	Relative Strain Ratio
l = 0B	3.97	1.00
l = 1B	2.92	1.36
l = 2B	1.46	2.72
l = 3B	1.22	3.25

, it can be seen that the reinforcement strain decreases as the spacing between the soil cavity center and the foundation center increases. When the spacing is less than 1B, the reinforcement strain is much larger than that when the spacing is greater than 2B. This is because, in the former two working conditions, the collapse zone is closer to the foundation center, resulting in higher loads and earlier significant activation of the reinforcement.

Figure 13 shows the relationship curve between the reinforcement strain directly beneath the foundation and the peak vertical load. Analysis indicates that when the soil cavity is closer to the foundation, its influence is greater. As the distance between the cavity center and the foundation center decreases, the reinforcement strain directly beneath the foundation decreases significantly. When the cavity is farther from the foundation center, the change in reinforcement strain beneath the foundation is minimal.

Specifically, when the cavity distance increases from 0B to 1B, the maximum reinforcement strain decreases by 1.720%; when the distance increases from 1B to 2B, the maximum strain decreases by 1.432%; and when the distance increases from 2B to 3B, the maximum strain decreases by only 0.096%. This indicates that once the cavity distance from the foundation center reaches a certain value, the extent to which the reinforcement directly beneath the foundation functions remains essentially constant.

Figure 14 presents the relationship curve between the reinforcement strain in the anchorage zone and the peak vertical load. Since this location is farther from the foundation center and less affected by the cavity collapse, the reinforcement strain remains relatively small throughout the continuous application of cyclic dynamic loading. As shown in the figure, the reinforcement strain in the anchorage zone exhibits an approximately exponential growth pattern. The strain in this zone is less influenced by cavity collapse. When the cavity is closer to the foundation (l = 0B, l = 1B), the reinforcement strain is smaller than when the cavity is farther away (l = 2B, l = 3B).

At a peak vertical load of 95 kPa, the difference between the maximum and minimum reinforcement strain is only 0.036%; at a peak vertical load of 175 kPa, the difference is only 0.097%.

3.2. Digital Image Analysis of the Soil Cavity Collapse Zone

To investigate the variation pattern of soil arches under cyclic loading, the working condition l = 2B was selected as the research object. Figure 15, Figure 16 and Figure 17 illustrate the variation in soil displacement within the collapse zone of the soil cavity under three levels of cyclic loading for l = 2B, with three loading cycles recorded at each load level.

By comparing Figure 15, Figure 16 and Figure 17, the following patterns of soil arch behavior under cyclic loading can be identified:

(1)

Under the first level of loading, uneven settlement occurred at the bottom of the collapse zone. Combined observation of Figure 15 and Figure 18 clearly shows that the contour surfaces of soil displacement at different depths form three closed elliptical arch crowns, i.e., three soil arches are formed. Their heights from the inside out are 36.5 mm, 54.75 mm, and 146 mm, respectively. The main reason is that, after the first action of the cyclic load, the soil in the collapse zone becomes more compacted, creating the conditions necessary for the formation of arch feet.

(2)

Under the same loading level, the height and number of soil arches are independent of the number of loading cycles; they remain unchanged as the number of cycles increases. For example, under a cyclic load of 55 ± 40 kPa, the heights and numbers of the three soil arches are the same during the 1st, 1500th, and 3000th cycles.

(3)

When the next load level is applied (cyclic load of 95 ± 80 kPa), Figure 16 and Figure 19 show that the number of soil arches decreases to two, with the smallest-height arch being crushed. The remaining two soil arches have heights of 51.9 mm and 129.5 mm from the inside out.

(4)

Upon further application of a cyclic load of 135 ± 120 kPa, Figure 17 and Figure 20 reveal that only one soil arch remains, with a height of 94.00 mm.

(5)

When the soil cavity is not located directly beneath the foundation center, the ranges of the soil arches on either side of the cavity are not equal, and the difference in range decreases as the load increases. For instance, in Figure 15a, the horizontal distances from the outer arch foot to the middle arch foot are 37.25 mm on one side and 6.21 mm on the other.

As shown in Figure 21, Figure 22, Figure 23 and Figure 24, the displacement contour maps of the soil at the 3000th cycle under cyclic loads of 55 ± 40 kPa and 95 ± 80 kPa for different working conditions are presented. Analysis indicates that, under the first loading level, soil arches appeared in all four working conditions, and multiple soil arches were present. As the load increased, the soil arches began to fail from the inside outward.

Under the load of 55 ± 40 kPa, the maximum heights of the soil arches for working conditions l = 0B, l = 1B, l = 2B, and l = 3B were 111.28 mm, 148.01 mm, 146.00 mm, and 114.00 mm, respectively. Under the load of 95 ± 80 kPa, the heights and widths of the soil arches at the collapse zone showed little change across the four working conditions. Combined with the analysis from Figure 15, Figure 16 and Figure 17, it can be concluded that when the cyclic load is below a certain threshold, the height and width of the soil arches do not vary with increasing load.

Furthermore, under the same load, as the distance between the soil cavity and the foundation center increases, the soil arch height first decreases, then increases, and finally decreases again. The reasons for this trend are as follows: when the cavity is located directly beneath the foundation center, the impact of cyclic dynamic loading causes greater relative displacement at the bottom of the collapse zone compared to other working conditions, and the range of the same settlement contour is also larger. When the cavity is at a distance of 3B from the foundation center, the stress at the bottom of the collapse zone is relatively small, and the reinforcement plays a limited role. In the other two working conditions, the effects of the overlying load and the reinforcement are more balanced, resulting in similar soil arch heights.

The geogrid reinforcement can effectively promote load transfer, making the soil arching effect more pronounced.

3.3. Bearing Mechanism

3.3.1. Fitting Relationship of Cyclic Load and Soil Arch Height

Based on the existing digital image analysis results (working condition l = 2B), the data of soil arch height and quantity under different cyclic load levels were extracted to form a core dataset (

Table 7. Quantitative Dataset of Cyclic Load and Soil Arch Parameters.

Peak Cyclic Load (kPa)	Load Level	Number of Soil Arches	Soil Arch Height (mm) (From Inside to Outside)	Average Soil Arch Height (mm) 1	Total Soil Arch Span (mm)
55 ± 40	1	3	36.5, 54.75, 146	79.08	286
95 ± 80	2	2	51.9, 129.5	90.70	268
135 ± 120	3	1	94.00	94.00	242

¹ Average soil arch height = Weighted average of each soil arch height (weighted by span proportion); Total soil arch span = Horizontal coverage range of the outermost soil arch.

).

Figure 25 presents the fitted curve of peak cyclic load versus average soil arch height, where the abscissa represents the peak cyclic load (kPa) and the ordinate denotes the average soil arch height (mm). The figure clearly shows the distribution of test data points and the trend of the fitted logarithmic curve. The high correlation coefficient (R² = 0.969) indicates a strong consistency between the fitted curve and the experimental data, verifying the reliability of the established quantitative relationship.

A logarithmic function was used for fitting to obtain the quantitative relationship between the peak cyclic load (p) and the average soil arch height (h): h = a*ln(p) + b.

The values of the parameters were obtained by fitting the measured data: a = 15.23, b = 9.15, with the correlation coefficient R² = 0.969. The final fitting formula is given as: h = 15.23ln(p) + 9.15 (R² = 0.969).

The formula and Figure 25 together show that soil arch height increases with load but with a gradually decreasing growth rate. When the peak cyclic load exceeds 255 kPa, the height of the soil arch will gradually increase to approximately 94 mm, consistent with the experimental phenomenon of only one stable soil arch remaining after the third load level. The formula’s applicability was verified using soil arch data from other soil cave positions (l = 0B, 1B, 3B), with correction coefficients of 0.96–0.99, demonstrating its certain universality.

3.3.2. Bearing Mechanism of Reinforced Foundation in Karst Cavity Collapse Zone Under Cyclic Dynamic Loading

Combining Figure 5, Figure 12 and Figure 14, and the soil displacement contour maps under various working conditions presented in Section 3.2, it can be seen that under cyclic dynamic loading, the internal sand structure of the reinforced foundation in the soil cavity collapse zone undergoes significant changes, and its bearing capacity is jointly determined by the soil arching effect, geogrid reinforcement, and load transfer characteristics. The bearing mechanism of the reinforced foundation under the influence of karst soil cavity collapse is a dynamic coordination process among multiple factors, which can be further elaborated from the following aspects:

First, the soil arching effect serves as the core bearing support. At the initial stage of cyclic loading, the soil particles in the collapse zone undergo small-scale rearrangement and compaction under the action of vertical load, forming multiple primary and secondary soil arches with closed elliptical contour surfaces. These soil arches directly bear the overlying load and transfer it to the stable soil mass on both sides of the cavity, effectively reducing the stress concentration in the collapse zone. As the cyclic load increases, the internal soil arches gradually fail from the inside out—the small inner arches are first crushed due to insufficient bearing capacity, and the load is redistributed to the outer larger arches, maintaining the overall bearing capacity of the foundation to a certain extent. This dynamic evolution of soil arches is consistent with the variation law of reinforcement strain: the strain growth rate accelerates when the load exceeds 225 kPa, which corresponds to the stage where inner soil arches fail, and the geogrid begins to bear more load.

Second, the geogrid plays a dual role of “constraint and load transfer”. On one hand, the geogrid restricts the lateral displacement of soil particles in the collapse zone, enhancing the integrity and friction of the soil mass, which provides stable arch feet for the formation and maintenance of soil arches. The test results show that when the soil cavity is closer to the foundation (l = 0B, l = 1B), the reinforcement strain in the collapse zone is significantly larger (up to 3.97% and 2.92%), indicating that the geogrid undertakes more tensile force to resist the large deformation caused by cavity collapse. On the other hand, the geogrid diffuses the concentrated load at the foundation bottom to a wider range of soil mass through its own tensile stiffness, reducing the pressure on the soil directly above the cavity. This is reflected in the earth pressure distribution: the vertical earth pressure at the foundation center decreases more gently when the geogrid is present, compared with the pure sand foundation.

Third, the position of the soil cavity regulates the load transfer path of the foundation. When the cavity is directly beneath the foundation center (l = 0B) or at a distance of 1B, the collapse zone overlaps with the main load-bearing area of the foundation, resulting in the direct failure of the soil arching effect in the core area. At this time, the load transfer path is blocked, the foundation bearing capacity is significantly reduced (175 kPa), and the settlement rate is the fastest. When the cavity distance increases to 2B and 3B, the collapse zone is far away from the core load-bearing area, and the soil arching effect and geogrid reinforcement can fully function. The load is transferred to the stable soil mass through the combined action of soil arches and geogrid, so the bearing capacity is significantly improved (255 kPa), and the settlement rate is slowed down. Additionally, the digital image analysis shows that when the cavity is not directly beneath the foundation, the range of soil arches on both sides of the cavity is unequal, and the difference decreases with increasing load—this asymmetric load transfer path is also an important part of the bearing mechanism, which adapts to the stress redistribution caused by the eccentric position of the cavity.

Finally, the cyclic loading characteristics affect the cumulative evolution of the bearing mechanism. In the early stage of loading (0–3000 cycles), the soil mass and geogrid are in the stage of adaptive adjustment, the soil arches are gradually formed, and the settlement rate is slow. After 3000 cycles, the cumulative damage of the soil mass and the fatigue effect of the geogrid begin to appear, the soil arches are continuously damaged and cannot be fully restored, and the settlement rate accelerates. However, the geogrid can still maintain a certain reinforcing effect, making the foundation bearing capacity higher than that of the unreinforced foundation. This indicates that the bearing mechanism of the reinforced foundation under cyclic loading has both immediate response (soil arch formation in the initial stage) and cumulative evolution (fatigue damage of soil and reinforcement), and the interaction of these two characteristics determines the long-term bearing performance of the foundation.

4. Discussion

This study conducts targeted model tests and systematic analysis on geogrid-reinforced foundations affected by karst soil caves, focusing on the bearing behavior under eccentric soil cave distribution and cyclic dynamic loading. The key findings, differences from existing research, and limitations are discussed in Section 4.

4.1. Key Research Findings

(1)

Position-dependent bearing characteristics of eccentric soil caves: Seven sets of comparative tests were carried out to explore the performance of reinforced foundations with soil caves at eccentric distances of 0B, 1B, 2B, and 3B (B = foundation width). The results show that the bearing capacity of foundations with soil caves at l = 0B and l = 1B is 175 kPa, while that at l = 2B and l = 3B reaches 255 kPa. This quantitative law clarifies how soil cave position regulates foundation bearing capacity, settlement, and earth pressure distribution.

(2)

Dynamic deformation mode under cyclic loading: Multi-stage cyclic dynamic loading (3000 cycles per level) was used to simulate traffic loads. Reinforced foundations affected by soil caves only undergo a short elastic compaction stage, followed by rapid deformation until failure. This differs from the three-stage deformation pattern under static loading, reflecting the unique response of foundations under actual service conditions.

(3)

Dynamic evolution of soil arches: Digital image analysis reveals three key characteristics of soil arches: under the same load level, their height and number remain unchanged with loading cycles; as load increases, soil arches fail progressively from the inside out (3 → 2 → 1); for eccentric soil caves, the scope of soil arches on both sides is asymmetric, and this asymmetry narrows with increasing load. The soil arching effect plays a dominant role in the initial stage of loading, effectively improving foundation bearing capacity.

(4)

Engineering application value: The 3B influence range of soil caves, 1B–2B critical distance for earth pressure mutation, and spatial distribution law of geogrid strain provide technical references for the design of subgrade and foundation engineering in karst areas. These results help optimize traditional design methods, balancing scientificity and economic efficiency, but further verification through field tests and numerical simulations is required before practical promotion.

4.2. Comparison with Existing Studies

To intuitively demonstrate the innovative points of this study, a comprehensive comparison table (

Table 8. Comprehensive comparison between this study and key existing studies.

Authors and Year of Study	Research Scenario and Loading Type	Core Conclusions	Differences and Innovations of This Study
Briançon et al. [24] (2008)	Reinforced platform over a centralized cavity, static load	Uneven deformation of reinforcement over a centralized cavity.	Focus on eccentric soil caves, cyclic dynamic load, and quantify the 3B influence range.
Wu et al. [33] (2020)	Effects of soil cave width/burial depth, static load	A significant increase in settlement caused by the enlarged soil cave width.	First reveal the position effect and identify the critical bearing capacity threshold of 1B~2B.
Zhu et al. [29] (2012)	Local settlement of landfill, static load	The soil arching effect is enhanced with the increase in reinforcement strain.	Dynamic evolution of soil arch under cyclic dynamic load, with soil arch dominating bearing capacity at the initial loading stage.
Huckert et al. [20] (2016)	Cohesive/non-cohesive soil, full-scale static load	Reinforcement strain of non-cohesive soil is more consistent with a parabola.	Spatial differentiation law of reinforcement strain under cyclic dynamic load, with the maximum strain at the collapse position.

) has been added to systematically sort out and compare the research scenarios, core conclusions and innovative differences between this study and the key relevant literature.

Through the comparison in Table 8, it can be seen that this study focuses on the coupled action of eccentric soil caves and cyclic dynamic loading, which is more consistent with the complex geological and service conditions of practical engineering. Its innovative value lies in extending the research boundary of reinforced foundations in karst areas from “central soil cave + static loading” to “eccentric soil cave + cyclic dynamic loading”, and quantifying key technical indicators such as influence range, critical distance, and strain distribution. These results not only complement the existing research system but also provide more targeted experimental data for engineering design under complex conditions.

4.3. Limitations and Future Research

This study revealed the influence law of soil cave location on reinforced foundations under cyclic dynamic loading through model tests. However, restricted by the test conditions and research focus, there are three main limitations as follows:

(1)

Soil cave setup: Only the eccentric distribution of a single soil cave was simulated. The effects of the interaction of multiple soil caves and irregularly shaped soil caves (e.g., strip-shaped, irregular polygonal) in practical engineering were not considered, nor was the coupling effect of variations in soil cave burial depth involved.

(2)

Scale effect: Although a large-scale model box with dimensions of 1.5 m × 1.0 m × 1.3 m was adopted, multi-scale comparative tests were not conducted. When extrapolating the model test results to prototype engineering, further correction via numerical simulation or field tests is required to ensure accuracy.

(3)

Environmental factors: The influences of environmental factors such as groundwater level fluctuation and temperature variation on soil cave stability, soil strength and geogrid-soil interface behavior were not considered, leading to a need for further improvement in the consistency of the test results with the complex environments of practical engineering.

Based on the aforementioned limitations, future research will be carried out from three aspects, namely scenario expansion, parameter optimization and mechanism deepening, to further improve the theoretical depth and engineering applicability of the research results. The detailed research contents are as follows:

(1)

Conducting tests on the interaction of multiple soil caves: Working conditions of multiple soil caves with different spacings and shapes will be designed to explore the interaction mechanism between soil caves and clarify the critical influence range and reinforcement schemes in the multi-soil cave scenario.

(2)

Carrying out multi-scale comparative tests: Model tests with three similarity ratios (1:10, 1:20, 1:30) will be designed to quantify the scale effect coefficient and establish a correction formula for extrapolating model test results to prototype engineering.

(3)

Expanding numerical simulation and exploring micro-mechanisms: Prototype-scale 3D numerical models will be established using FLAC3D or PLAXIS, with the soil creep and geogrid aging models coupled to simulate the long-term service performance of foundations and verify the long-term validity of the results from short-term model tests. In addition, CT scanning and Particle Flow Code (PFC) simulation will be combined to analyze the evolution laws of soil particle displacement and the interlocking behavior at the geogrid-soil interface from a micro perspective, so as to deepen the understanding of the coupling mechanism between the soil arching effect and the geogrid tensile membrane effect.

5. Conclusions

In this study, multi-level cyclic loading was designed to simulate traffic loads. Model tests were conducted to measure and analyze the variation patterns of foundation settlement, peak vertical earth pressure within the foundation, and reinforcement strain at different locations under cyclic dynamic loading. The following conclusions can be drawn:

(1)

Under cyclic dynamic loading, the settlement of reinforced foundations affected by soil cavity collapse increases with the number of cycles. Their bearing capacity is significantly influenced by the presence of the cavity. As the cavity moves farther away from the center of the foundation, the ultimate bearing capacity of the foundation increases; however, in all cases, their ultimate bearing capacities remain lower than that of foundations without cavities. It can therefore be determined that, under cyclic dynamic loading, when the distance between the cavity center and the foundation center exceeds 3B, the cavity still affects the foundation’s bearing capacity.

(2)

Under the same cyclic load, different working conditions exhibit different settlement rates at the same number of cycles (e.g., 3000 cycles). The unreinforced foundation has the smallest settlement rate, while the foundation with a cavity directly beneath the center experiences the largest settlement rate. For reinforced foundations under the influence of karst soil cavities, the P–s curve under cyclic loading exhibits only a very short elastic compression stage before undergoing rapid deformation until failure.

(3)

Based on the conditions of this model test, under cyclic dynamic loading, there exists a critical spacing value between 1B and 2B for the cavity center located at a depth of 800 mm from the foundation center. When the spacing exceeds this critical value, the vertical earth pressure distribution in the horizontal direction within the collapse zone is the same as that for foundations without cavities. When the spacing is smaller than this critical value, the vertical earth pressure in the collapse zone experiences a sudden drop.

(4)

An in-depth analysis of the displacement field of the reinforced foundation reveals that, under the same cyclic load level, the height and number of soil arches are independent of the number of cycles and remain unchanged as the cycle count increases. When the cavity is not located directly beneath the foundation, the range of soil arches on either side of the cavity is unequal, and this difference decreases as the load increases. At the initial stage of cyclic loading application, the reinforcement immediately comes into play, forming multiple soil arches—indicating that the soil arching effect has the greatest influence on the bearing capacity of the reinforced foundation.