Experimental Study on the Vertical Bearing Characteristic Model of Pile Groups in Complex Interactive Karst Pile Foundations

Abstract

In order to study the bearing characteristics of pile groups under the coupling of multiple caves, the influence of the interaction between the crossing cave, the underlying inclined cave, the pile-side cave, and the underlying cave on the ultimate bearing capacity, axial force, lateral friction, and load sharing ratio of the pile group was analyzed based on the model test. The research results show the following: (1) Due to the existence of the underlying cave, the Q-S curves of the pile groups are all steep drop types, and they show the characteristics of end-bearing piles. The influence of other caves is not obvious; the existence of beaded caves, lower crossing caves, underlying inclined caves, upper crossing caves, and pile-side caves will reduce the ultimate bearing capacity of the pile group. The reduction in the ultimate bearing capacity is 7.38%, 4.94% for the lower crossing cave, 2.59% for the underlying inclined cave, 2.27% for the upper crossing cave, and 0.74% for the pile-side cave. (2) When the pile body passes through the cave, the axial force changes slightly in the overburden layer, changes greatly in the limestone layer, and remains unchanged in the cave; under the same load level, the axial force of the pile close to the underlying inclined cave and the pile-side cave is smaller than that of the pile farther away. (3) Under the same load level, the lateral friction of the pile foundation shows a decreasing trend in the sand layer and limestone layer. The friction inside the sand layer is small. After entering the lime layer, the lateral friction increases sharply. The lateral friction is approximately 0 within the cave range. After passing through the cave, the lateral friction increases sharply. (4) The underlying inclined cave and the pile-side cave do not affect the position of the peak point of the pile foundation. The existence of the cave makes the pile foundation increase the peak point at the exit of the cave; under the same load level, the lateral friction of the pile close to the underlying inclined cave and the pile-side cave is larger than that of the pile farther away. (5) The existence of beaded caves, lower crossing caves, underlying inclined caves, upper crossing caves, and pile-side caves will increase the proportion of pile end resistance by 6.95%, 4.23%, 0.94%, 0.77%, and 0.62%, respectively. (6) This study systematically analyzed the differences in the degree of influence of different types of caves (including crossing caves, underlying inclined caves, and pile-side caves) on the bearing characteristics of pile foundations under the condition of the existence of underlying caves. It was found that beaded caves > lower crossing caves > underlying inclined caves > upper crossing caves > pile-side caves, which provides a priority decision-making basis for the optimal design of cave treatment schemes in engineering practice.

1. Introduction

China is one of the countries with the most extensive karst development in the world, but construction in karst areas will face engineering geological problems such as collapse and surface deformation [1,2,3]. Pile foundations have high bearing capacity, good stability, can effectively control uneven settlement, and have good seismic performance, so they are widely used in karst area engineering construction [4,5,6,7,8,9,10,11,12,13,14,15,16]. However, the complex and changeable karst environment will affect the bearing capacity of pile foundations to varying degrees, and in most cases will reduce the bearing capacity of pile foundations [17,18,19]. Therefore, research on the bearing characteristics of karst pile foundations is of great significance to engineering design in karst areas.

At present, scholars at home and abroad conducted relevant research on the bearing characteristics of pile foundations in karst areas. A. Yacine et al. [20] and He et al. [21], respectively, established and solved the differential equation of a single pile under static load based on the existing pile foundation load transfer theory, and achieved theoretical innovation in the analysis of the Q-S curve of a single pile; H. Gharsallaoui et al. [22] discussed the hole expansion theory based on the H-Cek-Brown failure criterion, and finally obtained a calculation method for the ultimate bearing capacity of the pile end; N.Z. Gotman et al. [23] proposed a method for calculating the bearing capacity of a pile foundation acting on a karst cavity considering the deformation of the underlying roof; Li [24] studied the influence of pile diameter, the ratio of roof thickness to pile diameter, and the ratio of karst cavity width to pile diameter on the stability of the karst roof through finite element analysis. Wu et al. [25] proposed the mechanism of reducing the side friction resistance by the karst cavity on the pile side; Feng et al. [26] analyzed the influence trend of the geometric parameters of the underlying karst cavity on the ultimate bearing capacity of the pile foundation through numerical simulation, and used the metabolic GM (1,1) model to derive a pile foundation bearing capacity prediction formula with a relative error of 0.06% compared with the ordinary model; He et al. [27] used the grey theory and combined the numerical simulation results to study the influence of the thickness-span ratio and karst cavity size on the ultimate bearing capacity of a single pile. Feng et al. [28] studied the relationship between the span of the karst cavity and the vertical bearing capacity and the end resistance ratio of the pile foundation based on actual projects by numerical simulation. Chen et al. [29] studied the influence of the pile foundation passing through the beaded karst cavity on the load transfer relationship and ultimate bearing capacity through centrifugal tests and attributed the sensitivity of the vertical bearing capacity of a single pile to three factors; Wang et al. [30] used numerical simulation to study the influence of the height and span of the underlying karst cavity on the bearing capacity of the super-long pile foundation. J.L. Benito Olmeda et al. [31] used numerical simulation to study the influence of different karst cavity locations and sizes, rock types, rock mass strength, and rock mass state on pile foundation bearing capacity and found that the parameter with the greatest influence was the relative eccentricity of the karst cavity. Chen et al. [32] used static load tests, finite element analysis, and mechanical models to study the influence of karst cavity height, span, and top plate thickness under a bridge pile foundation on the vertical bearing characteristics of a single pile. Sheng et al. [33] studied the influence of karst cavity height and span on a single bearing capacity based on physical model tests and finite element numerical simulations and revealed the mechanism of bearing capacity reduction. Li Longqi et al. [34] analyzed the influence of different karst cavity heights and radii on the load transfer and bearing capacity of each pile foundation in the karst area when a pile group passes through a string of beaded karst cavities based on physical model tests and finite element numerical simulations.

Although existing research covers a variety of karst conditions, most scholars’ research focuses on the ultimate bearing capacity of pile foundations under the underlying karst cavities under single piles, the thickness of the safe top plate of the karst cavities, and the comparison of bearing mechanisms under single karst conditions. In contrast, there are relatively few studies on the deformation characteristics and bearing mechanisms of pile groups, and especially the analysis of the influence of the interaction of multiple karst conditions on the bearing characteristics of pile foundations is even more lacking. Based on this, the author relies on a karst pile group in a bridge project, designs an indoor model test of a pile group with multiple karst cavities according to the similarity ratio, and studies the vertical bearing characteristics of pile group foundations when beaded karst cavities, underlying inclined karst cavities, pile-side karst cavities, and underlying karst cavities coexist in order to provide guidance for the design of karst pile group foundations.

2. Methods

2.1. Experimental Assumptions

When the indoor model test simulates the actual project, the similarity of load, geometric parameters, physical quantities, as well as boundary conditions and constraints should be considered. In order to ensure the rationality and feasibility of the test, the following assumptions are made:

(1)

The pile body, the cap, the rock mass around the pile, and the soil are all continuous and a uniform single media;

(2)

The pile body and the cap are made of the same material, and the pile spacing is 2 d (d is the pile diameter);

(3)

The shape of the karst cavity is a regular cylinder. The filling of the karst cavity is not considered, and the interior of the karst cavity is regarded as a complete cavity;

(4)

The top plate of the karst cavity is complete and has a thickness of 2 d.

2.2. Similarity Relationship

According to the calculated size of the model pile and the geometric factors of the buried depth, the material properties of the model pile, the properties of the soil around the pile, and the initial stress state, the model scale n = 20 is determined under the conditions of satisfying the boundary conditions, the minimum pile spacing, and the particle size effect. The similarity relationship of each physical quantity in the model test is shown in

Table 1. Similarity relations of physical quantities in model tests.

Physical Quantity	Similarity Ratio	Physical Quantity	Similarity Ratio
Length	20	Cohesion	26
Unit weight	1.3	Elastic modulus	26
Internal friction angle	1	Strain	1
Friction coefficient	1	Poisson’s ratio	1
Compressive strength	26	Compressive strength	26

.

2.3. Model Pile Design

Based on the parameters and dimensions of the cap and pile of the prototype work site, according to the similarity ratio, aluminum–magnesium alloy is selected as the material of the cap and pile, with an elastic modulus of 40 GPa. Then, the dimensions of the cap and model pile are determined. The cap plate is made of an aluminum–magnesium alloy plate with a size of length × width × height = 240 mm × 240 mm × 40 mm. The cap plate has a hole with a diameter of 1 cm penetrating the entire length and a circular groove with a diameter of 60 mm and a depth of 20 mm. The model pile uses an aluminum–magnesium alloy hollow tube with a pile length of L = 1 m, an inner diameter d of 40 mm, an outer diameter D of 60 mm, and a pile group spacing of 2 d = 120 mm. In order to simulate the rough surface of the bored pile in real conditions, the surface of the aluminum alloy pile is embossed. The steel base is a stainless steel round table with an upper diameter of 40 mm and a height of 10 mm, and a lower diameter of 60 mm and a height of 20 mm, which plays the role of the bottom seal. Figure 1 is a schematic diagram of the various parts of the pile foundation.

Table 2. Pile parameters of the model.

	Length (m)	Diameter (m)	Density (kg.m−3)	Elastic Modulus (E/GPa)	Poisson’s Ratio
Model pile	1	0.06	2.8	40	0.25–0.30

is a parameter table of the model pile body.

2.4. Karst Cavity Design

Figure 2 is a schematic diagram of a karst cavity simulation. The karst cavity is simulated by a hollowed-out cylindrical foam, which is assembled from three parts: the upper, lower, and middle hollow ring. Its strength is negligible relative to bedrock. The karst cavity diameter is 6 d (360 mm) and the height is 2 d (120 mm). Figure 3 shows the layout of the karst cavity. The customized karst cavity model is nested in the corresponding position of the pile model to determine the relative position of the karst cavity and the pile foundation, and is then further fixed with epoxy resin glue; the underlying karst cavity and the underlying inclined karst cavity are directly fixed on the steel tray, and the pile-side karst cavity is directly buried in the predetermined position.

2.5. Rock and Soil Layer Design

Guided by similarity theory, a similarity ratio of 1:20 was selected. The overlying sand layer of the test selected was medium sand of uniform size, and the particle grading curve is shown in Figure 4. Considering the operability and boundary effect of the test, the bedrock material ratio that meets the similarity ratio was selected, and finally the sand: cement: gypsum: light calcium carbonate: water = 1:0.15:0.1:0.1:0.33 was obtained. According to the unconfined compressive strength test, direct shear test, etc., the material density ρ, elastic modulus E, Poisson’s ratio μ, cohesion c, and friction angle φ were measured, and the relevant parameters are shown in

Table 3. Rock and soil parameters of the model.

	Cohesion (Kpa)	Internal Friction Angle (°)	Poisson’s Ratio	Density (kg.m−3)	Elastic Modulus (MPa)
Overlying sand layer	1.2	26	0.25	1.8	28
Limestone layer	1.5	29	0.25	1.95	15,000

.

2.6. Model Solution

In order to study the changes in the bearing characteristics of pile groups under the coupling of multiple karst cavities, the karst cavity model is simplified on the basis of fully considering the test objectives and test operability. The size of all karst cavities is a cylinder with a diameter of six times the pile diameter and a height of two times the pile diameter. The karst cavities are embedded in the limestone layer = 48 cm, the top plate thickness is two times the pile diameter, the distance between the karst cavities crossed by the pile foundation is two times the pile diameter, the distance from the bottom of the karst cavity to the bottom of the pile is one times the pile diameter, and the distance from the pile-side karst cavity and the left side of the underlying inclined karst cavity to the pile body is four times the pile diameter. The specific situation is shown in Figure 5.

2.7. Loading and Testing System

2.7.1. Measurement of Loads on the Cap, Pile Top and Pile Bottom

The arrangement of the pile body is shown in Figure 6. The pile bottom pressure sensor is fixed to the steel base with tape, and the steel base is directly sleeved on the pile bottom. The load measurement of the cap and the pile bottom adopts a spoke-type pressure sensor. The pressure sensor model of the cap surface is HZC-30A-200T, and the pressure sensor model of the pile bottom is HZC-30A-5T, with a diameter of 58 mm, equipped with a digital display, which can read the value in real time with an accuracy of 0.01 KN. The pile top load measurement adopts a round pancake-shaped pressure sensor with a diameter of 28 mm and a range of 2 MPa. The sensor is placed in the groove opened on the cap, and then the model pile is sleeved on the remaining part of the groove on the cap, as shown in Figure 7.

2.7.2. Measurement of Settlement on the Cap and Pile Bottom

The settlement of the cap and pile bottom is measured by a BL-100NZ laser displacement sensor with a measuring range of 100 mm. The displacement meter is fixed horizontally on the displacement guide frame through a movable base and can be moved as required. The displacement guide frame is placed in the model slot and is not affected by the loading system. The displacement meter measures the settlement values of the four corners of the cap, and the average value is the cap settlement value.

The displacement guide rod is composed of an M5 full-length screw with a diameter of 6 mm and a length of 1.1 m and a displacement guide piece. A nut is welded on the steel base to connect and fix the screw. The screw extends from the cap hole, and the displacement guide piece is clamped by a nut at the extended part. A displacement sensor is set above the guide piece to measure the vertical displacement of the guide piece. The vertical displacement of the horizontal guide piece is the pile bottom settlement. The displacement guide rod is shown in Figure 8.

2.7.3. Measurement of Axial Force Along the Pile Shaft and Side Friction

In the preliminary preparation of the test, the surface of the model pile was polished with sandpaper, and 11 groups of strain gauges were symmetrically arranged around the pile, with 2 in each group, and attached to the pile wall with 502 glue. To protect the strain gauges, a layer of epoxy resin was applied, as shown in Figure 9 and Figure 10; the axial force of each section of the pile body and the pile-side friction resistance were calculated using the data measured by the BX120-10AA strain gauge. The pile body axial force and pile-side resistance can be calculated by the following formulas:

$$Q=E\epsilon A$$

(1)

$$T=(Q_i-Q_{i=1})/(\pi Dh)$$

(2)

where E is the elastic modulus of the model pile, $\epsilon$ is the average value of the two strain data at the same depth, Q is the axial force of the pile, T is the pile-side resistance strength, D is the outer diameter of the model pile, and h is the distance between the two strain gauge measuring points.

2.8. Experimental Procedures

2.8.1. Model Preparation

(1)

Pour fine sand, cement, gypsum, and light calcium carbonate into a mixer according to the proportion and add water to mix thoroughly.

(2)

After sufficient mixing, use a pump to pour the materials into a wooden model box, using a layered filling method, with each layer being 2 cm to ensure compaction.

(3)

To ensure that the pile is vertical and will not tilt, first pour the part below the pile end, wait for it to have a little strength, place the model pile in the predetermined position, and then pour the embedded rock section. After pouring, check whether the foundation is level. After each pouring, check the position of the karst cavity, and adjust it in time if there is any deviation.

(4)

After pouring, remove the mold after it has reached a certain strength, cover it with geotextile, maintain a good curing environment, and water it every day. After 28 days of curing, conduct a test.

(5)

After curing, put the component in a detachable acrylic box, fill the upper part with fine river sand evenly to a predetermined height using a sand filling machine, and put it in the loading device for a loading test.

The main experimental procedures are shown in Figure 11.

2.8.2. Test Operation and Loading Termination Criteria

Referring to DBJ/T 15-60-2019 “Code for Testing of Building Foundations” [35], the slow sustained load method was used to carry out destructive tests with vertical graded loading. Before loading, the estimated ultimate load value was obtained by numerical simulation. Each load level was set to 10 kN, with a total of eight levels. The data acquisition work was completed by three DH3816N 36-channel data acquisition instruments. The displacement sensor reads once every 5 min. When the displacement change of the pile top under each load level is less than 0.01 mm/5 min or the cumulative value does not exceed 0.1 mm/h, the next level of loading can be carried out until the underlying top plate is damaged. According to the “Handbook of Pile Foundation Engineering” [36] and the similarity relationship between the model test, the ultimate bearing capacity of the pile foundation can be taken as the load corresponding to the pile top settlement of 4% D.

2.9. Experimental Working Conditions

This test considers the influence of the interactive distribution of different karst cavities in the stratum on the vertical bearing capacity of the pile foundation. The interactive effects of different karst conditions are shown in

Table 4. Working conditions.

Front View
Top View
	a. Working Condition 1	b. Working Condition 2	c. Working Condition 3	d. Working Condition 4
Front View
Top View
	e. Working Condition 5	f. Working Condition 6	g. Working Condition 7	h. Working Condition 8

Note: For ease of calculation and analysis, the average values of piles 1 and 3 are taken as pile A data, and the average values of piles 2 and 4 are taken as pile B data.

.

3. Results

3.1. Vertical Bearing Capacity of Pile Groups

The load-settlement curves of the pile groups under various working conditions are shown in Figure 12, and the Q-S curves of various working conditions are shown in Figure 13. The load-settlement curves of the pile top and pile end under different working conditions are consistent, and the settlement values of the pile top and pile end are basically consistent, with a difference of less than 0.5 mm; however, due to the existence of pile-side friction, the force transmitted to the pile end under each load level is attenuated, and as the load increases, the side friction gradually fully exerts its effect, and the attenuation continues to increase.

According to the load-settlement curves under various working conditions, it can be seen that under different working conditions, as the vertical load increases, the settlement continues to increase. When the load is small, the curve is almost linear; as the load continues to increase, the compression and deformation of the rock mass at the pile end increase, and the slope of the curve gradually increases, with a more obvious mutation point. When the load transmitted to the pile end reaches the ultimate bearing capacity of the underlying top plate, a mutation failure will occur, so the last point of the P-S curve at the pile end is the ultimate bearing capacity of the top plate.

Compare the Q-S curves of working conditions 1, 2, 3, and 4. It can be seen that compared with working condition 1 where there is no karst cavity crossing, the settlement values of the conditions crossing the karst cavity under the same level of load are significantly increased, among which the settlement of crossing the double-layer karst cavity is greater than that of the single-layer karst cavity. This is because the pile foundation in the rock layer passes through the karst cavity, and the lack of rock mass on the pile side increases the instability of the pile, and the settlement will increase under the action of the top load. Comparing the load-settlement curves of the pile top and pile end, it can be seen that with the increase in the number of karst cavity layers, the pile-side resistance decreases, resulting in an increase in the force transmitted to the pile end under the same level of load. Under the condition of a certain load on the underlying top plate, the ultimate bearing capacity of the pile will decrease with the increase in the number of layers.

Among them, for working conditions 2 and 3 that pass through a single-layer karst cavity, due to the different locations of the karst cavity (one is located at the front end of the rock layer and the other is located near the pile end), their Q-S curves have a large difference, and the settlement of working condition 2 is greater than that of working condition 3. The curve trend of working condition 3 is close to that of working condition 1, while the trend of working condition 2 is close to that of working condition 4. The reason for this is mainly because the karst cavity is close to the pile end, which has a greater impact on the instability of the pile foundation, so the settlement will be larger.

By comparing the three groups of the Q-S curves of working conditions 2 and 5, working conditions 3 and 6, and working conditions 4 and 7, it is found that the Q-S curve of the former in each group is similar to the latter, and the settlement value of the Q-S curve of the former can be obtained after a certain increase. The underlying inclined karst cavity reduces the stability of the rock mass at the pile end, and the bearing capacity of the rock mass at the pile end will become smaller, and the shear resistance will become weaker. With the continuous increase in the upper load, the settlement becomes larger, and the degree of friction resistance on the side of the pile body decreases; the increase range of the three groups is approximately equal, which can be regarded as the role played by the underlying inclined karst cavity being equal.

By comparing working conditions 7 and 8, it is found that the Q-S curves of the two are similar, and the settlement value of the former can be obtained after a certain increase in the latter. The influence of the pile-side karst cavity on the pile foundation is mainly that the lack of the side rock mass leads to lower density and worse stability of the rock mass near the pile at the same depth. Under the action of the load, the settlement of the pile foundation will increase.

Due to the existence of the underlying karst cavity, the Q-S curves of working conditions 1-8 are all mutation types, and the ultimate bearing capacities are 52.45 kN, 51.26 kN, 49.8 kN, 48.58 kN, 49.98 kN, 48.67 kN, 46.96 kN, and 46.57 kN, respectively. Compared with working condition 1, the ultimate bearing capacity change caused by the upper karst cavity is 1.19 kN, the lower karst cavity is 2.59 kN, and the beaded karst cavity is 3.87 kN. The underlying inclined karst cavity is 1.36 kN, and the pile-side karst cavity is 0.74 kN. The reduction in the ultimate bearing capacity caused by each karst cavity is 7.38% for the beaded karst cavity, 4.94% for the lower crossing karst cavity, 2.59% for the underlying inclined karst cavity, 2.27% for the upper crossing karst cavity, and 0.74% for the pile-side karst cavity. In this case, the degree of reduction in the ultimate bearing capacity of the karst cavities is as follows: beaded karst cavity > lower crossing karst cavity > underlying inclined karst cavity > upper crossing karst cavity > pile-side karst cavity [37].

3.2. Axial Force Along the Pile Shaft

The distribution law of the bearing capacity of pile groups under different working conditions is shown in Figure 14. It can be seen that for the same pile depth, as the pile top load continues to increase, the pile shaft axial force also increases, and the axial force gradually decays along the depth; due to the gradual exertion of the pile shaft side friction resistance, when the pile top load is small, there is no relative displacement between the pile and the soil, and the pile shaft axial force decays slowly with depth; when the pile top load increases step by step, due to the interaction between the pile and the soil, the pile shaft side friction resistance gradually exerts itself, and the pile shaft axial force decays faster with depth. Under the same level of load, the axial force gradually decreases along the pile depth, and the axial force of the pile shaft changes less in the overburden layer. The axial force suddenly decays at the boundary of the soil layer because the overburden layer and the limestone layer have different mechanical properties. The limestone layer has greater cohesion and shear strength, and the pile–rock friction coefficient is greater than the pile–soil friction coefficient. The side friction that can be provided is greater, resulting in a sudden decrease in the axial force after entering the rock.

By comparing the axial force curves of working conditions 1, 2, 3, and 4, it can be seen that the attenuation law of the axial force under different working conditions is roughly the same. The axial force continues to decrease when it is transmitted to the limestone layer. The axial force remains unchanged in the karst cavity. After passing through the karst cavity, the axial force is further exerted and gradually decreases. Since the pile body is not in contact with the soil or rock in the karst cavity and is in an air-free state, it cannot generate side friction, resulting in a decrease in side friction and a worse overall degree of side friction, resulting in no change in the axial force in the karst cavity.

By comparing the three groups of axial force curves of working conditions 2 and 5, working conditions 3 and 6, and working conditions 4 and 7, it is found that the axial force curves of piles A and B in the former and the latter show the same pattern, the axial force curve of pile A is approximately equal, and the axial force of pile B close to the underlying inclined karst cavity is greater than that of pile A. The lack of rock mass at the pile end reduces the side friction of the pile foundation and increases the axial force accordingly, which has a greater impact on pile B and a negligible impact on pile A.

Comparing the axial force curves of working conditions 7 and 8, it can be seen that the axial force curves of pile A in working conditions 7 and 8 are approximately equal, the axial force of pile B is greater than that of pile A, the lack of rock mass around the pile affects the side friction of pile B, and the axial force increases accordingly; the reduction rate of the axial force curve of pile B in the rock-embedded section is roughly the same, and there is a significant difference in the karst cavity section on the pile side: working condition 7 shows a slightly decreasing trend, working condition 8 will have a significant reduction after passing through the karst cavity, and it shows a nonlinear reduction in the second half. The main reason for this is that the existence of the karst cavity on the side of the pile makes the side friction of the pile body in this area different from that in the ordinary rock-embedded section.

3.3. Side Friction Along the Pile Shaft

The distribution law of the side friction resistance of the pile group under each working condition is shown in Figure 15. Under the same load level, the side friction resistance inside the sand layer is small. After entering the lime layer, the side friction resistance increases sharply. The side friction resistance drops sharply within the karst cavity range. After passing through the karst cavity, the side friction resistance increases sharply. The side friction resistance of the pile body under each load level is slightly different. As the load applied to the pile top increases, the side friction resistance near the pile end area gradually stops, and the extreme range of the side friction resistance of the pile body slowly develops upward. This is because as the upper load increases, more and more loads are transferred to the pile end, causing the rock mass in the pile end area to expand on both sides after being compressed and causing the deformation and settlement of the underlying top plate under the load, resulting in a gap between the pile and the rock, which cannot provide side friction resistance. Therefore, when the load on the pile top increases to a certain extent, the axial force near the pile end is almost not attenuated. For working conditions 1-8, since there are karst cavities underneath, the distribution in the rock-embedded section is a step-type distribution of “decrease–increase–decrease”, and reaches an extreme value near the top plate in the second half of the rock-embedded section. The depth range is between 0.82 and 0.94 m. However, due to the existence of karst cavities, the degree of side friction under different working conditions is quite different [38].

Comparing the side friction curves of working conditions 1, 2, 3, and 4, it is found that in working condition 2, the karst cavity is close to the pile end, and the side friction of the rock-embedded section shows a trend of decreasing with depth until it drops to zero in the karst cavity section; the side friction reaches the extreme value in the bottom area of the karst cavity. The main reason for this is that due to the existence of the karst cavity, the relative displacement between the pile and the rock increases, and more load is transmitted downward. At the same time, due to the combined influence of the underlying karst cavity roof, the rock stratum will bend and become tensile after the pile foundation is embedded in the rock stratum again, thereby squeezing the pile end, resulting in a more full play of the side resistance in this section. In working condition 3, the side friction of the pile body will increase significantly after entering the rock, and suddenly drop to zero after reaching the karst cavity section; the side friction reaches the extreme value after the hole is penetrated, which is caused by the increase in the mutual displacement between the pile and the rock; then, due to the existence of the underlying karst cavity, the latter half presents a step-type distribution of “decrease–increase–decrease”, and its play mechanism is consistent with working condition 1, so the trend of its axial force in the latter half is the same as that of working condition 1. In working condition 4, the side friction increases in the rock-embedded section and becomes zero after reaching the karst cavity section; the side friction increases significantly after crossing the first karst cavity, then decreases to zero again after reaching the second karst cavity, and reaches an extreme value in the rock-embedded section after crossing the karst cavity.

By comparing the side friction resistance curves of working conditions 2 and 5, working conditions 3 and 6, and working conditions 4 and 7, it is found that the side friction resistance curves of piles A and B in the former and the latter show the same pattern, the side friction resistance curve of pile A is approximately equal, and the side friction resistance of pile B close to the underlying inclined karst cavity is bigger than that of pile A. The lack of rock mass at the pile end reduces the bearing capacity of the pile foundation and the degree of side friction resistance. The impact on pile B is large, while the impact on pile A is negligible.

By comparing the side friction resistance curves of working conditions 7 and 8, it can be seen that the side friction resistance curves of pile A in working conditions 7 and 8 are approximately equal, and the side friction resistance of pile B is bigger than that of pile A, which is caused by the lack of rock mass around the pile; the reduction rate of the axial force curve of pile B in the rock-embedded section is roughly the same, but there is a significant difference in the karst cavity section on the pile side: the increase in side resistance in working condition 8 is greater than that in working condition 7.

3.4. Variation in the Proportions of Pile End Resistance

The distribution law of the bearing capacity of pile groups under various working conditions is shown in Figure 16. It can be seen that with the increase in the cap load, the pile end resistance of the pile foundation shows a trend of gradual increase, and the inflection point of the pile end resistance change is more obvious. The displacement required for the end resistance to exert is greater than the displacement required for the pile-side resistance to exert, and the pile-side resistance exerts itself before the pile end resistance. When the pile top load continues to increase and the pile foundation continues to settle, the pile end resistance replaces the pile-side resistance as the main bearer of the pile top load. The maximum values of the end resistance ratios under various working conditions are 82.66%, 84.97%, 83.33%, 86.6%, 85.9%, 83.6%, 87.5%, and 88.12%, respectively, showing the characteristics of typical end-bearing piles. By comparing working conditions 1, 2, 3, and 4, it can be seen that when the pile passes through the karst cavity, the rock mass is missing, the side friction decreases, and the corresponding proportion of the end resistance increases. The increase is as follows: working condition 4 > working condition 2 > working condition 3. The rock mass loss in the beaded karst cavity is the most serious. The rock mass-missing area of the lower crossing karst cavity is located in the area with large side friction. Therefore, the range of change in the end resistance ratio of the lower crossing karst cavity is greater than that of the upper crossing karst cavity. By comparing working condition 2 and working condition 5, working condition 3 and working condition 6, working condition 4 and working condition 7, and working condition 7 and working condition 8, it can be seen that the existence of the underlying inclined karst cavity and the pile-side karst cavity causes the rock mass around the pile to be missing, affecting the performance of the pile-side resistance and increasing the proportion of the end resistance.

Under the ultimate load, compared with working condition 1, the proportion of pile end resistance in working conditions 2–8 increases by 2.31%, 0.67%, 3.94%, 3.24%, 0.94%, 4.84%, and 5.46%. The existence of beaded karst cavities, lower through karst cavities, underlying inclined karst cavities, upper through karst cavities, and pile-side karst cavities will increase the proportion of pile end resistance to 3.94%, 2.31%, 0.67%, 0.69%, and 0.62%, respectively, with an increase of 7.38%, 4.94%, 2.59%, 2.27%, and 1.17%, respectively.

4. Discussion

Although this paper achieved some research results, there are still some limitations and shortcomings: this paper only studies 2 × 2 low-cap pile groups, which cannot fully meet the theoretical needs of actual engineering; when quantitatively comparing the influence of underlying karst, through karst, and pile-side karst through model tests, this paper does not consider the eccentricity of the underlying inclined cave and the distance between the pile-side cave and the pile foundation, which are key parameters affecting the cave effect.

Based on the above research deficiencies, future research work can be carried out from the following aspects:

(1)

Conduct 3 × 3 or more pile group test studies and take into account parameters such as pile spacing and high (low) caps when designing the scheme to improve the engineering applicability of the results.

(2)

Use numerical simulation to establish a test scheme with the eccentricity of the underlying cave and the distance between the pile-side cave and the pile foundation as parameters, study the parameter mutation points of the cave effect, and supplement the conclusions of the model test in this paper.

(3)

It was determined that the influence of crossing caves is relatively large. In the future, a more in-depth comparative analysis of various parameters of crossing caves (cave height, cave type, and number of caves) will be carried out through numerical simulation and other means.

5. Conclusions

Through indoor model tests investigating the bearing characteristics of pile foundations under eight different karst cavity interaction conditions, load-settlement curves, axial force distribution, side friction distribution, and variation in the proportions of pile end resistance were analyzed. The main conclusions are as follows:

(1)

Due to the existence of underlying caves, the Q-S curves of pile groups are all steeply descending and show the characteristics of end-bearing piles. The influence of other caves is not obvious; the existence of beaded caves, lower through caves, underlying inclined caves, upper through caves, and pile-side caves will reduce the ultimate bearing capacity of pile groups.

(2)

When the pile body passes through the cave, the axial force changes slightly in the overburden layer, changes greatly in the limestone layer, and remains unchanged in the cave; under the same level of load, the axial force of piles close to the underlying inclined cave and the pile-side cave is smaller than that of piles farther away.

(3)

Under the same level of load, the lateral friction resistance of the pile foundation shows a decreasing trend in both the sand layer and the limestone layer. The friction resistance inside the sand layer is small. After entering the lime layer, the lateral friction resistance increases sharply. The lateral friction resistance is approximately 0 within the cave range. After passing through the cave, the lateral friction resistance increases sharply.

(4)

The underlying inclined cave and the pile-side cave do not affect the peak point position of the pile foundation. The existence of the through cave increases the peak point of the pile foundation at the exit of the cave. Under the same level of load, the side friction resistance of the pile close to the underlying inclined cave and the pile-side cave is greater than that of the pile farther away.

(5)

The existence of beaded caves, lower through caves, underlying inclined caves, upper through caves, and pile-side caves will increase the proportion of pile end resistance.

(6)

This study systematically analyzes the differences in the degree of influence of different types of caves (including through caves, underlying inclined caves, and pile-side caves) on the bearing characteristics of pile foundations under the condition of the existence of underlying caves. It is found that the beaded caves > lower through caves > underlying inclined caves > upper through caves > pile-side caves provide a priority decision basis for the optimal design of cave treatment schemes in engineering practice.