Research on Bearing Capacity Characteristics of Cave Piles

Abstract

To investigate the load-bearing characteristics of a pile foundation with multiple piles passing through karst caves and the extent of the caves’ influence, this study takes the Qihe Bridge, a key project of the second section of the Anhe Expressway, as a case study. Field tests on the bearing capacity of the pile foundation, passing through underlying karst caves, were conducted. Piles passing through the caves were selected as test piles, and a finite element analysis of the Qihe Bridge pile foundation structure was performed using Midas GTS NX 2022 software. After verifying the accuracy of the software’s calculation results, this study further explored the distribution patterns of factors such as axial force, side friction resistance, settlement, and relative displacement between the pile and soil with respect to the position of the pile. Special attention was given to monitoring locations at the interface between rock and soil layers, as well as within the depth range of the karst caves. The horizontal axial force on the piles was found to increase with the depth of the caves. By analyzing the distribution patterns of axial force, side friction resistance, settlement, and pile–soil relative displacement, the study clarifies the mechanism by which karst caves affect the load-bearing behavior of pile foundations.

1. Introduction

The karst areas of our country are widely distributed, and the construction of bridge structures in karst cave areas is very difficult. With the increase of bridge construction in karst areas in our country, more and more attention is being paid to the research on bridge pile foundation construction in karst areas.

In most foreign studies, the bearing capacity of a pile foundation is studied through comprehensive analyses of karst caverns. N.Z. Gotman et al. [1] proposed a method to determine the additional load on the pile according to the distance from the pile bottom to the karst soil roof and the predicted diameter of the hole in the karst soil. Feng et al. [2] explored the changing trends of the ultimate bearing capacity, the side friction resistance of piles within the range of karst caves, and the proportion of end resistance as the span of the karst caves increased. In addition, some scholars have studied the bearing capacity of pile foundations through experiments or model calculations. Erdi Abi et al. [3,4] analyzed the interface load transfer characteristics of rock-socketed piles through pile–mudstone interface shear tests. Based on the limit analysis theorem, Raffaele Di Laora et al. [5] proposed a method to determine the ultimate bearing capacity of non-uniformly distributed pile groups. A. Serrano et al. [6], based on the plastic theory, proposed a calculation method for the ultimate bearing capacity of rock-socketed pile tips, considering the three-dimensional characteristics. According to the first limit state, Sharapov et al. [7] calculated the sectional stress of piles under different conditions and determined the horizontal forces and bending moments of the piles, thus verifying the bearing capacity of pile foundations in the karst cave area.

Domestic scholars have made use of various finite element analysis software. Yang [8] used the finite element analysis software to carry out numerical calculations on the load transfer mechanism and the bearing characteristics of bridge pile foundations in the karst cave area and obtained the variation rule of the bearing capacity. Cui Junqiang et al. [9] used ABUQUS to establish a nonlinear model of a single pile and a pile group and studied the effects of axial force, the pile–soil stress ratio, and the pile–soil differential settlement on the single pile and the pile group. Zhang et al. [10] studied the generation mechanism of the soil arch effect in detail and analyzed the factors affecting the soil arch effect and the pile–soil stress-sharing ratio. Xie [11] deeply analyzed the physical and mechanical characteristics of the surrounding rock of pile foundations and the engineering characteristics of rock-socketed piles and proposed a mechanical model of the pile–rock stress characteristics of bridge pile foundations in karst areas under different geological conditions. Xiao et al. [12] used the modified Hoek–Brown criterion to describe the nonlinear characteristics of rock mass and analyzed the influence of various parameters on the ultimate bearing capacity coefficient. Gong et al. [13] analyzed the composition characteristics of the ultimate bearing capacity of bridge foundation piles and the failure mode of pile ends in karst areas and proposed a method to determine the ultimate bearing capacity of bridge foundation piles in karst areas. Liu et al. [14] proposed a reduction in the load distribution at the top of piles with cave foundations at the end of the piles by reasonably designing the bearing beam and the pile diameter of each pile. Taking the pile foundation project of Xiongchu Street in Wuhan City as the background, Huang et al. [15] obtained the deformation and stress conditions of pile foundations under different diseases by using ANSYS R16.0 software and evaluated the treatment effect of karst caves by comparing the deformation of pile foundations before and after filling the karst caves. Taking the Yonghe Bridge project in Ji’an as an example, Wu [16] proposed the design countermeasures for the bearing layer and rock socking depth in areas with a strong karst development. Professor Feng Zhongju’s team from Chang’an University [17,18,19,20] conducted a systematic and in-depth study on the fundamental research of bridges in karst areas, carried out field tests and numerical simulation studies on the stress of karst cave pile foundations constructed by the backfill method, and verified the change law of negative friction resistance caused by the consolidation of backfill materials. The effect of the coupling effect of steep slope and karst on the vertical bearing characteristics of pile foundations was studied. A coupling model of the karst cave–pile–rock mass was established, and the effects of different treatment measures on the bearing characteristics of pile foundations were compared and analyzed. The influence of soil moisture content change and concrete side coatings on the negative friction resistance of pile foundations was studied using large shear tests. Maryam Mardferi et al. [21] used the finite element method, considering pile–soil interactions, to study the nonlinear characteristics of the lateral load foundation of a single pile. The simplified linear finite element analysis method of piles was also studied, and the influence of the calculation of the pile diameter in the simplified linear finite element model was evaluated. Younhho Kim et al. [22] used the lateral load transfer method (p-y curve) to study the load distribution and the deflection of large-diameter piles. It was shown that a rigorous numerical analysis can overcome the limitations of the existing p-y method, to a certain extent, and take into account the effect of the actual three-dimensional combination of the pile and soil forces.

On the whole, (1) most of the research on bridge pile foundations in the karst area was carried out on the basis of single piles, and the research on pile groups is insufficient; (2) most studies on end-bearing piles ignore the friction pile characteristics presented in the early stages of construction; (3) the research on the large upper loads of long-span, continuous, rigid-frame bridges is insufficient. Based on the actual situation of the Qihe Bridge, this paper takes bridge pile foundations in the karst area as the research object and studies the influence of different factors on the bearing capacity characteristics of pile foundations in the karst area through numerical simulation and theoretical analyses, so as to provide a reference for the design and construction of bridge pile foundations in the same type of area in the future.

2. Field Tests

During the pile foundation construction phase, strain gauges are installed inside the piles and the wiring is routed to the surface by binding it with the reinforcement cage, allowing for the easy reading of the measurements. This setup helps monitor the stress state of the pile foundation at each construction stage.

2.1. Selection of Test Piles

Based on the geological conditions at the bridge location and the structural characteristics of the bridge, the Z1-1 pile within the karst cave area beneath Pier 1 of the Qihe Bridge, as well as the 20-RD5 karst cave it passes through, were selected as the research objects.

2.1.1. Stratigraphic Distribution of the Pile Foundation at Pier 1

Pier 1 of the Qihe Bridge is located on the northern bank of the Qihe River. The edge of the pile foundation cap is approximately 15 m from the northern hillside and 30 m from the southern riverbank. The ground elevation (i.e., the cap top elevation) is 161.0 m, the pile top elevation is 156.7 m, and the pile bottom elevation is 136.7 m. From top to bottom, the strata consist of the following layers: loose (mixed) fill soil, slope-deposited gravelly soil, moderately weathered karst limestone, strongly weathered karst limestone, a second layer of moderately weathered karst limestone, and moderately weathered limestone. The karst caves are roughly located within the strongly weathered karst limestone layer and the second moderately weathered karst limestone layer, as shown in the Figure 1, below.

2.1.2. Test Piles and Karst Cave Parameters

Under Pier 1 of the Qihe Bridge, a group pile foundation consisting of 24 bored piles arranged in a 6 × 4 grid was used. The diameter of each pile is 2 m, with a center-to-center spacing of 2.5 m between adjacent piles. The pile length is no less than 20 m, and the embedded depth into the rock is at least 2.5 times the pile diameter. The karst cave area has an approximate height of 6 m and a square plan dimension of about 8 m. This area covers the Z1-1 and Z1-2 piles, as shown in Figure 2. The interior of the karst cavity is mainly filled with cohesive soil, mixed with gravel, pebbles, etc., and is generally in a semi-filled state. In the actual project, to avoid the impact of subsequent drilling on the already-constructed piles, the drilling sequence for the pile foundation was carried out symmetrically along both the transverse and the longitudinal directions of the bridge. Specifically, when the Z1-1 pile was drilled, the karst cavity was filled, and by the time the Z1-2 pile was drilled, the original karst cavity area had already been filled. However, considering that only the pile foundation load was present at this point and that the karst fill had not fully settled, in order to ensure safety, the Z1-2 pile was still treated as passing through the void area. In the subsequent numerical simulation, the construction process was simplified as if both the Z1-1 and Z1-2 piles were drilled into the unsaturated karst cavity. The parameters for the test piles, karst cavity, rock layers, and soil mechanics are shown in

Table 1. Test pile and cave parameters.

Pile length L/m	20.1
Pile Diameter D/m	2.0
Concrete strength class	C30
Embedded rock depth h/m	>5 (2.5 D)
Cave height Hc/m	6
Cave size range Bc × Lc/m2	8 × 8
Cave type	Semi-filled cavern
Cave backfill material	Crushed stone, schist, clay, concrete, etc.

and

Table 2. Mechanical parameters of rock and soil layers.

Soil Layer Type	Capacity γ /kN·m−3	Modulus of Compression E/MPa	Cohesive Force c/kPa	Internal Friction Angle φ/°	Side Friction qik/kPa	Uniaxial Saturation Compressive Strength frk/MPa
Plain fill	16.6	2.0	15	14	15	/
Silty clay	17.2	3.8	26	16.2	45	/
Sloping gravel soil	19.2	15.7	16	33	66	/
Moderately weathered limestone	25.3	2661	240	51	195	28.7
Intermediately weathered limestone	22.3	1300	150	46	117	16.4
Highly weathered limestone	21.6	650	78	37	85	8.9
Cave filling material	18.3	13.5	20	25	58	/

.

2.2. Pile Foundation Measurement Point Arrangement

2.2.1. The Arrangement of the Strain Gauges Inside the Pile

For the test, vibrating wire strain gauges were selected. A measurement point was arranged at every 1 m interval along the pile body, with additional measurement points placed at the interface between the soil and rock layers, as well as at the top and the bottom of any karst cavities. Each measurement point was equipped with three strain gauges, evenly arranged in the radial direction of the cross section, and the average reading was taken as the strain value for that specific depth of the pile. The overall arrangement is shown in Figure 3.

The strain gauges were placed on the surface of the main reinforcement and welded into place, allowing them to accurately reflect the strain at the monitoring points on the pile, which can then be converted into the axial force of the pile. The installation of strain gauges was carried out after the reinforcement cage was fully tied and welded. During the installation process, it is essential to ensure a tight connection with the main reinforcement, with the wires wrapped around the reinforcement and extended from the top of the pile, leaving enough length for later connections. During the placement of the reinforcement cage and concrete pouring, care must be taken to prevent damage to the strain gauges and wires. During the binding and placement of the foundation slab reinforcement, the wires should be attached to the structural reinforcement and led out of the foundation slab area nearby. Additionally, PVC pipes were used to protect the wires at the pile–foundation slab junction and where the wires exit the foundation slab area.

2.2.2. Test Loading Scheme

According to the Code for Design of Highway Bridges and Culverts Foundations (JTG 3363-2019) [23], for large and super-large bridges with complex geological conditions, where the pile-bearing capacity is difficult to determine, static load tests should be conducted to determine the single pile-bearing capacity. Based on the load-bearing characteristics of piles in karst regions, the loads borne by these piles mainly come from the gradually increasing superstructure loads during construction. Therefore, following the construction sequence of the Qihe Bridge, the loading conditions corresponding to different construction stages were used to replace the load testing.

Combined with the construction process, the construction was divided into six main stages: after the pile construction; after the pile and cap construction; after the pile, cap, and lower hollow section of the pier body construction; after the pile, cap, and complete pier body construction; after the pile, cap, complete pier body, and No. 0 segment construction; and after the pile, cap, complete pier body, No. 0 segment, and all cantilever sections were constructed. The cantilever section construction was further divided into four sub-stages, based on the different segment lengths: Segments 1–2, Segments 3–10, Segments 11–18, and the two-sided closure segment.

Since the construction of the left and right pier bodies and the cantilever sections were carried out symmetrically, the effects of eccentric loads and bending moments were not considered. The weights of the various parts of the bridge structure are shown in

Table 3. The weights of the various components of the bridge structure.

Structure	Pile	Pile Cap	Pier	0#Beam
Weights (KN)	1576.53	48,540.22	79,948.17	14,125.72
Structure	1, 2 Beams	3–10 Beams	11–18 Beams	Closure
Weights (KM)	13,927.76	52,006.64	41,160.00	2281.44

:

The axial force of the pile body in the overall pier construction stage and the prior stages was converted based on the measured data. For the other construction stages, due to the limitations of the construction’s progress, the axial force of the pile body was obtained through a numerical simulation after verifying the accuracy and the safety of the constructed model. According to the “Code for Design of Building Foundations” (GB50007-2011) [24], the vertical force at the pile tops of individual piles in a highway bridge pile group should be calculated using the following formula:

$$Q_k=(F_k+G_k)/n$$

(1)

• F_k—The vertical force acting on the top surface of the pile foundation bearing when corresponding to the standard combination of the action of the load, (kN);
• G_k—The standard value of the self-weight of the pile foundation-bearing platform and the self-weight of the soil on the bearing platform, (kN);
• Q_k—Corresponding to the vertical force of any single pile under the action of the axial vertical force at the standard combination of actions, (kN);
• n—The number of piles in the pile foundation.

In the construction process of the Qihe Bridge, F_k in Formula (1) was the weight of pier and superstructure. In order to simplify the construction phase, beams 1 and 2 were regarded as the first cantilever section, and the load was loaded once. Beam sections 3~10 were the second cantilever section, and the load was divided three times on average. Beam sections 11~18 were regarded as the third cantilever section, and the load was divided into two average loads. The load size of a single pile corresponding to each construction stage is shown in

Table 4. Loads for each construction stage.

Construction Phase Loading	Load Size (kN)
1 The weight of a single pile.	1576.53
2 The weight of the bearing platform.	2022.51
3 The weight of the bearing platform and the first section of the lower part of the pier.	2855.31
4 Bearing platform+ pier lower overall deadweight.	3688.10
5 Bearing platform+ lower part of pier+ first section of self-weight on upper part of pier.	4520.89
6 Bearing platform+ pier body overall self-weight.	5353.68
7 Bearing platform+ pier +weight of 0#block.	5942.25
8 The bearing platform+ pier + zero block + self-weight of the first cantilever section.	6522.58
9 Bearing platform+ pier + block zero + first cantilever section + 33% self-weight of second cantilever section.	7244.89
10 Bearing platform+ pier + block zero + first cantilever section + 67% self-weight of second cantilever section.	7967.21
11 Bearing platform+ pier + block zero + first cantilever section + 100% self-weight of second cantilever section.	8689.52
12 The bearing platform+ pier + zero block + first and second cantilever section + 50% of the self-weight of the third cantilever section.	9547.02
13 The bearing platform+ pier + block zero + first and second cantilever section + 100% of the third cantilever section deadweight.	10,404.52
14 Bearing platform+ pier + zero block + all cantilever section weight before merging.	10,499.58

. Through calculation, the design values of the vertical force of a single pile at each stage met the requirements of the bearing capacity of the pile, based on the concrete strength.

During the construction of the whole substructure of the Qihe Bridge, six readings were recorded according to the actual project progress. Among them, a reading was carried out after the completion of the bored pile construction; a reading was carried out after the completion of the cap; the hollow section of the lower part of the pier was measured and recorded twice, according to the construction progress milestones of 50% and 100%; and the hollow section of the upper part of the pier was also recorded twice, according to the construction progress milestones of 50% and 100%.

2.3. Analysis and Processing of Test Data

2.3.1. Conversion of Test Data

The axial force of the pile was converted from the reading of the strain gauge, and the following assumptions were made: The compression direction of the pile is vertical; that is, the section of the pile at each depth is perpendicular to the pile axis. The strain gauge is closely combined with the steel bar and the concrete, and the strain gauge reading is the strain size of the steel bar and the concrete. Both the reinforcement and the concrete are elastic materials and are in the stage of elastic deformation, satisfying Hooke’s law.

Based on the above assumptions and the provisions in the Code for Design of Reinforced Concrete and Prestressed Concrete Bridges and Culverts for Highways (JTG 3362-2018) [25], the stress of the steel bars in the longitudinal body is equal to the product of the steel bar strain and its elastic modulus, and the axial force of a pile is calculated as follows:

$$Q=n{F}_S+{\displaystyle \frac{E_C{A}_C}{E_S{A}_S}}{F}_S$$

(2)

• F_S—The reinforcement’s axial force, (kN);
• n—The number of pile reinforcements;
• E_C—The modulus of the elasticity of the pile concrete, (kPa);
• E_S—The modulus of the elasticity of the reinforcement, (kPa);
• A_C—The pile’s cross sectional area, (m²);
• A_S—The reinforcing steel’s cross sectional area, (m²).

2.3.2. Analysis of Pile Axial Force

According to the on-site measurement results and Equation (2), Stage one through six correspond to the first six phases in Table 4, the axial force of a pile under the load of each construction stage is shown in Figure 4:

Based on Figure 4, from the overall trend of the pile shaft axial force changes, for pile Z1-1, during the stage when all the drilled and bored piles were completed, the axial force of the pile increased with depth, then decreased. The maximum axial force occured at a depth of approximately 13.2 m, at the bottom of the dissolution cavity. In other stages, the pile axial force showed a pattern of first increasing, then decreasing, followed by another increase and decrease, with two corresponding peak values. These peaks were located at a depth of about 5 m, where the soil layer meets the rock layer, and at a depth of about 13.2 m, at the bottom of the dissolution cavity. As the upper load increased, the maximum axial force position of the pile shifted upwards from within the dissolution cavity to the interface between the soil and rock layers.

From the rate of change in axial force, for the same construction stage, the pile axial force increased rapidly within the colluvial gravel soil layer, but the rate of increase gradually slowed as the depth increased. Within the rock layers above and below the dissolution cavity, the rate of axial force decay was faster, with slower decay within the dissolution cavity itself. The axial force decay rate in the upper rock layer was relatively constant, while in the lower rock layer near the pile end, there were slight fluctuations in the axial force decay rate. During different construction stages, with the increase in upper load, the rate of increase and decrease in axial force within each soil and rock layer became faster.

The cause of the above axial force variation pattern is as follows: the magnitude of the pile axial force is related to the upper load and the pile–soil interaction. The fundamental cause of the pile–soil interaction is the difference in the settlement between the two, which generates lateral friction resistance, leading to the increases and decreases in the pile axial force. After the construction of the cap, the lower colluvial gravel soil layer undergoes significant vertical compression under the weight of the cap and the pile itself, resulting in a settlement greater than that of the pile in this range, thus generating downward negative friction. Under the influence of negative friction, the pile axial force gradually increases within the colluvial gravel soil layer. As the depth increases within the soil layers, the vertical compression per unit depth gradually decreases, resulting in smaller settlement differences between the pile and the surrounding soil, which leads to less negative friction and a slower increase in axial force. At the interface between the soil and rock layers, the settlement of the pile matches the settlement of the surrounding soil, and the lateral friction resistance at this depth is zero, causing the pile axial force to reach its maximum. Subsequently, the lateral friction resistance becomes positive, and the axial force begins to decrease. Within the dissolved rock layers, the rock’s ability to resist deformation is strong, and its vertical compression is smaller than the pile’s settlement, thus providing upward positive friction, which leads to a gradual reduction in the pile axial force within the entire rock layer. Within the dissolution cavity, the axial force decay rate slows, but no negative friction is generated, indicating that the settlement of the filling material in the dissolution cavity is less than the relative settlement of the pile, providing a small amount of positive friction. Within the moderately weathered rock layer, the rock structure is relatively intact and can provide significant lateral friction, leading to the faster decay of the pile axial force.

Additionally, from the value of the maximum axial force, the colluvial gravel soil layer between the piles under the cap provides a considerable portion of the vertical bearing capacity when compressed. Although according to design standards, considering the potential for soil cavitation between the cap and the piles in the later stages, the cap effect is not included in the bearing capacity calculation during the design of the pile group foundation, the cap effect should not be ignored in the analysis of the bearing capacity during the early construction phases.

3. Research on Bearing Capacity Characteristics of Pile Group Foundation Based on Finite Element Method

3.1. The Establishment of Finite Element Model

Midas/GTS is a special finite element analysis software for geotechnical tunnel structures, developed by Beijing Midas Technology Co., Ltd. (Beijing, China) The software has the characteristics of a Chinese interface, interactive operation, powerful visualization, etc. According to the actual situation of the Qihe Bridge project, Midas GTS NX can simulate the condition of the pile cave under the pile foundation and the pile body passing through the cave more accurately.

The 3D solid model is used to simulate the elastic semi-infinite space foundation, and the degrees of freedom in the X, Y, and Z directions are limited. The overall model size limits the degrees of freedom in the X and Y directions but does not limit the degrees of freedom in the Z direction. In the selection of the model size, the size of the X and Y directions was set to 80 × 80 m, and the size of the Z direction was set to 40 m.

The soil was assumed to be an elastic-plastic material conforming to the Mohr–Coulomb criterion, the pile concrete was assumed to be a linear elastic material, and the contact form was set as a face-to-surface contact. After the geometric modeling was completed, it was divided into different layers by segmentation instructions, and the correct contact form between the geometry was ensured by a Boolean operation. According to the different depths of each layer, different sizes were selected to divide the grid, and the mesh size was reduced at the contact position between the stratum and the pile group foundation to ensure the accuracy of the calculation results. We selected a larger mesh size at the geometry boundary to reduce the total number of equations. The finite element model of Figure 1 is shown in Figure 5 below.

3.1.1. Construction of Pile Foundation and Cap

The length of the pile foundation is 20.1 m, the pile diameter is 2.0 m, the pile concrete is C30 underwater concrete, the bulk weight is 24 kN/m³, the elastic modulus is 3 × 10⁴ MPa, and the Poisson ratio is 0.2. The cap is 25.7 m long, 16.7 m wide, and 4 m high; the concrete used is C40 concrete; the bulk weight is 24.2 kN/m³; the elastic modulus is 3.25 × 10⁴ MPa; and the Poisson ratio is 0.25.

During the pile-modeling process, a 1D beam unit was used. During the selection of the mesh sizes, the mesh size of the pile, cap, and cave parts was set to 1 m, the formation mesh size was set to 2 m, and the size of the weathered rock in the lowest part was set to 3.m, and the sizes were automatically matched between similar contact surfaces. The finite element model of pile group foundation is shown in Figure 6.

3.1.2. The Building of the Pier

The lower part of the pier is made of C40 concrete, the top of the pier is made of C55 polyacrylonitrile fiber concrete within 3 m range, the bulk weight is 24.5 kN/m³, the elastic modulus is 3.55 × 10⁴ MPa, and the Poisson ratio is 0.3. The mesh partition size is 3 m. The self-weight load of the superstructure acts on the pier top in the form of uniform distribution pressure. The completed model is shown in Figure 7:

3.2. Calculation of Pile Axial Force in Different Construction Stages

3.2.1. Axial Force of Pile Foundation When It Is Built

The resulting data at each depth were extracted and the axial force diagram of each pile under the action of its own weight was drawn, as shown in Figure 4, where Z1-1 and Z1-2 are piles passing through the karst cave, and Z1-9, Z1-16, Z1-23, and Z1-24 are piles passing through the karst rock formation:

According to Figure 8, (1) under the action of its self-weight, the axial force of the pile without passing through the karst cave gradually increases with the increase in depth. The axial force grows faster within the depth of the slope gravel soil layer, while the axial force grows slower within the range of the rock layer. (2) The axial force of the Z1-1 and Z1-2 piles passing through the cave first increases and then decreases with the increase in depth, and the axial force grows faster within the cave range, reaching the maximum axial force at the junction between the bottom of the cave and the moderately weathered limestone layer.

3.2.2. Axial Force of Pile Under Load

When processing the data, the influence of pile self-weight was removed, and only the axial force of the pile under load was retained. After the pier was completed, the numerical simulation results of the axial force distribution of each pile on Pier No. 1 of the Qihe Bridge were shown in Figure 9:

Figure 9 showed that (1) the axial force of the pile without passing through the karst cave first increases and then decreases with the increase in depth and reaches the maximum value at the junction of the sloped gravel soil layer and the medium-weathered karst limestone layer; (2) the axial force of the piles passing through the cave increases first and then decreases with the depth, but the axial force attenuation rate within the depth range of the cave is significantly lower than that within the range of the upper and lower rock strata. The difference in the axial force between the karst cave piles and the non-karst cave piles is mainly reflected in the axial force attenuation rate within the cave range.

3.3. Comparison and Analysis of Numerical Simulation Results of Pile Axial Force with Field Test Results

Through a comparative analysis of the measured axial force data from each construction stage and the results of numerical simulations in Figure 10, the variation pattern of the axial force in the Z1-1 pile, as shown by both methods, was generally consistent. After excluding the influence of the pile’s self-weight, under the action of external loads, the axial force in the pile at all the stages exhibited a trend of increasing and then decreasing with depth. Specifically, within the range of the colluvial gravel soil layer, the axial force gradually increases, while in the bedrock and karst cave areas, the axial force decays at different rates. The maximum axial force in the pile during all the construction stages occurs at the interface between the soil layer and bedrock at a depth of approximately 4–5 m and increases with the applied upper load. The rate of change in the axial force also showed a generally consistent pattern, i.e., the axial force in the colluvial gravel soil layer increases at a gradually slowing rate with depth, while the axial force decays quickly in the upper and lower bedrock layers surrounding the karst cave and decays more slowly within the karst cave itself, at depths between 7.2 m and 13.2 m. For the different construction stages, the rate of change in the axial force within each soil and rock layer increases as the upper load increases.

A notable difference is that the axial force results from the numerical simulation were generally larger than the measured data. This discrepancy is considered reasonable due to several factors: the numerical simulation does not account for the layered construction intervals of the pile cap, the time factors such as the concrete strength development, the initial settlement of the strata during the symmetric drilling process, and the fact that the load is applied all at once without considering the long-term creep effect of the reinforced concrete material. Therefore, the results are deemed reasonable, considering the methodological constraints.

4. Superstructure Construction Phase Simulation

4.1. Axial Force of Pile During Construction of Superstructure

For the convenience of research, construction stages 7~14 in Table 4 were named as upper stage I and upper stage viii, respectively, according to the loading sequence of the superstructure construction loads.

4.1.1. Axial Force Distribution of Pile Z1-1 (Through Karst Cave)

As can be seen from Figure 11, the axial force distribution of pile Z1-1 under the construction load of the superstructure was similar to that in the previous construction stage. The axial force also increased in the range of the slope gravel soil layer and gradually decreased after reaching the maximum value above the junction of the soil layer and the rock layer. With the increase in the load, the axial force increased and the speed of attenuation increased, and the axial force attenuation increased obviously in the lower moderately weathered limestone layer, which indicates that the lateral resistance of the rock block below the bottom of the cave can be better exerted with the continuous increase in the load. However, the axial force attenuation rate of pile remained almost constant within the cave range, which indicates that the lateral friction resistance provided by the cave filling material has reached the limit, and the influence of the cave on the axial force of pile has gradually decreased. At the same time, the axial force of pile became more uniform when the load of the same size was increased. The maximum axial forces of the Z1-1 piles in each construction stage were 3694 kN, 4079 kN, 4557 kN, 5036 kN, 5514 kN, 6087 kN, 6658 kN, and 6723 kN. Differently from the construction stage of the substructure, the axial force of the Z1-2 pile in each construction stage was about 1.4% higher than that of Z1-1 pile, and the maximum axial force difference between the two piles was basically constant as the load continued to increase. The axial forces of the bottom plate were 2768 kN, 3056 kN, 3416 kN, 3775 kN, 4135 kN, 4566 kN, 4996 kN, and 5044 kN.

4.1.2. Axial Force Distribution of Pile Z1-9 (Without Passing Through Karst Cave)

As can be seen from Figure 12, under the action of the superstructure construction load, the axial force of pile Z1-9 first increased and then decreased, and the greater the upper load, the faster the axial force increased and decreased. The maximum axial forces of each construction stage were 3866 kN, 4271 kN, 4774 kN, 5278 kN, 5781 kN, 6368 kN, 6948 kN, and 7009 kN. The axial forces corresponding to the depth of the bottom plate of the cave were 2322 kN, 2565 kN, 2868 kN, 3170 kN, 3473 kN, 3825 kN, 4175 kN, and 4211 kN.

4.1.3. Axial Force Distribution of Pile

The maximum axial force of the Z1-9 piles in each construction stage of the superstructure was 4.66%, 4.72%, 4.77%, 4.81%, 4.85%, 4.61%, 4.36%, and 4.25% higher than that of the Z1-1 piles. Combined with the axial force difference of the two piles in each construction stage of the substructure, it can be found that the maximum axial force difference increases first and then decreases. The difference of the five axial forces in the construction stage of the superstructure reached the maximum value of 4.85%. The axial force difference between the piles passing through the cave and other piles was constant in the range of the weathered limestone below the cave, and the maximum axial force difference increased first and then decreased. Because a difference in axial force often means that the settlement is uneven, the influence of the upper load on the stability of the pile group foundation is mainly reflected in the increase in the uneven settlement between the piles passing through the cave and the other piles. Therefore, during the construction of the Qihe Bridge, the settlement monitoring of the piles in the range of the maximum axial force and the cave depth should be emphasized.

4.2. Lateral Friction Resistance of Pile During Superstructure Construction

4.2.1. Z1-1 Pile Side Friction Distribution (Through Karst Cave)

As can be seen from Figure 13, The friction resistance of pile Z1-1 is small in the inner range of the karst cave but large in the inner range of the rock layer. The maximum lateral frictional resistance in each stage was 10.66 kPa, 11.76 kPa, 13.13 kPa, 14.49 kPa, 15.85 kPa, 17.47 kPa, 19.07 kPa, and 19.25 kPa. The lateral friction resistance of the pile was basically constant over the whole range of the medium-weathered limestone layer, and the stages were 39 kPa, 43 kPa, 48 kPa, 53 kPa, 58 kPa, 64 kPa, 70 kPa, and 71 kPa. With the increase in the load, the lateral friction resistance in the cave was gradually increased, indicating that the lateral friction resistance provided by the cave filling material had not reached the limit.

4.2.2. Z1-9 Pile Side Friction Distribution (Not Through the Cave)

According to Figure 14, at the same construction stage, the side friction resistance of the Z1-9 pile increased with the increase in depth, and the side friction resistance at the same depth also increased with the increase in the upper load. The maximum side friction occurred at the pile bottom, and the maximum values were 33.57 kPa, 37.08 kPa, 41.45 kPa, 45.82 kPa, 50.19 kPa, 55.29 kPa, 60.34 kPa, and 60.86 kPa. In the range of the moderately weathered limestone beds, the lateral friction resistance still presented a relatively obvious increasing trend. This indicates that with the continuous increase in the load, the lateral resistance of the rock-socketed section of pile Z1-9 is further exerted, and the closer the position is to the pile bottom, the more fully exerted the lateral resistance becomes.

4.2.3. Distribution Law of Pile Side Friction Resistance

(1) Under the action of superstructure construction load, the lateral friction resistance provided by the cave filling material does not reach the limit; (2) with the increase in the load, the lateral friction of the rock-socketed section increases significantly. The pile passing through the karst cave has greater lateral friction resistance in the rock-socketed section below the karst cave; (3) the lateral friction resistance of the pile located in the center of the cap is larger and tends to increase with the increase in depth.

5. Axial Force Distribution of Piles with Different Depths

In this paper, the axial force of the pile body at depths of 0.3 m (close to the pile top), 13.0 m (close to the cave bottom), and 19.0 m (close to the pile bottom) was extracted for exploration.

5.1. Axial Force at 0.3 m

As can be seen from Figure 15, the axial force connection of the pile body resembles a convex curve, and the axial force in the direction of the transverse bridge presents the rule of middle pile > side pile, and the axial force in the direction of the axial force along the bridge presents the rule of side pile > middle pile. The axial force of the Z1-1 and Z1-2 piles passing through the cave was smaller than that of the piles in the symmetrical position of the transverse bridge. On the whole, the axial force of each pile near the top of the pile is as follows: middle pile of the bridge > side pile of the bridge > corner pile > cave pile.

The top of the pile is mostly located in the range of the slope gravel soil layer, and the negative friction caused by the soil compression being greater than the pile settlement is the main factor causing the increase in the axial force of each pile. The pile passing through the karst cave has a large settlement under the action of the load of the cap. Because the soil between the piles is squeezed by the surrounding piles, the dissipation effect of the stress is weaker than that of the soil outside the cap, resulting in the compression of the soil between the piles is greater than that outside the cap. Under the combined action, the negative friction force and the axial force of cave pile are minimum. The negative friction force and the axial force of the pile along the bridge are small.

Figure 16 shows the axial force at 0.3 m of each pile in the different construction stages, and the distribution law is basically the same as that at the stage of cap construction. However, with the increase in the load, the axial force difference between any two piles at the same depth increases.

5.2. Axial Force at 13.0 m

As can be seen from Figure 17, the axial force distribution of each pile at a depth of 13.0 m (close to the bottom of the cave) presents a completely different law from that of the pile top. In addition to the two piles passing through the cave, the axial force distribution shows the middle pile > side pile > side pile. The axial force of the two piles passing through the cave is significantly greater than that of the other piles, and the axial force of the Z1-2 piles is slightly greater than that of the Z1-1 piles. From the overall distribution, the axial force distribution of the pile near the soleplate with the location is as follows: cave pile > bridge to center pile > bridge to side pile > corner pile.

Compared with the axial force distribution near the pile top, the axial force distribution at the bottom of the cave is different, mainly in the direction along the bridge and the cave pile. This is because the soil on the side of the pile at this depth already provides positive upward friction and because the lateral friction provided by the cave filling material is less than that provided by the strongly weathered limestone; the two piles in the cave generate greater compression and axial force. Because of the existence of the cave, the continuity of the soil on the side of the pile is interrupted, resulting in the overall strength of the soil being reduced. As a result, the horizontal force on the pile under the influence of the cave is different, thus reducing the side friction resistance and slightly increasing the axial force.

According to Figure 18, the distribution law of the pile axial force with the position in the subsequent construction stage is consistent with that in the stage of cap construction, and the difference in the axial force increases significantly with the increase in the load.

5.3. Axial Force at 19.0 m

As shown in Figure 19, in the direction of the cross bridge, the axial force of side piles near the cave > middle piles > side piles far from the cave > side piles; in the third, fourth, and fifth rows of the piles near Z1-2 along the bridge, the axial force of the piles near the cave > the piles on the side of the cave > the piles away from the cave > the piles on the side of the cave, and the axial force of the piles on the sixth row > the piles on the side of the cave; at the same time, the axial force of the pile body in the range of the karst cave is the largest. On the whole, the axial force distribution at 19 m is as follows: cave pile > cave side pile > cave side pile > bridge side pile > cross bridge side pile > corner pile. The influence range of the karst cave near the pile bottom is larger than that at the depth of 13 m.

The reason for the above phenomenon is that the total lateral friction resistance of the karst cave pile is less than that of the other piles, so the axial force is significantly higher than that of the other piles. Because of the rock-socketed section of pile foundation at this depth, the stress dissipation ability of the rock mass on the side of the pile is weaker than that of the soil, and the existence of the karst cave leads to the uneven settlement of the pile.

As can be seen from Figure 20, with the increase in the load, the distribution law of the pile axial force at 19 m depth, along with the location, is consistent with that at the stage of cap construction, and the difference in the axial force increases with the increase in the upper load. This shows that the distribution law of axial force and the influence range of the karst cave have nothing to do with the load size but only have something to do with the position and depth of pile.

6. Settlement Distribution and Non-Uniform Settlement

Under the action of loads, pile settlement at different depths in different construction stages is shown in the figure below.

6.1. Pile Top Settlement

According to Figure 21a, after the cap is built, the settlement distribution of the pile top of each pile presents a pattern of the karst cave pile > middle pile > side pile > corner pile; that is, except for the two karst cave piles, the settlement of the pile top of the overall pile group foundation presents a concave curved surface.

According to Figure 21b, with the increase in the load, there is no obvious difference in the settlement distribution law of each pile, and the influence range of the karst cave is also consistent with the stage after the cap is built, but the significant value of the settlement difference increases. Since the pile group foundation of the Qihe Bridge is a large-diameter, rock-socketed pile and the rock layer at the bottom has a good bearing capacity, the overall settlement amount is not large. However, considering that the settlement difference between the two corner piles reaches about 20%, it is still necessary to strengthen the settlement monitoring of the piles within the influence range of the karst caves to prevent potential risks caused by additional internal forces.

6.2. Subsidence at the Bottom of the Cave

According to Figure 22, the settlement law at the bottom depth of the karst cave in the different construction stages of the piles is the same: karst cave pile > middle pile > side pile > side pile. From the influence range of the cave, the piles affected at the depth of the cave floor are two side piles across the bridge, one side pile, and two side piles along the bridge, which is consistent with the influence range of the cave at this depth on the axial force of the piles.

6.3. Pile Bottom Settlement

According to Figure 23, the settlement distribution of the pile bottom of each pile in the different construction stages is consistent, which is also the karst cave pile > middle pile > side pile. The maximum settlement difference occurs between piles Z1-1 and Z1-24, and the influence range of the cave is the same as the depth of the cave floor.

6.4. Summary of Settlement Distribution and Influence Range of Karst Caves

The settlement distribution law of each pile does not change with the change in the depth, and the karst cave pile is prominent in the whole pile depth range, and the other piles are similar to the settling basin of the “pot bottom”. At the same time, the influence range of the cave on the pile settlement does not increase with the increase in the load, nor does it change with the change in depth. The coverage range is always two side piles across the bridge, one side pile, and two side piles along the bridge.

7. Relative Vertical Displacement of Pile Side Soil

7.1. Vertical Relative Displacement of Pile Top

According to Figure 24, the relative displacement of the pile and the soil at the top of each pile in the different construction stages is consistent with the distribution law of the location, showing the law of high middle, low around, and smallest cave pile, namely, middle pile > side pile > side pile > corner pile > cave pile.

7.2. Vertical Relative Displacement at the Depth of the Cave Floor

According to Figure 25, except for Z1-1 and Z1-2, which are significantly smaller, the relative displacement of the piles and soils at the depth of the pile soleplate is basically the same, showing a law that the transverse bridge is higher in the middle and the two sides are lower in the middle, while the longitudinal bridge is slightly higher at the two sides and the middle is slightly lower. Generally speaking, side piles > middle piles > side piles > side piles > side piles > side piles > corner piles > cave piles, and the distribution law of each construction stage is the same.

Compared with the pile top, the relative displacements between the piles and soil on the sides of the piles at the depth of the cave floor are smaller, which is because the non-cave piles are located in the intensely weathered limestone layer, have stronger deformation resistance than the soil layer, and can provide enough side friction resistance. The relatively small pile side displacement is due to the fact that the settlement of the cave filling material is significantly greater than that of the strongly weathered limestone, so the relative displacement of the pile body is small.

7.3. Vertical Relative Displacement of Pile Bottom

From Figure 26, the relative displacement of the pile side soil at the pile bottom of the two construction nodes has the same distribution law as the location. In addition to the obvious protrusion of the karst cave piles, the relative displacements of the piles at the pile bottom and the pile side soil present a distribution form of higher in the middle and lower in the periphery. Meanwhile, some piles near the karst cave are slightly higher than those in symmetrical positions. In general, the pattern is the karst cave piles > middle piles > side piles > side piles > corner piles.

7.4. The Distribution Law of the Vertical Relative Displacement of the Pile Side Soil and the Influence Range of the Karst Cave Are Summarized

The vertical relative displacement distribution of the pile side soil at the same depth in the different construction stages remains unchanged, but the vertical relative displacement distribution of the pile side soil at different depths is different; that is, the top position of the pile is the middle pile > side pile > side pile > corner pile > cave pile, and the base position of the cave is along the bridge side pile > middle pile > side pile > cross bridge side pile > corner pile > cave pile. The bottom of the pile is cave pile > middle pile > side pile > side pile > corner pile. The existence of the karst cave has a significant influence on the relative displacement of the pile side soil within the soil layer, but in the rock layer, the influence on the relative displacement of the pile side soil around the pile body can be ignored.

8. Conclusions and Prospect

8.1. Conclusions

In view of the fact that most studies on bridge pile foundations in the karst area are carried out on the basis of single piles, and the simulation of individual piles passing through karst caves is insufficient, this paper, respectively, explored the distribution law of axial force, pile end force, settlement, and the vertical relative displacement of the soil on the sides of 24 piles with their location and explored the influence of karst caves on various parameters. The mechanism of pile–soil interactions under the influence of karst caves was revealed by analyzing and comparing the distribution of the parameters at different depths and their mutual relationships. The following conclusions were drawn:

(1) From the simulations of the superstructure and the output, the axial force, the side friction, and other results, it was found that the difference in the maximum axial force between the cave pile and the middle pile in the construction stage of the superstructure increases first and then decreases. Therefore, according to the different construction stages, the junction of the pile rock layer and the soil layer and the part within the depth of cave should be monitored.

(2) The position distribution law of axial force has nothing to do with the load size and is only related to the position and the depth of the pile.

(3) The settlement distribution law of each pile does not change with the change in depth, and the karst cave pile is prominent across the whole pile depth range, and the other piles are similar to the settling basin of the “pot bottom”. At the same time, the influence range of the cave on the pile settlement does not increase with the increase in the load, nor does it change with the change in depth. The coverage range is always two side piles across the bridge, one side pile, and two side piles along the bridge.

8.2. Prospect

This paper studies the bearing capacity characteristics of a pile group foundation in an underlying cave by combining field tests with numerical simulations. However, the research content on the bearing capacity characteristics of pile group foundations passing through a cave is extensive and very complicated, and my knowledge is limited, and the investigation was limited by the research time and the actual construction progress, and there are still some problems to be improved in this study.

(1) Considering the disturbance effect on the surrounding soil or rock mass during the construction of bored pile, the stability analysis of the karst cavern’s surrounding rock under the dynamic load during the drilling process can be increased in the future to ensure the safety of the overall pile foundation construction process.

(2) Considering the limitation of the actual construction schedule, the stress and deformation of key positions on the whole bridge can be monitored during the subsequent construction process of the bridge superstructure and the opening and operation stage, so as to further determine the accuracy and applicability of the finite element numerical simulation results, so as to facilitate the application of the research results in practical projects.