#### Abstract

Concrete expanded-plate piles have significant advantages in the bearing capacity, settlement, and construction period. The added bearing expanded plate is the key reason for their many advantages; moreover, the slope angle (*α* angle: the maximum diameter of the bearing expanded plate and the angle formed on the plate) of the bearing expanded plate is the main factor to control the longitudinal symmetry. However, the concrete expanded-plate piles in practical engineering do not exist in a rigid body state, and elastic deformation will occur under variable engineering conditions. In addition, the research in this paper mainly focuses on a flexible concrete expanded-plate pile (F-CEP pile). The flexible pile mentioned in this paper refers to the bending deformation of the pile body under horizontal load, which produces large pile top displacement. This study uses the two methods of small-scale half-plane pile model test and finite element simulation analysis of ANSYS, after referring to the equipotential pile test at the actual site. In this paper, the variation law of the displacement curve and the failure law of the soil around the pile under the horizontal force when the *α* angle changes are analyzed, and the calculation model of the bearing capacity of F-CEP pile under the *α* angle change is put forward. This research aims to verify the reliability of existing research and provides strong support for the application, promotion, design, and research of F-CEP piles in construction engineering.

#### 1. Introduction

Variable cross section piles have been studied by engineering scholars because of their flexible application in complex foundation soil in various regions of China [1, 2]. They include DX piles [3, 4], squeezed branch piles [5, 6], and concrete expanded-plate piles [7]. The concrete expanded-plate pile is a new type of pile that is highly suitable for multiterrain and multiregion. Such a pile type is widely accepted for its good bearing capacity, low settlement, and engineering economy and has gradually attracted increasing attention and discussion from scholars at home and abroad. The actual construction site and stress mechanism are shown in Figure 1.

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At present, most scholars’ research mainly focuses on the two aspects of tensile and compressive strength [8, 9]. However, in practical engineering, there will be a situation that the restraint of the reinforced concrete pile cap is not large enough to the pile, resulting in the pile body not only bearing the vertical force but also the horizontal displacement at the top of the pile [10]. Therefore, the damage of building foundation is often accompanied by more complex damage, such as punching and torsion of the pile caused by the horizontal force [11, 12]. Meanwhile, due to the properties of reinforced concrete and other materials [13], when the pile is damaged due to the horizontal load, a bending phenomenon will occur rather than simple rigid failure [14, 15]. Therefore, the bearing mechanism of a flexible concrete expanded-plate pile (F-CEP pile) in the horizontal direction should be studied [16, 17].

Considering that the bearing mechanism of an F-CEP pile is determined by many factors [18, 19], the *α* angle of the expanded plate determines the longitudinal height of the plate, which directly affects the bearing performance of the F-CEP pile. Thus, this research analyzes the antioverturning bearing capacity of F-CEP piles with different *α* angles under the horizontal force [20]. Based on the model test and finite element analysis [21, 22], the displacement and stress values obtained by a single pile without a concrete pile cap under the horizontal load were drew and compared, and the displacement law, stress change [23, 24], and failure state of the F-CEP piles and the soil around the piles are analyzed [25, 26]. This research lays a foundation for the further study of concrete expanded-plate piles and has certain practical engineering guiding significance for the construction and bearing capacity of F-CEP piles [27, 28]. The actual site map and model diagram of a pile are shown in Figure 1.

#### 2. Experimental Study on a Small-Scale Half-Face Pile Model

##### 2.1. Selection of Undisturbed Soil and Fabrication of a Model Pile

###### 2.1.1. Selection of Undisturbed Soil

Soil is one of the important factors that affects test results. Test soil parameters should be consistent with actual construction soil parameters to improve the test accuracy. In accordance with the geological survey report provided by the construction unit, this research collects field survey records of undisturbed soil and selects the second layer of silty clay on the undisturbed soil site as the test soil. The second layer of silty clay in this exploration has a layer thickness of 2.20 m to 12.40 m, and its soil properties are gray-brown, gray-black, high compressibility, and plastic soft-to-soft plastic state. The second layer of silty clay in this exploration has a layer thickness of 2.20 m to 12.40 m, and its soil properties are gray-brown, gray-black, high compressibility, and plastic soft-to-soft plastic state.

In this experiment, a special soil extractor is used as a soil removal tool and a soil container. When taking soil, the soil extractor is placed at intervals on the leveled silty clay layer site. This research uses a machine to press into the soil evenly and slowly, digs out after a period of time, and utilizes a waterproof plastic film to seal the soil extractor for storage and transportation. During the entire borrowing process, the soil properties should not be destroyed and remain in the original state. The borrowing process is shown in Figure 2.

###### 2.1.2. Model Pile Production

This research mainly evaluates the influence of different *α* angles on F-CEP piles under the horizontal load with the *α* angle as the single control variable. Therefore, four groups of test model piles with *α* angles of 30°, 35°, 40°, and 45° are set [29]. They are named P1, P2, P3, and P4. The material is made of aluminum alloy with properties relatively close to those of reinforced concrete, and the size is reduced in accordance with the actual demonstration project at a ratio of 1:30. To facilitate the application of the horizontal load to the test model pile, a 20 mm hole position should be reserved at the top of the pile. The test model pile is shown in Figure 3, and the specific number and size are shown in Table 1.

##### 2.2. Test Process Analysis

First, the test model pile is buried in the soil. Then, the glass plate is fixed on the soil surface of the soil extractor such that the pile–soil interaction during the test can be observed and recorded. The test bench after installation is shown in Figure 4.

In this test, a horizontal load is applied step by step such that the displacement of the pile and the damage of the soil can be observed clearly. A vertical load is applied first, followed by a horizontal rightward load. Slow down, press down during loading, and pause the loading once each time the pile top produces 1 mm displacement. At this time, photos are taken, and the horizontal force is recorded until the soil around the pile loses its effect on the pile. P3 pile is regarded as an example, and the loading process and soil damage state are shown in Figure 5.

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The test process is analyzed, as shown in Figure 5. When a vertical load is applied to the pile, the upper part of the bearing plate begins to separate from the soil, and a watermark appears at the end of the pile. When a horizontal load is applied, the pile body is bent first, as shown in Figure b. With the increase in the load, the expanded piles show an overturning phenomenon and begin to rotate at 1/2 of the pile body under the plate. The pile top continuously squeezes the soil on the right side, the left side of the bearing plate, and the soil around the pile. The cracks continue to expand until complete destruction in Figure e. Owing to the existence of the bearing plate in the entire process, the bending moment of the pile end generated by the expanded plate pile during the rotation process is much smaller than that of the pile top. Accordingly, the pile end displacement is smaller than the pile top displacement.

Figure f shows the soil damage. Cracks are mainly distributed on the top of the pile, the bearing plate, and the end of the pile. The cracks on the top of the pile and the soil on the top of the pile are wider. Owing to the mutual compression of the bearing plate and the soil, the phenomenon that the top of the pile body is bent first and overturned afterward is evident.

##### 2.3. Analysis of Test Results

The four groups of test model piles are loaded at different *α* angles separately. The four groups of soil around the piles under limit state loading are recorded and compared, as shown in Figure 6.

Figure 6 illustrates that when the ultimate bearing capacity is reached, the watermark outline range appears on the top of the pile, the right side of the bearing plate, and the left side of the bottom of the pile. The damage state of the soil around the four groups of test model piles is roughly the same. When the *α* angle increases, the affected soil area around the bearing plate also increases. That is, the larger the *α* angle is, the wider area the bearing plate will have on the surrounding soil, and the bearing capacity of the pile will also increase.

#### 3. ANSYS Finite Element Simulation Research

##### 3.1. Model Establishment

In the finite element analysis process, to facilitate comparative analysis with the test, four groups of model piles with different values of *α* angles of 30°, 35°, 40°, and 45° are also set up, and the number is the same as the test number. The difference from the experiment is that the size of the ANSYS model pile has 1:1 ratio from the actual demonstration project to ensure the practical applicability of the finite element simulation experiment. The ANSYS model pile size and ANSYS model soil parameters are shown in Tables 2 and 3, respectively. The ANSYS model is shown in Figure 7.

Once the model is built, the next step is meshing. Meshing is the most important part of the finite element simulation process, and the accuracy of the meshing affects the accuracy of the simulation results. The meshing of this study is based on the sweeping meshing. The meshed graph is shown in Figure 8.

##### 3.2. Displacement Result Analysis

The four sets of ANSYS model piles are loaded step by step. To compare and analyze the displacement of different *α*-angle model piles, displacement cloud diagrams when the four sets of loading are all in the ultimate load state are extracted. The displacement cloud images are shown in Figure 9.

The displacement cloud diagrams in Figure 9 show that the overall displacement trends of the model piles with different *α* angles are the same. The displacement influence area mainly appears on the top of the pile, the right side of the bearing plate, and the left side of the bottom of the pile. As the *α* angle increases, the area affected by the displacement of the pile top gradually decreases. Therefore, the finite element simulation displacement results are consistent with the experimental results.

#### 4. Comparative Analysis of Results

The analysis of the test failure status of the test model pile and the displacement cloud diagram of the ANSYS model pile basically lead to the same conclusion. On this basis, the load and displacement data from the test and finite element simulation are sorted and analyzed, and the load–displacement curve diagram can be obtained. A comprehensive comparative analysis of the curve change rules of the two is performed to verify the reliability of the test. The load-displacement curves are shown in Figure 10.

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The two sets of graphs in Figure 10 are compared and analyzed, and the following conclusions are drawn:

The overall trends of the curves are the same. As the load increases, the pile top displacement increases, but the growth trend is nonlinear. In Figure a, before the displacement reaches 6 mm, the pile top loads at various slope angles are inconsiderably different, indicating that the bearing plate plays a minimal role in the early stage of loading. The curve trend in Figure b is similar to that in Figure a. In the early stage of horizontal load loading, the pile top displacement curves are completely overlapped. The pile top displacements at different slope angles are extremely small, which prove that the test and simulation results are the same.

Curve analysis indicates that when the concrete expanded pile reaches the ultimate load (refers to the maximum load corresponding to the occurrence of deformations that are not suitable for continued bearing), although the bearing capacity (refers to the lateral bearing capacity of the pile, that is, the bearing capacity of the pile when it is forced perpendicular to the axis of the pile) increases as the *α* angle increases, the difference in the top displacement of the pile at different *α* angles is small. Figure a is regarded as an example, and the difference between the pile top displacement of P4 and P1 is only 0.95 mm. When the pile top displacement reaches 11 mm during the test, the difference in load is only 0.2 kN. The conclusions in the experiment and simulation are the same; that is, the limit displacement values of the pile tops with different *α* angles are minimally different. Thus, the *α* angle has a low efficiency in improving the horizontal bearing capacity of F-CEP piles.

#### 5. Calculation Mode for Single Pile-Bearing Capacity

From the test and ANSYS finite element simulation results, an F-CEP pile will bend first and then overturn under a horizontal load. Accordingly, the force mode of the F-CEP pile is determined [30, 31], as shown in Figure 11.

Given that the pile body will bend in the early stage when the horizontal load is applied and the pile itself will resist part of the bending moment, the calculation mode for the single pile bearing capacity of an F-CEP pile iswhere is the horizontal displacement of the pile; is the calculated width of the pile; is the total length of the expanded pile; is the length of the main pile on the bearing plate; is the area pile length.

Under the action of the horizontal load, the soil under the end of the pan will produce slipping failure. In accordance with the slip line theory, the strain field of the Prandtl area is established, as shown in Figure 12.where is the horizontal bearing capacity of the soil under the bearing plate per unit width; is the diameter of the bearing plate and diameter of the main pile, respectively; is the cohesion of the soil around the pile; *φ* is the internal friction angle of the soil around the pile; *θ* is * α *+90°.

When the bearing capacity of the pile body is calculated, the principle of linear elastic body deformation is adopted. Then, we obtainwhere is the material modulus of elasticity; is the maximum pile top displacement when the pile body is bent; and ——the moment of inertia of the pile.

In accordance with the above formula and Figure 11, the *θ* value in the disk end calculation mode is the radian value of *α* + 90°. Therefore, when the *α* angle of the bearing plate increases, its *θ* value increases, and the horizontal bearing capacity of the plate end also increases. Likewise, the horizontal bearing capacity of F-CEP piles increases with the increase in the *α* angle. However, given that the *θ* value is the radian value after angle conversion, when the *α* angle increases by 5°, the *θ* value increases to 0.08722. From the calculation, the maximum growth rate of the bearing capacity of a single pile with different *α* angles is 0.8%, and the bearing capacity changes minimally. Hence, the *α* angle has a certain influence on the horizontal bearing capacity of F-CEP piles, but the influence degree is relatively small.

#### 6. Conclusions

Through the research in this article, the following conclusions can be drawn:

The failure state of the soil around F-CEP piles with different *α* angles is basically the same. That is, under the action of the horizontal load, the pile body bends first; as the load increases, the pile body overturns again. Under the action of the horizontal load to the right, the location of soil is on the right side of the pile top and under the right side of the plate. Meanwhile, the left side of the bottom of the pile resists the horizontal load.

The displacement of the pile top decreases as the *α* angle increases, but the difference value is small. The factor *α* angle has a minimal effect on the horizontal bearing capacity of F-CEP piles.

According to the test results, the single pile bearing capacity mode of F-CEP pile is and , and the *α* angle is the main parameter in the calculation, but it has less impact on the calculation result.

In summary, it can be seen that the *α* angle has less influence on the bearing performance of F-CEP piles under the horizontal load. In the future, the design of piles should also comprehensively consider geological conditions, engineering requirements, and other conditions. In particular, in the actual project, we should try to choose a reasonable angle, we must consider the *α* angle and strength of reinforced concrete, construction costs, and other factors at the same time.

#### Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

#### Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

#### Acknowledgments

This work was financially supported by the National Natural Science Foundation of China (nos. 52078239and 52008185).