Displacement and force analyses of piles in the pile-caisson composite structure under eccentric inclined loading considering different stratum features

Abstract

A novel anchorage for long-span suspension bridges, called pile-caisson composite structures, was recently proposed by the authors in an attempt to reduce the construction period and costs. This study aims to investigate the displacement and force behavior of piles in a pile-caisson composite structure under eccentric inclined loading considering different stratum features. To this end, both 1g model tests and three-dimensional numerical simulations were performed. Two groups of 1g model tests were used to validate the finite-element (FE) method. Parametric studies were then performed to investigate the effects of groundwater level, burial depth of the pile-caisson composite structure, and distribution of soil layers on the performance of the pile-caisson composite structure. The numerical analyses indicated that the influence of the groundwater level on the stability of the caisson was much greater than that of the piles. In addition, increasing the burial depth of the pile-caisson composite structure can assist in reducing the displacements and improving the stability of the pile-caisson composite structure. In addition, the distribution of soil layers can significantly affect the stability of the pile-caisson composite structure, especially the soil layer around the caisson.

Graphical abstract

Keywords

composite structure / piles / foundation / suspension bridge / 1g model test / finite-element analysis

1 Introduction

It is well recognized that the suspension bridge has the advantages of large span, beautiful shape, and high economy. Currently, the main span of numerous long-span suspension bridges exceeds 1000 m [1–7]. Moreover, the caisson anchorage has been widely adopted to support many long-span suspension bridges, such as the caisson anchorage on the Awajishima side of the Akashi Kaikyo Bridge [8], Jiangyin Yangtze River Bridge’s north anchorage [9], and Taizhou Yangtze River Bridge’s south anchorage [10]. However, as the suspension bridge span increases, the anchorage foundation volume increases, and its construction cost increases. To shorten the construction cycle and reduce costs, the authors recently proposed a new design for a composite anchorage foundation to sustain long-span suspension bridges. By significantly lowering the caisson’s height and adding bored piles beneath it, this foundation, known as the pile-caisson composite structure, improves upon the traditional caisson anchorage foundation. Based on the Nanjing Xianxin Road (NXR) Bridge with a traditional caisson foundation at the prototype scale, the authors performed finite-element (FE) analyses to explore the feasibility of the pile-caisson composite structure. The numerical results show that the horizontal and vertical displacements of the pile-caisson composite structure are both less than those of the conventional caisson foundation, indicating that the pile-caisson composite structure is suitable for the north anchorage of the NXR Bridge. Furthermore, the impacts of pile diameter, pile length, and pile arrangement on the responses of bored piles for the pile-caisson composite structure were further investigated using parametric analyses with Plaxis 3D software [11].

In addition, the behaviors of caisson foundations have been extensively investigated [12–18]. Therefore, this study focused on the load behaviors and displacements of the pile group. Despite a plethora of previous investigations on the behavior of pile groups applied to eccentric lateral loading [19–22], eccentric vertical loading [23–26], or eccentric inclined loading [27,28], the response of pile groups with numerous piles in the pile-caisson composite structures has received little attention.

Moreover, the mechanism of soil−pile interaction has been studied using many 1g model tests. Yavari et al. [29] studied the mechanical behavior of an energy pile in saturated clay. Liang et al. [30] investigated the mechanisms of the pile−soil−cap−goaf and settlement characteristics. Zhang et al. [31] performed quasi-static model tests using two 1/8-scale bridge-pier models. A large number of large-scale 1g model tests were conducted by Rizvi et al. [32] to investigate the behavior of the soil–pile system under an axial load.

Numerical simulations were also conducted to deepen the understanding of the loading behavior of piles. Mroueh and Shahrour [33] performed numerical simulations to investigate the effects of urban tunnel construction on nearby pile foundations. Achmus et al. [34] outlined a numerical model and investigated monopile deformation response under cyclic lateral loads. Lam et al. [35] performed numerical analyses of centrifuge model tests, considering the elasto-plastic slip at the pile−soil interface. Cui et al. [36] studied the effects of anchorage displacement on the loading behavior of a bridge based on a verified FE model. Zhang et al. [37] conducted a FE study of pile groups with various layouts of individual piles.

In addition, extensive studies [10,38,39] have been conducted using the FE method to evaluate the safety of anchorage foundations during loading, without considering the construction stages. Because the authors’ time and energy are limited, this study focuses on the displacement and force analyses of piles in the pile-caisson composite structure under eccentric inclined loading without considering the characteristics of the construction stage. Installation effects have been proven to be significant for the capacity of piles [40,41]. The authors will conduct future investigations on the installation effect of piling works for the pile-caisson composite structure.

This study aims to comprehensively investigate the induced lateral behavior (i.e., pile deflection and pile shear force) of piles in a pile-caisson composite structure. In this study, based on the project of the north anchorage of the NXR Bridge in China, two groups of 1g model tests were first conducted. The model test results were then used to validate the three-dimensional finite, and parametric analyses were performed. The parametric analyses focused on the effects of groundwater level, burial depth of the pile-caisson composite structure, and soil layers on the responses of piles in the pile-caisson composite structure. The mechanism of the lateral effects on the piles was given special attention when the pile-caisson composite structure was subjected to the designed load from the main cable.

2 Project description

The NXR Bridge is a long-span suspension bridge with a main span of 1760 m in Nanjing, China. The north anchorage foundation adopted by the NXR Bridge, which consists of an anchorage block and a caisson, was constructed on the north bank of the Yangtze River. To reduce the construction period and cost, the structure of the north anchorage foundation is optimized by decreasing the caisson height from 49.5 to 29.5 m and arranging bored piles below the caisson. The optimized structure was termed the pile-caisson composite structure. Fig.1(a) and Fig.1(b) show the elevation and plan views of the pile-caisson composite structure at the prototype scale, respectively.

3 1g model tests

The on-site responses of a full-scale pile-caisson composite structure can be forecast using model tests. The scaling laws for the 1g model tests in this study were reported by Gudehus and Hettler [42]. It should be noted that for the 1g model tests, it is challenging to follow all similarity laws. Tab.1 presents the scaling factors used in the model tests.

Fig.2 depicts the profiles of the pile-caisson composite structure at the model scale. The model box used in this paper was 4.0 m long, 2.0 m wide, and 1.2 m high. The model caisson was 70 cm long, 50 cm wide, and 29.5 cm high. The distance from the front side of the caisson (i.e., facing the direction of the applied load F_a) to the inner side of the model box was 1750 mm, which ensured that the distance from the edge of the pile-caisson composite structure to the edge of the model box was longer than the half-width of the anchorage [10]. The model piles were 45 cm in length.

Moreover, extensive research on pile groups in model tests was conducted, and the ratio of the distance between the bottom of the pile group and the bottom of the model box to the diameter of piles was less than 12 in most studies [43–45]. In this study, the ratio of the distance between the pile toe and the bottom of the model box is 12.75, which is larger than 12.

In this study, two types of model tests were performed for the pile-caisson composite structure. The only difference between the two model tests was the number of piles. Fig.3 presents the bottom view of the pile-caisson composite structure in the two model tests. Scheme A denotes the pile-caisson composite structure with 35 piles, whereas Scheme B denotes that with 54 piles.

3.1 Experimental program and setup

The model sand originated from the Gand Canal, China. Tab.2 summarizes the mechanical properties of the model sand.

Fig.4 shows a typical model setup including a monitoring system. As shown in Fig.4, a hand chain hoist was used to apply the load, which was controlled using a tensile force gauge. The monitoring system depicted in Fig.4 consists of a noncontact laser displacement sensor and a data acquisition system with an accuracy of 0.01 mm. Moreover, one side of the model box was set to be transparent for the convenience of observing foundation displacements.

3.2 Model piles

As shown in Fig.5, the model pile in each test was fabricated from an acrylic tube with an outer diameter of 2 cm, inner diameter of 1.8 cm, and a length of 45 cm. The pile surface was polished with 0.125 mm sandpaper to simulate the roughness. In addition, the essential governing property to be satisfied in this study is the pile’s bending stiffness (EI). The Young’s modulus (E_m) and bending stiffness (E_mI_m) of the model pile are 3.0 GPa and 8.103 N·m², respectively. The corresponding bending stiffness (E_pI_p) of a real bored pile in the prototype is 1.013 × 10⁵ MN·m².

The sand in the model tests was prepared in layers, and the thickness of each layer was 5 cm. The density of the sand model was controlled by its weight and volume. When the model sand was filled to the elevation of the pile toe, the pile group was temporarily fixed at its designed location through a location plate (see Fig.6) with holes of the same size as the model piles in the model caisson bottom. Therefore, model piles are “wished-in-place” in the sand bed.

3.3 Model caisson and construction

In the north anchorage foundation project of the NXR Bridge, the anchorage block was located above the soil surface and had no contact with the surrounding soil. Therefore, the anchorage block and caisson were considered in the model tests. The total dead weight and center of gravity of the anchorage block and caisson were equivalent to those of the simplified caisson and counterweight plate fabricated from alloy steel.

In addition, as the strength and stiffness of the anchorage block and caisson in the prototype scale are much larger than those of the soil, the simplified model caisson was considered as a rigid body in the model tests. As shown in Fig.7, the components of the model caisson include the caisson cover, frame, and bottom. Moreover, a layer of sand with grain sizes from 0.9 to 2.3 mm was adhered to the surface of the caisson frame and caisson bottom to simulate the frictional nature of the caisson’s contact with the surrounding soil. Fig.8 shows the procedure of the model test for the pile-caisson composite structure. The following is a description of construction details of the model caisson.

After completing the construction of the model piles, model caisson bottom was placed in, closely followed by installing the counterweight plate, caisson frame, and caisson cover, which were assembled using steel and nuts. Hereafter, the model sand is filled to the designed elevation. Additionally, as shown in Fig.8(e), Targets A and B for the displacement were installed on the caisson cover.

4 Numerical model

To investigate the displacement and force of piles in the pile-caisson composite structure, numerical simulations of the model tests were performed using Plaxis 3D software in this study.

4.1 Meshing and boundary conditions

A three-dimensional FE mesh of the pile-caisson composite structure for Schemes A and B is depicted in Fig.9. All the dimensions in the mesh were the same as those in the 1g model tests. The analysis results show that expanding the mesh boundary used in this study did not affect the responses of the pile-caisson composite structure. For the boundary conditions, the horizontal movements of the vertical boundaries were restricted in this study. Furthermore, the embedded pile beam elements in Plaxis 3D software can be conveniently used to simulate a large number of piles, which is a significant advantage.

The model piles used in this study were hollow. However, the embedded pile beam element in Plaxis 3D was adopted to simulate a solid pile, which was modeled as an elastic material. Therefore, Young’s modulus (E_m) of the hollow piles was equivalent to that of the embedded piles in Plaxis 3D. The Young’s modulus (E_n) of the embedded piles can be obtained using Eq. (1):

(1)E_{\text{m}}{I}_{\text{m}}\text{=}{E}_{\text{p}}{I}_{\text{p}},

where E_{\text{m}} represents the Young’s modulus of the hollow piles in the model tests, I_{\text{m}} represents the area moment of inertia of the hollow piles in the model tests, E_{\text{n}} represents the Young’s modulus of the embedded piles, and I_{\text{n}} represents the area moment of inertia of the embedded piles.

Tab.3 lists the parameters of the embedded piles used in the FE analysis.

4.2 Soil parameters

To simulate the stress–strain behavior of soils, the Hardening Soil (HS) model [46] was adopted in Plaxis 3D software, which considers both frictional and cap hardening characteristics and has been applied in numerous studies [47–49]. Tab.4 lists the parameters of the model sand adopted in the FE analysis.

It is worth noting that the magnitudes of the tangential stiffness from oedometer primary loading (E_{\text{oed}}^{\text{ref}}), secant stiffness in standard drained triaxial tests (E_{50}^{\text{ref}}), and loading-unloading stiffness (E_{\text{ur}}^{\text{ref}}) are derived from their empirical relationship with the compression modulus (E_{\text{s}}) [50,51]:

(2)E_{\text{s}}\text{:}{E}_{\text{oed}}^{\text{ref}}\text{:}{E}_{50}^{\text{ref}}\text{:}{E}_{\text{ur}}^{\text{ref}}=\text{1 : 1 : 1 : 5}.

4.3 Procedures of numerical modeling

The procedure of the numerical modeling follows that of the 1g model tests. The details of the numerical modeling procedure are summarized as follows.

1) Set up the initial boundary and initial stress conditions.

2) Activate the bored piles, caisson bottom, caisson frame, counterweight plate, and caisson cover in order (modeled as “wished-in-place”).

3) Apply load with an increment of 310 N (i.e., 0.5 times the designed load) until the foundation displacement increases abruptly.

5 Three-dimensional numerical back-analysis

5.1 Measured and computed displacement

For the convenience of describing the development of the load applied to the pile-caisson composite structure, the ratio between the applied load and the designed load is introduced and given by

(3)R=F_{\text{a}}/F_{\text{d}},

where F_a is the applied load and F_d is the designed load (i.e., 620 N).

Fig.10 and Fig.11 compare the measured and computed displacements of Targets A and B in the model tests for Schemes A and B, respectively. The measured horizontal and vertical displacements were in good agreement with the results of the FE analysis. This slight discrepancy may have been caused by the conservative estimates of the values of E_{\text{oed}}^{\text{ref}}, E_{50}^{\text{ref}}, and E_{\text{ur}}^{\text{ref}}.

5.2 Comparison of response of piles in different positions

In this study, limited by the test equipment, model tests that did not consider the water load were constructed to validate the FE method. However, in engineering practice, the caisson anchorage foundation is usually constructed on a river beach with a high groundwater level. The stability of the pile-caisson composite structure is considerably affected by the groundwater load. To this end, new numerical models that consider the water load were established.

It is noteworthy that the parameters of the soil used in the new numerical models are the same as those listed in Tab.4, unless stated otherwise. The reason for this was to provide a hypothetical soil layer for numerical parameter analyses.

Moreover, empirical formulae [52] can be used to calculate the secant stiffness (E₅₀).

For fill and sand,

(4)E_{50}\text{=}250(N_{\text{SPT}}+15).

The values of E_{50}^{\text{ref}} can be obtained by [52]:

(5)E_{50}^{\text{ref}}\text{=}{E}_{50}/({\sigma }_3^{\prime }/p^{\text{ref}}),

where {\sigma }_3^{\prime } represents the effective confining pressure, p^{\text{ref}} represents the referential pressure, and p^{\text{ref}}\text{=}100\text{kPa}.

Moreover, the most influential parameters are E_{\text{s}}, E_{\text{oed}}^{\text{ref}}, E_{50}^{\text{ref}}, E_{\text{ur}}^{\text{ref}} for the HS model. Therefore, the influence of water level on the soil parameters is not considered in this study.

The parameters of the embedded piles used in the FE analyses are listed in Tab.3.

Fig.12 shows the distributions of the maximum axial force in the pile-caisson composite structure under the designed load for Schemes A and B. According to Fig.12, the maximum axial force of the piles in Scheme A is larger than that in Scheme B, indicating that increasing the number of piles can reduce the axial load borne by the piles in the pile-caisson composite structure. In addition, the caisson may have rotated or have a tendency to rotate when the pile-caisson composite structure is subjected to the designed load, further resulting in a gradual reduction in the maximum axial force of piles from the first row (i.e., Row 1) to the last row (i.e., Row 7 for Schemes A and Row 9 for Scheme B) in the x-direction. Additionally, in the y-direction, the piles are placed symmetrically below the caisson in the pile-caisson composite structure; thus, the maximum axial forces of the piles are almost symmetric.

Fig.13 shows maximum shear forces of piles for Schemes A and B when the pile-caisson composite structure is subjected to the designed load. As a sign convention, a positive shear force induced along the pile shaft faces the x-direction. It is well known that when the pile group is solely applied to lateral force, due to the shadowing effect (see Fig.14), the first row (i.e., Row 1 in Fig.3) bears the maximum shear force. However, Fig.13(a) and Fig.13(c) show that from the first row (i.e., Row 1) to the last row (i.e., Row 7 for Scheme A and Row 9 for Scheme B), the maximum shear force amplitudes in piles first decline before increasing. Besides, as shown in Fig.13(b) and Fig.13(d), in the y-direction, the maximum magnitudes of shear force in piles decrease gradually from Columns 1 to 3 for Schemes A and B. The edge effect (Fig.14) can be used to explain this phenomenon.

The influence of the edge effect on the piles in the pile-caisson composite structure in this study is the same as that on laterally loaded pile groups [53–56]. However, the leading row of piles has the highest resistance in the laterally loaded pile groups, whereas the piles in the leading row (i.e., Row 1) and the last row (i.e., Rows 7 and 9) in the pile-caisson composite structure have the highest resistance of any of the rows in the group. This phenomenon may be attributed to the comprehensive effects of the uneven vertical load borne by the piles ((Fig.12), shadowing effect (Fig.14), and additional bending moment of the piles induced by the applied load. It is noteworthy that the caisson was designed with uneven gravity using the counterweight plate in the model test to counterbalance the tension force of the main cable.

6 Parametric analyses

Based on the results of Scheme B, parametric analyses were performed to explore the effects of groundwater level, burial depth of the pile-caisson composite structure, and soil layers on the response of the pile-caisson composite structure, especially on the pile performance. Additionally, it can be observed in Fig.13(c) and Fig.13(d) that corner pile P₁ (Fig.3) had the largest shear force, whereas the center pile P₂ (Fig.3) had the smallest shear force, as presented in Subsection 5.2. Therefore, two typical piles (P₁ and P₂) were chosen for analysis in this section.

6.1 Effects of groundwater level

To investigate the effect of groundwater level (H) on the displacements of the pile-caisson composite structure and the mechanical behaviors of piles, the considered magnitudes of groundwater level are 0.1, 0.0, –0.1, –0.2, –0.3, and –0.4 m. Note that the elevation of the soil surface is defined as 0.0 m. Besides, the value of the pile soil relative stiffness E_n/E_s in this section is 0.10.

Fig.15 shows the displacements of Target A when the pile-caisson composite structure is subjected to different applied loads at different groundwater levels. As illustrated in Fig.15, the displacements of the pile-caisson composite structure decrease significantly when H decreases from 0.1 to –0.3 m. However, the decrease rate slows down when H decreases from –0.3 to –0.4 m. Fig.16 presents horizontal displacements of piles when the pile-caisson composite structure is subjected to the designed load at different groundwater levels. According to Fig.16, the horizontal displacement values of piles for the pile-caisson composite structure are greater than 0, indicating that the effective pile length of the embedded pile is the entire length of the pile (i.e., 45 cm). Moreover, there is a negligible difference in the horizontal displacements of piles P₁ and P₂ when H decreases from –0.3 to –0.4 m. This might be explained by the fact that the caisson’s impact on the groundwater level is substantially greater than that on the piles in the pile-caisson composite structure. This phenomenon might be because the influence of the groundwater level on the caisson is much larger than that on the piles in the pile-caisson composite structure. As the caisson bottom elevation is –0.295 m, the effect of groundwater level on the displacements of the pile-caisson composite structure is marginal when the groundwater level is smaller than −0.295 m.

Fig.17 shows shear forces of piles when the pile-caisson composite structure is subjected to the designed load at different groundwater levels. It can be observed from Fig.17 that the groundwater level produces minor effects on the shear forces of piles. Consequently, compared with the load borne by piles in the pile-caisson composite structure, the groundwater level exhibits greater influence on the load borne by the caisson.

6.2 Effects of the burial depth of the pile-caisson composite structure

To evaluate the effects of the burial depth of the pile-caisson composite structure (z_s) on the response of the pile-caisson composite structure, five cases with the burial depth of the pile-caisson composite structure ranging from –0.1 to 0.1 m at an interval of 0.05 m were considered, which was achieved by changing the height of the model sand while keeping the elevation of the pile-caisson composite structure being constant in the five cases. It is noteworthy that the burial depth of the pile-caisson composite structure is defined as the height from the sand surface to the caisson cover. As a sign convention, in this study, a positive burial depth means that the soil surface is above the caisson cover. The pile soil relative stiffness E_p/E_s in this section was 0.10.

Fig.18 shows the displacements of Target A when the pile-caisson composite structure is subjected to different applied loads with different burial depths. As illustrated in Fig.18, increasing the burial depth can effectively reduce the displacements of the pile-caisson composite structure. Moreover, the displacements decrease significantly when z_s was increased from 0.0 to 0.05 m, indicating that burying the pile-caisson composite structure completely in the soil is beneficial to limiting its displacement. In addition, the horizontal displacement values of piles for the pile-caisson composite structure are greater than 0, indicating that the effective pile length of the embedded pile is the entire length of the pile (i.e., 45 cm).

Fig.19 shows the horizontal displacements of piles when the pile-caisson composite structure is subjected to the designed load with different burial depths. As expected, horizontal displacements of piles reduce significantly with the increase of the burial depth.

In addition, as depicted in Fig.20, the burial depth of the pile-caisson composite structure has a significant impact on the shear forces of the piles, especially when z_s ≤ 0.0 m. This phenomenon is attributed to the fact that the stability of the pile-caisson composite structure is heavily reliant on the caisson’s gravity and the soil resistance offered by the surrounding soil. Therefore, decreasing the burial depth reduces the soil resistance of the caisson when the soil surface is below the caisson cover. Consequently, the lateral load borne by the piles increased.

6.3 Effects of soil layers

The distribution of soil layers in engineering practice is usually an alternate layer of clay and sand [14–16,57]. Therefore, we conducted an exploratory study on the behavior of the pile-caisson composite structure in different soil layers at the model scale.

Four arrangements of soil layers were considered in this section, as depicted in Fig.21. In addition, Tab.5 lists the parameters of the two typical soil layers selected from the construction site of the north anchorage of the NXR Bridge [11]. Therefore, the value of the pile soil relative stiffness E_p/E_s for clay was 0.277, whereas it was 0.657 for sand in this section.

Fig.22 shows the displacements of Target A when the pile-caisson composite structure is subjected to different applied loads in different soil layers. According to Fig.22, the sand layer can significantly improve the stability of the pile-caisson composite structure.

Fig.23 and Fig.24 show the horizontal displacements and shear forces of the piles, respectively, when the pile-caisson composite structure is subjected to different applied loads in different soil layers. As shown in Fig.23, the horizontal displacement values of piles for the pile-caisson composite structure are greater than 0, indicating that the effective pile length of the embedded pile is the entire length of the pile (i.e., 45 cm). In addition, the horizontal displacements and shear forces of the piles in clay are much larger than those in sand, indicating that sand can provide more lateral resistance than clay. In other words, stiffer soil can considerably reduce the deformation and internal forces of piles. Consequently, the pile-caisson composite structure may be more suitable for construction in soils with high strength.

7 Discussion of application prospects

A novel anchorage foundation (i.e., the pile-caisson composite structure) for long-span suspension bridges was proposed to reduce the construction period and costs and achieve low carbon energy and environmental protection. Furthermore, the water load, burial depth of the pile-caisson composite structure, and distribution of soil layers can significantly influence the stability of the pile-caisson composite structure. The numerical analyses indicate that decreasing the groundwater level, increasing the burial depth of the pile-caisson composite structure, and increasing the soil stiffness can help to reduce the displacements and increase the stability of the pile-caisson composite structure. Consequently, in practical engineering, it is preferable to construct a pile-caisson composite structure in a stratum with a lower groundwater level. In addition, on the premise that the surrounding soil around the caisson has a higher strength, the burial depth of the pile anchorage composite structure should be increased as much as possible.

It is known that caisson foundations have the advantage of good stability and can withstand large horizontal and vertical loads. However, a caisson foundation is suitable for construction in shallow soil layers. Moreover, it is difficult for the caisson to be embedded in the rock. In contrast, the construction technology for bored piles is mature and widely applied to different types of strata.

In addition, bored piles have the characteristics of lower cost and shorter construction period. Therefore, combining the advantages of caissons and bored piles may reduce the cost of materials and construction.

8 Conclusions

The conclusions that can be drawn from this study are summarized as follows.

1) When the pile-caisson composite structure is subjected to the designed load, the corner piles in the leading and last rows bear the largest lateral loads in the pile group. Therefore, to ensure the stability of the pile-caisson composite structure, reinforcement is required for these corner piles.

2) The influence of the groundwater level on the caisson is much larger than that on the piles in the pile-caisson composite structure. Decreasing the groundwater level considerably improves the stability of the caisson and reduces the displacement of the pile-caisson composite structure.

3) In the pile-caisson composite structure, increasing the burial depth can significantly increase the lateral load that the caisson bears and decrease the lateral load borne by the piles. Moreover, as the burial depth increased, the displacements of the pile-caisson composite structure decreased effectively.

4) The distribution of soil layers exhibits significant influence on the stability of the pile-caisson composite structure, especially the soil layer around the caisson. The better the properties of the soil around the caisson, the smaller the displacement of the pile-caisson composite structure.

5) The values of the horizontal displacements of the piles for the pile-caisson composite structure are greater than 0, indicating that the effective pile length of the embedded pile is the entire length of the pile (i.e., 45 cm). Consequently, the piles in the pile-caisson composite structure can sufficiently mobilize the resistance of the surrounding soil to counteract the eccentric inclined load from the main cable.

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