Influencing factors and control measures of excavation on adjacent bridge foundation based on analytic hierarchy process and finite element method

Abstract

Many uncertain factors in the excavation process may lead to excessive lateral displacement or over-limited internal force of the piles, as well as inordinate settlement of soil surrounding the existing bridge foundation. Safety control is pivotal to ensuring the safety of adjacent structures. In this paper, an innovative method is proposed that combines an analytic hierarchy process (AHP) with a finite element method (FEM) to reveal the potential impact risk of uncertain factors on the surrounding environment. The AHP was adopted to determine key influencing factors based on the weight of each influencing factor. The FEM was used to quantify the impact of the key influencing factors on the surrounding environment. In terms of the AHP, the index system of uncertain factors was established based on an engineering investigation. A matrix comparing the lower index layer to the upper index layer, and the weight of each influencing factor, were calculated. It was found that the excavation depth and the distance between the foundation pit and the bridge foundation were fundamental factors. For the FEM, the FE baseline model was calibrated based on the case of no bridge surrounding the foundation pit. The consistency between the monitoring data and the numerical simulation data for a ground settlement was analyzed. FE simulations were then conducted to quantitatively analyze the degree of influence of the key influencing factors on the bridge foundation. Furthermore, the lateral displacement of the bridge pile foundation, the internal force of the piles, and the settlement of the soil surrounding the pile foundation were emphatically analyzed. The most hazardous construction condition was also determined. Finally, two safety control measures for increasing the numbers of support levels and the rooted depths of the enclosure structure were suggested. A novel method for combining AHP with FEM can be used to determine the key influencing aspects among many uncertain factors during a construction, which can provide some beneficial references for engineering design and construction.

Graphical abstract

Keywords

deep foundation pit excavation / adjacent bridge foundation / influencing factors / analytic hierarchy process / finite element

Introduction

China has become the largest user of commercial high-speed rail. The velocity of high-speed trains has increased drastically from 200 to 350 km/h, which has been a milestone for China’s development. The number of high-speed railways used in bridge projects over seawaters, lakes, and rivers has increased with the implementation of the national “Belt and Road Initiatives” strategy. The adjacent parallel rails of operation and construction lines are booming in coastal areas. The distance between an operation line and a construction line can reach 2.5–7.5 m in engineering practice. Construction lines often involve deep foundation pit excavations, retaining the construction and internal support design of the structure, which are very complex and important in a system engineering project. A deep foundation pit construction may cause a large deformation of the foundation, an insufficient bearing capacity of pile foundation, and an excessive ground settlement surrounding the operation line, which will inevitably affect the safety of the driving train [1,2].

The coastal areas of China have widely distributed soft clay, which has the poor engineering characteristics of high moisture content, a large void ratio, high compressibility, low permeability and strength, rheological properties and structural characteristics [3]. The thickness of the clay layer can reach approximately 7–15 m, which demonstrates the complexity of the geological conditions of engineering projects in such areas [4,5]. Moreover, engineering practice shows that as the foundation pit excavation depth deepens, the excavation environment becomes more complicated and changeable with the development of infrastructure construction [6,7]. When a foundation pit is excavated, the stress of soil is altered, resulting in an excessive lateral displacement of the enclosure structure, an overlarge settlement at the periphery of the foundation pit, and an uplift of the foundation pit bottom. An excessive foundation pit displacement will lead to an over-limit deformation of an adjacent bridge foundation and even a failure of the bridge foundation.

Originally, most scholars systematically studied single foundation pits without considering the surrounding complex construction environment [8–12]. As early as the 1920s, Terzaghi and Peck were the first to propose the concept of deep foundation pit engineering. During the 1940s, the total stress method was proposed to predict the supporting force and excavation stability of retaining structures. Analyzing a large number of monitoring data on the foundation pit in Singapore, Liu and Hou [13] classified the deformation types of foundation pits into triangular and parabolic shapes and put forward an empirical formula for estimating the ground settlement of soil mass behind the retaining wall. Hsieh et al. [14,15] developed out a method for predicting the deformation of a retaining wall during the foundation pit excavation based on the deformation behavior of continuous beams. Coupled with a finite element (FE) simulation, Ahmad et al. [16] analyzed the contribution of the excavation length and the excavation sequence to a retaining wall deformation. Zhuang et al. [17] studied the problem of hydraulic fracturing using a method of fracture mechanics and multi-field coupling and analyzed the propagation law of rock cracking during excavation. In addition, the support structure was established using an FE, and the reduced modulus action (RMA) parameter was underlined by Wang et al. [18] to analyze the stability of the foundation pit.

However, with an unprecedented development of urbanization, foundation pits have often been excavated in infrastructure intensive zones, where the surrounding environment is complex, and many uncertain factors have affected such pits. Therefore, most scholars have been concerned with the stimulus from deep excavations on the adjacent bridge pile foundations [19–21]. For example, Kok and Huat [22] used a two-dimensional FE simulation to obtain the bending moment of an adjacent pile foundation. Combined with a numerical simulation and field testing, Wang et al. [23] used a finite difference method (FDM) to analyze the lateral displacement of a pile foundation, and demonstrated that adjacent pile foundation showed a larger negative friction resistance and greater pile foundation settlement. Zhang et al. [24] studied the two-stage analysis method to deduce the analytical solution matrix expression and FE iterative format, which can consider the lateral displacement response of the neighboring pile foundation during a deep exaction. Combined with the FE results, Zheng et al. [25] applied the lateral displacement development of the back row and retaining piles, and found that the deformation curve shapes for both were similar, which also demonstrated that a deep excavation resulted in an excessive lateral displacement at the peripheral pit.

In fact, there have been many uncertain factors affecting the safety of adjacent bridge foundations during deep excavation, i.e., soil properties, depth of the enclosure structure, stiffness of the internal support system, foundation pit size, foundation pit stability, and surrounding environment of the foundation pit [26,27]. However, as the main culprit for the failure of a surrounding bridge foundation, the key influencing factors are difficult to be determined among the many different factors. Therefore, determining the key influencing factors among complex uncertain factors is crucial to investigating the deformation of the adjacent bridge foundation affected by the deep foundation pit excavation. A numerical simulation is an important approach to influencing a factor analysis applied in a quantitative study. Tong et al. put forward the pore water pressure in the artesian aquifer of silty soil layers, which was regarded as one of the main influencing factors based on an FE simulation [28]. Li et al. [29] employed an FEM to comparatively study the different construction methods for deep excavations, and determined that a divided alternate excavation method (DAEM) is the optimal construction method. Through an analysis, it was found that the number of influencing factors subjectively determined through the numerical simulation method was generally less than four. In addition, the FEM requires a significant calculation time and increases the design cost for more types of influencing factors. Furthermore, some experts used an AHP to establish the index system of influencing factors and analyzed the weight of influencing factors in the field of geotechnical engineering management for decision making. For example, a novel AHP model was established by Peng et al. [30] to evaluate the risk of a tunnel water inrush. It was proved that the evaluation results of a water-rich fault tunnel were consistent with the actual situation, and the reliability of the evaluation model was verified. Kuo and Chao [31] suggested a general evaluation framework of a hierarchical structure composed of four groups of 21 factors. They utilized the AHP to generate weighting factors and ratings for pile installation methods.

At present, few experts have applied the combined AHP with the FEM to a deep foundation pit engineering design, and they have generally only been carried out separately. The AHP can effectively deal with a huge number of influencing factors for determining the key influencing factors. The FE method can quantitatively analyze the mechanical behavior of the pile foundation. Therefore, a novel method for combining the AHP with the FEM is proposed in this study. Based on the advantages of both methods, the AHP was employed to determine the main factors affecting the deformation and internal force of the bridge foundation around the deep foundation pit. The FEM was then adopted as a case study to quantitatively simulate the neighboring bridge foundation affected by a deep excavation in terms of the key factors. In addition, compared with monitoring data and the numerical simulation data, a typical foundation pit case was selected to illustrate the correctness of the numerical model. Finally, according to the construction contract, two safety control measures were put forward as achieving the most advantageous construction conditions. The research results can provide guidelines for a similar engineering construction and design.

Analysis of influencing factors using analytical hierarchy process (AHP)

The analytic hierarchy process (AHP) is a semi-quantitative method. There was no inconsistency in the decision-making process. The weight was determined by a pairwise relative comparison [32]. It was characterized by organizing all types of factors in complex problems by dividing them into interrelated and orderly levels, and quantitatively describing the importance of the comparison between the two elements of the first level. Then, the weight reflecting the relative importance ranking of each level element was calculated using a mathematical method, and the relative weight of each element was calculated and sorted according to the total ranking among different levels. The AHP consists of six steps: 1) break down target into the influencing component factors, 2) arrange all influencing component factors in a hierarchic order to form the AHP index system, 3) assign the expert score for all factors, 4) establish a comparison matrix, 5) calculate the normalized principal eigenvector and give the weight of each factor, and 6) carry out a consistency check.

The AHP index system was subdivided into the (A) target layer, (B) criterion layer, and (C) index layer. Clearly, the target layer (A) can reflect the research goal, a deformation of the bridge foundation around a deep foundation pit is chosen. All indexes in the criterion layer should be consistent with the request of the target layer. According to the construction conditions, the factors affecting the deformation of the bridge foundation around a deep foundation pit can be classified into six categories for the criterion layer: the (B1) groundwater and soil engineering characteristics, (B2) retaining structure system, (B3) internal support system, and the (B4) size, (B5) stability, and (B6) surrounding environment of the foundation pit.

The behavior of the soil layer was clearly an important link to determine the accuracy of numerical calculation results for the deformation of bridge foundation around the deep foundation pit. The factors affecting the soil properties included the (C1) groundwater, (C2) soil density, (C3) internal friction angle, and (C4) cohesive force.

The thickness and type of retaining structure will directly affect its stiffness. The deformation and displacement of the retaining structure were affected by the active earth pressure, and therefore the settlement of the soil around the deep excavation pit and the deformation of the bridge foundation were affected. The soil penetration ratio of the retaining structure will affect the influence of a passive retaining structure, the deformation and stability of the supporting structure, the settlement of the soil around the deep foundation pit and the deformation of the bridge foundation. Therefore, the (C5) stiffness of the retaining structure, the (C6) enclosure depth rooted in soil, and (C7) the retaining structure style were considered under (B2) the retaining structure system.

The stiffness and plane layout of the internal support system will affect the internal force and deformation of the retaining structure, and the internal support number and elevation will affect the excavation sequence, the soil settlement surrounding the deep foundation pit, and the bridge foundation deformation. The (C8) stiffness of the internal support, the (C9) numbers of the internal support, the (C10) elevation location, and the (C11) layout were taken into account under the (B3) internal support system.

The foundation pit size included the plane size, the depth, and shape of the deep foundation pit excavation. The active earth pressure, retaining structure and internal support stiffness, soil settlement surrounding the deep excavation, and the bridge foundation deformation were directly affected by the foundation pit size. Therefore, the (C12) influence of the plane size, (C13) excavation depth, and (C14) shape of the pit were considered under the (B4) foundation pit size.

When the foundation pit failed, the soil settlement around the deep foundation pit and the bridge foundation deformation were large. It was necessary to ensure that the foundation pit was not destroyed by instability during the deep excavation. The (C15) effects of the integral stability, (C16) anti-uplift stability, (C17) stability against tilting, (C18) anti-slip stability, and (C19) seepage resistance stability were considered.

The (C20) influence of distance between the foundation pit and bridge foundation, and (C21) overloading on the ground, were considered in the (B6) surrounding environment of the foundation pit. The index system determined by AHP was summarized in Fig. 1.

Through the analysis, the comparison matrix satisfied the consistency test. The weight of each criterion layer to the target layer was calculated, which can determine the key influencing factor in the index layer. A total of 21 indexes were sorted according to the degree of their impact on the target layer. The total ranking matrix is given in Table 1.

Based on the total ranking, the most important factor was the depth of the foundation pit, followed by the distance between the foundation pit and the bridge foundation. The weights of the two key influencing factors were 0.224 and 0.227, respectively. Therefore, combined with the case study, this paper emphasizes the two aforementioned key factors in Section 4. Before the numerical simulation, the correctness of the numerical model should be verified in Section 3.

Field monitoring and FE model verification

Overview of the viaduct project

The viaduct project was situated in the northeast of Fujian Province, China, and on the northwest coast of Taiwan Strait, China. It is a vital place connecting two economically developed regions of the Yangtze River Delta and the Pearl River Delta, as shown in Fig. 2. The starting and ending mileage of the viaduct project was 18746.92 m in total with 550 piers and 549 spans. The newly built project was a viaduct project in the parallel section of the existing railway. The nearest distance between the twin line (the operation and construction lines) was approximately 2.5 m. The deep excavation depth was 5–9 m.

The construction of newly built viaducts will face the following challenges.

1) The engineering geological conditions were complex, and the thickness of the soft clay deposit was large. Once the excavation is unloaded, it may cause instability to the bridge foundation.

2) To guarantee a normal operation of the high-speed train, the trainload interfered with the construction line, and the mutual interference had consequences on the challenge for the foundation pit construction.

3) The close parallel distance between the construction line (newly built viaduct project) and the operation line (the existing high-speed train railway) led to a narrow construction site, and the thorny problem of the entrance and transfer of large-scale machinery was prominent.

Owing to the importance of the project and the complexity of the surrounding environment, the project had yet to be constructed when the distance between the foundation pit and pile foundation was less than 10 m. Therefore, it was urgent to analyze the feasibility of the construction scheme based on an FE simulation. In addition, the construction contract stipulated that the limitation of the lateral displacement of the bridge pile foundation was 12 mm, the upper bound of the soil settlement at the peripheral pile should not exceed 20 mm, and the maximum differential settlement should not exceed 8 mm. Moreover, the internal force of the bridge pile should be recalculated and verified.

Field monitoring and monitoring result analysis

The foundation pit, which is more than 10 m away from the bridge foundation, will be constructed first in the engineering practice. To calibrate the validity of the model, we chose a representative foundation pit 30 m away from bridge foundation. The influence of the excavation on the surrounding bridge foundation can be ignored.

The dimensional size of the foundation pit was 12.5 m × 10 m × 6 m (length × width × depth), as plotted in Fig. 3. An FSB-IV steel sheet pile was used as the enclosure structure. The section size of steel sheet pile was 400 mm × 170 mm × 15.5 mm (width × height × thickness), rooted 12 m under the ground. The internal support system was composed of a waist girder (H× W = 400 mm × 400 mm), corner struts (φ426 mm × 10 mm), and middle struts (φ426 mm × 10 mm).

The construction of the foundation pit was mainly divided into five steps. 1) Steel sheet pile construction: The single steel sheet pile was assembled as a whole, rooted underground to the target depth using a vibratory driver (construction time of 10 d). 2) Dewatering and excavation: The water elevation was reduced to 0.5–1.0 m below the excavation surface, and the excavation was then carried out to a depth of 0.5 m below the corresponding support level (construction time of 10 d). 3) Strut connection: Combined with the design requirement, the middle and corner struts were set and connected at the desired depth (construction time of 10 d). 4) Repeating Steps 2 and 3: Steps 2 and 3 were duplicated once the excavation depth achieved the specified depth. It would take 20 d to excavate to desired depth owing to the rainfall weather. 5) Casting the bottom concrete, caps, and piers (construction time of 15 d).

According to the results proposed by Wang et al. [18], the steel sheet pile had inherent characteristics of the RMA, and the lateral displacement of the pile head was the largest. Four monitoring points of #1–4 were set in the middle part of steel sheet pile head. The instrument of the electronic total station (ETS) was adapted to measure the lateral displacement of the steel sheet pile. The lateral displacement observation should be conducted every 3 d according to the construction contract.

The normal direction outside the foundation pit was specified as positive for the lateral displacement of the steel sheet pile. The monitoring results showed that the steel sheet pile inclined inward at the foundation pit because the monitoring data of the lateral displacement were all negative. The deformation of a steel sheet pile under different construction steps is depicted in Fig. 4. Figure 4 showed that the lateral displacement increased with the time and construction steps, which was basically consistent for four monitoring points. When the construction time approached the 60th d, the maximum lateral displacements of #1–4 could reach 43.70, 41.66, 44.46, and 44.21 mm, respectively. Clearly, the steel sheet piles suffered from a positive earth pressure. The steel sheet pile can be equivalent to a continuous beam for a geotechnical design. According to Eq. (1), the positive earth pressure of the steel sheet pile increased gradually with the excavation depth. This demonstrated that the positive earth pressure was the main reason for the increase in the lateral displacement of the steel sheet pile.

(1)p_{\mathrm{a}}=\gamma z{\tan }^{\mathrm{2}}(45°-{\displaystyle \frac{\phi }{\mathrm{2}}})-\mathrm{2}c\tan \left(45°-{\displaystyle \frac{\phi }{\mathrm{2}}}\right),

where p_a was the positive earth pressure, and g, \varphi, and c were the unit weight, internal friction angle, and cohesion, respectively, which belonged to the soil property.

FE model baseline and verification

The numerical simulation provided a new engine for the engineering design and construction. The key factors determined by the AHP can be considered to evaluate and predict the engineering risks quantitatively. To illustrate the correctness of the FE model, this part focused on the comparative analysis of the differences between the numerical predicted results and the measured results. A commercial FE software package, Plaxis 3D, developed at Delft University of Technology in the Netherlands, was employed to develop foundation pit models as a model baseline.

Figure 5 shows that the size of the model was 90 m × 70 m × 25.19 m (length × width × height), and a tetrahedral element with 10 nodes was selected for the three-dimensional model. The free mesh technique was adopted, the element distribution was the refined denseness, and the foundation considered by the project was partially encrypted. The maximum element size was 11.22 m, and the minimum element size was 0.25 m. There are 25142 elements and 38382 nodes in the entire model. The displacement boundary was fixed at the bottom (Z_min) but free at the top (Z_max). The displacement boundaries at X_min, X_max, Y_min, and Y_max were fixed in the horizontal coordinate but free in the vertical coordinate. The FE analysis employed a fully implicit time-marching scheme and allowed the large-strain consolidation to be evaluated. The calculation of large-strain deformation was based on a Lagrangian formulation that updated the FE mesh and the stiffness matrix at the beginning of each iteration [33].

The constitutive model of “hardening-soil” (HS) was adopted, which can simulate the irreversible compressive deformation of soil under the main compression condition [34]. The stress dependence of soil stiffness can be considered, and belongs to the second-order hyperbolic elastic-plastic constitutive model. The elastic constitutive model was used for the internal support, pile, and enclosure structure. The point-to-point bolt element was employed to imitate the corner struts and middle struts. The “plate” element was selected to simulate the enclosure. The detailed layout of the foundation pit and the bridge foundation are shown in Fig. 5.

There were four soil layers below the ground where the foundation pit was located. The parameters of each soil layer were selected according to the engineering geological investigation report. The relevant physical parameters and constitutive parameters were determined as shown in Table 2.

A steel sheet pile (model no., FSB-IV) was used for the enclosure structure. The material properties of the enclosure structure and internal bracing system were determined based on the Chinese Code for the Design of Concrete Structures (GB50010-2010) (Ministry of Housing and Urban-Rural Construction of the People’s Republic of China) in Table 3 [35].

Figure 6 shows that the soil settlement around the foundation pit increases with the excavation depth. The settlement surrounding the steel sheet pile is greater than that of the other zones, and the predicted value is in good agreement with the monitoring data. To further explain the correctness of the model, the averaged monitoring data of the lateral displacement at four monitoring points and the FE results are compared and analyzed. Figure 7 shows that when the excavation depth is 3 m, the average measured value is 28.75 mm and the predicted value is 30.63 mm. The relative error is 6.54%, which is the largest error in this situation. Whereas the excavation depth is up to 6 m, the measured value is 43.51 mm, the predicted value is 44.24 mm, and the relative error is 1.68%. It was found that the predicted value is consistent with the measured value, which demonstrates the validity of the model.

Numerical analysis of key influencing factors

Establishment of numerical model and simulation scheme

The excavation depth and distance between the foundation pit and the bridge foundation had the greatest impact on the behaviors of the bridge foundation around the foundation pit based on an analysis of the AHP. Nine engineering construction conditions were simulated and analyzed, and are summarized in Table 4. According to the field construction, the excavation depth was 5.0, 7.5, and 9.0 m, and the distance between the foundation pit and the edge of the cap was 2.5, 5.0, and 7.5 m, respectively.

A pile was used as the existing bridge foundation, and the width and length of the cap were 12 and 20 m, respectively. The length of the pile was 14 m, which belonged to the rock-socketed pile, and the depth of the embedded granite was 3 m. A harmonic load with an amplitude of 1 kPa and a vibration frequency of 10 Hz was exploited to simulate the high-speed railway load. In addition, caps of the bridge foundation were subjected to a pressure of 20 kPa when considering the weight of the concrete. The plane size of the foundation pit was 17.8 m × 12.5 m (length × width), and the rooted depth of the enclosure was 10 m.

The size of the model was 140 m × 90 m × 25.19 m (length × width × height), and the constitutive model and boundary condition were consistent with the model baseline. The beam element was chosen to imitate the bridge pile, reflecting the axial force and bending moment of the bridge pile, as shown in Fig. 8.

Analysis of numerical results for the key influencing factors

The influence mechanism of the foundation pit on the surrounding pile foundation, lateral displacement of the pile foundation, the internal force of the pile foundation, and the settlement of the soil around the pile foundation were systematically researched for the key influencing factors described in this section.

Influence mechanism of foundation pit on surrounding pile foundation

The excavation of the foundation pit on one side of pile foundation is equivalent to the unloading, which will lead to an uneven soil settlement around the foundation pit within a certain range. The uneven settlement will further have an impact on the pile foundation to bear a large additional stress, and then cause the excessive deformation or failure of the pile foundation. This is a crucial challenge for a geotechnical design. To solve the problem, Ding and Wang proposed the concept of a zone of influence [36]. In combination with the research results and construction contract of the project, the zone with a ground settlement of more than 10 mm is defined as the zone of influence.

Figure 9 shows that the larger distance between the foundation pit and the pile foundation will lead to a smaller zone of influence. For example, when the excavation depth is 9.0 m, the zone of influence has a range of 9.34, 9.19, and 9.03 m when the corresponding distance between the pit and bridge foundation is 2.5, 5.0, and 7.5 m, respectively. Moreover, the larger the excavation depth is, the larger the deformation of soil around the foundation pit, which shows a larger zone of influence. When the distance is 2.5 m, the corresponding range of the zone of influence is 7.03, 8.18, and 9.34 m for an excavation depth of 5.0, 7.5, and 9.0 m, respectively.

Lateral displacement of pile foundation

As Fig. 10 shows, the pile foundation performs a rotational movement for distances of 2.5 and 5.0 m and a bending deformation for a distance of 7.5 m. The lateral displacement at the pile top is the largest, whereas the lateral displacement at the pile bottom is basically zero. In addition, the pile tends to incline toward the foundation pit. The lateral displacement of the pile increases gradually with the excavation depth. When the distance between the foundation pit and bridge foundation is 2.5 m and the excavation depth is 9.0, 7.5, and 5.0 m, the maximum lateral displacement at the pile top is 19.2, 15.12, and 10.56 mm (less than 12 mm), respectively. Clearly, the excavation depth is equal to 5 m, and the lateral displacement at the pile top can meet the requirement of the construction contract. When the distance is from 5 to 7.5 m, the lateral displacement at the pile top decreases from 11.34 to 4.26 mm.

As the reason why the lateral displacement of the bridge foundation is larger, the uneven deformation of soil outside the foundation pit is produced during the excavation. The stress of the soil surrounding the bridge foundation changes, some additional stress is generated inside the bridge pile with the increase in the excavation depth. In addition, once the lateral displacement of the bridge foundation occurs, the lateral displacement of the pile head will be slightly larger than that of the other parts. Moreover, with the increasing development of the lateral displacement of soil around the piles, the additional lateral pressure on the bridge piles increases continuously, and this additional stress will also cause an unbalanced lateral force acting on the piles. This will increase the horizontal stress of the bridge foundation, and the unbalanced lateral force may also cause a large lateral displacement of the bridge foundation.

When the excavation depth is 9.0 m, the lateral displacement of the pile is the largest, which tends to result in engineering accidents. Therefore, an excavation depth of 9.0 m is selected to illustrate the influence of the distance on the lateral displacement of the pile. Figure 10 also shows that the closer distance is, the larger the lateral displacement of the pile. When the distance between the foundation pit and the bridge foundation is 2.5 m, the largest lateral displacement of the pile top is 19.56 mm. By contrast, when the distance is 7.5 m, the maximum lateral displacement of the pile top equals 4.56 mm. Obviously, the difference between the lateral displacement reaches 15 mm for a distance of 2.5 and 7.5 m. When the distance is 5.0 m, the extreme lateral displacement of the pile top remains 11.82 mm, which meets the engineering requirement of the lateral displacement (less than 12 mm).

Internal force of pile foundation

Because of the unloading of the soil after the pit excavation, the stress of the soil in the pit is released, and the soil around the pit will move toward the foundation. The soil deformation has a diffusion and transmission effect, which will cause a deformation of the soil near the end-bearing pile at the lower part of the bridge pier. The movement and deformation of the stratum will have an additional effect on the pile and cap. Therefore, the internal force of the pile foundation must be carefully considered during a deep excavation. The internal forces of the bridge pile foundation used to prevent the pile from breaking owing to the additional axial force, shear, or bending moment are summarized in Table 5. As Table 5 demonstrates, the greater excavation depth contributes to the greater internal force of the pile. When the distance between the foundation pit and the bridge foundation is 2.5 m and the excavation depth is 9.0 m, compared with the excavation depth of 5 m, the axial force is increased by 8.69%, the positive shear force is amplified by about twofold, the negative shear force is enlarged by 19.54%, and the positive and negative bending moment are augmented by 65.13% and 10.59%, respectively.

Similarly, Table 5 also shows that the smaller the distance between the foundation pit and bridge foundation, the larger the internal force of the pile foundation. When the excavation depth is 9.0 m, the distance is 2.5 m, the axial force is increased by 20.81%, the shear force is augmented 2.31-fold, and the bending moment is enlarged 2.26 times that of the internal force for a distance of 7.5 m. As mentioned above, the closer the distance is from the foundation pit, the larger the deformation of the soil around the pile and the greater the additional stress of the bridge pile foundation produced. Ding et al. [36] also determined that there is a safe distance for the influence of the foundation pit excavation on the surrounding bridge foundation. The additional stress should be considered during an excavation within a distance of 10 m between the foundation pit and the bridge pile foundation. Therefore, engineers should calculate the internal force of piles during the process of construction and design; otherwise, it will easily lead to the problem of an insufficient bearing capacity of the pile foundation.

Soil settlement surrounding the pile foundation

In this study, the section coordinates (−17.5, 4, 0), (37.5, 4, 0) are selected to illustrate the soil settlement surrounding the pile foundation. The section coordinate is shown in Fig. 8. The relationship between the settlement and the location of the bridge foundation is illustrated in Fig. 11. It was found that the settlement increases gradually from left to right and increases gradually with the excavation depth. The maximum settlement around the foundation pit can reach 24.9 and 22.1 mm, consistent with the excavation depth of 9.0 and 7.5 m, which cannot fulfill a request of the construction contract. By contrast, when the excavation depth is 5.0 m, the soil settlement around the pile complies with the requirements of the construction contract.

Figure 11 also shows that a closer distance between the two lines tends to cause a larger soil settlement surrounding the pile foundation. When the distance is 2.5 m, the largest soil settlement at the peripheral foundation pit can reach 24.9 mm, and the differential settlement is 14.4 mm. By contrast, when the distance is 7.5 m, the settlement of soil around the pile foundation is 18.2 mm, and the differential settlement is 10 mm. Although the closest distance reaches up to 2.5 m, the demand for engineering construction is not satisfied. Therefore, soil settlement around the foundation pit and pile foundation should be strengthened in engineering practice.

Safety control measures

When the excavation depth is 9.0 m and the distance between the foundation pit and the bridge foundation is 2.5 m, the lateral displacement of the pile and settlement of soil around the pile foundation cannot satisfy the requirements of the construction contract, and the internal force becomes larger for the viaduct project. Therefore, this study considered the control measures under this condition, and two safety measures are put forward based on engineering practice, i.e., increasing the insertion depth of the enclosure structure and increasing the support level numbers.

The embedding depth of the enclosure structure will affect the deformation of the foundation pit, which will bring about a settlement and deformation of the surrounding soil. Combined with the actual needs of the project, the two selected depths are 12 and 15 m. More support level numbers can reduce the deformation of the enclosure structure. Numbers of internal support levels of four, five, and six were selected to illustrate the influence of the support level number on the construction safety. Therefore, six simulated conditions are compared and analyzed in this section. The optimal construction scheme is selected to provide a reference for engineering construction.

Increase the number of support levels

Figure 12 demonstrates that increasing the support level numbers can effectively reduce the lateral displacement of the piles. When the number of support levels increases to four, the maximum lateral displacement of the piles is 2.68 mm. However, when the number of support levels is five or six, the lateral displacement of the pile is within the permission scope, and is 1.9 and 1.81 mm, respectively. Compared with three support levels, the maximum lateral displacement of the pile decreases by 41.7% and 44.5%, respectively. This suggests that the support level number should be increased to five or six during the concrete construction process.

Table 6 shows that the internal force decreases with the increase in the number of support levels. Compared with three support levels, the maximum difference of bending moment is 546.24 kN·m for five support levels. Although when the number of support levels is five or six, the difference in lateral displacement is small, and there are significant differences in the internal forces of the piles. Therefore, the bearing capacity of piles with five support levels should be emphatically analyzed in the engineering design.

Figure 13 shows that when five or six support levels are used, the soil settlement around the pile can meet the requirements of the construction contract. When five or six support levels are applied, the maximum soil settlement around the pile is 15.08 or 14.69 mm, and the differential settlement is 8.52 or 7.80 mm, respectively.

Rooted depth of enclosure structure

Figure 14 shows that the increase of pile lateral displacement can be well restrained when the rooted depth of the retaining structure is 15 m. When the rooted depth is 15 m, the maximum lateral displacement of the pile is 11.16 mm, which is less than 12 mm and within the safety range. Compared with the insertion depth of 9.0 m, the settlement displacement of the pile body is decreased by 42.9%. When the insertion depth of the enclosure is 12 m, the maximum lateral displacement of the pile is 17.16 mm. It has been suggested that the enclosure structure should be located approximately 6 m from the bottom of the foundation pit in engineering practice.

Table 7 demonstrates that the internal force of the pile decreases with the increase in the rooted depth of the enclosure structure. Compared with an enclosure rooted depth of 10 m, when the rooted depth is 15 m, the maximum axial force and shear force decrease by 57.43 and 59.28 kN, respectively. Although the bending moment decreases, the change is not obvious. This shows that the increase in the embedding depth of the retaining structure cannot effectively reduce the pile bending moment.

Figure 15 shows that increasing the rooted depth of the retaining structure can reduce the soil settlement around the bridge foundation. When the rooted depth is less than 12 m, the settlement is more than 20 mm. When the rooted depth is 15 m, the maximum settlement is 15.86 mm, and the differential settlement is 9.17 mm.

Based on a comparative analysis of the two simulated plans, adding the number of internal supports is more conducive to ensure the safe operation of the railway and the safe engineering construction. In terms of the current construction technology, the common forms of internal support include a corner brace, ring beam support, and truss support. Adding an internal support can increase the relative stiffness of the supporting structure, which helps the retaining wall bear more uniform active earth pressure and reduce the deformation of the surrounding soil.

Conclusions

An innovative approach using an AHP combined with an FEM is proposed in this paper. This method includes two aspects: The AHP method is used to find the key factors among the many uncertain influencing factors and the FEM is employed to simulate the different construction conditions for a viaduct project based on the key influencing factors. Safety control measures are provided for viaduct projects that have not yet been constructed. The following conclusions are obtained.

1) The most important factor is the excavation depth, followed by the distance between the foundation pit and the bridge foundation. The weights of the two key influencing factors are 0.224 and 0.227, respectively.

2) The lateral displacement of a bridge pile foundation, the internal force of the piles, and the settlement of the surrounding soil are emphatically analyzed using the FEM.

A greater excavation depth of the foundation pit leads to larger lateral displacement, greater internal force of the piles, and a settlement of the surrounding soil of bridge pile foundation. Compared with an excavation depth of 5 m, the maximum lateral displacement of the pile is increased by 43.2%. The maximum internal shear force is enlarged by about twofold. The maximum settlement around the pile foundation is increased by 12.7% for an excavation depth of 9 m.

The closer the foundation pit is to the bridge foundation, the larger the lateral displacement, the internal force of the piles, and the settlement of the soil surrounding the pile. When the distance decreases from 7.5 to 2.5 m, the maximum lateral displacement of the pile is increased by threefold, the maximum internal force of shear force is amplified by 2.31-fold, and the maximum settlement around the pile foundation is augmented by 36.8%.

3) Two safety control measures for increasing the number of support levels and the rooted depth of the enclosure structure are suggested. The number of support levels should be increased to five or six and the rooted depth of the enclosure structure should be increased to 15 m during the construction process, which can effectively reduce the lateral displacement of the bridge foundation, the internal force of the piles, and the ground settlement surrounding the pile.

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