# Deformation Characteristics of the Foundation Pit of the Underpass Viaduct and Grey Relational Analysis of the Maximum Horizontal Deflection of the Retaining Wall

Authors: Shoubang Sun; Songhong Yan; Xiaoping Cao; Xiaozhong Li
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

With the rapid development of rail transit, the excavation of new foundation pits will inevitably approach or pass through existing structures. Therefore, choosing a reasonable support scheme can effectively control the deformation of the foundation pit and ensure the safety of existing structures. This paper investigates the excavation of a typical foundation pit in Guangdong that underpasses a viaduct as the research object. This study uses field monitoring and numerical simulations to analyze the deformation characteristics of the supporting structure and introduces grey relational analysis (GRA) to investigate the key factors that influence the maximum horizontal deflection of the retaining wall. The results indicate that all monitored values are substantially less than the warning value specified in the code. Moreover, the horizontal deflection of the retaining wall and the horizontal displacement of the top of the wall at the measuring points near the existing bridge piles are smaller than at other measuring points. This support system has a high safety factor and a large space for optimization. The main factors affecting the maximum horizontal deflection of the retaining wall are as follows: second strut horizontal spacing > first strut horizontal spacing > layered excavation thickness > retaining wall thickness > retaining wall stiffness. The results of this study will provide technical guidance for the design of similar projects and optimization of their construction.


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## Body

## 1. Introduction

With the rapid development of urban construction in China, the need to alleviate the urban traffic and space crisis is motivating an increasing number of projects to excavate underground spaces near viaducts, high-rise buildings, subway tunnels, and the upper or lower parts of municipal pipelines [1]; this trend inevitably leads to complex foundation pit engineering.As the excavation of a foundation pit can easily destroy the initial stress balance state of the soil at the site, excavation unloading redistributes the stress state of the surrounding rock, causing horizontal displacement of the soil layer and uneven settlement of the surface. If the support is improper, instability of the foundation pit and destruction of the existing structure occur. Therefore, the deformation caused by foundation pit excavation must be controlled within the allowable range. To explore the deformation characteristics of excavations and adjacent facilities, previous researchers used theoretical analysis to analyze the deformation characteristics of supporting structures during foundation pit excavation [2, 3]. As data measured in the field can reflect actual deformation during projects, researchers used large amounts of data to analyze the deformation characteristics of supporting structures and environments caused by excavation and dewatering processes [4–8]. These field data are extremely valuable and can be used to calibrate numerical simulations of similar projects in the future. There are generally two shapes of the settlement trough during excavation, as shown in Figure 1.Figure 1
Different settlement trough shapes (replot based on Ou et al. [9]).
(a)
(b)To comprehensively evaluate the characteristics of the excavation of a large-scale foundation pit, measurements were conducted in the field. They focused on the maximum deflection of the underground diaphragm wall, support plate, column, and wall, surface settlement, and the force of the public pipeline during the entire excavation process. It was concluded that pouring the bottom plate restrained the internal displacement of the wall and the subsequent horizontal movement of the ground [10]. On this basis of that study, combined with 16 similar examples, a general relationship between the excavation area and the wall deflection was proposed. It was concluded that zoned excavation can reduce the ratio of depth to width for a single pit and thus effectively control the deformation of the sidewall and wall. When the maximum horizontal displacement and maximum axial force are substantially less than the control value, the foundation pit structure and building are in a safe state; the supporting structure layout is reasonable; and the design safety factor of the foundation pit is high [11, 12].In recent years, the finite element method (FEM) has been widely used in solving practical engineering problems [13, 14]. It can be applied to investigate the influence of the excavation method, soil properties, excavation geometry, retaining wall type, and support system on the excavation response and the influence of adjacent structures [15–17]. In addition, the FEM can be used to develop three-dimensional fluid-solid coupling models to investigate complex foundation pit seepage problems and predict the influence of seepage and dewatering on ground settlement and the surrounding environment [18–20]. However, due to the complexity of strata, it is often necessary to compare field monitoring data with numerical results to correct the finite element model and verify the reliability of the model simulation [21–23]. Reference [24] proposed a simplified semiempirical model and used it to predict the maximum wall deflection, maximum surface settlement, and surface settlement profile caused by excavation in soft clay. In addition, multifactor analysis of foundation pit deformation characteristics can be carried out through reliable numerical models [25], including the influence of excavation geometry, wall system stiffness, support stiffness, wall thickness, wall depth, wall spacing, and the normalized undrained shear strength of clay on wall deflection. A simplified method was established to predict the wall deformation with or without cross-wall excavation [26], mainly simulating the influence of the soil type, wall stiffness, excavation length, excavation depth, and excavation width on the deflection envelope of the horizontal wall.Due to the complexity of geotechnical engineering, the stability of a structure is affected by various factors. Researchers have introduced mathematical models, conducted qualitative and quantitative analyses of each influencing factor, and identified major risk factors in systems [27–29]. In addition, a hybrid mathematical model was established based on artificial intelligence technology to accurately predict the impact of various parameters on construction [30, 31]. The application of these mathematical methods provides an incredibly valuable reference for construction risk control and management.The above research mainly provided the characteristics of the support structure and surface deformation during the excavation of foundation pits in different geologies and environments through the combination of theoretical analysis, field monitoring, and numerical analysis. However, studies of the deformation characteristics of the foundation pit of the underpass viaduct, the variation characteristics of the maximum horizontal displacement of the retaining wall under the consideration of various influencing factors, and the quantification of the degree of each influencing factor are relatively lacking. Therefore, the focus of this study was the engineering of the foundation pit of a rail transit underpass viaduct in Guangdong. First, field monitoring of the special project was comprehensively conducted, and the variation characteristics of the horizontal deflection of the retaining wall, the horizontal displacement of the top of the wall, the vertical displacement of the wall, the surface settlement, and the axial force of the struts were analyzed. Second, according to the actual working conditions, a 3D finite element model was established, and the reliability of the numerical simulation results was verified by the measured data. Third, considering the maximum horizontal deflection of the retaining wall as an important inspection index [32, 33], the influence of different factors on the maximum horizontal deflection of the retaining wall was discussed based on the numerical model. Finally, the degree of influence of each factor on the maximum horizontal deflection of the retaining wall was analyzed by grey correlation analysis. The research results will provide an important theoretical basis and practical guidance for the design and optimization of similar construction projects.


## 2. Project Background

A typical rail transit system in Guangdong passes through a high-speed viaduct; the average depth of the foundation pit is 12.5 m; the width of the foundation pit is 15.4 m; and the oblique intersection angle between the foundation pit and the high-speed viaduct is 66°38′34″. The north side of the foundation pit is the N76 pile of the existing bridge; the bridge pile closest to the tunnel is N76-A; and the horizontal net distance from the tunnel is 2.067 m. The south side of the foundation pit is the N77 pile of the existing bridge, of which the N77-D1 pile foundation partially intersects the sidewall of the main structure of the tunnel. The intrusion distance is approximately 0.29 m, which enables the use of active underpinning for pile foundations. The location of the foundation pit and its adjacent environment are shown in Figure2. In GDK10 + 260∼GDK10 + 260 mileage, the foundation pit is located relatively close to the existing N76 and N77 bridge piles. In this range, the support and deformation monitoring are intensified, and grouting reinforcement is performed at certain positions before the excavation of the foundation pit.Figure 2
Site plan of the project and instrumentation layout.To ensure the safety of the surrounding structures during the excavation of the foundation pit, the retaining structure of the foundation pit should be able to resist the deformation caused by excavation, and the structural deformation should be controlled to the allowable range. The construction site is shown in Figure3. According to the surrounding environment and geological conditions of the foundation pit, the following supporting scheme was adopted:(1)
The retaining wall of the foundation pit adopted Ф1200@1350 bored, cast-in-place piles, and Ф600 jetting piles were installed between every two piles to stop the water.(2)
Foundation pit support system: the first strut of the foundation pit was supported by 0.6 × 0.8 m reinforced concrete with a spacing of 6 m; the second strut of the foundation pit was constructed of steel pipe supports with Ф600,t = 16 mm, and spacing of 3 m. The first support and second support were located 1.6 m and 6.6 m, respectively, below the surface, as shown in Figure 4.(3)
In the process of foundation pit excavation, layering and partial excavation were adopted, and the length of the subdivision was less than 3 m to fully utilize the “time-space effect.”Figure 3
Construction site.Figure 4
Typical excavation cross-section.


### 2.1. Geology and Hydrogeology

The distribution of the soil layer and a typical section of the retaining structure in the foundation pit excavation are shown in Figure4. According to the geological exploration report, the soil properties of different soil layers downwards from the surface were as follows: Plain fill ①₁—grey, brownish-yellow, loose, and mainly composed of cohesive soil and sand; silty clay ②₂—marine alluvial silty clay, silt, plastic flow, marine alluvial silty clay, soft plastic, marine alluvial silt, saturated, slightly dense; fully weathered argillaceous siltstone ⑥₁—reddish-brown, the original rock is heavily weathered to be soil-like, and there are strongly weathered rock fragments at the bottom; strongly weathered argillaceous siltstone ⑥₂—brown–red, blue–grey, grey–white, developed fissures, from broken to relatively broken; weakly weathered argillaceous siltstone ⑥₃—blue–grey, grey–white between brown and red, well-developed fissures, relatively complete to complete rocks. Below the weakly weathered argillaceous siltstone is gravel-bearing sandstone. Groundwater mainly consists of sand layer water and bedrock fissure water, with a small water volume and a buried depth in the range of 0.20∼1.4 m. The replenishment mode of groundwater is mainly supplied by atmospheric precipitation; its drainage mainly occurs by atmospheric evaporation; and the formation permeability is weak. Therefore, the influence of groundwater was not considered in this study. The physical and mechanical parameters of the stratum and support are shown in Table 1.Table 1
Physical and mechanical parameters of the soil layers and supporting structures.
Material
Unit weight,γ (kN·m−3)
Quick shear test
Poisson’s ratio (µ)
Modulus of elasticity,E (MPa)
C (kPa)
φ (°)
Plain fill
18.0
10.0
10.0
0.33
20
Muddy silty clay
16.6
10.8
8.9
0.42
21
Muddy siltstone whole-weathered
19.5
27
21.5
0.30
28
Muddy siltstone strong-weathered
21.0
28
40
0.25
120
Muddy siltstone slight-weathered
23.0
32
50
0.25
150
Retaining wall
26.0
—
—
0.2
3.1e4
Crown beam
26.0
—
—
0.2
3.0e4
Concrete support
26.0
—
—
0.2
3.1e4
Steel support
78.0
—
—
0.3
2.1e5


### 2.2. Instrumentation and Construction

The design safety rank of the pit support was first class. According to the specification [34] and the characteristics of this test project, the main monitoring items of the foundation pit were as follows:(1) Horizontal deflection of the retaining wall, (2) horizontal displacement of the top of the retaining wall, (3) vertical displacement of the retaining wall, (4) ground settlement around the foundation pit, and (5) axial force of the struts. To improve the measurement accuracy, all instruments were carefully calibrated and installed prior to construction. The layout of the monitoring points is shown in Figure2, and Table 2 lists the monitoring items, the corresponding monitoring instrument points, and the accumulated deformation alarm value. To ensure the safety of the existing bridge piles near the foundation pit, strict requirements were proposed for the deformation of the foundation pit, in which the warning value of the deep horizontal displacement of the retaining wall was set to 6 mm (substantially less than the warning value of 30 mm stipulated in the code). CX denotes the measuring points for the deep horizontal displacement of the retaining wall; WY denotes the measuring points for the horizontal displacement of the top of the retaining wall; QD denotes the measuring points for the vertical displacement of the top of the retaining wall; DC represents the ground settlement measurement points behind the retaining wall (the distances from the retaining wall were 3, 6, and 11 m, respectively); and ZL denotes the measuring points for the axial force of struts (such as ZL1-2, which means that the second strut was measured at point ZL1).Table 2
Description of monitoring.
Monitoring contents
Icon
Amount
Alarm value
Lateral deflections of retaining walls
CX
7
6 mm
Horizontal displacement of the top of the retaining wall
WY
8
30 mm
Vertical wall movements
QD
8
30 mm
Ground surface settlement
DC
24
30 mm
Axial force of struts
ZL
4
3,000 kNTo reduce the settlement deformation of bridge piles and surrounding buildings, sleeve valve pipe grouting was performed to reinforce the soil around the bridge piles before foundation pit excavation, as shown in Figure5. The grout material consisted of cement slurry and 42.5 grade ordinary Portland cement with a water-cement ratio of 1:0.75∼1:1, grout diffusion radius R = 0.5 m, grouting hole spacing 0.8 m, plum pattern layout, and minimum reinforcement depth 1.5 d at the bottom of the existing bridge pile, where d is the existing bridge pile diameter.Figure 5
Sleeve valve pipe grouting.The construction of the excavation was conducted by the open cut method. To protect the existing bridge piles, the foundation pit excavation was separated into sections and layers; each section and layer did not exceed 3 m in length. Before the foundation pit excavation, the bored piles were constructed first, followed by the construction of the jet grouting piles outside of the bored piles to act as a waterproof curtain, and then the crown beam was constructed. More details about the excavation sequence are summarized in Table3.Table 3
Main construction stages.
Stage
Construction activity
1
Excavation to 2.16 m BGS
2
Bracing the struts at first level at 1.66 m BGS
3
Excavation to 7.16 m BGS
4
Bracing the struts at the second level at 6.66 m BGS
5
Excavation to 12.5 m BGS (base level)
6
Pouring concrete bottom plate with a thickness of 0.2 m
Note. BGS means below the ground surface.


## 2.1. Geology and Hydrogeology

The distribution of the soil layer and a typical section of the retaining structure in the foundation pit excavation are shown in Figure4. According to the geological exploration report, the soil properties of different soil layers downwards from the surface were as follows: Plain fill ①₁—grey, brownish-yellow, loose, and mainly composed of cohesive soil and sand; silty clay ②₂—marine alluvial silty clay, silt, plastic flow, marine alluvial silty clay, soft plastic, marine alluvial silt, saturated, slightly dense; fully weathered argillaceous siltstone ⑥₁—reddish-brown, the original rock is heavily weathered to be soil-like, and there are strongly weathered rock fragments at the bottom; strongly weathered argillaceous siltstone ⑥₂—brown–red, blue–grey, grey–white, developed fissures, from broken to relatively broken; weakly weathered argillaceous siltstone ⑥₃—blue–grey, grey–white between brown and red, well-developed fissures, relatively complete to complete rocks. Below the weakly weathered argillaceous siltstone is gravel-bearing sandstone. Groundwater mainly consists of sand layer water and bedrock fissure water, with a small water volume and a buried depth in the range of 0.20∼1.4 m. The replenishment mode of groundwater is mainly supplied by atmospheric precipitation; its drainage mainly occurs by atmospheric evaporation; and the formation permeability is weak. Therefore, the influence of groundwater was not considered in this study. The physical and mechanical parameters of the stratum and support are shown in Table 1.Table 1
Physical and mechanical parameters of the soil layers and supporting structures.
Material
Unit weight,γ (kN·m−3)
Quick shear test
Poisson’s ratio (µ)
Modulus of elasticity,E (MPa)
C (kPa)
φ (°)
Plain fill
18.0
10.0
10.0
0.33
20
Muddy silty clay
16.6
10.8
8.9
0.42
21
Muddy siltstone whole-weathered
19.5
27
21.5
0.30
28
Muddy siltstone strong-weathered
21.0
28
40
0.25
120
Muddy siltstone slight-weathered
23.0
32
50
0.25
150
Retaining wall
26.0
—
—
0.2
3.1e4
Crown beam
26.0
—
—
0.2
3.0e4
Concrete support
26.0
—
—
0.2
3.1e4
Steel support
78.0
—
—
0.3
2.1e5


## 2.2. Instrumentation and Construction

The design safety rank of the pit support was first class. According to the specification [34] and the characteristics of this test project, the main monitoring items of the foundation pit were as follows:(1) Horizontal deflection of the retaining wall, (2) horizontal displacement of the top of the retaining wall, (3) vertical displacement of the retaining wall, (4) ground settlement around the foundation pit, and (5) axial force of the struts. To improve the measurement accuracy, all instruments were carefully calibrated and installed prior to construction. The layout of the monitoring points is shown in Figure2, and Table 2 lists the monitoring items, the corresponding monitoring instrument points, and the accumulated deformation alarm value. To ensure the safety of the existing bridge piles near the foundation pit, strict requirements were proposed for the deformation of the foundation pit, in which the warning value of the deep horizontal displacement of the retaining wall was set to 6 mm (substantially less than the warning value of 30 mm stipulated in the code). CX denotes the measuring points for the deep horizontal displacement of the retaining wall; WY denotes the measuring points for the horizontal displacement of the top of the retaining wall; QD denotes the measuring points for the vertical displacement of the top of the retaining wall; DC represents the ground settlement measurement points behind the retaining wall (the distances from the retaining wall were 3, 6, and 11 m, respectively); and ZL denotes the measuring points for the axial force of struts (such as ZL1-2, which means that the second strut was measured at point ZL1).Table 2
Description of monitoring.
Monitoring contents
Icon
Amount
Alarm value
Lateral deflections of retaining walls
CX
7
6 mm
Horizontal displacement of the top of the retaining wall
WY
8
30 mm
Vertical wall movements
QD
8
30 mm
Ground surface settlement
DC
24
30 mm
Axial force of struts
ZL
4
3,000 kNTo reduce the settlement deformation of bridge piles and surrounding buildings, sleeve valve pipe grouting was performed to reinforce the soil around the bridge piles before foundation pit excavation, as shown in Figure5. The grout material consisted of cement slurry and 42.5 grade ordinary Portland cement with a water-cement ratio of 1:0.75∼1:1, grout diffusion radius R = 0.5 m, grouting hole spacing 0.8 m, plum pattern layout, and minimum reinforcement depth 1.5 d at the bottom of the existing bridge pile, where d is the existing bridge pile diameter.Figure 5
Sleeve valve pipe grouting.The construction of the excavation was conducted by the open cut method. To protect the existing bridge piles, the foundation pit excavation was separated into sections and layers; each section and layer did not exceed 3 m in length. Before the foundation pit excavation, the bored piles were constructed first, followed by the construction of the jet grouting piles outside of the bored piles to act as a waterproof curtain, and then the crown beam was constructed. More details about the excavation sequence are summarized in Table3.Table 3
Main construction stages.
Stage
Construction activity
1
Excavation to 2.16 m BGS
2
Bracing the struts at first level at 1.66 m BGS
3
Excavation to 7.16 m BGS
4
Bracing the struts at the second level at 6.66 m BGS
5
Excavation to 12.5 m BGS (base level)
6
Pouring concrete bottom plate with a thickness of 0.2 m
Note. BGS means below the ground surface.


## 3. Field Measurement of the Foundation Pit

### 3.1. Lateral Deflections of the Retaining Walls

To investigate the dynamic change in the deep horizontal displacement of the retaining wall during the construction stages, 7 inclinometers were arranged before the excavation of the foundation pit. Positive values and negative values indicated displacement away from the foundation pit and towards the foundation pit, respectively.Figure6 shows the variation of measuring point CX3 with the construction stages, and the distribution of measuring point CX3 is shown in Figure 2. Figure 6(a) shows that the value of the CX3 measuring point was the cantilever type at the initial stage of excavation, at which time the strut had not been installed. As the construction progressed, the horizontal displacement of the retaining wall continued to increase and develop at great depths. Figure 6(b) shows the change rate of measuring point CX3 at each depth. Notably, stages 3 and 5 (the two stages were the excavation of soil layers) had large rates of displacement increase into the pit. Since the excavation of soil layers caused a redistribution of the stress field, it was necessary to control the excavation thickness of each layer at this stage. This project required that the excavation thickness of each layer not exceed 3 m. After the base plate was poured at stage 6, the deformation rate tended to be 0 mm/d, and the maximum horizontal displacement of the CX3 measuring point was −5.8 mm, which was near the warning value of 6 mm in this project. There were moving loads (such as cranes) near the measuring point, as shown in Figure 3, that caused a certain increase in the displacement of the measuring point.Figure 6
Deformation feature ofCX3 measuring point: (a) deflection during construction and (b) deflection rate during construction.
(a)
(b)Figure7 shows the values monitored by the remaining 6 inclinometers as shown in Figure 2; CX6, CX8, and CX10 were positioned near the N76 bridge pile on the north side of the foundation pit, while CX5, CX7, and CX9 were located near the N77 bridge pile on the south side of the foundation pit. The horizontal displacement of the retaining wall presented a typical parabolic shape. The deformation increased as the construction progressed; the struts limited the horizontal displacement of the wall towards the pit; and the displacement value below the foundation pit underwent a minimal change and basically fluctuated at approximately 0 mm. The maximum horizontal displacements of CX5, CX7, CX8, and CX9 were −3.6, −1.9, −0.8, and −3.5 mm, respectively, approximately 3 m belowground. The maximum horizontal displacements of measuring points CX6 and CX10 were −3.4 and −2.6 mm, respectively, occurring near the ground, mainly due to the extra lateral pressure on the retaining wall near the ground caused when the ground moving load squeezed soil. However, the values of all measuring points were less than the project’s control value of 6 mm. In particular, the values monitored by CX7 and CX8 underwent small changes throughout the construction process, and their maximum values were less than half those of other measuring points. As CX7 and CX8 were relatively close to the existing bridge piles (as shown in Figure 2), the bridge piles functioned as soil-retaining piles and restricted the horizontal displacement of the soil layer to a certain extent. This finding showed that the safety factor of the support structure was relatively high.Figure 7
The monitoring value of each inclinometer against different construction stages.During the construction process, the horizontal deflection of the retaining wall is a key factor in judging the stability of the overall structure. To further investigate the relationship between the maximum horizontal deflection of the retaining wallδhm and the excavation depth of the foundation pit H, in addition to the monitoring data of this project, field data with geological conditions similar to those in this study were analyzed for comparative analysis, as shown in Figure 8.Figure 8
Maximum wall deflection versus excavation depth.All the data measured in this study were betweenδhm=0.005%He and δhm=0.05%He; they were significantly smaller than data from the following: the Chicago case where the excavation was carried out in soft clay [35]; data from a statistical analysis of 30 excavation cases where all the excavations were carried out in soft or medium clay [24]; data from the Hangzhou case, where the excavation was carried out in soft clay [10] and a cross wall was constructed to limit the horizontal displacement of the retaining wall in soft clay [26]; data from the Shenzhen case [36]; data from the Guangzhou case [7]; and data from the Changsha case, where the excavation was carried out in marshland [23]. For this project, the maximum horizontal displacement of the retaining wall was less than the warning value and the value reported in the literature, mainly for the following reasons: (1) to avoid the adverse impact of excavation on the existing bridge piles, the stratum was reinforced by grouting in a certain range before excavation, and the grouting depth reached 11.5 m. The existing pile foundation was also reinforced (see Figure 5); (2) during the excavation process, the excavation thickness of each layer was strictly controlled not to exceed 3 m, and struts were erected promptly; (3) the existing piles played the role of isolation piles and shielded a portion of the horizontal displacement of the soil layer. Through the detection of the existing pile foundation, the average pile length was approximately 13 m, which was greater than the depth of the foundation pit excavation He=12.5m.


### 3.2. Lateral Displacement of the Top of the Retaining Wall

Figure9 shows the change in the lateral displacement of the top of the retaining wall with application time. A negative value indicates displacement inside the pit, and a positive value indicates displacement outside the pit. The lateral displacement increased as the excavation progressed, and the lateral displacement slowly increased in stages 1–2and underwent sharp increase—slow decrease—rapid increase in stages 3–5; the slowly decreasing stage occurred as the second support was applied to prevent displacement into the pit. Displacement was significantly reduced at stage 6 due to the enhanced integrity of the support structure attributed to the pouring of the base plate, thus providing better resistance to the lateral earth pressure. Measuring points WY7 and WY8 were located relatively near the existing bridge piles, and the maximum values at the two measuring points were 0.012% He and 0.024% He, respectively (He was the final excavation depth of the foundation pit), which were only 20%–50% of the maximum values of other measuring points. The existing bridge piles had a certain retaining effect. Although the displacement variation of measurement points WY4 and WY6 was consistent with that of other measurement points, their displacement values were 2–3 times that of other measurement points. This was mainly due to the dynamic load near the excavation. Construction machines such as cranes were operated near the excavation system, and they produced numerous vibrations, referred to as a dynamic load (see Figure 3). The dynamic load near the excavation was the highest risk factor identified through the risk evaluation of the excavation [27]. Therefore, sufficient attention should be given to the static and dynamic loads around the foundation pit during construction. The maximum horizontal displacement of the top of the wall was between 0.012% He and 0.155% He, which was smaller than the value measured by the excavation of foundation pits in Nanjing, Shanghai, Taipei, and Singapore [32]. Notably, the values of all of the measured points were substantially less than the warning value, that is, 30 mm.Figure 9
Horizontal displacement of the top of the retaining wall.


### 3.3. Vertical Wall Movements

During the excavation of the foundation pit, the retaining wall may move up or down [8] as the uneven settlement of the top of the retaining wall causes damage to the structure. Thus, it is necessary to analyze the vertical displacement of the top of the retaining wall and strictly control the vertical displacement in the actual project. The main factors affecting the vertical displacement of the retaining wall are the springback of the foundation pit foundation, the self-weight of the structure, and the construction load [10].Figure10 shows the development of the vertical displacement of the top of the retaining wall during the whole construction process of QD3∼QD10. The settlement trend of each measuring point was consistent, with the slight settlement, uplift, and then substantial settlement. Initially, due to the relatively small excavation depth and limited springback stress of the foundation, the self-weight of the retaining wall had a leading role, so the retaining wall produced a small settlement. With the increase in the excavation depth, the rebound effect of the stratum was enhanced, and the retaining wall was uplifted by a maximum of 2.3 mm, which was approximately 50% smaller than that reported in the literature [7, 8]. This finding was mainly attributed to the grouting reinforcement of the surrounding strata in advance and the retaining effect of the existing bridge piles; thus, the stress release effect caused by excavation was small. With the construction of the support, the self-weight of the support structure increased, and the top of the wall underwent obvious settlement over time. Moreover, the integrity of the structure was strengthened after the bottom plate was poured, and the vertical displacement of the retaining walls tended to stabilize. The final settlement value of the retaining walls on the north and south sides increased along the large mileage direction (i.e., from QD3 to QD9, from QD4 to QD10), and the final average settlement values of the retaining walls on both sides were similar, −6.43 and −6.32 mm. In addition, the figure shows that the displacement values of all measuring points were substantially less than the accumulated warning values.Figure 10
Vertical displacement of the top of the retaining wall.


### 3.4. Ground Surface Settlement

During the construction process, the ground settlementδv was closely monitored. Figure 11 shows the development of surface settlement during the excavation of the foundation pit. Unfortunately, due to the surrounding construction, some of the measuring points were damaged, and no data were available. As shown in the figure, the settlement variation was divided into four stages: slowly change – dramatic change – slow change – stabilization. During stages 3 and 5, excavation induced relatively large surface settlement increments, and the retaining wall produced relatively large lateral displacement increments, as shown in Figure 6(b). This finding indicated that the ground settlement outside the pit was usually synchronized with the deflection deformation of the retaining structure. This relationship was consistent with the corresponding description in related studies. Therefore, the suppression of wall deformation in practical engineering was helpful to minimize the surface settlement caused by excavation. At stage 6, the surface settlement slowly changed and stabilized, which was mainly attributed to the reinforcement of structural integrity obtained by pouring the bottom plate to resist soil deformation. Thus, pouring the bottom slab in time during construction helped reduce surface settlement. Notably, the accumulated maximum settlement value of all measuring points was substantially less than the accumulated warning value.Figure 11
Development of the ground surface settlement.To further explore the settlement range and the maximum surface settlement value caused by excavation, Figure12 shows the relationship between the normalized settlement δvm/He and the normalized distance x/He from the retaining wall, where δvm represents the maximum settlement value of each surface settlement measuring point behind the retaining wall, x represents the distance from the top of the wall, and He represents the depth of the foundation pit. The surface settlement had a typical concave profile, which corresponded to the type shown in Figure 1(b); and δvm mainly occurred between 0.25 He and 0.87 He behind the wall. The measured δvm values ranged between δvm = 0.02% He and δvm = 0.13% He, which were smaller than that those reported in the literature [6, 7, 10, 36]. When x/He=0.48, δvm increased and reached the maximum value in the region where 0≤x/He≤0.48 and gradually decreased in the region where 0.48≤x/He≤1.9. Notably, the range of surface settlement in this study was narrower than that reported in the literature, which should be related to the existing pile foundation and the stratum grouting reinforcement before excavation, which are also reflected in the relatively small deflection of the retaining wall. This finding fully demonstrated the good performance of the foundation pit and showed that the reinforcement measures with timely support were effective, stratified excavation was reasonable, and the support structure had space for further optimization.Figure 12
Relationship between the normalized settlement and normalized distance from the retaining wall.


### 3.5. Axial Force of Struts

Figure13 shows the variations with time of three measuring points (ZL1-1, ZL2-1, and ZL3-1) for the first strut and one measuring point (ZL1-2) for the second strut, where a negative value represents tension and a positive value represents compression. As shown in the figure, the force on the first strut sharply increased during stages 2∼3 and increased to 1,915 kN. After the second strut was erected, the axial force of the first strut gradually decreased, tended to stabilize, and then remained approximately 1,500 kN. The axial force of the second strut slowly increased and basically remained at approximately 300 kN for a certain period. However, it sharply increased when the bottom of the pit was excavated and reached 1,735 kN. Subsequently, the axial force of each strut tended to stabilize in the floor pouring stage. The values at all measuring points were substantially less than the warning value of 3,000 kN.Figure 13
Development curve of axial force of struts over time.


## 3.1. Lateral Deflections of the Retaining Walls

To investigate the dynamic change in the deep horizontal displacement of the retaining wall during the construction stages, 7 inclinometers were arranged before the excavation of the foundation pit. Positive values and negative values indicated displacement away from the foundation pit and towards the foundation pit, respectively.Figure6 shows the variation of measuring point CX3 with the construction stages, and the distribution of measuring point CX3 is shown in Figure 2. Figure 6(a) shows that the value of the CX3 measuring point was the cantilever type at the initial stage of excavation, at which time the strut had not been installed. As the construction progressed, the horizontal displacement of the retaining wall continued to increase and develop at great depths. Figure 6(b) shows the change rate of measuring point CX3 at each depth. Notably, stages 3 and 5 (the two stages were the excavation of soil layers) had large rates of displacement increase into the pit. Since the excavation of soil layers caused a redistribution of the stress field, it was necessary to control the excavation thickness of each layer at this stage. This project required that the excavation thickness of each layer not exceed 3 m. After the base plate was poured at stage 6, the deformation rate tended to be 0 mm/d, and the maximum horizontal displacement of the CX3 measuring point was −5.8 mm, which was near the warning value of 6 mm in this project. There were moving loads (such as cranes) near the measuring point, as shown in Figure 3, that caused a certain increase in the displacement of the measuring point.Figure 6
Deformation feature ofCX3 measuring point: (a) deflection during construction and (b) deflection rate during construction.
(a)
(b)Figure7 shows the values monitored by the remaining 6 inclinometers as shown in Figure 2; CX6, CX8, and CX10 were positioned near the N76 bridge pile on the north side of the foundation pit, while CX5, CX7, and CX9 were located near the N77 bridge pile on the south side of the foundation pit. The horizontal displacement of the retaining wall presented a typical parabolic shape. The deformation increased as the construction progressed; the struts limited the horizontal displacement of the wall towards the pit; and the displacement value below the foundation pit underwent a minimal change and basically fluctuated at approximately 0 mm. The maximum horizontal displacements of CX5, CX7, CX8, and CX9 were −3.6, −1.9, −0.8, and −3.5 mm, respectively, approximately 3 m belowground. The maximum horizontal displacements of measuring points CX6 and CX10 were −3.4 and −2.6 mm, respectively, occurring near the ground, mainly due to the extra lateral pressure on the retaining wall near the ground caused when the ground moving load squeezed soil. However, the values of all measuring points were less than the project’s control value of 6 mm. In particular, the values monitored by CX7 and CX8 underwent small changes throughout the construction process, and their maximum values were less than half those of other measuring points. As CX7 and CX8 were relatively close to the existing bridge piles (as shown in Figure 2), the bridge piles functioned as soil-retaining piles and restricted the horizontal displacement of the soil layer to a certain extent. This finding showed that the safety factor of the support structure was relatively high.Figure 7
The monitoring value of each inclinometer against different construction stages.During the construction process, the horizontal deflection of the retaining wall is a key factor in judging the stability of the overall structure. To further investigate the relationship between the maximum horizontal deflection of the retaining wallδhm and the excavation depth of the foundation pit H, in addition to the monitoring data of this project, field data with geological conditions similar to those in this study were analyzed for comparative analysis, as shown in Figure 8.Figure 8
Maximum wall deflection versus excavation depth.All the data measured in this study were betweenδhm=0.005%He and δhm=0.05%He; they were significantly smaller than data from the following: the Chicago case where the excavation was carried out in soft clay [35]; data from a statistical analysis of 30 excavation cases where all the excavations were carried out in soft or medium clay [24]; data from the Hangzhou case, where the excavation was carried out in soft clay [10] and a cross wall was constructed to limit the horizontal displacement of the retaining wall in soft clay [26]; data from the Shenzhen case [36]; data from the Guangzhou case [7]; and data from the Changsha case, where the excavation was carried out in marshland [23]. For this project, the maximum horizontal displacement of the retaining wall was less than the warning value and the value reported in the literature, mainly for the following reasons: (1) to avoid the adverse impact of excavation on the existing bridge piles, the stratum was reinforced by grouting in a certain range before excavation, and the grouting depth reached 11.5 m. The existing pile foundation was also reinforced (see Figure 5); (2) during the excavation process, the excavation thickness of each layer was strictly controlled not to exceed 3 m, and struts were erected promptly; (3) the existing piles played the role of isolation piles and shielded a portion of the horizontal displacement of the soil layer. Through the detection of the existing pile foundation, the average pile length was approximately 13 m, which was greater than the depth of the foundation pit excavation He=12.5m.


## 3.2. Lateral Displacement of the Top of the Retaining Wall

Figure9 shows the change in the lateral displacement of the top of the retaining wall with application time. A negative value indicates displacement inside the pit, and a positive value indicates displacement outside the pit. The lateral displacement increased as the excavation progressed, and the lateral displacement slowly increased in stages 1–2and underwent sharp increase—slow decrease—rapid increase in stages 3–5; the slowly decreasing stage occurred as the second support was applied to prevent displacement into the pit. Displacement was significantly reduced at stage 6 due to the enhanced integrity of the support structure attributed to the pouring of the base plate, thus providing better resistance to the lateral earth pressure. Measuring points WY7 and WY8 were located relatively near the existing bridge piles, and the maximum values at the two measuring points were 0.012% He and 0.024% He, respectively (He was the final excavation depth of the foundation pit), which were only 20%–50% of the maximum values of other measuring points. The existing bridge piles had a certain retaining effect. Although the displacement variation of measurement points WY4 and WY6 was consistent with that of other measurement points, their displacement values were 2–3 times that of other measurement points. This was mainly due to the dynamic load near the excavation. Construction machines such as cranes were operated near the excavation system, and they produced numerous vibrations, referred to as a dynamic load (see Figure 3). The dynamic load near the excavation was the highest risk factor identified through the risk evaluation of the excavation [27]. Therefore, sufficient attention should be given to the static and dynamic loads around the foundation pit during construction. The maximum horizontal displacement of the top of the wall was between 0.012% He and 0.155% He, which was smaller than the value measured by the excavation of foundation pits in Nanjing, Shanghai, Taipei, and Singapore [32]. Notably, the values of all of the measured points were substantially less than the warning value, that is, 30 mm.Figure 9
Horizontal displacement of the top of the retaining wall.


## 3.3. Vertical Wall Movements

During the excavation of the foundation pit, the retaining wall may move up or down [8] as the uneven settlement of the top of the retaining wall causes damage to the structure. Thus, it is necessary to analyze the vertical displacement of the top of the retaining wall and strictly control the vertical displacement in the actual project. The main factors affecting the vertical displacement of the retaining wall are the springback of the foundation pit foundation, the self-weight of the structure, and the construction load [10].Figure10 shows the development of the vertical displacement of the top of the retaining wall during the whole construction process of QD3∼QD10. The settlement trend of each measuring point was consistent, with the slight settlement, uplift, and then substantial settlement. Initially, due to the relatively small excavation depth and limited springback stress of the foundation, the self-weight of the retaining wall had a leading role, so the retaining wall produced a small settlement. With the increase in the excavation depth, the rebound effect of the stratum was enhanced, and the retaining wall was uplifted by a maximum of 2.3 mm, which was approximately 50% smaller than that reported in the literature [7, 8]. This finding was mainly attributed to the grouting reinforcement of the surrounding strata in advance and the retaining effect of the existing bridge piles; thus, the stress release effect caused by excavation was small. With the construction of the support, the self-weight of the support structure increased, and the top of the wall underwent obvious settlement over time. Moreover, the integrity of the structure was strengthened after the bottom plate was poured, and the vertical displacement of the retaining walls tended to stabilize. The final settlement value of the retaining walls on the north and south sides increased along the large mileage direction (i.e., from QD3 to QD9, from QD4 to QD10), and the final average settlement values of the retaining walls on both sides were similar, −6.43 and −6.32 mm. In addition, the figure shows that the displacement values of all measuring points were substantially less than the accumulated warning values.Figure 10
Vertical displacement of the top of the retaining wall.


## 3.4. Ground Surface Settlement

During the construction process, the ground settlementδv was closely monitored. Figure 11 shows the development of surface settlement during the excavation of the foundation pit. Unfortunately, due to the surrounding construction, some of the measuring points were damaged, and no data were available. As shown in the figure, the settlement variation was divided into four stages: slowly change – dramatic change – slow change – stabilization. During stages 3 and 5, excavation induced relatively large surface settlement increments, and the retaining wall produced relatively large lateral displacement increments, as shown in Figure 6(b). This finding indicated that the ground settlement outside the pit was usually synchronized with the deflection deformation of the retaining structure. This relationship was consistent with the corresponding description in related studies. Therefore, the suppression of wall deformation in practical engineering was helpful to minimize the surface settlement caused by excavation. At stage 6, the surface settlement slowly changed and stabilized, which was mainly attributed to the reinforcement of structural integrity obtained by pouring the bottom plate to resist soil deformation. Thus, pouring the bottom slab in time during construction helped reduce surface settlement. Notably, the accumulated maximum settlement value of all measuring points was substantially less than the accumulated warning value.Figure 11
Development of the ground surface settlement.To further explore the settlement range and the maximum surface settlement value caused by excavation, Figure12 shows the relationship between the normalized settlement δvm/He and the normalized distance x/He from the retaining wall, where δvm represents the maximum settlement value of each surface settlement measuring point behind the retaining wall, x represents the distance from the top of the wall, and He represents the depth of the foundation pit. The surface settlement had a typical concave profile, which corresponded to the type shown in Figure 1(b); and δvm mainly occurred between 0.25 He and 0.87 He behind the wall. The measured δvm values ranged between δvm = 0.02% He and δvm = 0.13% He, which were smaller than that those reported in the literature [6, 7, 10, 36]. When x/He=0.48, δvm increased and reached the maximum value in the region where 0≤x/He≤0.48 and gradually decreased in the region where 0.48≤x/He≤1.9. Notably, the range of surface settlement in this study was narrower than that reported in the literature, which should be related to the existing pile foundation and the stratum grouting reinforcement before excavation, which are also reflected in the relatively small deflection of the retaining wall. This finding fully demonstrated the good performance of the foundation pit and showed that the reinforcement measures with timely support were effective, stratified excavation was reasonable, and the support structure had space for further optimization.Figure 12
Relationship between the normalized settlement and normalized distance from the retaining wall.


## 3.5. Axial Force of Struts

Figure13 shows the variations with time of three measuring points (ZL1-1, ZL2-1, and ZL3-1) for the first strut and one measuring point (ZL1-2) for the second strut, where a negative value represents tension and a positive value represents compression. As shown in the figure, the force on the first strut sharply increased during stages 2∼3 and increased to 1,915 kN. After the second strut was erected, the axial force of the first strut gradually decreased, tended to stabilize, and then remained approximately 1,500 kN. The axial force of the second strut slowly increased and basically remained at approximately 300 kN for a certain period. However, it sharply increased when the bottom of the pit was excavated and reached 1,735 kN. Subsequently, the axial force of each strut tended to stabilize in the floor pouring stage. The values at all measuring points were substantially less than the warning value of 3,000 kN.Figure 13
Development curve of axial force of struts over time.


## 4. Numerical Analysis and Verification

According to the above analysis of field data, all monitoring values of the supporting structure were substantially less than the early warning values. To examine the relationship between the maximum horizontal deflection of the retaining wall and various influencing factors, a 3D finite element model was established, and the simulated values were compared with the monitored values to verify the reliability of the model. Next, a multivariate analysis was conducted.


### 4.1. Numerical Model

A 3D finite element model was established by MIDAS-NX according to the actual working conditions on site, as shown in Figure14. The depth of the model was 54 m, which was almost 5 times the depth of the foundation pit. The length of the model was 124 m; that is, the distance between the edge of the foundation pit and the model boundary was approximately 4 times the width of the excavation of the foundation pit. The width of the model was 59 m, which minimized and eliminated the boundary effect. The main research area was the excavation area of the foundation pit, so a nonuniform grid was utilized. The advantage of this grid was that fewer elements were applied in the model, which improved the calculation efficiency. The boundary conditions of the model were assumed as follows: the ground surface was free, the side surfaces had roller boundaries, and the vertical displacement on the undersurface of the model was fixed. The rock mass and existing bridge piles were simulated by solid elements; the retaining wall was simulated by plate elements according to the principle of equivalent stiffness; and the crown beams and struts were simulated by beam elements.Figure 14
3D finite element model: (a) model, (b) structure, and (c) mesh of the finite element model.
(a)
(b)
(c)The constitutive model adopted Mohr–Coulomb theory, which can predict the sidewall movement and surface settlement of the foundation pit with reasonable accuracy according to several references from the literature [37–39]. The main physical and mechanical parameters of the soil layer were selected according to Table 1. According to the hydrogeological conditions, no surface river was present at the project site, and the groundwater had minimal impact on the project. In addition, the retaining wall effectively stopped the flow of water. Therefore, the effect of seepage was not considered in the numerical simulation.The MIDAS-NX software “activation” and “passivation” functions were used to define the construction phases to simulate soil excavation and strut installation. First, the initial stress balance was carried out; the existing pile foundation and retaining wall were activated; and then the displacement was reset to zero. In accordance with the stages of the actual construction phases, the excavation simulation procedure was as follows:(1)
In stage 1, the retaining walls and crown beams were activated and excavated to −2.66 m.(2)
In stage 2, the first strut was activated at −1.66 m.(3)
In stage 3, excavation to −7.16 m was conducted. Since the layered excavation did not exceed 3 m, the excavation here was divided into two layers.(4)
In stage 4, the second support was activated at −6.66 m.(5)
In stage 5, excavation to the base −12.5 m was conducted; each layer did not exceed 3 m; and the excavation was completed in two layers.(6)
In stage 6, the concrete floor was activated, and the excavation was completed.


### 4.2. Model Verification

The monitoring data at inclinometer pointCX9; surface settlement measurement points DC9-1, DC9-2, and DC9-3; the first axial force measurement point ZL2-1; and the second axial force measurement point ZL1-2 were compared with the corresponding values from the numerical simulation, as shown in Figure 15.Figure 15
Comparison of values from the numerical simulation and measurements: (a) comparison with monitoring values at pointsCX9, DC9-1, DC9-2, and DC9-3; (b) comparison of axial force; and (c) comparison of maximum horizontal displacement.
(a)
(b)
(c)According to Figure15(a), the variation of the numerical simulation of the horizontal deflection and the monitored values were similar in each construction stage, which clearly showed the restricting effect of the support on the deflection of the retaining wall. The simulated maximum horizontal deflection appeared approximately 3 m below the surface, which was consistent with the monitoring and analysis results. The maximum value simulated at CX9 was 3.4 mm; the monitored value was 3.5 mm; and the error was 2.9%. The surface settlement increased with the progress of the construction stage; the settlement shape resembled a “groove”; and the maximum subsidence value was observed at a position 6 m from the edge of the foundation pit, which was consistent with the monitoring results. The maximum values of the surface settlement were 11.1, 15.8, and 13.7 mm at the distance of 3, 6, and 11 m from the foundation pit, and the errors were 4.7%, 2.0%, and 3.1%, respectively, compared with the measured values.Figure15(b) shows the comparison between the numerical simulation of the axial force and the monitored values. The actual monitored axial force changed over time and was a continuous process, while in the numerical simulation, the axial force changed according to the construction stage. However, the overall trends for changes in the two cases were consistent. As the construction stage continued, the axial force of the first support continued to increase. However, when the second support was applied, the axial force on the first support tended to stabilize and decrease, and the force on the second support gradually increased until it stabilized after the bottom plate was poured. The maximum simulated values of ZL2-1 and ZL1-2 were 1,932.2 and 1,778.4 kN, respectively, and the errors were 2.1% and 2.6%, respectively, compared with the measured values.The maximum horizontal deflection of the retaining wall at each corresponding measurement point in the numerical simulation was compared with the monitoring value, as shown in Figure15(c). The numerical simulation value was generally less than the monitoring value, with a maximum error of 9.6%.There were certain differences between the simulated and monitored values for two primary reasons. First, in an actual project, the monitoring data for foundation pit excavation are scattered and perturbed by many factors on the construction site. Second, the following influencing factors were not fully considered in the numerical model: (i) limitation of the model [18]; (ii) complex geological stratigraphic conditions; (iii) influence of loads around the foundation pit; and (iv) long-term effects of neighboring construction and water seepage [40]. It is necessary to further investigate ways to comprehensively consider the influence of these factors in numerical simulations.However, the trends in the changes in the numerical simulation were similar to those of the monitoring results. The comparison revealed that the difference between the numerical results and the field monitoring results was less than 10%, which validated the correctness of the numerical model.


### 4.3. Factors Affecting the Maximum Wall Deflection

The numerical model was employed to consider the variation of the maximum horizontal deflection of the retaining wall for different influencing factors (concrete grade of the retaining wall, thickness of layered excavation, thickness of the retaining wall, and horizontal spacing of the first and second struts), as shown in Figure16.Figure 16
Influence of various factors on the maximum horizontal displacement of the retaining wall: (a) grade of concrete for retaining walls, (b) excavation thicknesses, (c) wall thicknesses, (d) horizontal spacing of the first strut, and (e) horizontal spacing of the second strut.
(a)
(b)
(c)
(d)
(e)The grade of concrete in the retaining wall was taken asC25, C30, C35, C40, C45, and C50 and corresponding values of the elastic moduli were input into the numerical model, according to the code [41], as shown in Figure 16(a). The figure shows that the maximum horizontal deflection decreased with an increase in the concrete grade and that the maximum horizontal displacement of concrete decreased by 10.3% from C25 to C50.Different excavation thicknesses of each layer were used in the numerical model to analyze their influence on the maximum horizontal deflection, and thicknesses of 1 m, 1.5 m, 2 m, 2.5 m, 3 m, and 3.5 m were selected, as shown in Figure16(b). The maximum horizontal deflection increased with increasing excavation thickness of each layer. When the excavation thickness of each layer decreased from 2.5 m to 1 m, the maximum horizontal displacement decreased by 0.7%. When the excavation thickness of each layer decreased from 2.5 m to 3.5 m, the maximum horizontal displacement increased by 2.7%.Figure16(c) shows the influence of different thicknesses of the retaining wall on the maximum horizontal deflection of the retaining wall. Since the retaining wall was composed of bored piles, the diameters of the piles were 1,400, 1,300, 1,200, 1,100, 1,000, and 900 mm. However, in the numerical calculation, according to the principle of equivalent stiffness, the retaining wall was equivalent to a continuous wall with thicknesses of 1.16, 1.08, 1.00, 0.81, 0.74, and 0.67 mm, respectively. The maximum horizontal deflection decreased with increasing wall thickness. The thickness increased from 0.74 to 0.81 mm, and its value decreased from 5.56 to 4.56 mm, which was a decrease of 18.0%.Figure16(d) shows the influence of the first strut on the maximum horizontal displacement of the retaining wall for different horizontal spacings by setting the horizontal spacings to 5.0, 5.5, 6.0, 6.5, 7.0, and 7.5 m in the numerical model. The maximum horizontal deflection significantly increased with an increasing horizontal spacing of the first strut. When the horizontal spacing of the first strut increased from 6.0 to 7.0 m, the maximum horizontal deflection increased by 29.6%. When the horizontal spacing of the first strut decreased from 6.0 to 5.0 m, the maximum horizontal deflection decreased by 17.2%.Figure16(e) shows the influence of the second strut on the maximum horizontal displacement of the retaining wall for different horizontal spacings by setting the horizontal spacings to 2.0, 2.5, 3.0, 3.5, 4.0, and 4.5 m in the numerical model. The figure shows that the maximum horizontal deflection of the retaining wall significantly increased with an increasing horizontal spacing of the second strut. When the horizontal spacing of the strut increased from 3.0 to 4.0 m, the maximum horizontal deflection increased by 36.2%. When the support horizontal spacing was reduced from 3.0 to 2.0 m, the maximum horizontal deflection decreased by 21.5%.The Pearson correlation coefficient (PCC) was used to identify parameters that were strongly correlated with the target variable [42]; the PCC was calculated as follows:(1)ρx,yxi=n∑i=1nxiyi−∑i=1nxi∑i=1nyin∑i=1nxi2−∑i=1nxi2n∑i=1nyi2−∑i=1nyi2,where xi is the value of the influential factors, yi is the value of the predicted parameter, n is the total number of samples, and ρx,yxi is the PCC of the effect of the ith influential factor on output yi. The higher the absolute value of ρx,yxi is, the stronger the correlation between the predicted parameter and the influential factor.Table4 shows the PCC values of influential factors. Positive and negative PCC values indicate positive and negative correlations, respectively. The results showed that the excavation layer thickness, the horizontal distance of the first strut, and the horizontal distance of the second strut were the variables that were most strongly correlated with the maximum wall deflection. The different concrete grades and bored pile diameters had large negative correlations with the maximum wall deflection.Table 4
PCC values of influential factors.
Variables
Units
PCC values
Concrete grade
MPa
−0.97
Excavation layer thickness
m
0.92
Bored pile diameter
m
−0.85
First strut (horizontal distance)
m
0.99
Second strut (horizontal distance)
m
0.99


## 4.1. Numerical Model

A 3D finite element model was established by MIDAS-NX according to the actual working conditions on site, as shown in Figure14. The depth of the model was 54 m, which was almost 5 times the depth of the foundation pit. The length of the model was 124 m; that is, the distance between the edge of the foundation pit and the model boundary was approximately 4 times the width of the excavation of the foundation pit. The width of the model was 59 m, which minimized and eliminated the boundary effect. The main research area was the excavation area of the foundation pit, so a nonuniform grid was utilized. The advantage of this grid was that fewer elements were applied in the model, which improved the calculation efficiency. The boundary conditions of the model were assumed as follows: the ground surface was free, the side surfaces had roller boundaries, and the vertical displacement on the undersurface of the model was fixed. The rock mass and existing bridge piles were simulated by solid elements; the retaining wall was simulated by plate elements according to the principle of equivalent stiffness; and the crown beams and struts were simulated by beam elements.Figure 14
3D finite element model: (a) model, (b) structure, and (c) mesh of the finite element model.
(a)
(b)
(c)The constitutive model adopted Mohr–Coulomb theory, which can predict the sidewall movement and surface settlement of the foundation pit with reasonable accuracy according to several references from the literature [37–39]. The main physical and mechanical parameters of the soil layer were selected according to Table 1. According to the hydrogeological conditions, no surface river was present at the project site, and the groundwater had minimal impact on the project. In addition, the retaining wall effectively stopped the flow of water. Therefore, the effect of seepage was not considered in the numerical simulation.The MIDAS-NX software “activation” and “passivation” functions were used to define the construction phases to simulate soil excavation and strut installation. First, the initial stress balance was carried out; the existing pile foundation and retaining wall were activated; and then the displacement was reset to zero. In accordance with the stages of the actual construction phases, the excavation simulation procedure was as follows:(1)
In stage 1, the retaining walls and crown beams were activated and excavated to −2.66 m.(2)
In stage 2, the first strut was activated at −1.66 m.(3)
In stage 3, excavation to −7.16 m was conducted. Since the layered excavation did not exceed 3 m, the excavation here was divided into two layers.(4)
In stage 4, the second support was activated at −6.66 m.(5)
In stage 5, excavation to the base −12.5 m was conducted; each layer did not exceed 3 m; and the excavation was completed in two layers.(6)
In stage 6, the concrete floor was activated, and the excavation was completed.


## 4.2. Model Verification

The monitoring data at inclinometer pointCX9; surface settlement measurement points DC9-1, DC9-2, and DC9-3; the first axial force measurement point ZL2-1; and the second axial force measurement point ZL1-2 were compared with the corresponding values from the numerical simulation, as shown in Figure 15.Figure 15
Comparison of values from the numerical simulation and measurements: (a) comparison with monitoring values at pointsCX9, DC9-1, DC9-2, and DC9-3; (b) comparison of axial force; and (c) comparison of maximum horizontal displacement.
(a)
(b)
(c)According to Figure15(a), the variation of the numerical simulation of the horizontal deflection and the monitored values were similar in each construction stage, which clearly showed the restricting effect of the support on the deflection of the retaining wall. The simulated maximum horizontal deflection appeared approximately 3 m below the surface, which was consistent with the monitoring and analysis results. The maximum value simulated at CX9 was 3.4 mm; the monitored value was 3.5 mm; and the error was 2.9%. The surface settlement increased with the progress of the construction stage; the settlement shape resembled a “groove”; and the maximum subsidence value was observed at a position 6 m from the edge of the foundation pit, which was consistent with the monitoring results. The maximum values of the surface settlement were 11.1, 15.8, and 13.7 mm at the distance of 3, 6, and 11 m from the foundation pit, and the errors were 4.7%, 2.0%, and 3.1%, respectively, compared with the measured values.Figure15(b) shows the comparison between the numerical simulation of the axial force and the monitored values. The actual monitored axial force changed over time and was a continuous process, while in the numerical simulation, the axial force changed according to the construction stage. However, the overall trends for changes in the two cases were consistent. As the construction stage continued, the axial force of the first support continued to increase. However, when the second support was applied, the axial force on the first support tended to stabilize and decrease, and the force on the second support gradually increased until it stabilized after the bottom plate was poured. The maximum simulated values of ZL2-1 and ZL1-2 were 1,932.2 and 1,778.4 kN, respectively, and the errors were 2.1% and 2.6%, respectively, compared with the measured values.The maximum horizontal deflection of the retaining wall at each corresponding measurement point in the numerical simulation was compared with the monitoring value, as shown in Figure15(c). The numerical simulation value was generally less than the monitoring value, with a maximum error of 9.6%.There were certain differences between the simulated and monitored values for two primary reasons. First, in an actual project, the monitoring data for foundation pit excavation are scattered and perturbed by many factors on the construction site. Second, the following influencing factors were not fully considered in the numerical model: (i) limitation of the model [18]; (ii) complex geological stratigraphic conditions; (iii) influence of loads around the foundation pit; and (iv) long-term effects of neighboring construction and water seepage [40]. It is necessary to further investigate ways to comprehensively consider the influence of these factors in numerical simulations.However, the trends in the changes in the numerical simulation were similar to those of the monitoring results. The comparison revealed that the difference between the numerical results and the field monitoring results was less than 10%, which validated the correctness of the numerical model.


## 4.3. Factors Affecting the Maximum Wall Deflection

The numerical model was employed to consider the variation of the maximum horizontal deflection of the retaining wall for different influencing factors (concrete grade of the retaining wall, thickness of layered excavation, thickness of the retaining wall, and horizontal spacing of the first and second struts), as shown in Figure16.Figure 16
Influence of various factors on the maximum horizontal displacement of the retaining wall: (a) grade of concrete for retaining walls, (b) excavation thicknesses, (c) wall thicknesses, (d) horizontal spacing of the first strut, and (e) horizontal spacing of the second strut.
(a)
(b)
(c)
(d)
(e)The grade of concrete in the retaining wall was taken asC25, C30, C35, C40, C45, and C50 and corresponding values of the elastic moduli were input into the numerical model, according to the code [41], as shown in Figure 16(a). The figure shows that the maximum horizontal deflection decreased with an increase in the concrete grade and that the maximum horizontal displacement of concrete decreased by 10.3% from C25 to C50.Different excavation thicknesses of each layer were used in the numerical model to analyze their influence on the maximum horizontal deflection, and thicknesses of 1 m, 1.5 m, 2 m, 2.5 m, 3 m, and 3.5 m were selected, as shown in Figure16(b). The maximum horizontal deflection increased with increasing excavation thickness of each layer. When the excavation thickness of each layer decreased from 2.5 m to 1 m, the maximum horizontal displacement decreased by 0.7%. When the excavation thickness of each layer decreased from 2.5 m to 3.5 m, the maximum horizontal displacement increased by 2.7%.Figure16(c) shows the influence of different thicknesses of the retaining wall on the maximum horizontal deflection of the retaining wall. Since the retaining wall was composed of bored piles, the diameters of the piles were 1,400, 1,300, 1,200, 1,100, 1,000, and 900 mm. However, in the numerical calculation, according to the principle of equivalent stiffness, the retaining wall was equivalent to a continuous wall with thicknesses of 1.16, 1.08, 1.00, 0.81, 0.74, and 0.67 mm, respectively. The maximum horizontal deflection decreased with increasing wall thickness. The thickness increased from 0.74 to 0.81 mm, and its value decreased from 5.56 to 4.56 mm, which was a decrease of 18.0%.Figure16(d) shows the influence of the first strut on the maximum horizontal displacement of the retaining wall for different horizontal spacings by setting the horizontal spacings to 5.0, 5.5, 6.0, 6.5, 7.0, and 7.5 m in the numerical model. The maximum horizontal deflection significantly increased with an increasing horizontal spacing of the first strut. When the horizontal spacing of the first strut increased from 6.0 to 7.0 m, the maximum horizontal deflection increased by 29.6%. When the horizontal spacing of the first strut decreased from 6.0 to 5.0 m, the maximum horizontal deflection decreased by 17.2%.Figure16(e) shows the influence of the second strut on the maximum horizontal displacement of the retaining wall for different horizontal spacings by setting the horizontal spacings to 2.0, 2.5, 3.0, 3.5, 4.0, and 4.5 m in the numerical model. The figure shows that the maximum horizontal deflection of the retaining wall significantly increased with an increasing horizontal spacing of the second strut. When the horizontal spacing of the strut increased from 3.0 to 4.0 m, the maximum horizontal deflection increased by 36.2%. When the support horizontal spacing was reduced from 3.0 to 2.0 m, the maximum horizontal deflection decreased by 21.5%.The Pearson correlation coefficient (PCC) was used to identify parameters that were strongly correlated with the target variable [42]; the PCC was calculated as follows:(1)ρx,yxi=n∑i=1nxiyi−∑i=1nxi∑i=1nyin∑i=1nxi2−∑i=1nxi2n∑i=1nyi2−∑i=1nyi2,where xi is the value of the influential factors, yi is the value of the predicted parameter, n is the total number of samples, and ρx,yxi is the PCC of the effect of the ith influential factor on output yi. The higher the absolute value of ρx,yxi is, the stronger the correlation between the predicted parameter and the influential factor.Table4 shows the PCC values of influential factors. Positive and negative PCC values indicate positive and negative correlations, respectively. The results showed that the excavation layer thickness, the horizontal distance of the first strut, and the horizontal distance of the second strut were the variables that were most strongly correlated with the maximum wall deflection. The different concrete grades and bored pile diameters had large negative correlations with the maximum wall deflection.Table 4
PCC values of influential factors.
Variables
Units
PCC values
Concrete grade
MPa
−0.97
Excavation layer thickness
m
0.92
Bored pile diameter
m
−0.85
First strut (horizontal distance)
m
0.99
Second strut (horizontal distance)
m
0.99


## 5. Grey Relational Analysis (GRA) of the Influencing Factors of the Maximum Wall Deflection

Based on the satisfactory performance of the numerical model, a parametric analysis was performed, and the variation of the maximum horizontal deflection of the retaining wall with respect to different influencing factors was obtained. Through the quantitative analysis of the degree of influence of each influencing factor, the main factors affecting the maximum horizontal deflection were determined; these results can provide a reference for the optimization of support parameters. Therefore, GRA was introduced to analyze the correlation between each support variable and the maximum horizontal deflection of the retaining wall. In many monitoring projects, the maximum horizontal displacement of the retaining wall was selected as the reference factor, as it was the most important indicator reflecting the structural stability of the foundation pit [32, 33].


### 5.1. Grey Relational Theory

GRA is an effective measurement method from grey system theory that can accurately quantify the correlation between comparison factors and reference factors in the case of limited data. The degree of correlation between two factors is referred to as the degree of correlation. The greater the degree of correlation is, the stronger the relationship between the comparison factor and the reference factor. The specific steps are as follows [43–45].The impact factors (concrete grade of enclosure wall, depth of layered excavation, thickness of retaining wall, horizontal spacing of the first support, and horizontal spacing of the first and second struts) were defined as the comparable sequenceX and expressed as X=X1,X2,⋯,XmT. Accordingly, the maximum horizontal deflection of the retaining wall was defined as the reference sequence Y, which was expressed as Y=Y1,Y2,…,YmT. Each factor of column X,Y had several values, namely, Xi=Xi1,Xi2,⋯,Xin and Yi=Yi1,Yi2,⋯,Yin; thus, columns X, Y were written in matrix form as follows:(2)X=X1X2⋮Xm=X11X12⋯X1nX21X22⋯X2n⋮⋮⋮⋮Xm1Xm2⋯Xmn,Y=Y1Y2⋮Ym=Y11Y12⋯Y1nY21Y22⋯Y2n⋮⋮⋮⋮Ym1Ym2⋯Ymn.As the dimensions of each influencing factor differ, the order of magnitude is large, and there is no comparability, soXi and Yi must be dimensionless. In this paper, the interval relative value was employed for processing, and the calculation method was as follows:(3)Xi′=xi′1,xi′2,⋯,xi′n.Here,xi′j=Xij−minXij/maxXij−minXij, i=1,2,⋯m,j=1,2,⋯n; reference column Y was also dimensionless.The grey correlation difference information space of the matrix was determined, and the difference matrix was expressed as follows:(4)Δ=Δ1Δ2⋮Δn=Δ11Δ12⋯Δ1nΔ21Δ22⋯Δ2n⋮⋮⋮⋮Δm1Δm2⋯Δmn,where Δij=xi′j−yi′j, i=1,2,⋯m,j=1,2,⋯n. The difference sequence matrix Δ was constructed; the maximum and minimum values in Δ were extracted; Δmax=maxΔij; and Δmin=minΔij.To obtain the grey correlation coefficient matrix and grey correlation degree, the relationship coefficient was obtained by the following formula:(5)γij=Δmin+ξΔmaxΔij+ξΔmax,where ξ is the identification coefficient, ξ∈0,1, and ξ=0.5 is generally applied.Due to a large number of correlation coefficients and scattered information, the comparative analysis is difficult, so the degree of correlation is obtained by calculating the average value to compare the correlation of influencing factors. The correlation degree can be obtained by the following formula:(6)Ai=1n∑j=11γij.The degree of grey correlation represents the degree of correlation between the reference column and the comparison column, andAi∈0,1, which is the degree of external expression correlation of multifactor interactions. The grey relational grade also indicates the degree of influence that the comparability sequence could exert over the reference sequence. The greater the correlation degree of the influencing factors in the correlation degree sequence, the greater the degree of influence.


### 5.2. Grey Relational Analysis

According to the GRA method described in Section5.1, each influencing factor in Section 4.3 was selected as the comparison matrix, and the maximum horizontal deflection of the retaining wall was applied as the reference matrix.(7)X=X1X2X3X4X5=28.030.031.532.533.534.511.522.533.50.91.01.11.21.31.455.566.577.522.533.544.5,(8)Y=Y1Y2Y3Y4Y5=4.764.574.494.404.314.274.464.474.484.494.574.6111.265.654.573.783.362.953.784.174.575.085.926.313.583.934.575.326.226.61,where X1, X2, X3, X4, and X5 denote the different concrete grades, excavation layer thickness, bored pile diameter, horizontal spacing of the first strut, and horizontal spacing of the second strut, respectively. Y denotes the maximum wall deflection corresponding to X1, X2, X3, X4, and X5. The grey relational grade values were calculated by applying equations (3)–(6), which were expressed as the sequence matrix shown below for each impact factor:(9)Ai=0.520.810.510.920.93T.The relational grade values indicated that different concrete grades, excavation layer thicknesses, bored pile diameters, and horizontal spacings of the first and second struts had different impacts on the extent of the maximum wall deflection. The extent of the maximum wall deflection primarily depended on the horizontal spacing of the second support. The horizontal spacing of the first support was the second most significant factor; and the excavation layer thickness, different concrete grades, and bored pile diameter were the third, fourth, and least significant factors, respectively. This finding will provide future guidance and enable engineers to effectively, accurately, and economically control deformations of retaining walls and designs of similar projects.


## 5.1. Grey Relational Theory

GRA is an effective measurement method from grey system theory that can accurately quantify the correlation between comparison factors and reference factors in the case of limited data. The degree of correlation between two factors is referred to as the degree of correlation. The greater the degree of correlation is, the stronger the relationship between the comparison factor and the reference factor. The specific steps are as follows [43–45].The impact factors (concrete grade of enclosure wall, depth of layered excavation, thickness of retaining wall, horizontal spacing of the first support, and horizontal spacing of the first and second struts) were defined as the comparable sequenceX and expressed as X=X1,X2,⋯,XmT. Accordingly, the maximum horizontal deflection of the retaining wall was defined as the reference sequence Y, which was expressed as Y=Y1,Y2,…,YmT. Each factor of column X,Y had several values, namely, Xi=Xi1,Xi2,⋯,Xin and Yi=Yi1,Yi2,⋯,Yin; thus, columns X, Y were written in matrix form as follows:(2)X=X1X2⋮Xm=X11X12⋯X1nX21X22⋯X2n⋮⋮⋮⋮Xm1Xm2⋯Xmn,Y=Y1Y2⋮Ym=Y11Y12⋯Y1nY21Y22⋯Y2n⋮⋮⋮⋮Ym1Ym2⋯Ymn.As the dimensions of each influencing factor differ, the order of magnitude is large, and there is no comparability, soXi and Yi must be dimensionless. In this paper, the interval relative value was employed for processing, and the calculation method was as follows:(3)Xi′=xi′1,xi′2,⋯,xi′n.Here,xi′j=Xij−minXij/maxXij−minXij, i=1,2,⋯m,j=1,2,⋯n; reference column Y was also dimensionless.The grey correlation difference information space of the matrix was determined, and the difference matrix was expressed as follows:(4)Δ=Δ1Δ2⋮Δn=Δ11Δ12⋯Δ1nΔ21Δ22⋯Δ2n⋮⋮⋮⋮Δm1Δm2⋯Δmn,where Δij=xi′j−yi′j, i=1,2,⋯m,j=1,2,⋯n. The difference sequence matrix Δ was constructed; the maximum and minimum values in Δ were extracted; Δmax=maxΔij; and Δmin=minΔij.To obtain the grey correlation coefficient matrix and grey correlation degree, the relationship coefficient was obtained by the following formula:(5)γij=Δmin+ξΔmaxΔij+ξΔmax,where ξ is the identification coefficient, ξ∈0,1, and ξ=0.5 is generally applied.Due to a large number of correlation coefficients and scattered information, the comparative analysis is difficult, so the degree of correlation is obtained by calculating the average value to compare the correlation of influencing factors. The correlation degree can be obtained by the following formula:(6)Ai=1n∑j=11γij.The degree of grey correlation represents the degree of correlation between the reference column and the comparison column, andAi∈0,1, which is the degree of external expression correlation of multifactor interactions. The grey relational grade also indicates the degree of influence that the comparability sequence could exert over the reference sequence. The greater the correlation degree of the influencing factors in the correlation degree sequence, the greater the degree of influence.


## 5.2. Grey Relational Analysis

According to the GRA method described in Section5.1, each influencing factor in Section 4.3 was selected as the comparison matrix, and the maximum horizontal deflection of the retaining wall was applied as the reference matrix.(7)X=X1X2X3X4X5=28.030.031.532.533.534.511.522.533.50.91.01.11.21.31.455.566.577.522.533.544.5,(8)Y=Y1Y2Y3Y4Y5=4.764.574.494.404.314.274.464.474.484.494.574.6111.265.654.573.783.362.953.784.174.575.085.926.313.583.934.575.326.226.61,where X1, X2, X3, X4, and X5 denote the different concrete grades, excavation layer thickness, bored pile diameter, horizontal spacing of the first strut, and horizontal spacing of the second strut, respectively. Y denotes the maximum wall deflection corresponding to X1, X2, X3, X4, and X5. The grey relational grade values were calculated by applying equations (3)–(6), which were expressed as the sequence matrix shown below for each impact factor:(9)Ai=0.520.810.510.920.93T.The relational grade values indicated that different concrete grades, excavation layer thicknesses, bored pile diameters, and horizontal spacings of the first and second struts had different impacts on the extent of the maximum wall deflection. The extent of the maximum wall deflection primarily depended on the horizontal spacing of the second support. The horizontal spacing of the first support was the second most significant factor; and the excavation layer thickness, different concrete grades, and bored pile diameter were the third, fourth, and least significant factors, respectively. This finding will provide future guidance and enable engineers to effectively, accurately, and economically control deformations of retaining walls and designs of similar projects.


## 6. Conclusion

Through field monitoring, numerical analysis, and grey relational analysis of the foundation pit project for the underpass of a viaduct, the following main conclusions can be drawn:(1)
According to the analysis of the measured data, the horizontal displacement of the retaining wall and the displacement of the top of the wall were both less than the warning value. The maximum horizontal deflection of the retaining wallδhm was between 0.005%He and 0.05%He, which was substantially less than the value reported in the literature. The existing pile foundation shielded the soil layer displacement. Due to the integrity of the supporting system and the stratum grouting in this project, the maximum settlement δvm was between 0.02%He and 0.13%He; the subsidence affected area x/He was between 0 and 1.92; and the maximum subsidence value was observed at x/He=0.48.(2)
The struts played an important role in retaining the horizontal displacement of the retaining wall and surface settlement. The axial force on the first reinforced concrete strut increased sharply with the excavation and gradually decreased until it became stable after the second steel strut was erected. The axial force of the second strut increased gradually at first and then suddenly as the excavation reached the bottom of the pit. The maximum values of all the axial forces were less than the warning value.(3)
The changes in each monitoring value tended to stabilize after the bottom plate was poured. Therefore, timely pouring of the bottom plate can better restrain the inward movement of the retaining wall and enhance the integrity of the supporting structure. The horizontal displacement of the retaining wall was increased by the dynamic load near the excavation; thus, it is necessary to improve management during construction.(4)
The results of the numerical simulation were similar to those of field monitoring, and the variation trends were basically consistent, which verified the reliability of the numerical model. Based on this numerical model, the variation of the maximum horizontal deflection of the retaining wall was analyzed with respect to the following influence factors: retaining wall stiffness, layered excavation thickness, retaining wall thickness, and horizontal spacing of the first and second struts.(5)
The various factors had different impacts on the extent of the maximum horizontal deflection of the retaining wall. The horizontal spacing of the second strut was the main influencing factor, followed by the horizontal spacing of the first strut, the layered excavation thickness and retaining wall thickness, and finally the stiffness of the retaining wall.



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*Source: 1543698-2022-08-29.xml*