Analysis of the Influence of Deep Foundation Excavation on Adjacent Viaduct Pile Foundation Considering Train Dynamic Loads

Abstract

The development and utilization of underground space is an effective way to make intensive use of resources, solve "big city disease" and achieve high-quality development. The expansion and renovation of underground space in a central urban area is likely to cause serious damage to surrounding structures. In this study, a deep foundation excavation for the reconstruction of an urban subway station in the Greater Bay Area was chosen for analysis using the finite element method. Different from common excavation engineering, the interaction between the three coupling factors of train dynamic load, foundation excavation, and viaduct pile foundation were analyzed. Six different cases were calculated considering different working conditions of excavation depth and train dynamic load. Soil was evaluated using modified Cam-Clay model. The physical parameters of the soil were determined through on-site and laboratory tests. The results were compared with monitoring data, and the accuracy of the finite element model was verified. The settlement and influence range of the soil, and displacement and internal forces of viaduct piles were analyzed. The maximum settlement of the soil occurred in the direction of the short side of the foundation pit. The maximum value was approximately 0.53 times the excavation depth. The settlement increased by approximately 49% when applying the train load. The dynamic load had an aggravating influence on the horizontal displacement of the top of the pile, with a maximum increase of 51%. Moreover, the dynamic load increased the negative bending moment of the viaduct piles. This study provides a reference for the design and construction of geotechnical engineering projects.

1. Introduction

With the continuous construction and development of urban rail transit, conducting ultra-deep foundation excavation near operating traffic line is necessary. The excavation of a deep foundation pit is accompanied by ground settlement, causing varying degrees of damage to surrounding structures. Especially in the reclaimed stratum near the sea, the damage to the foundation soil will seriously affect the normal use of structures. The lateral displacement of the soil caused by excavation leads to additional deflection and bending moment of the viaduct pile foundation. Moreover, the vertical displacement of soil caused by excavation leads to negative friction of the viaduct pile foundation, resulting in uneven settlement of piles and deformation of superstructure. Therefore, it is of great significance to explore the deformation and stress distribution of adjacent viaduct foundation piles caused by the excavation of deep foundation in urban area.

Previous research on soil deformation of foundation excavation, and its influence on adjacent structures, started in the early 1920s. Terzaghi et al. [1] proposed a method, called the total stress method, to estimate the supporting force of the envelope structure and the stability of foundation excavation. This method was continuously improved and modified in later development, and has been commonly applied. Peck [2] calculated a set of empirical relationship curves of the surface settlement and settlement range behind the diaphragm wall, which was related to the soil properties and excavation depth, using an empirical estimation method that is still widely used. Hsieh and Ou [3] adopted an empirical analysis method to study and analyze the deformation law of the foundation pit envelope and the surrounding surface during the construction of a deep foundation pit. The surface settlement pattern behind the wall depended on the deformation pattern of the retaining wall. The soil deformation behind the wall was generally a triangular groove shape. Kung et al. [4] believed that uneven surface settlement caused by deep foundation pit construction was the main cause of damage to the adjacent buildings. A method for predicting the degree of damage to buildings, called the KJHH simplified evaluation method, was proposed. This method was used to evaluate the settlement form and the range of settlement around the foundation pit. Zhang et al. [5] established governing differential equations of a single pile and the pile group by considering the coupling effects of longitudinal and transverse deformations. A new theoretical method was proposed to estimate the displacement of soil with a constant field caused by foundation excavation using the modified method as the basic calculation data of the envelope deflection curve. Based on this, a two-stage analysis method was proposed to study the influence of foundation movement caused by excavation on the performance of the pile foundation. The effectiveness of the method was verified by comparing the calculated results with centrifuge test results. The empirical formula method also plays a crucial role in studying the surface deformation of foundation pits and predicting the deformation of adjacent structures [6,7]. For example, pile-soil interaction properties are widely studied using p–y curves, particularly in the clay soil [8,9]. However, the complexity of stratigraphic conditions limits the theoretical solution methods.

With the continuous development of technologies, the finite element method has gradually gained increasing interest because it can consider various factors to simulate the construction [10,11]. Huynh et al. adopted a finite element method to study deep excavations and damage to adjacent buildings, and they proposed and validated allowable horizontal displacements of retaining wall based on limited settlements of adjacent building with shallow foundations [12,13]. Faheem et al. [14] studied the stability of excavation in soft soil using a two-dimensional finite element analysis method. Factors affecting the stability of the foundation pit after excavation were determined. Yao et al. [15] explored the dynamic response of a steel pipe pile foundation during the construction process of an adjacent deep foundation pit using measured data and numerical calculation results. The results were in good agreement based on a comparison of the numerical simulation results with the measured results. Lee et al. [16] used three-dimensional finite element software to study the shielding effect of pile groups and the mechanical response of pile groups under soil deformation. The simulation result was compared with existing solutions. Liu et al. [17] simulated pile-soil interaction using a Timoshenko beam, and derived an explicit solution of the pile-soil interaction by using the finite difference method. The shear properties of piles and the non-uniformity of multilayer soil were further considered. Through numerical analysis and field monitoring data, the maximum errors of the predicted and simulated pile deflection under different excavation depths were 4.5% and 1.8%, respectively. Goh et al. [18] used finite element software to simulate the excavation process of a deep foundation pit to study the excavation effect of a deep foundation pit on an adjacent pile foundation. The results showed that the excavation of the foundation pit caused a large horizontal displacement in the adjacent pile foundation, with a maximum value up to 28 mm. Soomro et al. [19] adopted a method by coupling the consolidation parameter in three dimensions. The settlement and load transfer mechanisms of a single pile caused by different construction sequences of double-pile tunnels in rigid saturated clay were investigated. The results showed that the construction sequence of double-pile tunnels with different depths had a significant influence on the settlement and deformation of the pile, but had a small influence on the load transfer mechanism in the pile. Kok and Huat [20] and Khelifiz et al. [21] used finite element simulation to simulate the excavation process of the foundation pit, and concluded that the excavation of the foundation pit would cause an additional bending moment of the pile foundation. However, this method did not consider the shear fluidity of the soil around the pile. Therefore, the establishment of the finite element model seriously affected the correctness of the calculation results.

This study relied on a deep foundation excavation engineering in the Greater Bay Area in Shenzhen, south China. The minimum distance between the foundation excavation and adjacent viaduct foundation pile was only 2.1 m. Two-way double-track train loads run on both sides of the upper part of the viaduct every 4–6 min. The train load is considered to have an impact on the excavation deformation and pile foundation of the viaduct. The interaction between the three coupling factors of the train dynamic load, foundation excavation, and viaduct pile foundation cannot be ignored. Therefore, in this study, a large 3D finite element model was built. The train dynamic load operation of a two-way double-track train was simulated by a set of codes using the Fortran language. Combined with numerical simulation and construction monitoring, the influence of the dynamic load on the excavation of deep foundation excavation was explored. We propose reasonable suggestions for the construction of this project and provide a reference for urban subway station reconstruction.

2. Project Overview

2.1. Overview of the Excavation and Viaduct Foundation

A deep foundation excavation for the reconstruction project of an urban subway station in the Greater Bay Area was chosen for this study, as shown in Figure 1. The layout of foundation excavation and adjacent elevated station is shown in Figure 2. The nearest horizontal distance between the deep foundation excavation and pile foundation of the viaduct was 2.1 m, which results in a significant safety risk and challenge for the deep foundation excavation. Figure 3 shows the profile of the viaduct pile foundation. The AT01~AT12 of the viaduct pile foundation was a single truss structure with a span of 12 m. Most of the piles below the bearing platform were friction piles, with pile lengths of 23.0~38.0 m, and a few were end-bearing friction piles with lengths of 25.5~45.0 m.

2.2. Engineering Geological Conditions

The engineering geological conditions at the site are complex, and groundwater exists in the pores and fissures of the weathering zones of the quaternary alluvium, quaternary residual deposit, and mixed rock. At the site, the artificial fill is a moderate permeable stratum, and the quaternary alluvial (fine) medium sand and (coarse) gravel sand are strong permeable strata. Additionally, the other layers are weak permeable strata. The range of the groundwater level is 0.50–3.00 m. The stratum soil exposed by the foundation excavation for the station construction is plain-filled soil, silty clay, fully weathered sandstone, soil-like strongly weathered sandstone, massive strongly weathered sandstone, and moderately weathered sandstone. There is abundant underground water of three types. One type is loose rock pore water, which mainly occurs in the loose strata. Another type is bedrock fissure (structural fissure) water, mainly occurring in massive strong weathering, medium weathering zone and fault structure fissure, with slightly pressure bearing. The third type is karst water, which mainly occurs in carbonate karst caves and dissolved gaps. Generally, the ground water is located 1.8 m below the ground surface. The geological profile is shown in Figure 4 and Figure 5.

3. Numerical Model of Viaduct and Foundation Excavation

3.1. Assumptions

Due to the complex construction conditions and the environment of the foundation excavation, to simulate the conditions of foundation excavation after the geological and environmental investigation of the construction site, the following assumptions were made.

• All soil layers were assumed to be homogeneous and continuous elastoplastic materials, and the viaduct station, viaduct pedestal, and enclosure for foundation excavation were assumed to be homogeneous linear elastomers. Beam elements were used to simulate foundation piles and internal support of excavation pit [22].
• The function of piles used in the enclosure structure for the stability of foundation pit were similar to that of an underground diaphragm wall. According to the principle of the equivalent stiffness method, the enclosure pile was considered an underground diaphragm wall with a certain thickness based on Equations (1) and (2), and the underground diaphragm wall was regarded as a homogeneous elastic body. The formula used is expressed below.

  $$(D+t)h^3/12=\pi D^4/64$$

  (1)

  where $D$ is the diameter of the enclosure pile, $t$ is the distance between piles, and $h$ is the convert thickness of diaphragm wall. According to Equation (1), h can be obtained:

  $$h=0.838 \mathrm{D}\sqrt[3]{1/(1+t/D)}$$

  (2)
• The influence of the excavation process and time on the soil strength and mechanical properties were ignored.
• The influence of groundwater on foundation excavation was ignored in the calculation.

3.2. Calculation Model

A large three-dimensional numerical model was built as shown in Figure 6. The total length of deep excavation model of subway station is 304.8 m, the width is 70.5 m, and the maximum excavation depth is 26.42 m. To reduce the influence of boundary size on the calculation results, the relative position of the foundation excavation and the adjacent elevated station is fully considered. The distance between the boundary and the excavation in the calculation model is greater than three times the maximum excavation depth [23]. The final calculation model is 700 m long along the X-axis, 450 m wide along the Y-axis and 100 m deep along the Z-axis.

For the boundary condition of the model, horizontal constraints were selected on the four lateral side surfaces, vertical constraints were applied to the bottom surface, and the top surface was a free boundary. The soil parameters used in calculation were obtained by field tests and laboratory tests. Soil weight, cohesion, internal friction angle, elastic modulus, Poisson's ratio, and initial pore ratio were all obtained through field tests. The slopes of the critical state line $M$, normal consolidation line $\lambda$, and rebound line $\kappa$ were obtained through triaxial tests and isotropic consolidation tests.

3.3. Soil Constitutive Model and Parameters

In terms of the soil constitutive model, the modified Cam-Clay model was selected as the constitutive model of the soil. The modified Cam-Clay model adopts the law of isotropic hardening; that is, the shape of the yield surface does not change during the expansion process of plastic deformation, but the size changes and is only related to the plastic volume strain. The yield surface size is expressed by the hardening parameters. Thus, the completely modified Cam-Clay model can be expressed in Equation (3).

$$\left(1+\frac{q^2}{M^2+P^2}\right)P=P_a{e}^{\left(\frac{1+e_a}{k_1+k_2}{e}_a^p\right)}$$

(3)

There are three special physical parameters in the modified Cam-Clay model: the critical state line slope $M$, the normal consolidation line slope $\lambda$, and the rebound line slope $\kappa$. The slope parameter of the critical state line $M$ can be determined by the conventional consolidation undrained triaxial shear test. The parameters of normal consolidation line slope $\lambda$ and rebound line slope $\kappa$ can be determined by loading and unloading of various isotropic consolidation tests. The corresponding parameters of each soil layer used in the simulation are listed in

Table 1. Parameters of each soil layer.

Soil layer	ρ/ kN/m3	c/kPa	φ/°	E/MPa	μ	${\mathit{e}}_0$	$\mathit{\lambda }$	$\mathit{\kappa }$	$\mathit{M}$
Plain fill	18.5	23.7	24.7	6.6	0.23	1.046	0.179	0.0368	0.911
Silty clay	19.2	27.7	19.6	10.32	0.38	0.923	0.2531	0.0462	0.987
Silty-fine sand	19.2	25.1	21.8	22.51	0.33	1.01	0.0751	0.008	1.247
Strongly weathered sandstone (soil-like)	19.7	31.9	23.3	8.72	0.25	0.96	0.04	0.004	0.9
Strongly weathered sandstone (massive)	22	500	46	13	0.22	1.34	0.026	0.0026	0.9
Moderately weathered sandstone	27			27	0.17

.

3.4. Simulation of Construction Process

According to the site construction condition, the numerical calculation is determined as the following cases.

Working condition 1: The first concrete support was poured at 2 m depth after excavation.

Working condition 2: The second concrete support was poured when the excavation reached 8.3 m.

Working condition 3: The third concrete support was poured when the excavation reached 15.3 m.

Working condition 4: The fourth concrete support was poured at 21.6 m after excavation.

Working condition 5: Excavate to 26.42 m to achieve the designed depth of foundation excavation.

Working condition 6: Train dynamic load is applied synchronously under working condition 5.

4. Model of Train Load

The train load is a type of permanent fatigue load, which has the characteristics of reciprocation and instantaneity on the rail surface, with great randomness, and the load effect is uneven. Therefore, simulation of the random vibration load of a train is an important and complex factor for analyzing the foundation excavation. Extensive research has been carried out to solve the vibration problem caused by the rail transit. Grundmann et al. [24] equated the dynamic load of a train to a movable periodic load, applied the load on the roadbed, and studied the dynamic response of the roadbed. Hall [25] simulated the effect of train load vibration on road surfaces using a numerical simulation method, established 3D vibration models of trains at different speeds, and obtained changing rules of displacement and stress at different depths from the ground. Yu and Jia [26] studied the influence of vehicle load on the stability of the foundation pit in the process of excavation. Through engineering practices of foundation excavations near roads and bridges, they analyzed mechanical behavior during foundation excavation and adopted the 3D finite element analysis method to consider the combined action of the foundation excavation and soil pile foundation. The feasibility of the construction method and corresponding support measures were discussed. Babu et al. [27] analyzed the settlement of a pile foundation under a dynamic load considering soil-structure interaction. Fu et al. [28] used finite element method to analyze the dynamic response of a foundation excavation supporting structure under a vehicle load. The vehicle load was simplified as a half-wave sinusoidal load, and the internal force and displacement of the retaining structure of the foundation excavation under traffic loads were analyzed.

In summary, owing to the complexity of traffic load, the vibration traffic load can be simplified into a moving load and a half-wave sinusoidal load to obtain a useful analytical solution. The DLOAD in the ABAQUS dynamic analysis module was used to numerically simulate the internal force change and deformation rule of the foundation excavation under a half-wave sine load. A set of codes reflecting the two-way two-track train load operation was incorporated in the calculation program. Figure 7 shows the acceleration time history of vibration load when a train passes. Implicit time integration was used in the nonlinear dynamics analysis program of ABAQUS. The basic equation of the nonlinear dynamic analysis is as follows.

$$\left[M\right]\left\{\ddot{u}\right\}+\left[I\right]-\left[P\right]=0$$

(4)

$$\left[M\right]\left\{\ddot{u}\right\}+\left[C\right]\left\{\dot{u}\right\}+\left[K\right]\left\{u\right\}=\left[P\right]$$

(5)

$$\left[I\right]=\left[C\right]\left\{\dot{u}\right\}+\left[K\right]\left\{u\right\}$$

(6)

where $\left[M\right]$ is the mass matrix, $\left[C\right]$ is the damping matrix, $\left[K\right]$ is the stiffness matrix, $\left[I\right]$ is the viscosity effect term, considering damping, viscoplastic, viscoelastic, $\left[P\right]$ is the external excitation, $\left\{\ddot{u}\right\}$ is the node acceleration vector, $\left\{\dot{u}\right\}$ is the node velocity increment, and $\left\{\dot{u}\right\}$ is the node displacement increment.

5. Analysis Results

In the construction of subway foundation excavation, the excavation deformation and unloading rebound cause the soil around the foundation excavation to produce different degrees of displacement, bringing risk to the viaduct pile foundation. However, the influence of train random vibration load on the surrounding environment of foundation excavation is also an important factor. This section mainly analyzes the behavior of viaduct piles and soil from the following four aspects:

• The settlement of soil around the foundation excavation and the influence range.
• Horizontal displacement of viaduct pile foundation under different working conditions of foundation excavation and train dynamic load.
• Vertical displacement of viaduct pile foundation under different working conditions of foundation excavation and train dynamic load.
• Bending moment of viaduct piles under different working conditions of foundation excavation and train dynamic load.

The measuring locations selected for analysis of piles are point A under the pier of HT43, point B under the pier of AT01, point C under the pier of AT06 and point D under the pier of TA01. The layout of the pile foundation and measuring location are shown in Figure 8. Figure 9 illustrates the layout of the measurement points of soil settlement during the foundation excavation, which are points A1, B1, C1 and D1.

5.1. Surface Settlement and Influence Range around the Excavation

During foundation excavation for the reconstruction of subway stations, the stratum is inevitably disturbed, and surrounding surface settlement occurs due to the unloading action of the soil. According to practical engineering experience, there are two types of surface settlement: triangular and groove. Triangular surface settlement mainly occurs when cantilever excavation or deformation of the building enclosures is large. Groove surface settlement mainly occurs when the retaining structure has a large depth in the soil, is buried in a rigid stratum, or when there is a support at the top of the envelope. In the present case, the surface settlement around the main foundation excavation corresponds to groove settlement. Under the condition of train load operation, excavation has a significant influence on the soil settlement and structures. Figure 10 shows the distribution of vertical displacement at the bottom of the foundation excavation. Settlement measurement points A1, B1, C1 and D1 were selected for a systematic comparative analysis of settlement deformation. The surface settlement curve of each point under different working conditions is shown in Figure 11.

By comparing working conditions 5 and 6 at points A1, B1, C1, and D1, it is clear that the train dynamic load has a great impact on the soil settlement around the foundation excavation. The settlement of the short side of the foundation excavation increased by approximately 20% based on the comparison of points A1 and B1. By comparing points C1 and D1, the increment of the long side of the foundation excavation was greater than that of the short side, and the increment of the settlement at point C1 was approximately 41%. The settlement at point D1 increased by approximately 49% when applying the train load. Although points C1 and D1 were on the same side, different settlements were produced. This is because point D1 is near the station of Line 3. In the normal operation of the station, the flow of people generated additional loads to the structure and soil. Therefore, the settlement at point D1 is greater than that at point C1.

Comparison of Monitoring and Simulation Results

In situ construction monitoring was performed. Taking the most unfavorable working condition 6 as an example, the selected monitoring points were close to points A1, B1, C1, and D1. Figure 12 shows the comparison of the measured data and finite element calculation results when the excavation reached the depth of 26.45 m at the bottom of the excavation. In Figure 12, the monitoring data at the four points are in good agreement with the simulation results. The deformation trend is roughly the same, while there is a certain value difference between the monitoring and simulation results at points C1 and D1 so that the calculation results are slightly smaller than the monitoring data because the soil condition was simplified for convenient calculation, and the simulation working condition did not fully reflect the actual engineering construction. The results at points A1 and B1 are similar, and the maximum settlement located near points A1 and B1 in the short side direction of the foundation excavation were approximately 0.53 times the excavation depth.

5.2. Horizontal Displacement of the Bridge Piles along the Long Side of the Foundation Excavation

Figure 13 shows the distribution curve of the horizontal displacement of piles A, B, C and D along the long side of the foundation excavation under different working conditions. The calculated curves for each working condition were smooth. The positive and negative values in Figure 13 represent the deformation to the east and the west, respectively. As shown in Figure 13, the overall deformation of the pile foundation gradually increases as the excavation depth increases. The maximum horizontal displacement occurred at the top of the pile, and the displacement gradually decreased with increasing pile depth. Under the condition of working condition 5 (excavating to the bottom without the train load), the maximum displacement of the piles A and B occurred at the pile top, and the values were 0.77 and 0.99 mm, respectively. The maximum displacement of piles C and D with a curved shape occurred at the upper part of the pile body, and the values were 0.32 and 2.04 mm, respectively.

By comparing working condition 5 (excavating to the bottom without the train load) with working condition 6 (applying the train load when excavating to the bottom) of each pile foundation, the horizontal displacement of the pile foundation along the long side of the foundation excavation was aggravated by the train load. The dynamic load had a great influence on pile displacement, and the maximum deformation occurred at the top of piles. The maximum displacements of piles A and B were 1.03 and 1.4 mm, respectively, and the increasement percentages were 34% and 41%, respectively when considering the train load during excavation. Therefore, the amplification effect of the train dynamic load on the pile deformation is evident. The deformation of piles C and D also increased under dynamic load, and the maximum displacements were 0.43 and 2.64 mm, respectively. The increasement percentages were approximately 34% and 30%, respectively compared to the working condition 5 without train load.

5.3. Horizontal Displacement of the Bridge Piles along the Short Side Direction of the Foundation Excavation

Figure 14 shows the distribution curve of the horizontal displacement of points A, B, C and D along the short side of the foundation excavation under different working conditions. The calculated curves for each working condition are smooth. The positive value in Figure 14 represents deformation to the north (outside the pit), and the negative value represents deformation to the south (inside the pit). As shown in Figure 14, with increasing excavation depth of the foundation excavation, the overall deformation of the pile foundation gradually increased, and the maximum horizontal displacement under different working conditions was near the excavation face during the foundation excavation. With an increase in pile length, the displacement gradually decreased first, then increased, and then decreased. The deformation of pile foundations A, B, C and D all had a curved shape bent outward toward the pit. Under working condition 5 (excavating to the bottom without the train load), the maximum displacements of piles A, B, C, and D occurred in the middle of the pile body, which was sufficiently close to the bottom of the foundation excavation.

By comparing working condition 5 (excavating to the bottom without the train load) and working condition 6 (applying the train load when excavating to the bottom) of each pile, the train load increased the horizontal displacement of the pile foundation along the short-side direction of the foundation excavation. The dynamic load had little influence on the maximum horizontal displacement of the pile body, and the main influence was still reflected in the position of the pile top.

5.4. Vertical Displacement of Bridge Pile Foundation

Long piles are always used in bridge foundation, as opposed to short piles, and the soil has a negative friction effect on the pile body when the vertical displacement of soil is larger than the pile foundation settlement, which generates additional axial force inside the pile. When the ultimate bearing capacity of the pile is insufficient, this leads to further subsidence of the pile and poses a threat to the upper structure. In contrast, the direction of the negative friction is cut to the pile surface. In the case of the horizontal deformation of the pile, negative friction produces an additional bending moment, further reducing the safety of the pile. In the present case of long piles (i.e., pile foundation with a long pile greater than the excavation depth of the foundation excavation), the vertical displacement of the surrounding soil caused by the foundation excavation is dual. The pile body has the effect of friction resistance in two directions when settlement occurs at a certain depth. Above the boundary line, soil settlement was greater than the pile settlement, and the soil had negative friction on the pile. Below the boundary line, there was an upward friction resistance to the pile body, resulting in an upward pulling force. Therefore, the long piles adjacent to the deep foundation excavation may settle or lift during foundation excavation. As shown in Figure 15, the pile in the present case is a long pile with negative friction resistance; thus, the pile foundation presents a linear settlement trend.

Figure 15 shows the deformation curves of the top of piles A, B, C and D under different working conditions. In Figure 15, with increasing excavation depth of the foundation pit, the vertical displacement at the top of the pile increases, and the maximum vertical displacement at the top of the pile occurs when the excavation is completed. The maximum displacements of piles A, B, C and D were 0.24, 0.45, 0.58, and 0.3 mm, respectively.

The dynamic load had a significant influence on the vertical displacement of the pile foundation, which cannot be ignored, based on the comparison of the vertical displacement of the four piles under working condition 6 (applying a train dynamic load when excavating to the bottom). The maximum displacements of the pile top of piles A, B, C and D under dynamic load were 0.37, 0.64, 0.79, and 0.43 mm, respectively. Compared with condition 5 (excavation to the bottom without the train load), the increases were 54.1, 42.2, 36.2, and 43.3%, respectively. However, although the increases were large, the overall vertical displacement of each pile was small, and the influence of train vibration could be ignored.

5.5. Comparative Analysis of Monitoring Data and Calculated Results

Combined with the above simulations and analysis, a comparative analysis of the foundation displacement of the bridge pile and the actual construction monitoring data along the short-side direction of the foundation excavation was conducted. The selected monitoring points were located close to points A, B, C and D. The measured data and calculation results when excavating to the bottom of the foundation pit were compared and analyzed, as shown in Figure 16. Because the horizontal displacement of the pile was the largest at this time, and the excavation was more complete and better reflected the rationality of the finite element calculation results.

In Figure 16, the deformation calculation results of the four locations on the pile are almost the same as the on-site monitoring data, the difference being approximately 0.5–1 mm. The difference in the calculation of the pile body was very small compared to the measured results, and the deformation trends of the four piles were clearly consistent. The reasons for exploring the difference between the monitoring data and the calculated results are the influence of precipitation on the pit and creep effect of soil mass. At the early stage of foundation excavation, the range of disturbed soil increases as the excavation depth gradually increases, further increasing soil displacement. Coupled with the seepage effect caused by gradual precipitation, the deformation of the pile gradually increased. After completing the excavation, the deformation of the soil does not stop immediately because of the creep property of the soil. Under the subsequent deformation of the soil, the pile deformation continued to increase, indicating a clear time effect. This preliminary analysis shows that under the fourth and fifth working conditions, the construction progress of the foundation excavation accelerated, eliminating the soil creep effect to a certain extent.

5.6. Internal Force of Bridge Piles

The test points selected for analysis were measuring point A under HT43 pier and measuring point C under AT06 pier.

Figure 17 shows the change of bending moments at two different locations of points A and C under different working conditions. The bending moments at the two positions are relatively small since the pile top is connected to the pier cap and the bottom of the pile is embedded in a solid rock layer. With an increase in the excavation depth, the bending moment of the pile increased, and the pile position corresponding to the maximum bending moment gradually decreased. There are two backbend points at point A and one backbend point at point C. The maximum negative bending moment of the two piles was produced in the upper part of the pile, indicating that the outer part of the pile was subjected to tension and the inner part suffers compression. The maximum positive bending moment occurred in the lower part of the pile, which indicates that the lower part of the pile was compressed outside and tensioned inside.

The bending moment curves of the pile at points A and C were close to each other under every working condition, as shown in Figure 17. From the figure, the maximum negative bending moment at point C is greater than that at point A, which is thought to be related to the tight arrangement of the pile at point C, and the spacing between two piles is much smaller than that of pile A. A tight arrangement may result in the superposition effect of the pile group bending moment.

For comparison of the bending moment curves of piles A and C under working condition 6 (applying the train load when excavating to the bottom), despite the negative bending moment of the upper pile body or the positive bending moment of the lower pile body, the value at point C was larger than that at point A. This indicates that the pile group effect exists regardless of whether the pile is subjected to a dynamic train load. The dynamic train load influences the increase in the bending moment value of the viaduct pile foundation, especially the change in the negative bending moment, based on the comparison of the maximum positive and negative bending moments at locations of A and C under the action of working conditions 5 and 6.

6. Conclusions

Based on a deep foundation excavation for the reconstruction of urban subway station project, the influence of foundation excavation on the viaduct pile foundation considering the train dynamic load was analyzed numerically. The results were compared with monitoring data. The main conclusions are as follows.

1. The maximum settlement of soil around the excavation occurred at approximately 0.53 times of the excavation depth, which was named the “groove type”. The dynamic load had a significant influence on soil settlement. The main influence area was near the station, and the settlement increased by approximately 49% compared to the case without the train load.

2. The horizontal displacement of the pile along the long side of excavation gradually increased as the excavation depth increased. The dynamic load had the greatest influence on the top displacement of piles A and B, and the displacement increased by 34% and 41%, respectively. For the influence on the piles C and D, and the displacement increased by 34% and 30%, respectively.

3. For the horizontal displacement of the piles along the short side of the foundation excavation, the maximum displacement of the piles gradually moved from the top of the pile to the deep pile with an increase with the excavation depth. The final maximum displacement occurred in the middle of the pile body when excavating to the bottom. The dynamic load had an intensified influence on the horizontal displacement of the pile, and the most influential part was at the top of the pile. Compared with the condition without train load, the displacement of piles A, B, C and D increased by 46, 47, 43, and 51%, respectively.

4. The vertical displacement of the pile was analyzed. The pile in this study was a long pile with a negative friction resistance such that the pile showed a settlement trend. However, the vertical displacement of each pile was small, and had a small influence on the superstructure.

5. By analyzing the internal forces and bending moment of piles A and C with an increase in the depth of the excavation, the bending moment of the piles increased, and the position of the pile corresponding to the maximum bending moment moved down. The maximum negative bending moment of the two piles occurred in the upper part of the pile. The maximum positive bending moment occurred in the lower part of the pile. Particularly, the negative bending moment significantly increased when applying the train load.

6. Compared to the on-site monitoring data, the calculation results are in good agreement with the monitoring data, verifying the accuracy and applicability of the numerical analysis. The finite element simulation can reflect the general behavior of excavation deformation, and provide reliable data for foundation excavation in the construction of subway station.