Numerical analysis of the impact of excavation for undercrossing Yellow River tunnel on adjacent bridge foundations

2.1 Project introduction

The Phase 1 project of Line 1 of Lanzhou Urban Rail Transit in Lanzhou City spans from Chenguanying to Donggang, with a total length of 26641.213 m. The entire line is located underground. The Yingmentan to Matan section is situated between Yingmentan in Anning District and Matan in Qilihe District, with a designed mileage ranging from YCk13 + 149.926 to YCk15 + 055.880. The total length of this section is 1,905.954 m, as shown in Figure 1.

Figure 1

Yingmentan-Matan District passes through the Yellow River.

This section passes underneath the Yellow River near the upstream of the Yintan Yellow River Bridge, with the left line ranging from 38 to 49 m from the upstream boundary of the Yintan Bridge, as shown in Figure 1.

The main bridge and approach bridge foundations are constructed using 1.5 m diameter bored cast-in-place piles. The pile design is based on friction piles. For the main bridge, Piers 6 and 7 are located within the Yellow River channel, with a design requirement of 26 piles per pier, totaling 52 piles. The designed effective pile length is 110 m, while the actual borehole depth is 120 m. The length-to-diameter ratio is 120:1.5 = 80:1, indicating an extra-long slender pile. The lateral spacing between pile centers is 2 m, and the longitudinal spacing is 3.55 m, arranged in a staggered pattern. For the abutments, 6 piles are designed with a lateral spacing of 12.75 m and a longitudinal spacing of 4 m.

In this section, the second crossing of the Yellow River occurs near the upstream of the Yintan Yellow River Bridge. The length of the tunnel section beneath the Yellow River is 404.0 m. The design elevation of the track ranges from 1492.226 to 1512.647 m, with a bottom plate depth ranging from 9.78 to 35.3 m. The maximum depth of the tunnel crown in the Yellow River section is 36 m. The entire section consists of a dual-track tunnel with a spacing of 6.8 m between the two tracks. The left line is located 38 to 49 m from the upstream boundary of the Yintan Bridge. The tunnel is constructed using the shield tunneling method. The diameter of the shield machine is 6.48 m, with a length of 96 m. The lining pipes used have an outer diameter of 6.2 m, a width of 1.2 m, and a thickness of 0.35 m.

2.2 Geological and topographic features of the site

The primary geomorphic units in the area are the high floodplain, low floodplain, and riverbed of the Yellow River. The elevation of the high floodplain on the north bank of the Yellow River ranges from 1527.94 to 1528.44 m, with a relatively flat terrain. On the south bank of the Yellow River, the elevation of the high floodplain ranges from 1521.8 to 1526.88 m, and the terrain exhibits relatively significant undulations. During the survey period, the water level ranged from 1519.3 to 1521.1 m, the riverbed width was approximately 404 m, and the water surface width was around 200 m. The high floodplain on both banks was approximately 5 m higher than the water level.

The riverbed consists of Quaternary alluvial deposits from the Neogene period. The first layer, identified as Unit ② gravel layer, has a thickness ranging from 1.5 to 3.2 m. The second layer, known as Unit ③ gravel layer, is part of the lower Quaternary alluvial deposits, and its thickness exceeds 60 m, which was not fully penetrated during the exploration. The tunnel only intersects with the Unit ③ gravel layer. The soil parameters are presented in Table 1.

3.1 Simplification of topography and landform and model establishment

As shown in Figure 1, the tunnel in the section from Yingmentan to Matan is curved, with distances of 49 and 38 m from the main bridge pier and the abutment foundation, respectively. The tunnel depth is shallow on the south bank of the Yellow River and deep on the north bank. Therefore, simplifications are made to the actual conditions to facilitate modeling. The actual computational model boundaries do not include both banks, and the elevations on the south and north banks are set to ±0.000 m. The riverbed at the bottom is uneven, and the south bank of the Yellow River extends to 271 m on the north bank, which is simplified as a horizontal riverbed with an elevation of −6.000 m. From 271 to 404 m, the riverbed is lower in the middle and higher on both sides. At 327 m, the elevation of the top layer of the gravel layer (②) is lowered to −14.9 m to simulate the riverbed, with a water level elevation of −8.500 m.

3.2 Establishment of finite element model

A three-dimensional model was created using PLAXIS3D to simulate the undercrossing of the Yellow River. The soil model for the undercrossing section consists of three layers. The first layer is composed of ① miscellaneous fill soil with a thickness ranging from 0.8 to 14.5 m. The second layer is composed of ② gravel soil with a thickness ranging from 3 to 11.9 m. The third layer is composed of ③ gravel soil with a thickness of 117.1 m. The water level is set at −8.500 m. The model configuration is depicted in Figures 2 and 3.

Figure 2

Main bridge pile foundation and tunnel model.

Figure 3

Side bridge pier foundation and tunnel mode.

The pile foundations of the main piers and abutments were simulated using Embedded pile models, with a diameter of 1.5 m and a length of 120 m. Both the main piers and abutments were provided with pedestals, and the pedestal surfaces were subjected to distributed loads to mimic the self-weight of the superstructures. The surface of the pedestals was subjected to a distributed load of −260 kN/m², while the abutment pedestals were subjected to a distributed load of −90 kN/m².

To establish the models, the tunnel is simplified as a horizontal tunnel based on the tunnel roof depth at the closest distance to the bridge foundations. Taking the midpoint of the bridge foundations as the reference point, a 60 m extension is created on both sides along the tunnel alignment for the shield tunneling simulation. Two separate models are developed to simulate the main piers and abutments. In the main pier model, the distance between the main pier and the tunnel centerline is 49 m, with a tunnel roof depth of 23.5 m. The model dimensions are 90.5 m in the transverse direction, 120 m along the tunnel alignment, and 135 m vertically. In the abutment model, the distance between the abutment and the tunnel centerline is 38 m, with a tunnel roof depth of 23.5 m. The model dimensions are the same as the main pier model.

3.3 Model calculation

The soil model adopts the HSS model, which is superior to commonly used constitutive models in describing shear hardening, compression hardening, loading or unloading, and small-strain behaviors. It is more suitable for simulating excavation problems.

Both the main pier and side pier models simulate the excavation of the left-line tunnel, considering only half of the tunnel in the simulation. The main pier model has a total excavation length of 106.8 m, with an excavation step size of 2.4 m, totaling 32 steps. The side pier model has a total excavation length of 99.6 m, with an excavation step size of 2.4 m, totaling 29 steps. During the construction phase, the initial position of the Tunnel Boring Machine (TBM) is established, with an already excavated length of 18 m set to avoid boundary effects.

The TBM advancement phase is then created. Since the advancement process essentially involves the transfer of construction loads and the stiffness of the shield machine, plate elements representing the TBM advance one ring at a time. The lining of the already excavated section is activated, while other parameters remain the same as in the initial position. Figure 4 shows the TBM advancement stage 32.

Figure 4

TBM promotion phase 32.

The face equilibrium pressure is the pressure exerted by the shield machine on the excavated soil. Insufficient pressure can cause settlement of the soil ahead, while excessive pressure can lead to a heave of the soil and have a significant impact on surrounding structures. The face equilibrium pressure is essentially equal to the horizontal earth pressure at the excavation face. Based on the selected values of earth pressure at the excavation face [13], calculations are conducted using the saturated unit weight of the soil and the unit weight of water above the soil, with a value of 0.3 MPa. The grouting pressure is set at −0.3 MPa, as the direction of the grouting pressure is opposite to the interface of the simulated shield machine plate elements. Therefore, a negative value is assigned. The jacking force is set at −0.64 MPa, with its direction opposing the advancement direction of the shield machine. Once all construction steps are defined, calculations are performed at monitoring points selected along the pile body.

4.1 Analysis of deformation in main pier piles

The analysis of the foundation pile deformation was conducted for both the main pier and the side pier. Figures 5 and 6 illustrate the deformation of the selected foundation piles in the main pier along the X- and Y-axes, respectively, as the tunnel excavation progresses to different positions. The X-axis is perpendicular to the direction of the shield tunneling, while the Y-axis is parallel to the tunneling direction. Figures 7–9 represent the displacement curves of the foundation piles along the X, Y, and Z axes, respectively. The displacement changes at nine different tunneling positions were chosen for analysis.

Figure 5

Displacement of the pile along the X-axis when the tunnel is excavated at different positions.

Figure 6

Displacement of the pile along the Y-axis when the tunnel is excavated at different positions.

Figure 7

The displacement of the pile along the X-direction.

Figure 8

The displacement of the pile along the Y-direction.

Figure 9

The displacement of the pile along the Z-direction.

Figure 5 illustrates the deformation of the main pier foundation piles at different positions of the shield tunnel: initial position, 58.8, 87.6, and 106.8 m. From the figure, it can be observed that at the initial position of the shield tunnel, the displacement at the pile head is the largest and decreases as the pile depth increases, deviating from the tunnel. When the shield tunnel reaches 58.8 m, the displacement at the pile head continues to increase, while the displacement along the pile body remains relatively small. As the shield tunnel advances to 87.6 m, the displacement at the pile head further increases in the direction away from the tunnel, while the displacement of the pile body and pile toe develops towards the direction closer to the tunnel, with the maximum displacement always occurring at the pile head.

Figure 6 illustrates the deformation of the pile along the Y-axis during the excavation process, where the positive sign indicates deformation in the positive direction of the Y-axis, consistent with the direction of the TBM. From the graph, it can be observed that the deformation in the Y-direction is greater than the deformation in the X-direction, and it is distributed throughout the entire length of the pile. The maximum displacement occurs at the pile cap and decreases with increasing depth. The majority of the displacement in this direction occurs prior to the arrival of the TBM. There are two main reasons for the significant displacement in this direction: first, the inclined riverbed alters the original state of the surrounding soil structure during pile group construction, resulting in a redistribution of soil stresses. This leads to uneven soil pressure acting on the pile cap in the Y-direction. When the soil pressure is sufficiently high, the pile cap tends to move towards the direction of lower soil pressure, which is the positive direction of the Y-axis, thereby increasing the displacement at the pile cap. Second, the TBM induces disturbances in the surrounding soil as it advances, causing displacement of the pile in the direction of tunnel advancement. The proximity between the TBM and the pile amplifies this effect, resulting in the maximum displacement occurring when they are closest to each other. The main causes of foundation pile deformation are as follows: (1) non-uniform distribution of superimposed loads: Uneven distribution of loads on the superstructure can lead to differential settlements and uneven deformation of the foundation piles. (2) Flexure of the raft and deformation of surrounding piles: the flexural behavior of the raft and the deformation of neighboring piles can also influence the deformation of the specific foundation pile. (3) Poor soil properties within the raft area: the soil properties within the area of the raft (within the envelope of the pile group) may be inferior, resulting in weak constraints on the foundation pile. (4) Redistribution of soil stresses during shield tunneling: when the shield tunneling disrupts the original soil equilibrium, there is a redistribution of soil stresses. The non-uniform soil pressures exerted on the foundation pile can cause deformation. These factors, either individually or in combination, contribute to the deformation of foundation piles. It is important to consider these factors in the analysis and design of foundation systems to ensure the stability and integrity of the structure.

As shown in Figure 7, the displacement of the pile cap is the smallest at the initial position of the TBM, measuring 2.45 mm. From the curves above −55 m, it can be observed that as the TBM advances, the upper part of the pile deviates further away from the tunnel. At the completion of the tunnel boring, the maximum displacement at the pile cap reaches 5.95 mm, representing a 142.8% increase. It is noticeable that the closer the TBM is to the pile, the faster the displacement increases, as indicated by the spacing between the curves. The displacement of the pile shaft below −55 m develops towards the direction of the tunnel as the TBM progresses. The maximum displacement of the pile shaft occurs at −80 m, measuring 0.75 mm. The influence of the TBM decreases with increasing depth, and the displacement at the pile toe is already formed prior to tunnel excavation, remaining unaffected by the TBM.

The decrease in pile displacement as the TBM continues to advance is primarily due to the diminishing influence of the machine on the pile with increasing distance. Additionally, the reinforcement of the tunnel helps to control soil deformation, resulting in reduced soil rebound and consequently smaller pile displacements.

Figure 8 illustrates the displacement curve of the piles along the direction of TBM advancement. The density of the displacement curve indicates a significant influence of the machine on the surrounding and upper soil. The displacement at the pile head increases as the TBM advances, reaching a peak of 7.03 mm at the closest distance. This represents a 20.9% increase compared to the pre-tunneling condition. However, as the TBM continues to advance, the pile displacement starts to decrease. At a distance of 106.8 m, the displacement reduces to 6.45 mm, which is an 11% increase compared to the initial position of 5.81 mm. The displacement of the pile body initially decreases and then increases during the advancement process. Taking the example of −80 m, the initial displacement is 5.34 mm, reaching the minimum value of 4.9 mm when the TBM advances to 78 m. Subsequently, the displacement starts to increase again, reaching 5.02 mm at the end of the tunnel boring process. Overall, the tunneling process leads to a 5.9% reduction in displacement.

Figure 9 illustrates the variation of vertical displacement of the piles with the advancement of the TBM. To highlight the vertical displacement changes, the difference between the vertical displacement at each advancement stage and the initial stage is plotted. The negative sign indicates an increase in displacement, while the positive sign indicates a decrease. From the graph, it can be observed that as the TBM advances, the vertical displacement of the piles slightly increases. At the end of the tunnel boring process, the maximum increment of vertical displacement at the pile head is 0.18 mm, which represents a 0.93% increase compared to the initial position. The growth rate of displacement becomes faster as the distance to the TBM decreases. Moreover, the rate of increase in vertical displacement decreases with the increasing depth of the piles.

The two main factors contributing to the significant initial vertical displacement of the piles are as follows: the first factor is the disturbance of the soil’s original structure during the construction of the pile group. This leads to a lower soil performance within the inner envelope of the pile group compared to the soil outside the pile group. Consequently, the axial forces of the piles cannot be effectively transferred to the soil through lateral frictional resistance. The second factor is the overlapping stress between adjacent piles, resulting in an elevation of stress levels and a deepening of the compression layer below the pile toe. This leads to greater settlement and a longer duration of settlement for the pile group compared to individual piles, known as pile group effects.

4.2 Analysis of pile deformation in abutment piers

Figure 10 illustrates the deformation of the abutment piles along the X-axis. At the initial position of the TBM, the maximum deformation occurs at the pile head with a magnitude of 0.81 mm, pointing towards the tunnel. As the TBM advances, the pile head displacement starts to develop in the direction away from the tunnel, while the pile body displacement develops towards the tunnel. At the end of the tunnel boring process, the pile head deformation increases to 3.97 mm, diverging from the tunnel, with a change of 4.09 mm. The maximum deformation of the pile occurs at −17.9 m, with a magnitude of 4.07 mm, diverging from the tunnel, with a change of 4.31 mm. The pile body deformation reaches its maximum value of 0.53 mm at −89.79 m, compared to the initial position of 0.05 mm, resulting in an increase of 0.48 mm in deformation.

Figure 10

Displacement of the pile along the X-axis when the tunnel is excavated at different positions.

As shown in Figure 11, the maximum displacement occurs at a pile depth of −17.9 m, which is the furthest distance from the tunnel. The pile body displacement increases with the advancement of the TBM and reaches a peak of 0.53 mm at −89.79 m, slightly smaller than the displacement of the main pier piles. Examining the displacement curves within the range of pile heads, it can be observed that the curve spacing is denser during the TBM advancement from 30 to 46.8 m, indicating a slower deformation rate of the pile head and a lesser influence from the TBM. However, as the TBM continues to advance from 56.4 to 94.8 m, the spacing between the displacement curves along the X-axis widens, indicating an accelerated deformation rate of the pile head and a greater influence from the TBM. As the TBM further progresses, the growth of pile head deformation slows down, suggesting a diminishing impact from the TBM.

Figure 11

The displacement of the pile along the X-direction.

Figures 12 and 13 depict the deformation and displacement of the edge pier piles along the tunnel direction. By comparing the displacement curves before and after the TBM advancement, it can be observed that the piles above −20.64 m are significantly affected by the machine. The maximum displacement of the pile head occurs at 66 and 75.6 m of advancement, reaching a peak of 2.87 mm. This represents a 41.4% increase compared to the initial displacement of 2.03 mm. However, as the TBM continues to advance, the displacement decreases, reaching 2.31 mm at the end of the process. Overall, the tunneling process results in a 13.8% increase in pile head displacement. On the other hand, the displacement of piles below −20.64 m remains smaller than the initial displacement. The largest change in pile body displacement occurs at −51.4 m, where the displacement before the TBM advancement is 1.89 mm, decreasing to 1.39 mm at the end of the process, a reduction of 26.5%. The magnitude of displacement change for the piles below −51.4 m decreases with increasing depth, indicating a diminishing influence from the TBM.

Figure 12

The displacement of the pile along the Y-direction.

Figure 13

The displacement of the pile along the Y-direction.

Figure 14 illustrates the vertical displacement of the edge pier piles. To highlight the variations in vertical displacement, the displacement differences between each advancement stage and the initial stage are plotted, with a negative sign indicating an increase in displacement and a positive sign indicating a decrease. From the graph, it can be observed that the vertical displacement of the piles decreases with increasing depth. As the TBM progresses, the vertical displacement slightly increases for depths above −55 m. The maximum increase occurs at −40 m, with a magnitude of 0.02 mm, representing a 2.1% increase. However, for depths below −55 m, the vertical displacement starts to decrease as the TBM advances. The maximum reduction occurs at −89 m, with a magnitude of 0.074 mm, indicating a 52.8% decrease compared to the initial displacement.

Figure 14

The displacement of the pile along the Z direction.

4.3 Analysis of pile axial force variation

Figure 15 illustrates the variation of axial force in the main pier piles as the TBM advances to different positions. It can be observed from the graph that the axial force of the piles initially increases and then decreases with increasing depth. This phenomenon is attributed to the significant disturbance caused by the construction of the pile group, which reduces the mechanical properties of the surrounding soil. As a result, the transfer of axial force from the pile body to the soil is not efficient, leading to an increase in axial force for piles located above −33 m depth, under the influence of upper loads and self-weight. In contrast, the soil below −33 m depth experiences less disturbance and can effectively transmit the axial force from the pile body to the soil, resulting in a decrease in axial force. As the depth exceeds 60 m, the rate of axial force reduction accelerates, and the bearing capacity of the pile toe begins to play a role, leading to a rapid decrease in axial force until it reaches its minimum value.

Figure 15

Axial force variation of main pier pile foundation.

Based on Figure 15, it can be observed that the axial force of the main pier piles decreases as the TBM advances. Taking the pile head axial force as an example, the axial force before tunneling is 1962 kN, which decreases to 1867 kN at the end of the tunneling process, resulting in a reduction of 4.8%. The maximum axial force of the piles decreases from 2014 to 1915 kN, representing a reduction of 4.9%. According to the calculated data from the model, it is evident that the location of the maximum axial force shifts upward as the TBM advances. Prior to tunneling, the maximum axial force occurs at a depth of −33 m, whereas at the end of tunneling, the maximum axial force occurs at −29 m. It can be concluded that as the piles go deeper, their axial force is less affected by the TBM.

Based on Figure 16, the axial force variation of the side pier piles during the advancement of the TBM is shown. The axial force of the piles increases with increasing depth for depths greater than −20 m, reaching a maximum value of 2034.5 kN. However, for depths below −20 m, the axial force decreases with increasing depth. As the TBM advances, the rate of axial force attenuation accelerates. specifically, the pile head axial force decreases from 2005.4 kN before tunneling to 1826.4 kN at the end of the tunneling process, representing a reduction of 8.9%. The maximum axial force of the piles decreases from 2034.5 to 1793.2 kN, resulting in an 11.8% reduction. At a depth of −85.84 m, the pile experiences the greatest variation in axial force. The axial force decreases from 1417.14 kN before tunneling to 291.02 kN, representing a significant reduction of 79.46%.

Figure 16

Axial force variation of side pier pile foundation.

The variation in axial force between the main pier piles and the side pier piles is significant. There are two main reasons for this difference. First, the main pier piles have a larger number of piles compared to the side pier piles, which makes them more stable and less affected. Therefore, the axial force of the main pier piles decreases at a slower rate along the pile shaft compared to the side pier piles. Second, the impact of TBM advancement on the vertical displacement of the piles is greater for the side pier piles than the main pier piles. As the relative displacement decreases, the axial force also decreases. Therefore, as the TBM advances, the axial force of the side pier piles attenuates at a faster rate compared to the main pier piles.