Introduction

With the gradual maturity of underground transportation technology, shield method construction is more and more widely used in urban underground engineering. Pile foundation is one of the commonly used foundation forms for modern urban buildings, and shield tunneling through the pile foundation of a building is inevitable. Yang1 and Chen2 believe that shield tunneling through the pile foundation will extrude and loosen the neighboring soil, change the nature of the soil, and affect the carrying capacity of the pile foundation and the structural safety of the building. Yi et al.3 believe that the specific penetration resistance is measured through static touch tests, and the tested resistance is used to simulate the disturbance of the soil body during shield construction. Zhang et al.4 the bending pattern of the soil body traversed by the shield up and down line tunnels in soft soil areas was derived by comparing the monitored data with the simulation results using theory, modeling, and on-site monitoring. Liu et al.5 were develop a Pasternak foundation model to simulate the disturbance of the tunnel through the soil body, taking into account the shear effect and rotation effect, and compared with the field data. Wang et al.6 were develop a finite element analysis software model to calculate the resulting surface settlement using Peck’s formula, and to analyze the bending pattern of the soil body during the construction of bridge piers and pile foundations.

Many researchers believe that the shield tunnel crossing the soil body generates additional axial force and bending moment on the pile foundation, which produces a series of impacts and disturbances on the neighboring pile foundation. By establishing a calculation model containing the shield tunnel, pile foundation and soil body, it is proposed that tunnel excavation will cause the original pile foundation to deflect in the direction of the tunnel7,8,9,10. Zhou11 and Fu12 find that tunnel excavation will likewise cause the pile to tilt, with the lower part of the pile displaced away from the tunnel direction and the upper part of the pile tilted in the opposite direction. Many scholars believe that during the tunneling process of the shield, the thrust of the shield machine is the main factor affecting the tilting of the pile foundation13,14,15. Gao16 and Zi17 find that the maximum values displacement, the maximum values bending moment and the shear stress of the pile foundations occur opposite to the axis of the tunnel, and the regional values of their influence can be determined by their horizontal distance from the pile foundations and by spreading them at an angle of 45° + φ/2 Zheng et al.18 develop a computational model for the side penetration of group piles in layered soil shields and discover that the horizontal displacement and tilt of the pile foundation bearing platform increase and then decrease with pile-tunnel distance. Liang19 investigates the effect of double-lane shield tunnel side penetrating bridge piles using numerical simulation and discovers that pile horizontal displacement decreases as pile length, diameter, and pile top load increase, whereas tunnel depth is positively proportional to the bending moment. Jiang20 discovered through numerical simulation that the vertical settlement of the bridge piles in the middle of the twin tunnels caused by the side penetration of the double-mode shield piles is the greatest, and the top plate of the tunnels closest to the pile foundations is more affected by pile foundation settlement.

When the shield tunnel passes through the pile foundation, it is often treated by replacing the pile foundation of the original building21,22. Zhang et al.23 through theoretical analysis and numerical calculation, the range of foundation to be reinforced, the exposed length of excavated pile foundation and the role of each other during the construction of underpinned piles were studied. Li et al.24 the bending and settlement of the soil layer, pile foundation and the buttress beam during the construction process were monitored for a long time, and the bending law was proposed. Kou et al.25 proposed that the jack hydraulic force should be adjusted in time with the monitoring data when the pile foundation is replaced. Ding et al.26 proposed that under the geological conditions of soft soil, it is necessary to carry out reinforcement first before the construction of pile replacement. Bai et al.27 discovered using numerical simulation that the maximum settlement of the ground surface caused by the underpinned piless, combined with the shield directly cutting the piles, occurred at the center of the twin tunnels’ axis, and the piers underwent flexural deformation.

In order to deal with the situation of shield tunnel crossing pile foundation by underpinned piles, the existing studies have analyzed the vertical bending of building foundation, buttress beam and buttress pile foundation more, and the horizontal displacement of buttress beam has not been adequately investigated, and the horizontal displacement has a greater impact on the structural safety of the building, we set up different traversing angles on the computational model to carry out simulation calculations, focusing on the analysis of the shield traversing for the impact of the level of the pile foundation and determining the angle with the minimum impact of shield tunnel crossing28,29. In this paper, different crossing angles are set in the calculation model to simulate the calculation, focusing on analyzing the effect of shield crossing on the level of pile foundation, which provides a reference for the design and construction of shield tunnels. In addition, the workflow is shown in Fig. 1.

Fig. 1
figure 1

Study flowchart.

Full size image

Establishment of computing model

Metro Line 2 in Jinan, China is a city express line that runs east-west through Jinan, totaling 36.4 km in length. It significantly reduces east-west traffic congestion and promotes the city’s spatial expansion. The tunnel radius is 3 m, tube sheet thickness is 0.3 m, bridge piers are 2 m×2 m×5 m, and buttress beams are 20 m×4 m×3 m. Diameter of original pile is 1.5 m, length is 28 m; diameter of underpinning pile is 2 m, length is 30 m. The top and bottom of the original pile are cut off separately to allow the shield tunnel to pass through. The upper load of the pier is 5000kN. Figure 2 presents the dimensions of tunnels, pile foundations, and soil layers.

Fig. 2
figure 2

Profile of tunnels, pile foundations, and soil layers.

Full size image

Finite element mesh and boundary conditions

Based on Jinan Metro Line 2 engineering cases in China, the finite element analysis program midas GTS NX is used to develop a three-dimensional calculation model .To minimize computation, the mesh dimensions are 90 m (= 15 D) wide in the transverse direction, 20 m (≈ 3.33 D) in the longitudinal direction, and 42 m (= 7 D) deep in the vertical direction30,31. have shown that the impact of shield construction on pile foundations is mainly in the range of twice the tunnel diameter. The maximum distance from the longitudinal front and rear of the tunnel to the pile foundations is approximately 1.66D, which will not significantly affect the results. The replacement beam measures 20 m×4 m×3 m. Figure 3 depicts the calculation model, which includes the pier, replacement beam, original pile foundation, replacement pile foundation, tunnel, and soil body.

Fig. 3
figure 3

Numerical 3D computational model.

Full size image

The upper soil surface of the model is unconstrained, the bottom surface constrains the degrees of freedom in three directions, and the four lateral surfaces constrain the displacement in the normal direction.

Constitutive models and material parameter

The deformation caused by the construction of the shield tunnel near the side through the existing viaduct piles should be a small deformation problem, and the shear strain of the soil body should be controlled between 1.0 × 10− 4 and 1.0 × 10− 2, and the deformation of the soil body should be in a small strain state32. The constitutive model is Hardening Soil Small (HSS). with an excavation footage of 1 m, to simulate the construction process of the shield tunnel passing through the pile foundation under the condition of the replacement pile.

According to the geological survey report, the stratigraphy is divided into seven layers and the soil parameters are shown in Table 1.

Table 1 Physical and mechanical indexes of geotechnical body of 3D computational model.
Full size table

The pipe segments, supporting beams, and piles in this project are all reinforced concrete structures, with material properties shown in Table 2.

Table 2 Material and structural component attribute parameters.
Full size table

Simulation of construction process

The simulation in the construction stage uses passivation method to simulate tunnel excavation. Excavation footage is 1 m. When tunneling shield tunnels, jacks are usually used to squeeze the soil in front to obtain forward thrust. The digging pressure to take the value of 12 MPa. The tunneling pressure of the tunnel face grid group is applied by the face pressure. When each excavation face is excavated, the solid element will be passivated.

After the shield tunnel is excavated, the shield shell is added, and then the segment needs to be installed. When installing the segment, thrust is needed. At this time, a jack is needed to provide thrust. This force is applied to the shield segment, which is the jack thrust. After the installation of this segment is completed, there is no need to continue to apply thrust, because the segment itself is a plate and shell unit, and the unit needs to be passivated in the next step.

After the installation of the segment is completed, the grouting process needs to be carried out. The project grouting pressure is 15 MPa. The grouting pressure is applied through the surface pressure, and the grouting pressure always exists, so no passivation is required. The construction simulation steps are as Table 3.

Table 3 Simulation steps during the construction phase.
Full size table

Numerical Simulation Calculation and analysis

According to the variation of the angle between the shield tunnel and the axis of the support beams, different working conditions are set up, see Table 4, to analyze the effect of the shield tunnel on the soil and the pile foundation in the excavation process.

Table 4 Angle between the tunnel and the axis of the joist for each working condition.
Full size table

Effect of crossing at different angles on surface settlement

Shield tunnel in the construction process will produce a certain degree of disturbance to the soil, destroying the original balance of the soil, resulting in uneven settlement, the phenomenon of ground settlement is mainly due to the loss of stratum caused during the construction of the shield as well as the reconsolidation of the soil around the shield tunnel subjected to shear damage.

As can be seen from Figs. 4, 5, 6 and 7, when the shield tunnel is perpendicular to the plane of the axis of the buttress beam and the shield tunnel is crossing, the maximum values settlement value of the inner edge of the surface is 1.9 mm, and the maximum settlement value of the outer edge of the surface is 2.0 mm, the center of the surface is 0.7 mm due to the existence of the buttress beam; when the angle between the tunnel and the axis of the buttress beam is 80°, the maximum settlement value of the inner edge of the surface is 2.0 mm, the maximum settlement value of the outer edge of the ground surface is 2.2 mm, and the settlement value of the center of the ground surface is 0.75 mm; when the angle of pinch is 70°, the maximum values settlement value of the inner edge of the ground surface is 2.1 mm, the maximum values settlement value of the outer edge is 2.4 mm, and the maximum values settlement value of the center of the ground surface is 0.79 mm; when the angle of pinch is 60°, the settlement value of the inner edge of the ground surface is 2.2 mm, and the settlement of the outer edge is 2.5 mm, and the settlement value of the center of the ground surface is 0.86 mm.

Fig. 4
figure 4

Elevation of surface settlement when intersecting at different angles.

Full size image
Fig. 5
figure 5

Settlement curve of the inner edge of the ground surface.

Full size image
Fig. 6
figure 6

Settlement curve of the outer edge of the surface.

Full size image
Fig. 7
figure 7

Surface median settlement curve.

Full size image

It can be seen from the above settlement data: when the angle between the tunnel and the axis of the buttress beam is 90° (vertical crossing), the surface settlement is the smallest, and the smaller the angle between the axes, the larger the settlement is. observing the above settlement values, it can be found that under the above four working conditions, when the two are vertical, that is, 90°, the effect of shield tunnel crossing on surface bending is relatively little; In addition, due to the existence of underpinning beams and underpinning piles built before construction, the distribution of settlement values at the ground center lacks symmetry. The settlement values are relatively little where there are underpinning beams and piles, and relatively large where there are no underpinning beams and piles.

Effect of crossing at different angles on perpendicular displacement of underpinned piles

The shield tunnel crossing construction will have perpendicular effects on the building foundations and pile foundations, causing perpendicular displacement of the underpinned piles.

It can be seen from Figs. 8 and 9, when the shield tunnel and the axis of the buttress beam angle of 60°, shield tunnel crossing, the perpendicular displacement of the buttress pile is 1.17 mm; when the angle of 70°, the perpendicular displacement of 1.13 mm; when the angle of 80°, the perpendicular displacement of 1.05 mm; when the angle of 90°, the perpendicular displacement of 1.0 mm. It can be concluded that: the greater the angle of the tunnel and the axis of the buttress beam, the perpendicular displacement of the buttress pile caused by crossing the tunnel. It can be concluded that the larger the angle between the tunnel and the axis of the buttress, the smaller the perpendicular displacement of the buttress pile caused by crossing, and when the angle is 90°, the perpendicular displacement of the buttress pile is the smallest. Therefore, if only consider the effect of shield tunnel crossing on the pile, perpendicular crossing is the most suitable shield crossing method.

Fig. 8
figure 8

Vertical displacement of the underpinned piles base when intersecting at different.

Full size image
Fig. 9
figure 9

Vertical displacement curve of underpinned piles foundation.

Full size image

Effect of different angles of traversal on horizontal displacement of underpinned piles

Shield traversal can cause displacement of the underpinned piles in the horizontal direction, which adversely affects the structural safety of the building and should be given special attention.

As can be seen from Figs. 10, 11, 12 and 13, when the angle between the shield tunnel and the axes of the buttress beams is 60°, the maximum values horizontal displacement of the buttress beams perpendicular to the axes when the shield tunnel crosses is 0.99 mm, and that parallel to the axes is 0.027 mm; when the angle between the two is 70°, the horizontal displacements are 0.91 mm, 0.026 mm; when the angle is 80°, the horizontal displacements are 0.83 mm, 0.025 mm; when the angle is 90°, the horizontal displacements are 0.80 mm, 0.024 mm. When the angle is 80°, the horizontal displacement is 0.83 mm and 0.025 mm respectively; when the angle is 90°, the horizontal displacement is 0.80 mm and 0.024 mm respectively. It can be seen from the above data: the shield tunnel traversing angle for the horizontal displacement of the beam perpendicular to the axis is much larger than that of the parallel axis direction, which should be taken into account highly, and with the increase in the angle of the clamping angle, the horizontal displacement decreases. And in the wake of the angle, the horizontal displacement decreases, and when the angle is 90°, the horizontal displacement is the smallest, and the shield tunnel traverses the pile foundation vertically with the smallest impact on the safety of the building.

Fig. 10
figure 10

Horizontal displacement of the X-direction of the underpinned piles when intersecting at different angles.

Full size image
Fig. 11
figure 11

Horizontal displacement of the Y-direction of the underpinned piles when intersecting at different angles.

Full size image
Fig. 12
figure 12

Horizontal displacement curve in X-direction of underpinned pile foundation.

Full size image
Fig. 13
figure 13

Horizontal displacement curve of Y-direction of underpinned piles.

Full size image

Effect of shield tunnel penetration on axial force and bending moment of underpinned piles body

Tunneling can cause axial forces on the underpinned piles themselves, which vary depending on the depth of the underpinned piles.

According to Fig. 14: the axial force of the pile body is distributed in the form of mountain peaks, the axial force at the top of the pile is 1589kN, and with the increasing depth, the axial force gradually increases until it reaches the tunnel traversing part, the axial force reaches the maximum value of 2320kN, it becomes smaller, and it reaches a minimum at the bottom of the pile body, which is 1100kN. The structural load remains unchanged, the pressure allocated to the pile body of the buttress pile increases, and the axial force of the pile body increases with the increase of depth; the carrying capacity of the soil in the lower part of the shield tunnel changes less, and the axial force of the pile body decreases with the increase of depth; therefore, in the process of construction, particular attention should be paid to the additional axial forces in the upper pile of the shield tunnel.

Fig. 14
figure 14

Axial force curve of pile foundation.

Full size image

The shield tunnel will generate horizontal additional stresses in the soil when crossing the soil body, and the presence of pile foundation will hinder the stress transfer, and the pile foundation will be deformed horizontally, generating bending moments.

It can be seen from Fig. 15: the deformation moment of the top part of the pile body of the pile replacement pile increases with the increase of the depth, and then gradually decreases, reaches about 10 m, and increases in the opposite direction, in the position of the tunnel crossing, the deformation moment of the pile body reaches the maximum value of 330kN-m, then it slowly decreases., and the tail of the pile appears to be the opposite direction of the change. This is due to the tunnel through the ___location of the soil body horizontal bending is the largest, the pile body bending moment appeared to be the largest, the pile top and pile tail position, due to the end effect of the bending moment appeared to be the size and direction of the change.

Fig. 15
figure 15

Pile bending moment curve.

Full size image

Impacts of shield tunneling through group piles

According to the shield tunnel construction plan of vertically traversing the pile replacement, analyze the impact range of shield tunnel traversing the pile foundation according to the actual engineering situation, and set up the three-dimensional calculation model of group piles, with the model size of 100 m×100 m×51.4 m, including 6 pile foundation models of “double piles + carrying platforms”, numbered from 1 to 6 from the left to the right, with the shield tunnel traversing the pile foundation of No.4 pile using underpinned piles from the first pile, and the shield tunnel traversing the pile foundation of No.4 pile using underpinned piles. The shield traverses from the No.4 pile foundation which adopts buttress pile. According to the actual project, the jack thrust is set to 11 MPa, the digging pressure is 13 MPa, the grouting pressure is 15 MPa, and the superstructure load of 500 MPa is applied at the upper pier of each pile foundation, and the grid is divided according to the minimum permissible distance, and the number of grids is 164,062, which achieves the accurate value, see Fig. 16.

Fig. 16
figure 16

3D computational model of group pile.

Full size image

Shield tunneling through group piles will cause ground disturbance, which in turn affects the neighboring pile foundations and produces bending, and the pile foundations of piles No. 1–6 are all subject to a certain degree of settlement and bending.

As can be seen from Fig. 17: the perpendicular displacement of the top of pile foundation No. 1 is 0.98 mm, No. 2 is 1.01 mm, No. 3 is 1.03 mm, No. 4 is 1.05 mm, No. 5 is 1.04 mm, and No. 6 is 1.04 mm.

Fig. 17
figure 17

Vertical displacement curve of group pile foundation.

Full size image

According to the observed settlement data, the perpendicular displacement of the top of pile No.4 is the largest, and the perpendicular displacement of pile foundation on both sides decreases gradually with pile foundation No.4 as the center; the perpendicular displacement of the top of all foundations is the largest, and its perpendicular displacement value decreases gradually as the depth of pile foundation extends downward continually. The pile foundation No.4 is crossed by the shield tunnel, and the soil disturbance is the most intense, and as the distance increases, the pile foundation on both sides is disturbed by the shield crossing gradually weakened.

Settlement and displacement monitoring

After the completion of shield tunnel construction, the surface settlement, horizontal displacement of pile foundation and underpinning girder settlement were tested for 180 days. The numerical simulation data in this chapter are the results of the modeling of the shield tunnel through the group of piles, and the numerical model does not take into account the time effect. The detailed parameters of Midas gts nx are given in Sect. 3.5 Impacts of shield tunneling through group piles. The construction process is similar to that of a monopile, so it will not be described again.

Surface subsidence monitoring

According to the engineering practice of Baochang section of Jinan Metro Line 2, 7 monitoring points similar to the numerical model A1, A2, A3, A4, A5, A6 and A7 are set on the soil surface, as shown in Fig. 18.

Fig. 18
figure 18

Layout of monitoring points at surface subsidence locations.

Full size image

After 180 days of monitoring, the actual monitoring value is compared with the final surface settlement value obtained by the three-dimensional numerical model, as shown in Table 5. It can be seen that the difference between the two is small, and the monitoring data of each monitoring point is less than the data obtained by numerical simulation, both of which meet the requirements of the design specification.

Table 5 Numerical comparison of surface subsidence.
Full size table

Monitoring of horizontal displacement of pile foundation

Four monitoring points, B1, B2, B3 and B4, are set on the underpinning pile foundation, as shown in Fig. 19, and the horizontal displacement of the pile foundation is monitored by remote sensing.

Fig. 19
figure 19

The monitoring points for horizontal displacement of pile foundation and settlement of underpinning beam.

Full size image

Comparing the actual monitoring value with the horizontal displacement value of pile foundation obtained by the three-dimensional numerical model, see Table 6. It can be seen that the monitoring data of each monitoring point are similar to the numerical simulation results and smaller than the numerical simulation results.

Table 6 Numerical comparison of horizontal displacement of pile foundation.
Full size table

Settlement monitoring of underpinned girder

Five monitoring points, C1, C2, C3, C4 and C5, are set at the upper part of the underpinning girder, as shown in Fig. 19. Comparing the actual monitoring value with the final settlement value obtained by the three-dimensional numerical model, see Table 7. It can be seen that the difference between the two data is small.

Table 7 Numerical comparison of surface subsidence.
Full size table

Conclusion

The paper takes Metro Line 2 in Jinan, China as the engineering background. Based on the actual construction conditions, the 3D calculation model is established by midas GTS NX to research the surface settlement and vertical and horizontal displacement of underpinned piles caused by shield tunnel crossing under different angles with the axis of underpinned beams. The internal force distribution of the support pile body during shield tunnel crossing is analyzed, as well as the effects of the shield tunnel crossing on the neighboring group pile foundations. The surface settlement, horizontal displacement of the pile foundation, and settlement of the support beam in actual engineering are monitored, and the results of engineering monitoring and numerical simulation are compared. the main conclusions reached are as follows:

(1) When the shield tunnel crosses the underpinned piles at different angles, the degree of influence on the soil body is different, the smaller the angle with the axis of the buttress beam is, the larger the surface settlement is, and when the angle between the two is 90°, the amount of surface settlement is the smallest, but the overall caused surface settlement is not large, and the underpinned piles play a role in reducing the surface settlement.

(2) Shield tunnel crossing will have an impact on the vertical and horizontal displacement of underpinned piles, the smaller the angle with the axis of replacement beams, the greater the displacement, the angle of 90°, the minimum displacement, perpendicular to the axis of the direction of the horizontal displacement is larger, and will have a greater impact on the structural safety of the building, This impact should be paid attention to in the design and construction of the support pile.

(3) At the ___location where the shield tunnel passes through, the maximum bending moment and axial force of underpinned piles occur, which becomes a risk point for pile body damage; when the shield tunnel crosses the group piles, as the distance increases, the pile foundations on both sides are gradually weakened by the disturbance of the shield tunnel crossing underpinned piles.