During construction with the shield machine side-crossing pile foundations, the response of the adjacent bridge structure is a process of 3D dynamic change. With the excavation face moving forward, the bridge response constantly changes.
In some existing standards and specifications, the control value of deformation of bridge piers is stipulated. The requirements for allowable deformation of bridge foundation are not clearly specified. For this reason, the relevant provisions are taken as the standards for controlling deformation of bridge piers and foundation of the overpass during project construction using the shield machine passing by the pile foundations in this analysis, shown as follows,
(1) The uneven subsidence between the adjacent piers should not cause an additional longitudinal slope of the bridge deck greater than 0.2%, so the limit of uneven subsidence between two bridge piers in this project is ΔUz = 70 mm.
(2) The horizontal displacement on the top of piers along the overpass should meet the following formula.
where, L0 indicates the bridge span and its value can refer to relevant specifications. Through calculation, the limit of horizontal displacement on the top of piers along the overpass is ΔUx = 29.6 mm in this project.
(3) The allowable horizontal displacement of pile foundations on the ground is 10 mm, while it is 6 mm for the buildings that are sensitive to horizontal displacement.
4.1 Analysis on deformation of bridge piers
4.1.1 Analysis on vertical deformation of bridge piers
During shield tunneling, the change curve of vertical displacement of the adjacent bridge piers of the overpass is displayed in Fig. 5. As shown in the figure, due to difference of distances from the tunnel, the changes of vertical displacement on the top of two bridge piers are largely different and such a difference mainly appears in the range of 20~40 m of excavation length. Within this range, differential subsidence on the top of the two bridge piers obviously increases. As the excavation length of shield tunneling exceeds 40 m, differential subsidence on the top of the piers gradually tends to be stable. Based on calculation, the maximum differential subsidence on the top of the piers is only 0.68 mm during shield construction, which is much smaller than the specified value in the above specifications. Obviously, for this project, attributed to the long pile foundations of the overpass, differential subsidence of the bridge piers of the overpass caused by shield construction is unobvious. Furthermore, it is worth noting that a large difference in subsidence on the top of the two bridge piers is present before and after excavation length reaches 20 m. To be specific, within excavation length of 12~20 m, as the excavation face constantly moves forward, soil in front of the cutter is disturbed, so that subsidence on the top of the piers gradually rebounds. When excavation length is 22 m, the excavation face is in the range of bridge piers. In this case, the surrounding rock at the bottom of the tunnel is upheaved as a result of tunnel excavation, leading to rebound of the bridge piers from vertical displacement. Particularly, for QD-1, owing to the end of piles is located within the upheaval range of surrounding rock at the bottom of the tunnel, as shown in Fig. 6, the rebound is greater. As the shield machine advances, the excavation area gradually expands and rebound of bridge piers gradually increases till the shield tail depart completely from the range of bridge piers, namely excavation length L = 38 m.
4.1.2 Analysis on transverse deformation of bridge piers
Figure 7 demonstrates change curve of horizontal displacement of the bridge piers along the overpass with excavation length with the shield machine. It can be seen from the figure that compared with vertical deformation, transverse deformation of bridge piers caused by shield tunneling side-crossing pile foundations is more obvious. Transverse deformation on the top of the two bridge piers is shown as deviation to the tunnel, while vertical deformation of the same bridge piers develops in a similar trend. Transverse deformation of the bridge piers shows obvious stages and each development stage basically is a cycle of shield excavation. Owing to QD-1 is closer to the tunnel than QD-2, the influences of shield construction on QD-1 are greater. When excavation length with the shield machine is L = 50 m, transverse displacements on the top of the two bridge piers reach the maximum and are 10.71 mm and -9.16 mm, respectively. The relative horizontal displacement of bridge piers along the overpass is 19.87 mm, which is slightly smaller than the control value of 29.6 mm stipulated in the aforementioned specifications.
In the monitoring of field construction, 70% of the standard reference value is usually used for early warning for construction. On this basis, the early warning value of relative horizontal displacement of the adjacent bridge piers along the overpass in the shield construction crossing the pile foundations is 20.72 mm. It is obvious that the horizontal displacement of bridge piers easily reaches the early warning value during shield construction. Therefore, certain measures for protecting pile foundations of the overpass are required in the construction and shield tunneling parameters should be controlled reasonably at the same time.
4.2 Analysis on deformation of pile foundations
Table 3 lists the maximum transverse and vertical displacements of each pile foundation after shield construction. It can be seen from the table that deformation of pile foundations caused by shield construction is mainly dominated by the transverse deformation along the overpass and vertical subsidence. Of them, the maximum transverse deformation of pile foundations is located at the tunnel axis and characterized by deviation away from the tunnel. The maximum subsidence of pile foundations is mainly found on the upper part of pile foundations, which mainly results from subsidence on the top of piles induced by transverse bending and deformation of pile foundations. In addition, as illustrated in Table 3, due to the isolation effect of pile foundations in the front row, deformation of pile foundations in the rear row is obviously small.
Table 3 The maximum deformation of pile foundations after shield construction (mm)
Bridge pier
|
Pile
|
Ux,max
|
Uy,max
|
Uz,max
|
QD-1
|
QZ1-1
|
-9.74
|
+2.68
|
-5.59
|
QZ1-2
|
-9.98
|
+1.35
|
-5.12
|
QZ1-3
|
-8.04
|
+1.93
|
-4.35
|
QZ1-4
|
-8.15
|
+0.93
|
-3.91
|
QD-2
|
QZ2-1
|
+8.89
|
+1.91
|
-5.85
|
QZ2-2
|
+9.08
|
+1.07
|
-5.53
|
QZ2-3
|
+7.30
|
+1.36
|
-4.31
|
QZ2-4
|
+7.37
|
+0.70
|
-4.00
|
Because deformation of foundations under each bridge pier is similar, characteristics of transverse deformation of pile foundations on both sides of the tunnel during shield tunneling were analyzed by taking QZ1-1 and QZ2-1 as examples. Figs. 8 and 9 demonstrate transverse deformation curves of QZ1-1 and QZ2-1 when the excavation face lies in different positions. Owing to the length of six rings of segments is used as an excavation cycle in the calculation model, the lengths of the excavation face are L = 10 m, 22 m, 34 m and 46 m.
As illustrated in Figs. 8 and 9, deformation characteristics of pile foundations of the overpass on both sides of the tunnel are similar during the shield tunneling, showing obvious S-shaped transverse bending and deformation. Near the tunnel axis, pile foundations on both sides present lateral deflection far away from the tunnel. The top and end of a pile deviate to the tunnel and the closer the pile foundation to the tunnel, the more obvious the effects of shield construction on the end of the pile foundation. When the excavation face is located at 10 m in front of the pile (L = 10 m), transverse deformation of the pile foundation is small. As the excavation face passes by the pile foundation (L = 22 m), transverse deformation of the pile foundation gradually increases but does not develop rapidly due to protection of shield shell. When shield tail departs the pile foundation (L = 34 m), deformation of the pile foundation obviously rises. With further shield tunneling, transverse deformation of the pile foundation reaches the peak in the later stage of consolidation and settlement of surrounding rock.
By taking the selected working conditions for analysis as an example, when excavation length is L = 46 m, horizontal displacements on the top of QZ1-1 and QZ2-1 piles are 4.3 mm and 4.1 mm, respectively. Because the pile foundations of the overpass are structures sensitive to horizontal displacement, horizontal displacement of pile foundations caused by shield construction is slightly smaller than the control value in the above specifications but larger than the early warning value for construction.
Figure 10 shows transverse deformation curves of QZ1-1 and QZ1-3 under excavation lengths of L = 22 m, 34 m and 46 m. It can be observed from the figure that transverse deformation of the pile foundations on the same side is consistent during shield construction. However, due to isolation effect of pile foundations in the front row, response of the pile foundations in the rear row to shield construction obviously reduces.
4.3 Analysis on internal force of pile foundations
Transverse shear forces and bending moments of QZ1-1 and QZ1-3 when the excavation face is located at different positions are shown in Figs. 11 and 12. As demonstrated in the figures, owing to QZ1-1 is closer to the tunnel than QZ2-1, additional internal force of QZ1-1 induced by shield construction is larger. On the whole, the changes of additional internal force of pile foundations in the transverse direction are consistent with transverse deformation. However, it should be noted that compared with additional deformation of the pile foundation caused by shield construction, the additional internal force induced by shield tunneling increases slowly when the excavation face is ahead of the pile foundation. As shield tail at the pile foundation departs from the pile foundation (L = 34 m), additional internal force of the pile foundation obviously rises. Furthermore, in terms of the positions where the maximum shear force and bending moment appear, the maximum additional bending moment and the maximum transverse deformation of the pile foundation are found at the same position, slightly above the tunnel axis, while the maximum additional shear force is located below the tunnel axis.
Based on the selected working conditions for analysis in this section, when excavation length is L = 46 m, additional internal forces of QZ1-1 and QZ1-2 reach the maximum. The maximum shear forces are 141.3 kN and 65.5 kN, and the maximum bending moments are 422.3 kN·m and 276.9 kN·m, respectively.