In the TBM construction, the surrounding soil is disturbed during the forward movement, as manifested by ground subsidence and deformation. The ground surface deformation during the TBM operation is mainly manifested in three aspects: The deformation of the ground when the TBM cutter head reaches the tunnel face ；the deformation of the ground when the TBM cutter head reaches and passes through the tunnel face and consolidation at the later stage of the surface (Avunduk and Copur 2019).
5.1 Effect of driving speed
The variation in the final settlement of the ground surface under different driving speeds is shown in Fig. 9. The entire surface of the tunnel is under sinking state during the tunnel excavation, and the largest surface settlement occurs at the axis of the tunnel. Although the tunnel is constructed by double-line excavation, no two settlement grooves are symmetrical about the central axis on the surface, because the tunnel has a large burial depth, and the effect of the double-line tunnel excavation on ground settlement is weakened. The subsidence of the ground surface approximately 30 m away from the central axis of the tunnel is within 1 mm, which has minimal influence on the ground. The surface subsidence starts increasing sharply when the distance is less than 30 m. The figure shows that when the driving speed is 1700 s/m (2.55 m/h), 2000 s/ms (2.11 m/h), 2300 s/ms (1.8 m/h), 2600 s/m (1.56 m/h), and 2900 s/m (1.38 m/h), the surface settlement of the central axis is 3.22, 3.43, 3.63, 3.96, and 4.18 mm, respectively. Tunneling speed has an effect on the surface settlement; the settlement is small when the tunneling speed is high. To maximize the economic benefits in the TBM construction, the driving speed should be increased as much as possible (with control of other driving parameters) to reduce the ground subsidence and the impact on the surface structures (Arbabsiar et al. 2020).
5.2 Effect of heading pressure
According to the relevant literature (Nagel and Meschke 2011), subsidence occurs on the surface when the earth pressure is less than the active earth pressure, as shown in Fig. 10. When the earth pressure is greater than its passive value, the earth’s surface may exhibit an uplift. When the earth pressure is between its active and passive values, the ground surface neither sinks nor swells. In soft to plastic clay, a reasonable value of pressure (P) can be determined according to the following equation.
where k is the earth pressure coefficient which is normally in the range of 0.35–0.75; γ is the bulk density (weighted average) of the soil layer above the centerline of the shield; and H is the vertical distance of the central axis of the shield tunnel from the natural ground (Qin et al. 2018).
The graphs of the maximum settlement of the surface of the two tunnels and the centerline of the left and right tunnels under different driving pressures are shown in Figs. 11–14. With the increase in tunneling pressure, the maximum settlement of the surface of the tunnel center also increases. However, the settlement rate decreases first, suddenly increases after the 18th construction step, and then continues to decrease. This phenomenon occurs because the TBM construction in this section is conducted first on the left line and then on the right line, with the right-line excavation as the 18th construction step. As the construction of the left-line tunnel progresses, the surface settlement of the left-line tunnel is greater than that of the right-line tunnel; when the construction of the left-line tunnel is completed, the surface settlement value tends to stabilize；When the right-line tunnel is excavated, the later-excavated right-line tunnel will continue to cause the settlement of the surface soil in the center line of the left-line tunnel, and the left-line tunnel that has been excavated will cause the displacement field of the surrounding rock and soil of the right-line tunnel. The change has a certain impact on the construction of the right-line tunnel, causing the ground settlement during the construction of the right-line tunnel to be significantly greater than that of the single-line tunnel excavation, and the mutual disturbance effect of the two-line shield excavation is obvious. During the excavation of the left line, the maximum settlement line of the surface is always near the left tunnel surface. When the right line is excavated, the maximum settlement line of the surface is close to the surface of the center axis of the right line tunnel, thereby causing the maximum settlement of the ground on the central axis of the left and right tunnels to increase suddenly. A comparison of the maximum settlement curves on the surfaces of the left and right tunnels shows that when the tunneling pressure is 600 kN/m2, the maximum settlement values in the last construction step are 4.23mm, 3.77mm, and 3.66 mm. These values indicate that increasing the tunneling pressure increases the maximum settlement of the surface centerline; the double-line shield construction has the strongest influence on the surface settlement value of the centerline of the double-line tunnel. this should be avoided in actual projects to prevent damage to sensitive buildings on the surface of the midline of the double-lane tunnel and avoid potential safety hazards.
Fig. 15 shows that the cumulative subsidence of the surface decreases with the increase in driving pressure. The successively decreasing rates are 8.63%, 9.20%, 10.11%, and 11.28% at the same surface location. In practical engineering applications, the TBM driving pressure should be increased to maximize the economic effect and to reduce the surface subsidence and the impact on the surface structures.
5.3 Analysis of vertical displacement of abutment pile foundation
The vertical displacement cloud diagram of the pile foundation of the overpass under different driving pressures is shown in Fig. 16.
It can be seen from Fig. 16 that the values of the vertical displacement vary with driving pressure. The maximum displacement values at driving pressures of 120 kN/m2, 240 kN/m2, 360 kN/m2, 480 kN/m2, and 600 kN/m2 are -1.01 mm, -0.93 mm, -0.86 mm, -0.78 mm, and -0.70 mm, respectively. The minimum displacement values are -4.06 mm, -3.98 mm, -3.91 mm, -3.83 mm, and -3.76 mm corresponding to the above pressures. The negative sign indicates that the direction is downward, which refers to the settlement. While the vertical displacement under a driving pressure of 120 kN/m2 has exceeded the safe limit for pile foundation settlement by ± 4 mm, the value is not very large. The excavation of the new subway tunnel by the TBM process will lead to settlement of the pile foundation of the overpass; this does not meet the requirements of the actual engineering specification under the driving pressure of 120 kN/m2. By analyzing the settlement, it can be seen that as the driving pressure increases, the pile foundation settlement of the overpass decreases. From the values of the maximum settlement at different driving pressures, it can be seen that the rate of maximum settlement reduction is 2.01%, 1.79%, 2.09%, and 1.86%, and irrespective of the value of the driving pressure, the maximum displacement appears at the position of the low pile cap. The minimum displacement appears at the pile foundation of pile pier No. 1 with the greatest length, and the second is at the pile foundation of pile pier No. 2 with the second greatest length. It shows that the deeper the pier is, the closer it is to the interval line from the excavation tunnel, and the greater is the effect of excavation on the pier. This is a key point that should be considered in the project (Cao and Zhuge 2013).
In the process of TBM excavation, the left and right tunnels are excavated through pile foundations No. 1, No. 2, No. 3, and No. 4, in turn. The vertical settlement of the pile foundation caused by different driving pressures is shown in Figs. 17–20.
As can be seen from Figs. 17–20, the displacement curves of pile foundations of the piled bridge piers with different lengths and positions are different, and the trends of the vertical displacement curves of pile foundations No. 1, No. 2, and No. 4 are similar. With the progress of construction steps, the changes in vertical displacement stabilize first, and then accelerate; subsequently, the changes continue gradually, and finally accelerate again. The pile foundations No. 1 and No. 4 are approximately in a vertical plane. The effect of the TBM excavation on these foundations is similar. However, the lengths of the two pile foundations from the excavation surface of the subway are different. The pile foundation No. 1 is closer to the excavation tunnel, and hence its final vertical settlement is greater than that of pile foundation No. 4. Thus, the pile foundation close to the tunnel section line should be paid more attention during construction. For pile foundations No. 1 and No. 2, the length is greater, and they are located near the centerline of the left and right tunnels. The construction of the left and right lines has the same effect on pile foundations No. 1 and No. 2, but pile foundation No. 2 is relatively short in length, and hence the final settlement value is less than that in the case of pile foundation No. 1. For the vertical displacement curves of piles No. 1, No. 2, and No. 4, the settlement values increase significantly at the twenty-fifth step of construction. Considering that the left-line excavation is conducted before the right-line excavation, it can be concluded that the effect of the right-line construction on the pile foundation is greater than that of the left-line construction. The final settlement values of pile foundations No. 1, No. 2, and No. 4 are greater than that of pile foundation No. 3, and hence special attention should be paid to the change in the pile foundation settlement of pile column piers No. 1, No. 2, and No. 4 overpass during the right-line tunnel excavation. The vertical displacement of pile column pier No. 3 increases first and then becomes smooth until the final settlement value is approximately 2 mm, which is far less than the safe limit for pile foundation settlement (± 4 mm). For the vertical displacement curves of the pile foundations under different driving pressures, the foundations of piles No. 2 and No. 4 show significant changes in settlement values under different driving pressures, indicating that pile foundations No. 2 and No. 4 are more sensitive to changes in driving pressure; irrespective of the pile foundation, with the increase in driving pressure, the settlement value decreases.
5.4 Shield fuselage vibration analysis
5.4.1 Vibration control specifications
To date, no specific control standard has been established for the vibrations during TBM construction in China. To evaluate the effect of the vibrations on the structures, the main vibration frequency and peak vibration speed are normally used in China and other countries. Blasting safety regulations provide the allowable particle vibration speed of various building structures in different main vibration frequency ranges. With reference to this standard, a safety assessment of TBM construction vibration is conducted as follows (Avunduk and Copur 2019).
5.4.2 Analysis of simulation results
The velocity curves in the vertical (Vy) and horizontal (VX) directions at section DC2 in the ground are shown in Fig. 21.
The vertical vibration velocity is the smallest near the central axis of the two tunnels, and the largest above the respective tunnels. The maximum vibration speed is 3.32 mm/s near the left line and 1.94 mm/s near the right line; the speeds gradually decrease toward both sides. The horizontal vibration velocity is the largest near the left tunnel with a maximum value of 12.13 mm/s, which decreases gradually toward both sides. The horizontal vibration speed is always greater than the vertical vibration speed, and the maximum vibration speed does not exceed the general civil building requirement of 20 cm/s. Therefore, the ground vibration speed caused by tunneling is within the safe range; thus, the horizontal vibration plays a key role. In practical engineering applications, the impact of the horizontal vibration on surface vibration should be considered.
Points DC3 and DC4 at the upper and lower parts of the surrounding rock of the right-line tunnel are studied to analyze the effect of the vibration caused by TBM tunneling on the surrounding rock soil. Fig. 22 shows the curve of the vibration speed at DC3 and DC4, on the surface with the construction time. The vibration of the TBM excavation greatly influences the surrounding rock of the upper and lower tunnels. With continued excavation, the vibration speed shows the same increasing trend. The rate of increase of vibration speed is the highest in the first 1000 s and gradually decreases thereafter. The upper part receives a larger impact (higher by 1.5%) than the lower part. In actual construction, the upper surrounding rock vibration support must be considered to prevent hidden safety hazards.