Numerical Investigation into the Effects of Controlled Tunnel Blast on Dynamic Responses of the Transmission Tower

. At present, the drill-and-blast method is still one of the main construction means in the road tunnel excavation process. When the tunnel penetrates underneath sensitive structures such as high-voltage transmission towers, the blasting and supporting parameters must be strictly controlled to ensure the stability and safety of the surface structures. In this paper, numerical simulations based on a large-section shallow buried tunnel project in Zhuhai are conducted to study the efect of controlled tunnel blast on the dynamic response of transmission towers. Te numerical simulation results indicate that the blast vibration velocity of the rock generated by controlled blasting decreases rapidly along the tunnel excavation direction. Te blast vibration velocity of the high-voltage transmission tower and its pile foundation gradually increases with the propagation of the blast waves, and the maximum vibration velocity is about 1.24cm/s. Te results indicate that the controlled blasting design of this project can efectively restrain the vibration velocity induced by the blasting load and could ensure the stability and safety of the transmission tower.


Introduction
With the rapid development of highways in China, largesection tunnels are widely used in highway construction because of their ability to signifcantly reduce road mileage and improve transport efciency.Te tunnels would sometimes inevitably penetrate beneath sensitive structures, such as transmission towers and other existing structures, which poses challenges for the design and construction of large-section tunnels.
At present, the drill-and-blast method is still one of the main construction methods in the road tunnel excavation process [1][2][3].When the tunnel penetrates underneath sensitive structures such as high-voltage transmission towers, the blasting and support parameters need to be strictly controlled to ensure the stability and safety of the surface structures.To study the infuence of vibration caused by controlled blasting on rock mass and sensitive structures, site test and numerical simulation methods are widely used by researchers [4][5][6][7].Te site test can objectively refect the infuence of blasting vibration on the rock mass structure.However, due to the nonhomogeneity and the defects of the internal structure in the rock mass, the experimental conditions are difcult to control.Compared with the site tests, the numerical calculation can simulate the dynamic response problem in the complicated geological conditions, thus the numerical simulation method is widely used to analyze the blasting vibration response.Some studies [8][9][10] evaluated the vibration damage to transmission towers based on the fnite element method.Luo et al. [11] analyzed the dynamic characteristic of the tunnel for surface explosion of 100 and 300 kg TNT charge, respectively.Duan et al. [12] investigated the vibration characteristic of high-voltage tower under the infuence of adjacent tunnel blasting excavation.Beside the study on the infuence of vibration induced by controlled blasting on transmission tower, more research focuses on the dynamic responses of adjacent structures.Zhao et al. [13] used feld monitoring experiments and numerical simulation to study the efect of blast-induced vibration from adjacent tunnel on existing tunnel.Jiang et al. [14] investigate the efect of excavation blasting vibration on adjacent buried gas pipeline in a metro tunnel.However, the dynamic responses of the transmission tower system remain one of the most challenging tasks in the civil engineering as a complex, continuous, and mechanical system.
Based on a large-section shallow buried tunnel project in Zhuhai, China, this paper studies the efects of controlled tunnel blasting on the dynamic responses of high-voltage transmission towers.Tree-dimensional numerical analyses were conducted in the fnite diference program FLAC3D, and the dynamic responses of the tunnel surrounding rock and high-voltage transmission towers under the blast loading were studied.Te vibration velocity, deformation responses of surrounding rock and high-voltage transmission towers were predicted to provide scientifc basis and reference for relevant construction optimization and decision-making.

Overview of the Project
Te Black and White General Hill tunnel is a large-section shallow buried tunnel under construction in Zhuhai, China, which is built to enhance the transportation links between diferent districts in Zhuhai.Te exit section of the tunnel penetrates directly underneath a high-voltage transmission tower.A schematic view of the locations of the tunnel and transmission tower is shown in Figure 1.Te transmission tower is a 2F-SJ2 type tower with a total height of 41.5 m, supported by four piles with a diameter of 2.1 m and a length of 12 m.Te vertical distance from the top of the tunnel to the pile toe is about 7.5 m, and the smallest horizontal distance from the tunnel to the transmission tower is about 1.9 m.
Te surrounding rocks at the tunnel exit consisted of medium strongly weathered quartz amphibolite.Te arches and sidewalls of the tunnel exit are of poor stability, which could lead to rock collapse and drops at drill-and-blast excavation.Te uneven weathering of the surrounding rocks has an impact on the stability of the tunnel portal and the side slopes.Tese geological conditions would pose a threat to the stability of the transmission tower.
According to the geological survey, the soil stratum from top to bottom within the exploration depth is divided into clay, fully weathered, strongly weathered, medium weathered, and slightly weathered quartz amphibolite.Based on the results of the wave velocity test and other geotechnical tests, the physical properties of the soil and rock are shown in Table 1.

Numerical Model.
A 100 m range of tunnel exit (mileage YK4 + 820-YK4 + 920) is selected as the modelling area, with the tunnel and transmission tower included.Te numerical model built in FLAC3D is shown in Figure 2. Considering the infuence of tunnel depth and blasting, the total length and width of the model are selected as 100 m and 52 m, respectively, which could efectively reduce the boundary efect.Te axis used in the numerical model is defned as follows: X axis is along the direction of tunnel excavation; Y axis is along the cross-section of the tunnel; and Z axis is along the gravity direction.Te numerical model mainly consisted of the tunnel, surrounding rocks, transmission tower, and its fle foundation.It is noted that the transmission tower and its pile foundation are modelled using the structure elements implanted in FLAC3D to reduce model complexity and increase calculation speed.Te total number of zones in the 3D numerical model is 112,400, and the total number of nodes is 12033.
Te high-voltage transmission tower is built upon a hill which the tunnel penetrates through.Te curved surface of the hill needs to be considered in the numerical model to obtain a correct initial stress condition in the surrounding rocks.Te curved surface is generated in SketchUp by importing the contour lines of the hill.Ten, the 3D hill surface is exported to FLAC3D, and it connects with the tunnel model built in FLAC3D to form the 3D numerical model.Te process of model generation is shown in Figure 3. Te soil layer distribution is generated based on the geological data using the curved surface import method.

Constitutive Model and Material Parameters. Te
Mohr-Coulomb model is selected as the constitutive model for the soil and rock in this project.Te parameters of density, cohesion, and friction angle are adopted directly from the geological survey data, which is shown in Table 1.Te transmission tower is modelled with the beam element implemented in FLAC3D, which is a two-noded, straight, fnite element with six degrees of freedom per node.Te beam element has three material parameters, density, elastic modulus, and Poisson's ratio, which are set to be 7850 kg/m 3 , 200 GPa, and 0.3, respectively.Te pile foundation of the transmission tower is modelled using the pile element, which could efectively simulate the normal-directed 2 Advances in Civil Engineering (perpendicular to the pile axis) and shear-directed (parallel with the pile axis) frictional interaction between the pile and the soil.Te soil-pile interaction is considered by the shear and normal coupling springs.Te coupling springs are nonlinear, spring-slider connectors that transfer forces and motion between the pile and the grid at the pile nodes.Te shear behavior of the pile-grid interface is cohesive and frictional in nature.Te lining and anchors used as tunnel supporting are simulated with the liner element and cable element, respectively.Te parameters of the structure element (pile, liner, and cable) adopted in this paper are shown in Tables 2-4.

Blasting Load.
Due the short distance from the tunnel and the sensitivity of the transmission tower, the controlled blast and double-sided guide-pit method are adopted in the excavation and initial support of tunnel exit to ensure the stability of the transmission tower.Te detailed blast-hole distribution and blasting sequences for the double-sided guide-pit method are shown in Figure 4. Tere are about 330 blast-holes in each blast section, distributed in a crosssectional area of 305 m 2 .Te unit explosive consumption is about 0.9 kg/m 3 for the controlled blast design.In order to study the efect of controlled blast on the dynamic responses of the transmission tower and surrounding rock, the blast load generated by millisecond delay blasting needs to be applied at the tunnel.
In the process of blasting, the interaction of stress waves generated by blasting will make cracks spread along the connecting line of adjacent blastholes.With the growth of the blast induced crack and interpenetration throughout the rock, a new free surface will be created along the blasthole line, which is the designed blasting excavation boundary.Terefore, the blasting excavation boundary is taken as the inner boundary of the numerical model.Tus, the full scale blastholes are not included in this model, and the blasting pressure is applied equivalently to the excavation boundary, which avoids tremendous model meshing and computational work due to detonations of too many tiny blastholes.
In this paper, an equivalent pulse load of the multihole blasts is applied at the blasting excavation boundary of the tunnel.Tis simplifed equivalent load method certainly causes some deviation in the immediate vicinity of blastholes.However, this study is to investigate the dynamic responses of the transmission tower and surrounding rocks outside the blasting boundary rather than the explosioninduced rock fracture and fragmentation process around blastholes.Terefore, this equivalent pulse load simplifcation is acceptable to a certain degree.Following the procedure used by Yang et al. [15,16], the equivalent pulse load applied in this paper is shown in Figure 5.  Terefore, the numerical study chooses the condition where the tunnel has been excavated directly underneath the transmission tower, and the initial support and cables have been installed in the excavated part of the tunnel, which is shown in Figure 6.Te blast load generated by the frst section of the tunnel (as shown in Figure 4) beneath the transmission tower is applied at the numerical model, when the infuence of the blast on the transmission tower is the most obvious.
Before the blast loading is applied, the boundary of the numerical model is set to be fxed in their normal direction to calculate the initial stress condition.In static analysis, fxed boundaries applied here are realistic since the model size is large enough and the boundary is placed at some distance from the region of interest.However, such boundary conditions cause the refection of outward propagating waves back into the model and do not allow the necessary energy radiation.Terefore, the fxed boundary condition is converted into a viscous boundary by using independent dashpots in the normal and shear directions at the model boundaries in the dynamic loading stage.

Responses of the Surrounding Rock.
To ensure the stability of the transmission tower, the dynamic responses of the surrounding rock are analyzed frst.Figure 7 shows the time histories of blast velocities measured at diferent distances from the blast surface.Te maximum blast velocities along X, Y, and Z axis caused by controlled blasting of section 1 are about 9 cm/s, 0.58 cm/s, and 3 cm/s, respectively.It can be concluded that the control blasting of section 1 of the tunnel generates main vibration of surrounding rock in the tunnel excavation direction, while the Y and Z axis component is relatively small.Advances in Civil Engineering Advances in Civil Engineering

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Figure 8 shows the decay curves of the maximum blast velocity along the tunnel excavation direction caused by controlled blasting in section 1, where the red, blue, and green curves are the velocity components in X, Y, and Z direction, respectively.As shown in the fgure, the magnitude of blast velocity components in the three axes decreases rapidly in the range from 10 m to 20 m from the blast surface.Beyond that distance, the maximum blast velocity basically remains constant.
Figure 9 shows the blast velocity contour of the rock mass due to controlled blasting in section 1. Te four contour graphs are captured at 0.003 s, 0.012 s, 0.021 s, and 0.03 s after blasting.It can be seen that at 0.003 s after blasting, the rock disturbance caused by controlled blasting of section 1 is basically concentrated within 4 m of the tunnel perimeter.With the increase of time, the range of rock disturbance gradually expands, but its peak size decreases rapidly.After 0.02 s from the start of blasting, the blast velocity around the tunnel has basically decayed to zero, while the vibration velocity above the tunnel is the largest part of the rock mass at this time.Terefore, the controlled blasting design of this project can efectively control the blasting vibration velocity of the rock around the tunnel, which meets the safety requirements of the specifcation and can efectively ensure the safety and stability of tunnel blasting.
Figure 10 shows the maximum dynamic stress induced by the controlled blast, which is measured at 3 ms.As shown in the fgure, the maximum dynamic stress occurred at the surrounding rock located near the blast section, with a value about 10 MPa.Te dynamic stress decreases dramatically with the increase of distance from the blast section, with an  8 Advances in Engineering 80% reduction in the peak value at the location with a distance of two times the largest dimension of the blast section from the blast center.Advances in Civil Engineering controlled blasting of tunnel section 1, the blasting vibration in Z direction frst increases and then decreases, with a peak value of about 0.12 cm/s.Te blasting vibration velocity Vz in the Z-axis direction decreases to zero at about 0.2 s after the blasting.Terefore, the magnitude of velocity measured at the base of the transmission tower is relatively small and will not pose a threat to the stability of the transmission tower, which demonstrates the validity of the controlled blasting design.

Responses of the Transmission
Te diferential settlement of the transmission tower is a key factor to monitor in practice to ensure the stability of the transmission tower.Terefore, the vertical displacements of the tower base are measured at the end of blast loading.Figure 12 presents the vertical displacement at the four corner nodes of the tower base and their relative position to the blasting surface.Te maximum and minimum vertical displacements of the tower base are about 0.37 and 0.14 mm, respectively, which would result in a diferential settlement of 0.23 mm.It can be concluded that the diferential settlement would only cause a neglectable tilt angle and would not threaten the stability of the transmission tower.
Figure 13 shows contour of vibration speed of the transmission tower generated by controlled blasting.As can be seen, the maximum vibration speed of the transmission 10 Advances in Civil Engineering tower and its pile foundation is about 0.02 cm/s at 0.003 s after the controlled blasting.As the blast wave in the rock propagates to the surface, the vibration speed of the transmission tower and its pile foundation gradually increases and its maximum vibration velocity is about 1.24 cm/ s, which occurs at the location of the tower base 0.012 s after the blasting.Ten, the vibration speed gradually decreases.It can be concluded that the design of controlled blasting of this project can ensure that the vibration speed of the transmission tower is below the safe vibration speed of 3.5 cm/s in the Chinese specifcation.Due to the short distance between the pile foundation and the undercrossing tunnel, the dynamic responses of the pile foundation would also afect the stability of the transmission tower.Terefore, the maximum bending moment of the pile is measured during the controlled blasting, which is shown in Figure 14.Te peak value of the bending moment developed in the pile is about 920 N•m, which is developed at 7 m below the pile top.Terefore, the blasting wave generated by controlled blast would not signifcantly afect the internal force in the pile.Tis result indicates that the pile foundation and the transmission tower remained stable during the blasting construction.

Conclusions
Tis paper investigates the dynamic efects of controlled tunnel blasting on surrounding rock and high transmission tower.A three-dimensional numerical analysis of a large section shallow buried tunnel under a transmission tower was conducted.Te dynamic responses of the surrounding rock and the high transmission tower were analyzed in detail.Te main conclusions can be drawn as follows: (1) Te vibration speed generated by controlled blasting decays rapidly along the tunnel excavation direction (2) At 0.003 s after the start of blasting, the rock disturbance caused by controlled blasting of section 1 is basically concentrated within 4 m of the tunnel perimeter, and with the increase of time, the rock disturbance range gradually expands, but its peak size decays rapidly (3) As the blast wave in the rock mass propagates to the ground surface, the vibration speed of the transmission tower and its pile foundation gradually increases with a maximum vibration velocity of about 1.24 cm/s (4) Te controlled blasting design of this project can efectively restrain the vibration velocity of the surrounding rock and the transmission tower, which could ensure the stability and safety of the transmission tower.

Figure 1 :
Figure 1: Schematic view of the locations of the tunnel and transmission tower.

Figure 9 :
Figure 9: Blast velocity contour of the rock mass.

Figure 10 :
Figure 10: Te maximum dynamic stress measured at the blasting surface.

Figure 11 :
Figure 11: Vibration speed time histories at the tower base.

Figure 12 :
Figure 12: Vertical displacement measured at the tower base.

Figure 13 :
Figure 13: Vibration speed contour of the transmission tower.

Table 1 :
Property parameters of the soil.

Table 2 :
Parameters of pile elements.

Table 3 :
Parameters of liner elements.

Table 4 :
Parameters of cable elements.
Tower.Figure11shows the time histories of blasting velocity in Z direction at the corners of the base of the high-voltage tower.During the