Structural Dynamic Response of a Shield Tunnel under Aircraft Taxiing Load

Dynamic load is an important factor affecting the safety and stability of subway tunnel structures. To obtain the variation law of shield tunnel structure dynamic response under aircraft taxiing load, a three-dimensional numerical simulation of such tunnel under the action of aircraft taxiing load is performed on the basis of a project involving a shield tunnel orthogonal underpass taxiway. +e effects of sliding speed and tunnel depth on the structure of the shield tunnel are also analyzed. +e results show that the transverse displacement and acceleration response of tunnel segment exhibit evident time-space effect under the action of aircraft taxiing load. +e transverse displacement and arch waist acceleration of the shield segment increase first and then decrease.+e transverse displacement of the arch waist reaches its maximumwhen the aircraft taxis directly above the tunnel. +e sliding speed exhibits an evident influence on the dynamic response of shield tunnel structure. +e vertical and convergence displacements of tunnel segments increase with the increase in sliding speed. +e dynamic response of tunnel structure is significantly affected by the factors of tunnel buried depth. +e vertical and convergence displacements of tunnel segments decrease with the increase in tunnel buried depth.+erefore, the safety of the shield tunnel structure can be ensured by controlling the taxiing speed when the aircraft taxis directly above the tunnel. +e measures of increasing the buried depth of the tunnel or strengthening the tunnel structure need to be considered when the taxiing speed is large.


Introduction
Subway construction has effectively solved the problem of urban traffic congestion and has become the main way to effectively improve the function of the airport comprehensive transportation hubs. Given that aircraft load is a dynamic load that has a significant effect on the safety of shield tunnel structure, the structural dynamic response of a shield tunnel under aircraft taxiing load must be studied [1,2].
A number of undercrossing projects in aircraft movement areas have been successfully implemented in China and abroad; these projects include the Taipei Songshan Airport municipal road undercrossing project in an operating runway [3,4], the Shanghai Rail Transit Line 10 undercrossing project in Hongqiao Airport's runway [5], the Beijing Capital International Airport L taxiway crossing project [6], the British airport cargo corridor project [7], the German mining method tunnel undercrossing in an airport runway [8], and the Chengdu Metro Line 10 crossing in Chengdu Shuangliu International Airport [9]. With the increase in number of undercrossing projects in airports, scholars have conducted considerable research on tunnel projects in aircraft movement areas. Luo et al. [10] analyzed the variation law of horizontal and lateral displacement of soil under load based on the strain path and source-sink methods. Wang et al. [11] deduced the additional stress formula at any soil depth under aircraft load by using Boussinesq's solution and elastic layered theory. Under the premise that the tunnel surface structure of an aircraft movement area is coordinated and deformed with the subsidence of the foundation, Zhang et al. [12] developed the control formula in which shield construction causes no an antislope problem in the tunnel structure when crossing the runway of an aircraft movement area. Zhang et al. [13] used three-dimensional (3D) finite element numerical simulation to obtain the runway subsidence law caused by an underpassing in a two-line shield tunnel.
e above research mainly focused on the influences of tunnel excavation on structures and surface settlement in the airport area. However, studies on the structural properties of the shield tunnel under aircraft load are limited. Aircraft load will have an adverse effect on the tunnel when the tunnel structure is in the muddy stratum. erefore, ensuring the stability of tunnel structure and surrounding soil under aircraft taxiing load is an important problem. In this paper, the numerical simulation method is used to study the variation law of taxiing speed on the dynamic response of tunnel segments and analyze the dynamic response of tunnel segments under different buried depths. e deformation law of the existing tunnel under aircraft taxiing load is obtained, and the acquired findings are important to the design, construction, and operation of subway tunnels and provide reference for similar projects.

Project Background
A shield tunnel exists under the operated airport. e aircraft movement area has the reference code 4E. e taxiway material is asphalt concrete, with a thickness of 1 m, and the taxiway has a natural foundation. e field foundation soil is divided into five engineering geological layers in accordance with the results of drilling, in situ test, and laboratory test. From top to bottom, the layers are plain fill, sandy silt, silt, mucky clay, and muddy silt clay. e entire tunnel is in the mucky clay layer, which has the characteristics of large layer thickness, low strength, high compressibility, and poor engineering properties. e total length of the shield section is approximately 3,274 m, with a buried depth of 10-18 m and a diameter of 6.2 m. e width of the single ring segment is 1.2 m, with a thickness of 350 mm. e shield section crosses the taxiway at the position of K51 + 039.788-K51 + 315.216 on the right line and K51 + 050.228-K51 + 323.346 on the left line. Figure 1 illustrates the position relationship between the shield tunnel and taxiway.

Determination of Aircraft Load
Aircraft taxiing load refers to the dynamic load generated by aircraft self-weight and acceleration on the taxiway during takeoff and landing. e aircraft load is mainly borne by the main landing gear in accordance with the load distribution factor and transmitted to the pavement through tires. e main landing gear usually is uniaxial and double-wheeled, biaxial and double-wheeled, and triaxial and doublewheeled [14]. To simulate the adverse effect of taxiing load on tunnel structure to the greatest extent, the maximum aircraft A380-800F is selected as the calculation parameter, and its maximum takeoff weight is 5600 kN. Figure 2 shows the tire layout of the A380-800F model, and Table 1 provides the aircraft calculation parameters.

Wheel Pressure of the Single Tire of an Aircraft.
e wheel load on the main landing gear of the aircraft is calculated accordance with the following formula [15]: where P t is the wheel load assigned to a single tire on the main landing gear, kN; G is the aircraft quality, t; p is the distribution factor of the main landing gear load; n c represents the number of main landing gears; and n w represents the number of wheels on a landing gear.

Calculated Size of Aircraft Wheel Prints.
To facilitate the establishment of the model, the wheel printing is simplified into a rectangle using the following equations [15] and in accordance with the principle of area equivalence: where L t is the length of the aircraft wheel prints, W t is the width of the aircraft wheel prints, and q is the tire pressure. Figure 3 shows the shape of aircraft wheel prints.

Establishment of 3D Finite Element Model.
In this paper, a 3D numerical model of dynamic response of the shield tunnel under aircraft load is established using finite element software. e model is mainly composed of aircraft load, taxiway, and shield tunnel. According to the actual project, the buried depth of the tunnel is 10 m, the diameter is 6.2 m, the segment thickness is 350 mm, and the single ring segment width is 1.2 m. e aircraft load is simplified as the surface load acting on the taxiway, and the directional displacement is specified to simulate the aircraft taxiing. To reduce the influence of boundary on the model, the size of the 3D numerical model is set as 30 m × 90 m × 40 m. In addition, the bottom of the model adopts horizontal and normal fixed constraints, the four sides adopt horizontal fixed constraints, and the ground surface is a free boundary. Figure 4 shows the 3D numerical model of the shield tunnel under aircraft load.

Determination of Model Parameters.
According to the actual project, the foundation soil in the site area is plain fill, sandy silt, silt, mucky clay, and muddy silt clay from top to bottom. Assume that all the soil layers are distributed inhomogeneous horizontal regions. Soil layers of the same type and with similar basic parameters are simplified by combining and simplifying the weighted average algorithm. e small-strain soil hardening (HSS) constitutive model [16,17] is selected for mucky clay, and the specific parameters are shown in Table 2. e Mohr-Coulomb (M-C) constitutive model is selected for plain fill, sandy silt, silt, and muddy silty clay. Table 3 shows the specific physical and mechanical parameters of soil. Among the parameters, H is the thickness of the soil layer, c is the cohesive force of the soil mass, φ is the friction angle in the soil, E ref ode is the tangent modulus of the consolidation test, E ref 50 is the secant modulus, E ref ur is the unload-reload modulus, c 0.7 is the shear strain threshold, G ref 0 is the small-strain shear modulus, m is the power exponent, c is the natural gravity, c sat is the saturation gravity, E is the elastic modulus, and ] is Poisson's ratio.
Given that the aircraft load acts on the airport pavement through tires, the aircraft load is simplified as surface load, and its position is determined by the actual aircraft wheel seal. Aircraft taxiing is realized through the change in surface load position. To maximize the adverse effect of taxiing load         [18], the maximum aircraft load and taxiing speed are selected as basic parameters. e specific parameters are shown in Table 4.
In accordance with existing research results [19], the additional stress generated under the flexible pavement of asphalt concrete under the action of aircraft load will be greater than that generated under the rigid pavement of cement concrete. erefore, the constitutive M-C model is adopted for the airport pavement in this numerical model. e constitutive M-C model is adopted for the grouting layer of the shield tunnel, and the contact surface is set between the segment and the grouting layer. e segment is simulated by solid element + plate element. e stiffness of the segment is reduced to 75% to consider the weakening of the overall stiffness of the connector. To facilitate the internal force output of the segment, a layer of the flexible plate element is placed inside the segment's solid element. Its stiffness is regarded as 1/1000 that of the segment, and thus the internal force of the surrounding solid element can be obtained on the basis of the plate element without affecting the force of the segment's solid element. To obtain the changes in displacement and internal force of shield tunnel structure under aircraft taxiing, the monitoring points are arranged at the central arch crown, arch waist, and arch bottom of the tunnel, as shown in Figure 5. Table 5 shows the material parameters of pavement, segment, and grouting layer, and Table 6 provides the plate elements. Figure 6 shows the displacement distribution of shield tunnel segments under the action of aircraft taxiing load. e time-history curves of tunnel segment monitoring points are extracted and illustrated in Figure 7. Figures 6 and 7 show that the displacement of tunnel segments exhibits an evident space-time effect under the action of aircraft taxiing load. Different positions of the ring segment in the shield tunnel have settlement under the action of aircraft taxiing load, in which the maximum settlement of the arch crown is 128.1 mm, followed by the arch waist (95.9 mm). e transverse displacement of shield segments increases first and then decreases. When the aircraft taxis directly above the tunnel, the maximum transverse displacement of the arch waist on the left and right sides of the middle ring of the tunnel is −12.9 mm and 16.3 mm, respectively. Figure 8 shows the acceleration time-history curve at the waist of the ring arch in the shield tunnel under the aircraft taxiing load. Figure 8 also reveals that with the taxiing of the aircraft, the acceleration of the tunnel structure fluctuates greatly before 0.06 s. At 0.06-0.13°s, the acceleration of the arch waist increases first and then decreases. e acceleration reaches the peak when the aircraft taxis directly above the tunnel, at which the maximum acceleration on the right side of the tunnel is 0.38 cm/s 2 which is greater than the maximum acceleration on the left side (0.22 cm/s 2 ).

Soil Hardening Effect.
e mucky clay is shear hardened under aircraft taxiing load, which affects the structural properties of the tunnel. Figure 9 shows the distribution of soil shear hardening around the tunnel under aircraft load. Figure 9 also reveals that the shear hardening of soil around the tunnel mainly occurs at the arch foot without aircraft load and is conically distributed along with the tunnel trend. When the aircraft applies taxiing load on the ground, the shear hardening of soil is mainly concentrated in the upper part of the tunnel and the soil around the arch bottom.
e shear hardening of the soil mass becomes denser with the decrease in distance from the tunnel.

Discussion
Aircraft taxiing load has a significant effect on tunnel structure. Based on the model established above, the variation law of sliding speed on the dynamic response of tunnel segments is studied, and the dynamic response of tunnel segments under different buried depths is analyzed.

Influence of Aircraft Taxiing Speed.
According to the takeoff and landing speeds of civil aircraft, three groups of control groups with different taxiing speeds are set. e specific parameters are shown in Table 7.   Shock and Vibration Figure 10 shows the response time-history curve of the tunnel structure at dynamic times under the action of different taxiing speeds. Figure 10 Table 8 shows the specific parameters. Figure 11 shows the response time-history curve of tunnel segments under aircraft taxiing load at different tunnel depths. Figure 11

Conclusions
(1) e displacement of the tunnel segment shows an evident space-time effect under the action of aircraft taxiing load. With regard to space, the vertical displacement of the vault and transverse displacement of the arch waist are the largest. On the whole, tunnel deformation represents the deformation of vault sink and the expansion on both sides. With regard to time, the transverse displacement of the arch waist first increases and then decreases with taxiing of the aircraft load. e transverse displacement of the arch waist reaches its maximum when the aircraft taxis directly above the tunnel. (2) e acceleration response of the arch waist increases with the approaching aircraft load and decreases as the load moves away from it. e acceleration reaches the peak when the aircraft taxis directly above the tunnel, and the acceleration response on the right side of the tunnel is greater than that on the left side. (3) e influence of sliding speed on the dynamic response of shield tunnel structure is evident. e vertical and convergence displacements of the tunnel segments increase with the increase in sliding speed. e dynamic response of the tunnel structure is significantly affected by the factors of tunnel buried depth. e vertical and convergence displacements of tunnel segments decrease with the increase in tunnel buried depth. (4) e taxiing speed needs to be controlled when the aircraft taxis directly above the tunnel to ensure the safety of the shield tunnel structure. e measures of increasing the buried depth of the tunnel or strengthening the tunnel structure need to be considered if the taxiing speed is large.

Data Availability
All data used during the study appear in the submitted article.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.