Submerged floating tunnel (SFTs) are typically subjected to complex external environmental and internal loads such as wave currents and traffic load. In this study, this problem is investigated through a finite element method able to account for fluid-structure interaction. The obtained results show that increasing the number of vehicles per unit length enhances the transverse vibrational displacements of the SFT cross sections. Under ultimate traffic load condition, one-way and two-way syntropic distributions can promote the dynamic responses of SFTs whereas two-way reverse distributions have the opposite effect.

Compared with other underwater traffic structures, submerged floating tunnels (SFTs) enjoy from some advantages such as shorter length and higher cost-effectiveness as well as less sensitivity to climate, surrounding environment and navigation conditions [

At present, no SFT structure exists in the world. The SFT design scheme proposed in this work was mostly a large cross-sea traffic structure for internal passage of cars and/or trains with external support system to maintain the balance of the overall structure. Due to the complex external environmental conditions of SFTs, there are several dynamic load types during operation period which wave and current around SFT, water flow excitation loads of anchor cables and vehicle loads inside the structure are the most common dynamic loads. In existing research data, the dynamic responses of SFTs under wave and current load [

Tariverdilo et al. [

Mulas et al. [

Lin et al. [

During the operation period of SFT structures, heavy vehicles, fast moving vehicles, vehicle shock effects and other conditions had significant impacts on SFT vibrations decreasing the driving comfort and stability of structures. In addition, the combined action of wave-current and vehicle loads was also a major factor in the generation of vibration, damage and fatigue failure of long distance SFT structures, thus affecting their operation and service quality.

In this paper, vehicle loads inside SFT were adopted as research objects and finite element numerical simulation analysis method was applied to evaluate the influences of the distribution mode, shock effect and limit condition of vehicle load on the dynamics of SFT structures, so as to provide a reference for the subsequent design and related research of SFT structures.

Due to the lack of a real SFT structure in the world at present and their high complexity, it was necessary to simplify SFT structures into numerical simulation analysis and carry out relevant calculations under assumed conditions. Based on the existing design data and research results around the world [

In order to facilitate the research, an SFT structure with length L with elastic supports at equal spacing was assumed as an elastic foundation beam structure. Anchor cables were simplified to springs with stiffness K and damping, connections among anchor cables and SFT were assumed as hinge joints. Traffic load in SFT was simplified to vertical moving load F(t). The simplified SFT model is presented in

In this paper, the downstream (X direction) and cross-flow (Y direction) vibrations of SFT structures under traffic load were studied and corresponding vibration differential equations were obtained as [

where _{s}_{s}_{x}(z, t)_{y}(z, t)

According to the assumed conditions, SFT was considered as an equidistant elastic support beam. Galerkin method was applied to derive the vertical displacement equation of SFT under traffic load as:_{n}(_{n}(

where

Flexible connections were assumed among SFT pipe bodies. Based on simplified SFT model, the boundary and initial conditions of SFT could be determined as:

According to

The lateral displacement of SFT was calculated by a similar method.

In this research, the finite element analysis software ANSYS Workbench 17.0 was applied for numerical simulation calculations, mainly due to its high capacity of structural, fluid and coupling analyses. Based on the analysis characteristics of ANSYS Workbench 17.0, analysis modules such as Static Structural (static analysis), Modal (modal analysis), Transient Structural (transient dynamics analysis) and Fluent (fluid dynamics analysis) commands were applied [

SFTs are generally long, up to thousands of meters or even tens of kilometers. SFT structures are connected by several pipe segments and the length of a single pipe segment is mostly designed to be 100–200 m. In this research, one pipe segment with 100 m length was selected for numerical analysis. The cross-section of SFT was considered to be oval and road surface plate was set inside. The space below road surface plate was designed for filling ballast and placing other ancillary facilities. The specific size of the cross-section was adopted based on the existing design scheme and model test [

SFT structures are consisted of a tunnel pipe body, tension leg anchor cables, pipe segment connecting devices and anchoring devices, as shown in _{1}_{2}

Length of pipe (m) | H_{1} (m) |
H_{2} (m) |
A (°) | D (m) |
---|---|---|---|---|

100.0 | 20.0 | 30.0 | 30.0 | 50.0 |

After SFT segment model was established, it was also necessary to divide grids before numerical calculation, as shown in

The material parameters of SFT model are given in

Density/(kg/m^{3}) |
Modulus of elasticity/GPa | Poisson’s ratio | Damping of anchor cable/(N⋅s/m) | Stiffness of anchor cable/(N/m) |
---|---|---|---|---|

2500 | 30 | 0.2 | 2 × 10^{6} |
1 × 10^{9} |

In fluid model, wave and current effects were taken into account at the same time. Wave was assumed to be airy linear wave and current followed RNG

Current in fluid model was assumed as a steady flow; i.e., physical quantities such as velocity, pressure, temperature, density, etc., at any point in flow field were not changed with time. Related parameters of fluid model are summarized in

Height of wave/m | Length of wave/m | Velocity of current/(m/s) | Density of current/(kg/m^{3}) |
---|---|---|---|

2.0 | 32 | 3.0 | 1028 |

During the operation period of SFT, vehicle load is the most common functional load and the selection of vehicle load model is critical in studying structural dynamic responses [

In this paper, a single circle was adopted for the simulation of contact surface between wheels and road surface and the diameter of a single circle under different wheel loads was calculated using

In the numerical analysis model of SFT, traffic loads were uniformly distributed within a single circle and arranged along the one-way center line of road surface plate, as shown in

Vehicle loads on pavement board inside SFT were considered as moving vibration loads, which was determined by _{0}_{0}^{2}/m), _{1}_{2}^{−1}) and was calculated by

where _{c}

The calculated parameters of traffic load model are summarized in

_{0} |
_{0}^{2}/m) |
_{1} |
_{2} |
||
---|---|---|---|---|---|

60 × 103 | 300.0 | 12.0 | 0.004 | 80.0 | 0.012 |

Traffic volume has to be considered when studying traffic load in SFTs. Traffic volume was defined as the number of vehicles passing through a road section in a unit time. In the SFT numerical model developed in this research, traffic volume was assumed as the number of vehicles passing through an SFT section at a constant speed within a specified time.

In order to simulate different traffic volumes, differrent numbers of vehicles were assumed to pass through SFT section at the constant speed of 80 km/h in both directions. The number of vehicles was adjusted by changing the distance between adjacent vehicles and two traffic loading modes of two-way single-vehicle and two-way multi-vehicle were adopted, as shown in

In this research, vibration displacements at mid-span of SFT structures under different traffic volumes were analyzed. When there was no traffic load, the dynamic response increments of SFT under the actions of different traffic volumes were calculated and the influences of different traffic load modes on dynamic responses were studied. Dynamic response increments are shown in

It was seen from

It was seen from

In the process of driving, even when the vehicle is in starting, stopping and other braking states, vehicle tires have impacts on road surface due to uneven road surface. In this section, the influence of the impact caused by vehicle in SFT on the dynamic responses of the structure is studied.

According to simplified SFT model, a middle pipe segment was regarded as a continuous beam structure and the connection between anchor cable and pipe segment was assumed as the fulcrum of continuous beam. Considering the mechanical characteristics of continuous beam and the vibration mode of pipe segment in modal analysis, it was proposed to add impact load at the L/4 and mid-span of pipe segment to simulate the braking behavior of vehicles. It was assumed that two vehicles were driving towards each other at the constant speed of 80 km/h from the two ends of the pipe, then braked at the L/4 and mid-span of the pipe. Impact load was added into a short period of time (0.1 s) which was obtained by dynamic increment multiplying the moving vibration load when driving at constant speed. The schematic diagram of impact action of traffic load is presented in

Dynamic response increments of SFT under two different impact loading conditions were calculated, as shown in

It was seen from

In order to study the dynamic responses of SFTs under ultimate traffic load condition, three different traffic load conditions were designed according to China’s Highway Bridge Load Test Regulations (JTG/T J21-01-2015) [

Under the action of three different traffic load ultimate conditions, the dynamic response increments of vibration displacements along mid-span transverse and downstream directions were calculated; the obtained results are shown in

It was seen from

Under the ultimate traffic load condition of two-way reverse distribution, the incremental value of transverse vibration displacement in the mid-span was negative with the maximum amplitude of −0.16 mm, indicating that two-way reverse distribution suppressed transverse vibrations in mid-span. According to existing research results, two-way reverse distribution was closest to real traffic flow and transverse vibration displacement of pipe section in mid-span was mainly influenced by anchor cable material. Therefore, in SFT design, as long as the anchor cable parameters were properly selected, internal traffic load was in the form of normal traffic flow, which could restrain the transverse vibration of SFT to a certain extent.

It was seen from

In this research, finite element analysis method was applied to investigate the influences of traffic load distribution mode, impact action and limit condition on the dynamic responses of SFT structures and the following conclusions were drawn:

In traffic load distribution mode, the number of vehicles per unit distance was proportional to the amplitude of the dynamic response increment of SFT. Vehicle spacing encryption had a certain suppression effect on transverse vibration displacement in the mid-span of pipe, while it had unstable effect on downstream vibration displacement. The amplitudes of downstream vibration displacement increment curves varied greatly, which might be caused by the horizontal force of traffic load.

The impact of traffic load had an obvious enhancement effect on the transverse vibration displacement increment of the cross section. When a vehicle braked at L/4 and L/2 sections, the dynamic increments of transverse vibration displacements of the sections were 1.145 and 1.212, respectively. This indicated that traffic load had a certain influence on the dynamic response of SFT.

Under ultimate traffic load condition, one-way and two-way syntrop distributions promoted the dynamic responses of SFT, while two-way reverse distribution inhibited the increase of dynamic response.