Experimental Investigation of the Dynamic Behavior of Submerged Floating Tunnels under Regular Wave Conditions

Abstract

Submerged floating tunnels (SFTs) are an innovative traffic structure for transportation in deep and long-distance ocean environments. SFTs have the risk of being subjected to wave action in the complex ocean environment. Therefore, in order to ensure the safety and stability of SFTs during their service, the dynamic behavior of an SFT subjected to the action of waves is experimentally investigated in this study. Based on the wave–current flume, a physical scale-model experiment of an SFT for studying the dynamic behavior of an SFT subjected to regular waves interactions is deeply and thoroughly explored. The results show that the wave outputs from the wave-making system are verified to be reliable. The influence of major load parameters on the dynamic behavior of the SFT are deeply and thoroughly explored. The effects of wave height and wave period on acceleration, wave pressure, anchor cable force and displacement in an SFT are discussed. This experimental study has theoretical and practical significant for SFT design and safety.

1. Introduction

Submerged floating tunnels (SFTs) are a novel traffic structure suitable for deep and long-distance areas, according to theory. They are primarily composed of a tunnel tube suspended underwater, a mooring system that restricts tunnel movement, deep-water foundations and the revetment section linking both sides [1]. An SFT has its unique features and charm [2,3], including the facts that it will not be affected by bad weather, can be operated around the clock, can be more economically competitive and have a smaller impact on waterway navigation. Therefore, SFTs have become potentially one of the most competitive cross-sea constructions in the twenty-first century [4,5,6]. They are gaining more and more interest in academia. Although the concept of an SFT has been proposed for a long time, the actual engineering of SFTs have not been implemented due to safety and stability issues caused by various environmental loading excitations [7,8]. Therefore, the dynamic behavior of an SFT subjected to the action of waves is studied and understood. It is of practical significance to realize the engineering applications of SFTs as soon as possible.

So far, some research on SFTs subjected to wave–current action has been conducted. Based on the potential function of the flow field, Lai [9] and Tariverdilo et al. [10] derived a formula for the fluid forces acting on the tube body. The key parameters such as the stiffness, length, and anchorage stiffness were discussed by solving the differential equations of motion. Seo et al. [11] proposed a simpler theoretical approach to calculate the forces using linear wave theory and the Morrison equation. Mai carried out research on the dynamic response of SFTs under the action of wave currents and the dynamic response of vortex-induced structures. A finite element numerical computational model for the dynamic response of an SFT system and the solution method were established. The dynamic response of an SFT for the sea conditions, structural section form, placement depth and support form were calculated and analyzed [12,13]. The CR (co-rotational) columnar method of beam cells was used to analyze the effects of incidence wave direction, placement depth and section form on the dynamic response of an SFT under the conditions of a wave [14,15]. Xiang et al. [16,17] proposed a theoretical approach for investigating the nonlinear dynamic response of SFTs under the combined effect of parametric excitation and hydrodynamic excitation. When the current velocity reaches a particular value, the vortex-induced vibration (VIV) of the cable was thought to generate a significant resonance in the structure. The displacement amplitude of an SFT grew as the wave height rose. The intrinsic vibration frequency of an SFT was calculated by the buoyancy-weight ratio of the construction and the anchoring angle of the cable. Hong and Ge [18,19] investigated the effects of tunnel length and uniform incoming current velocity on the lateral vibration response of SFTs by establishing a computational model and using the Galerkin and fourth-order Runge–Kutta methods. The structural finite element model was established on the basis of considering the effects of nonlinear fluid resistance and nonlinear cable restoring forces. The influence of the tube body’s basic parameters on the dynamic behavior of the structure was explored. The BWR (buoyancy-weight ratio) of the tube body played a crucial role in the dynamic response of both the SFT and anchorage system. It ought to be given consideration in the design process. [20,21,22]. Davide [23] developed an algorithm to study the fluid–structure–vehicle interaction (FSVI). They show that displacement and acceleration can be controlled and kept inside the proposed boundaries under storm sea states. Papadopoulos [24] investigated the structural response of the Bjornefjord submerged floating tunnel in current flow. Hemel [25] developed a new model to study the dynamic response of the submerged floating tunnel due to fluid structure interaction. The sway and roll motions, containing accelerations, velocities and displacements, can be obtained.

For the submerged floating tunnel model test, the two-dimensional flume and pool test are mainly used. The model cross sections are mainly circular and the loads mainly earthquake and wave current. Fujita [26] and Venkataramana et al. [27] conducted SFT model tests in shallow water and concluded that the cable tension increased with wave period. Gan [28] tested SFTs under hydrostatic load and obtained the spatial stress distribution of the tube section. Chao et al. [29,30] carried out model tests on the cable fluid–solid coupling vibration section and overall impact response of SFTs. They observed the phenomenon of anchor cable vortex excitation vibration and found that the inclined arrangement of circular cables is beneficial to reduce the adverse effect of vortex resonance. Tian et al. [31] studied the dynamic response of SFTs under the wave force conditions of the internal ocean waves. Qin and Wang et al. [32,33] carried out an SFT model test and investigated the spatial stress and anchor cable axial force distribution law under current action. Wei [34] conducted an experimental study on the acceleration response characteristics of SFTs under wave action and analyzed the changes in the acceleration under different wave conditions. Wang [35] studied the mechanical response of the tube section when subjected to ocean currents by conducting SFT model tests. Yang et al. [36] constructed a longitudinal truncated SFT model test by using wave–current flumes and analyzed the effect of wave–current action on the motion response of SFTs. They obtained the vertical and lateral motion response characteristics of the tube body structure. Zhao et al. [37] used a physical model test method to experimentally study the dynamic response of a three-dimensional elastic SFT in a wave–current field. Deng et al. [38] carried out an experimental study of the vortex-induced vibration of a twin-tube submerged floating tunnel segment model. The influence of spacing ratio on VIV response, lift coefficient and torsional coefficient were mainly studied. Daniil [39] mainly studied water–structure interaction of submerged floating tubes in homogeneous and stratified flows, as well as gravity current development.

Overall, a great number of in-depth research studies have been conducted on the dynamic response of SFTs to external loads such as wave–current environments. However, the following deficiencies still exist. (1) In terms of research objects, the experimental validation of the wave–current-coupled SFT model and accumulation of technology are still not quite perfect. The simulation of the flume uniform current is not sufficiently fine in the model test research. (2) In terms of research methods, the current research on the structural dynamic response of SFTs is mainly based on theoretical derivation and numerical simulation. Few academics have conducted similar model experiments. Due to the limitation of experimental conditions, most of the existing similar model experiments are based on single factors and on a small scale. It is difficult to validate the theoretical calculations and numerical models effectively.

The dynamic behavior of SFTs exposed to wave action is experimentally investigated in this paper. Based on the wave–current flume, the experiments were conducted on an SFT model with a structure scale of 1:60 under the action of regular waves. A number of components, including experimental equipment, test model, instruments, wave conditions and data collection, are thoroughly introduced. The impacts of wave parameters on the dynamic response of SFT acceleration, wave pressure, displacement and cable forces are also explored based on the experimental data. Finally, conclusions are drawn based on the results of the study.

2. Experimental Setup

2.1. Experimental Facility

The experiment was conducted in the underwater tunnel laboratory of the China Merchants Chongqing Communications Technology Research and Design Institute Co., Ltd. The laboratory is equipped with a large wave–current flume with dimensions of 36.0 m × 31.0 m × 3.0 m, in which the wave maker area is 24.0 m × 5.0 m, the wave absorber area is 24.0 m × 2.0 m, the test area is 24.0 m × 24.0 m and the lower outlet is 1.5 m deep. This meets the test requirements for a wide variety of wave–current flumes, as shown in Figure 1. The wave-maker system consists of a wave generation train, servo motor, wave generator controller, computer control system and data acquisition system. Regular linear waves with periods from 0.5 to 2.0 s and wave heights from 2.5 to 20.0 cm and various nonlinear waves can be generated. The current-maker system consists of outlet valves, an axial flow pump array and a computerized control system. With a total flow of 14.1 m³/s and one pump operating at 2.82 m³/s, the combination of five pumps can accommodate various test flow needs. A large movable trailer is used to move test models and instruments. The wave absorbers are installed at the end of the flume. The outer frame of the wave absorber is made of an aluminum alloy material and filled with a plastic blind trench plate. It is mainly used to absorb wave energy and reduce wave reflection.

2.2. Test Model and Instrumentation

In this experiment, the prototype is an SFT scheme for the Qiongzhou strait passageway. The prototype size is shown in

Table 1. Prototype size.

Structure	Parameters	Numerical Value
Tube body	Segment length	120 m
	Long axis and short axis	45 m × 19 m
	Sectional area	671.5 m2
	Buoyancy (after scaling)	373.06 kg
	Bending rigidity	1456
	Elastic modulus	34.5 GPa
	Density	2000 kg/m3
	Buoyancy-weight ratio	1.3
	Damping factor	0.01
Anchor cable	Length	Determined according to water depth and angle
	Diameter	0.346 m
	Mass per unit length	1474.23 kg/m
	Density	7850 kg/m3
	Elastic modulus	210 GPa
	Initial tension	4.6 × 104 kN
	Damping factor	0.0018
Other	Water depth	132 m

. Based on the dimensions of the wave–current flume, a segmented model with a structural scale of 1:60 is designed for the SFT. The model scales of corresponding and other physical quantities are shown in

Table 2. The model scale of the physical quantities.

Physical Parameters	Comparison Relation	Unit
Length	lm = λlF	m
Time	tm = $\sqrt{\mathit{\lambda }}$tF	s
Structural mass	mm = λ3(ρm/ρF)mF	kg
Velocity	vm = $\sqrt{\mathit{\lambda }}$vF	m/s
Acceleration	am = aF	m/s2
Force	Fm = λ3(ρm/ρF)FF	N
Bending moment	Mm = λ4(ρm/ρF)MF	N * m

Note: $\mathit{\lambda }$ = 1:60.

. A detailed diagram of the experimental model is depicted in Figure 2. As can be seen in Figure 2a, the experimental instrumentation consists of a wave–current flume, model tubes, anchoring cables and data acquisition devices.

This experiment selects a typical elliptical section type based on the prior findings [40,41,42]. The model scaling is chosen to be 60 in accordance with a number of parameters, including the structural size of the test section, water depth and flume performance index. The BWR of this test is designed as 1.3 and the remaining buoyancy balanced by the anchor system. The long and short axes of the model are made according to 0.75 m × 0.317 m. In order to avoid the structural damage of the model, the thickness of the model is 8 mm. According to the experience of traditional hydrodynamic tests, the model material is acrylic. The internal partition is designed to increase the overall resistance to deforestation. The model is shown in Figure 2b. The model is installed in the middle of the wave–current flume. To enable proper wave propagation and development, it is around 12 m away from the wave-making pusher. It is about 14 m away from the wave absorber to prevent the influence of reflected waves.

As shown in Figure 2b,c. the instrumentation used in this experiment including: (I) A waterproof accelerometer, the accelerometer can measure the time history of SFT dynamic responses. Its maximum accuracy and range are 0.3% and 2.0 g. When the sampling rate reaches 4 kHz, an error can be ±0.1% F.S. The accelerometer is pasted directly above the end of the SFT. It is calibrated for direction by the internal leveling device. The Z-direction (vertical direction) of the accelerometer is in the same direction as the gravity acceleration direction, the Y-direction (transverse direction) is in the same direction as the wave propagation direction and the X-direction (longitudinal direction) is in the same direction as the length direction of the tube body, as shown in Figure 2a. The connection cable is taped tightly to the tube body with waterproof tape to avoid the influence of the sensor cable on the wave propagation and thus increase the accuracy of the test. (II) A waterproof pressure sensor. The pressure measurement system of the Nanjing Water Conservancy Research Institute was selected for this experiment. The measuring range of the system is 0–20 KPa, the resolution accuracy is 1% and the sampling frequency is 200 Hz. It can measure the wave pressure on the SFT. The numbers of the pressure sensors are named S1–S12, and the 12 waterproof pressure sensors are uniformly arranged in the middle of the tube section, as shown in Figure 2a. The mounting holes need to be reserved according to the dimensions. After the sensor is installed, it needs to be waterproofed to prevent the inflow of liquid. Its wiring is connected to the external channel collector through the reserved gap of the cover. (III) A tension sensor. The tension measurement system of the Nanjing Water Conservancy Research Institute was selected for this experiment. The main parameters of the tension measurement system are as follows: the measuring range is 0–30 kg, the resolution accuracy is 1% and the sampling frequency is 200 Hz. The overall anchor cable layout of the SFT is shown in Figure 2a. Referring to the test scale, the anchor cables are made from 5 mm-diameter stainless steel wire rope. The cables are named C1–C8. They are arranged at both ends of the model, where the C1 to C4 mooring cables are installed at one side of the SFT and the C5 to C8 mooring cables are installed at the other side of SFT. The mooring cables are attached to the model at the corresponding location by stainless-steel clevises. A series of pulley devices are installed at the bottom of the flume to ensure that the mooring cables are secured and installed on the seabed. After the mooring cable is connected to the tunnel, the other end passes through the bottom of the pulleys. The bottom of the pulley is reserved for the mooring cable to pass through and the pulley is smooth to ensure that the mooring cable can slide smoothly around the pulley under stress. The mooring cable passes through the pulley and is connected to the tension sensor by clamping with a stainless-steel collet. The water level in the flume is raised to 1.8 m and the SFT model floated on the water surface. The tension sensors and mooring cables complete the final installation. (IV) A waterproof displacement sensor. The displacement sensor can measure the horizontal and vertical displacement of the SFT. Its maximum range and sampling rate are 1000 mm and 200 Hz. After completing the installation of the tension sensors and mooring cables, the water level is raised to 2.2 m. At this time, the model is located at a depth of 0.4 m underwater. The drawstring displacement sensors are connected via two annular connections at the diagonal of the model. Two horizontal and vertical sensors are installed at each corner, as shown in Figure 2a. The horizontal displacement sensor is mounted using a special round tube mounted on the truss trailer. To facilitate the installation of the vertical displacement sensor, a fixed-size grid structure is laid on the mobile trailer.

2.3. Data Acquisition

Due to the length of the article, only the dynamic response characteristics of the SFT under regular wave action are studied here. In order to ensure the validity of the test results, the regular wave should consider the loading characteristics of the model and the actual water quality conditions. The parameters of regular waves generated in experiments are chosen in the experiments based on long-term observation data from China and previous research results [43].

In this paper, the main tests are designed as follows: (I) reliability verification for wave loading and (II) regular wave test. It is noted that, the water depth d of the wave–current basin is kept at 2.2 m. The wave propagation direction is always perpendicular to the SFT model longitudinal section, which is also the cross section formed by the X-axis and Z-axis in Figure 2a. The detailed test condition elements are shown in

Table 3. Test conditions.

Tests	Experimental Serial Number	Wave Height(m)	Wave Period(s)
Reliability analysis for wave surface	1~4	H = 0.06	T = 0.86, 0.96, 1.06, 1.10
	5~8	H = 0.07	T = 0.86, 0.96, 1.06, 1.10
	9~12	H = 0.08	T = 0.86, 0.96, 1.06, 1.10
	13~16	H = 0.09	T = 0.86, 0.96, 1.06, 1.10
Regular wave test	1~7	H = 0.05	T = 0.8, 0.86, 0.9, 0.96, 1.0, 1.06, 1.10
	8~14	H = 0.06	T = 0.8, 0.86, 0.9, 0.96, 1.0, 1.06, 1.10
	15~21	H = 0.07	T = 0.8, 0.86, 0.9, 0.96, 1.0, 1.06, 1.10
	22~28	H = 0.08	T = 0.8, 0.86, 0.9, 0.96, 1.0, 1.06, 1.10
	29~35	H = 0.09	T = 0.8, 0.86, 0.9, 0.96, 1.0, 1.06, 1.10
	36~42	H = 0.10	T = 0.8, 0.86, 0.9, 0.96, 1.0, 1.06, 1.10

.

3. Reliability Analysis for the Wave Surface

The wave-making system in the experiment creates the regular wave but the generated wave parameters will be affected by many factors. To assure the correctness of the generated waves, it is therefore required to test various wave-making system input parameters before the formal experiment. In the absence of an SFT model, the actual incident wave height is measured at the center of the model position by a capacitive wavemeter. The acquisition time history of the regular wavefront with multiple wave periods is compared with the theoretical solution of the linear wave theory, as shown in Figure 3. The test findings demonstrate that the test apparatus is capable of producing regular waves. Wave propagation under various circumstances is generally stable. The measured wavefront is in good agreement with the theoretical solution with a relative error of less than 5%.

4. Experimental Results and Analysis

4.1. Acceleration Response of the SFT

Figure 4 the time history of acceleration responses for the STF under a wave period of 1.0 s with various wave heights. Acceleration responses of the SFT measured in the experimental tests for three directions, longitudinal (X), transverse (Y) and vertical (Z), are presented in Figure 4. The three directions of the SFT accelerations are clearly exhibiting an escalating pattern of change. The reason for this phenomenon is that the greater the wave height, the greater the water particles at the same water depth are affected by the wave. The increased energy of the water particles leads to a greater acceleration. With increasing wave height, their longitudinal (X) accelerations also decrease. The variation pattern is approximately increasing and then decreasing in one wave cycle. There is a large correlation with wave action. This is mainly caused by the reflection of waves and the interaction between the waves and structures.

The transverse (Y) accelerations are much larger than the longitudinal accelerations. The primary cause of this phenomenon is that the regular wave propagates in the Y-direction. The transverse motion of the water particles drives the transverse motion of the SFT. The transverse (Y) acceleration gradually changes from a large positive acceleration to a negative acceleration much larger than the positive acceleration. It shows that the velocity of the SFT changes a lot in a short time. Additionally, negative acceleration has a significant impact in the huge wave height situation.

The vertical (Z) acceleration shows a more significant nonlinear periodic variation. As the wave height increases, the periodicity becomes more pronounced. Although an increase in wave height leads to an increase in wave steepness and thus wave breaking, the same wave periodicity leads to a more periodic and regular vertical acceleration of the SFT. The upward motion of the SFT tube body is inhibited by the restriction of the anchor cable, whereas the downward motion is more moderate.

Figure 5 shows the effects of waves with a height of 0.07 m and varied wave durations on the time history of acceleration responses for the STF. It can be clearly seen that the acceleration time history of the SFT shows high-frequency and multi-peak characteristics under the action of waves with small periods. Because the wave wavelength is smaller at small periods, this leads to an increase in the wave steepness value for the same wave height. It is induced for the wave breaking phenomena. On the other hand, the action of smaller wavelengths waves on the structure leads to a higher frequency motion of the SFT. The wavelength grows in step with the wave period as well. This leads to a decrease in wave steepness that attenuates wave breaking and energy dissipation. A discrepancy in the dynamic response of the SFT is also caused by variations in the wavelength to structure size ratio.

The above analysis of the time history of acceleration for the SFT tube body shows that the non-linear variation of the acceleration can be observed more clearly during the wave action. In order to further investigate the influence of wave height and period on the acceleration of the SFT, the variation in the maximum and minimum values of the acceleration is discussed below. The ratio of wave height to wavelength (H/L) is quoted in this paper. The wavelength $L$ under the action of regular waves is calculated according to the dispersion relationship of linear wave theory.

Because the acceleration maximum and minimum exhibit comparable tendencies, only the acceleration maximums are chosen for discussion here. Figure 6 shows the variation of the maximum values of the SFT in the three directions of acceleration for different H/L values. When the wave period is certain, the maximum value for the SFT acceleration increases with the increase in the H/L. When the wave height is known, the maximum SFT acceleration value rises and subsequently falls as the H/L value falls. The effect of waves on the SFT tube body is greatly amplified due to the rise in wave height. This phenomenon shows that with the increase in wave period, the influence of waves on the dynamic response of the SFT first increases and then decreases. The major reason for this is related to the ratio of wavelength to the structure. When the ratio reaches a certain value, the wave has the greatest effect on the dynamic response of the structure. It should be noted that the extreme values of longitudinal (X) acceleration are substantially less than the extreme values of transverse (Y) and vertical (Z) acceleration in a certain range. This phenomenon also again verifies the trend of the longitudinal acceleration time history variation. This is mostly due to the fact that the longitudinal acceleration is brought on by wave reflection and structure–wave interaction.

4.2. Wave Pressures on the SFT

As an example, consider the working situation with a fixed water depth of 2.2 m and a period of 1.0 s. The time history of wave pressure at point S5 on the wavefront, point S7 on the top surface and point S9 on the back surface of SFT at various wave heights is shown in Figure 7. The wave pressure time histories of the three places on the SFT tube body may be seen to exhibit more consistent fluctuations. At the same time, it can be found that the wave action time has a backward and forward sequence due to the different locations of the three measurement points. So, there is a certain phase difference in their time histories of the wave pressure. When the wave height is small, the time history of wave pressure on the SFT has many high-frequency components. This indicates that the interaction between the tube body and the wave is more obvious under the overall drive of water particles. The strong wave–structure interaction causes high-frequency vibrations of the wave pressure. As the wave height rises, the high-frequency component of the wave pressure decreases and the quasi-static wave pressure progressively replaces it. The high-frequency component only appears at the maximum and minimum values of the wave pressure and basically disappears at other time ranges. This phenomenon may be caused by the fact that the wave influence on the SFT steadily increases with wave height. This causes the movement of water particles to gradually reach a steady state. In addition, the periodicity of the time history of S7 is much better than that of S5 and S9. The wave pressure operating on the wave surface of the tube body is the biggest and the wave pressure acting on the back wave surface of the tube body is the smallest, according to a comparison of the quasi-static wave pressure at the three places.

The time history analysis of the wave pressure shows the high-frequency and quasi-static force components of the SFT’s tube body pressure. In order to further investigate the influence of wave height and period on the wave pressure in the SFT, the following discussion focuses on the variation of the maximum values of the wave pressure. Because the point pressure at the center of the top surface of the tube body (S7) basically maintains a more complete cycle variation, the extreme value of its wave pressure is selected for analysis. However, the variation trend of the point pressure with H/L is relatively vague; some wave heights and periods are selected to analyze here.

Figure 8 shows the variation in the maximum values of wave pressure for different wave heights and periods. It is clear that the variation of wave pressure with wave height and period is more complex than acceleration. Under various wave heights, it is discovered that the maximum point pressure changes with the wave period. The point pressure at the center of the top surface of the model varies dramatically, which is the primary cause of this phenomenon. That is, the wave force on the structure is more unstable when the wave period is short and the steepness is high. When the period is constant, the maximum value for the point pressure increases at first and then decreases. This demonstrates that the point pressure does not rise linearly as wave height rises. As a result, the point pressure of the SFT cannot be simply determined by the change in wave height alone; it must be combined with the comprehensive study of the interaction between the wave and the structure. When the wave height is small, the contribution of a high-frequency component leads to a great increase in maximum value. The high-frequency component gradually reduces at the peak as wave height rises and quasi-static forces make up the majority of the point pressure. Therefore, the point pressure lowers and wave height rises.

4.3. Cable Forces

Figure 9 gives the time history of the cable forces for C3, C4 and C6 in the SFT body under different wave heights, using situations with a water depth of 2.2 m and a wave period of 0.8 s as an example. The cable force numbers are shown in Figure 2a. The mooring cables C1–C4 are installed at one end of SFT and the mooring cables C5–C8 are installed at the other end. The three mooring cables selected can synthesize the maximum cable force variation of the eight mooring cables.

It can be seen that the general trend for the anchor cable force variation pattern is more consistent with the order of magnitude. This indicates that the anchor cable force is more equally distributed. Simultaneously, there is more high-frequency vibration in the anchor cable force time range. The dynamic reaction of the SFT and the wave action on the anchor cable is primarily responsible for this high-frequency component. The C6 mooring cable force is stronger and exhibits a significant periodic fluctuation when the wave height is minimal. The anchor cables below the SFT tube are more stressed in this anchor cable arrangement. The anchor cables located at the side of the SFT tube are relatively less stressed but still play a role in force distribution. This shows that the anchor cable design may more evenly distribute force. The risk of damaged cables is also reduced by this style of anchor cable construction. Moreover, the arrangement of multiple anchor cables on one side can facilitate anchor cable maintenance and replacement.

Because the acceleration maximum and minimum values exhibit comparable tendencies, only the cable force maximums are chosen for discussion here. The fluctuation of cable force extremes for the C3, C4, C5 and C6 mooring cables with various H/L values is shown in Figure 10. As can be observed, the maximum values for the four anchor cables show an increasing trend with the increase in H/L at a certain wave period. Additionally, the maximum values for anchor cable force increase suddenly at large wave heights. Among them, the force for the C4 mooring cable decreases when the wave height is 0.1 m. This indicates that the maximum value for the anchor cable force reaches a peak at this time. When the wave height is fixed, the maximum force for C3, C4, C5 and C6 mooring cables increases and then decreases with an increase in the wave period. All of these cables reach their peak force at a wave period of 1.0 s. This phenomenon indicates that the waves in this condition are quite likely to have severe vibrational effects in the SFT, which needs special attention in the project.

4.4. Displacement

The displacements measured by the two waterproof displacement sensors in Figure 2a are used as an example. The greatest vertical (Z-direction) and transverse (Y-direction) displacement variation of the SFT at various H/L values are shown in Figure 11. It should be noted that the maximum values here are the absolute maximum values, which means that the positive and negative directions are not taken into account.

When the wave period is certain, the maximum value for SFT displacement increases with an increase in H/L; when the wave height is certain, the maximum value for SFT displacement also increases with the decrease in H/L. The primary reason is that the increase in wave height enhances the effect of the wave on SFT displacement, whereas the increase in wave period increases the wavelength and the ratio of wavelength to structure size affects the dynamic response of the SFT. It is important to keep in mind that the ratio of wavelength to SFT size has a greater effect on the vertical displacement of the SFT than the transverse displacement for a certain range. Under wave loading, the vertical displacement of the SFT is larger than the transverse displacement. In some conditions, the vertical displacement is even two times more than the transverse displacement.

5. Conclusions

The dynamic behavior of an SFT under the influence of regular waves is experimentally explored in this paper. Based on the experimental results, the following conclusions and suggestions can be drawn:

(1) As wave height increases, the longitudinal, transverse and vertical acceleration time history of the tube increases. The time history of acceleration shows a high-frequency, multi-peak trend in small periods. The peak rises and then falls as the period lengthens. The extreme values for longitudinal (X) acceleration are substantially less than the extreme values for transverse (Y) and vertical (Z) acceleration in a certain range.

(2) When the wave height is small, the time history of wave pressure on the SFT has many high-frequency components. As wave height rises, the high-frequency component of wave pressure decreases and gradually gives way to the quasi-static wave pressure.

(3) With this multi-anchor cable placement technique, the anchor cables underneath the SFT tube are put under higher stress. The anchor cables located at the side of the SFT tube are relatively less stressed but still play a role in force distribution. This multi-anchor cable placement method can better distribute the cable force and reduce safety hazards. Moreover, it is easy to maintain and replace the anchor cables.

(4) The influence of waves on SFT displacement is amplified as wave height increases. The wavelength grows with wave period and the ratio of wavelength to structure size affects the dynamic response of the SFT. The ratio of wavelength to SFT size has a greater effect on the vertical displacement of the SFT than the transverse displacement for a certain range.

(5) We mainly carry out experiments on the hydrodynamic characteristics of local pipe joints. There is no research on the influence of anchor cable stiffness on hydrodynamic load and dynamic response, which is a limitation of this paper.