**2. Physical model test**

#### **2.1 Experimental installation and method**

The experiments are carried out in a wave flume which is 50m long, 3.0m wide and 1.0m deep. The sketch of experimental setup is shown in Fig. 1. Assuming the movements of the barges on the water surface are small and can be ignored, the immersion of the tunnel element is directly done by the cables from the fixed trestle over the wave flume.

The immersed tunnel element considered in this study is 200cm long, 30cm wide and 20cm high, which is a hollow cuboid sealed at its two ends. The tunnel model is made of acrylic plate and concrete and the cables are modeled by springs and nylon strings that are made to lose their elasticity.

Fig. 1. Sketch of experimental setup

It is known that the immersion of the tunnel element in practical engineering is actually done by the ballast water, namely negative buoyancy, inside the tunnel element. The weight of the tunnel element model used in this experiment is measured as 1208.34N. When the model is completely submerged in the water, the buoyancy force acting on it is 1176.0N. So the negative buoyancy is equal to 32.34N, which is 2.75 percent of the buoyancy force of the tunnel element. The negative buoyancy makes the cables bear the initial tensions.

Water depth (*h*) in the wave flume is 80cm. The normal incident irregular waves are generated from the piston-type wave generator. The significant wave heights (*Hs*) are 3cm and 4cm, and the peak frequency period of waves (*Tp*) 0.85s, 1.1s and 1.4s, respectively. The experiments are conducted for the cases of three different immersing depths of the tunnel element, i.e., *d*=10cm, 30cm and 50cm, respectively. *d* is defined as the distance from the water surface to the top surface of the tunnel element.

Corresponding to the three immersing depths of the tunnel element, three kinds of springs with different elastic constants are used in the experiment. According to the properties of cables using in practical engineering and the suitable scale of the model test, the appropriate

method. The motion responses of the tunnel element and the tensions acting on the

The time series of the motion responses, i.e. sway, heave and roll of the tunnel element and the cable tensions are presented. The results of frequency spectra of tunnel element motion responses and cable tensions for irregular waves are given. The influences of the significant wave height and the peak frequency period of waves on the motions of the tunnel element and the cable tensions are analyzed. Finally, the relation between the tunnel element

The experiments are carried out in a wave flume which is 50m long, 3.0m wide and 1.0m deep. The sketch of experimental setup is shown in Fig. 1. Assuming the movements of the barges on the water surface are small and can be ignored, the immersion of the tunnel

The immersed tunnel element considered in this study is 200cm long, 30cm wide and 20cm high, which is a hollow cuboid sealed at its two ends. The tunnel model is made of acrylic plate and concrete and the cables are modeled by springs and nylon strings that are made to

It is known that the immersion of the tunnel element in practical engineering is actually done by the ballast water, namely negative buoyancy, inside the tunnel element. The weight of the tunnel element model used in this experiment is measured as 1208.34N. When the model is completely submerged in the water, the buoyancy force acting on it is 1176.0N. So the negative buoyancy is equal to 32.34N, which is 2.75 percent of the buoyancy force of the

Water depth (*h*) in the wave flume is 80cm. The normal incident irregular waves are generated from the piston-type wave generator. The significant wave heights (*Hs*) are 3cm and 4cm, and the peak frequency period of waves (*Tp*) 0.85s, 1.1s and 1.4s, respectively. The experiments are conducted for the cases of three different immersing depths of the tunnel element, i.e., *d*=10cm, 30cm and 50cm, respectively. *d* is defined as the distance from the

Corresponding to the three immersing depths of the tunnel element, three kinds of springs with different elastic constants are used in the experiment. According to the properties of cables using in practical engineering and the suitable scale of the model test, the appropriate

tunnel element. The negative buoyancy makes the cables bear the initial tensions.

element is directly done by the cables from the fixed trestle over the wave flume.

controlling cables are tested.

**2. Physical model test** 

lose their elasticity.

Fig. 1. Sketch of experimental setup

water surface to the top surface of the tunnel element.

motions and the cable tensions is discussed.

**2.1 Experimental installation and method** 

springs are chosen. The relations between the elastic force and the spring extension are shown in Fig. 2. There are four strings that join four springs respectively to control the immersed tunnel element in the waves. Two strings are on the offshore side and the other two on the onshore side of the tunnel element. To measure the tensions acting on the strings, four tensile force gages are connected to the four strings respectively.

Fig. 2. Relations between the elastic force and the spring extension

The CCD (Charge Coupled Device) camera is utilized to record the motion displacements of the tunnel element during its interaction with waves. Two lights with a certain distance are installed at the front surface of the tunnel element, as shown in Fig. 3. When the tunnel element moves under irregular wave actions, the positions of the two lights are recorded by the CCD camera. Finally, the sway, heave and roll of the tunnel element are obtained from the CCD recorded images by the image analysing program.

Fig. 3. Photo view of the tunnel element at the wave flume. (a) wave is propagating over the tunnel element; (b) the tunnel element and CCD
