*2.1. Theory*

When using pressure sensing technology to continuously observe the height of the sea floor, the position of the observation point must first be determined. Assuming that the observation point is located at the trough of the initial position of a sand wave (solid line), under hydrodynamic action, the sand wave migrates to the left toward the dotted line (Figure 1). According to the pressure change law acting on the sand wave profile during this process, the bottom pressure (P*B*) at the observation point mainly includes the hydrostatic pressure determined by the sea floor surface height (H) and dynamic water pressure created by the waves and current (∆P*N*). The total pressure change (∆P*T*) is mainly shaped by changes in the soil–water pressure ratio's contribution to total pressure created by ∆H, and by changes in dynamic water pressure caused by waves and currents. Therefore, in combining the device arrangement depth of the in-situ observation (b) with the near-bottom pressure sensor mounting height (a), it can be deduced that there is a relationship (shown by Equations (1) and (2)) between ∆H, and ∆P*<sup>B</sup>* and ∆P*T*.

$$
\Delta \mathbf{H} = \left(\Delta \mathbf{P}\_B - \Delta \mathbf{P}\_N\right) / \rho\_w \mathbf{g}\_\prime \tag{1}
$$

$$
\Delta \mathbf{H} = \mathbf{a} \cdot (\Delta \mathbf{P}\_T - \Delta \mathbf{P}\_N) / (P\_{T0} - P\_{N0} - \rho\_w \mathbf{g} \mathbf{b}) / \tag{2}
$$

$$
\Delta \mathbf{P}\_T = \Delta \mathbf{H} \cdot \mathbf{y} + \Delta \mathbf{P}\_{\text{N}\prime} \tag{3}
$$

where ρ*<sup>w</sup>* is the density of seawater, g is gravity acceleration, γ is the buoyant unit weight of the seabed sediment; P*T*<sup>0</sup> is the total fixed-depth pressure level at the time of initial recording and P*N*<sup>0</sup> is the near-bottom pressure level at the time of initial recording. *J. Mar. Sci. Eng.* **2020**, *8*, x FOR PEER REVIEW 3 of 12

**Figure 1.** Pressure changes at key points during sand wave migration **Figure 1.** Pressure changes at key points during sand wave migration.

∆H = (∆P − ∆)/ρg , (1) ∆H = a ∙ (∆P − ∆)/(0 − 0 − ρgb) , (2) ∆P = ∆H ∙ γ + ∆ , (3) Thus, both P*<sup>T</sup>* and P*<sup>N</sup>* can be used to measure vertical height changes of the sea floor caused by sand wave migration. Based on this, we propose two tools for observing the vertical deformation of the sea floor caused by sand wave migration: (a) a fixed-depth total pressure recorder (TPRFD) kept at a certain depth within a sand wave at the observation point and (b) a surface synchronous bottom pressure recorder (BPRSS) kept at the surface of a sand wave at the point of observation.

#### where ρ is the density of seawater, g is gravity acceleration, is the buoyant unit weight of the *2.2. Experimental Set-Up and Arrangement*

seabed sediment; P T0 is the total fixed-depth pressure level at the time of initial recording and PN0 is the near-bottom pressure level at the time of initial recording. Thus, both P<sup>T</sup> and P<sup>N</sup> can be used to measure vertical height changes of the sea floor caused by sand wave migration. Based on this, we propose two tools for observing the vertical deformation of the sea floor caused by sand wave migration: (a) a fixed-depth total pressure recorder (TPRFD) kept at a certain depth within a sand wave at the observation point and (b) a surface synchronous bottom pressure recorder (BPRSS) kept at the surface of a sand wave at the point of observation. *2.2. Experimental Set-Up and Arrangement* To verify the feasibility of the above two methods, a physical model test was carried out in the wave flume (14.0 m × 0.5 m × 1.3 m) (Figure 2) housed at the Environmental Geotechnical Laboratory of the College of Environmental Science and Engineering, Ocean University of China. The 2.6 m wave-shaped test bed (Figure 2b) used to simulate sand wave terrain was filled with sand samples (Qingdao Beach, China) (Table 1). A wave generator with a wave frequency of 0.2 to 50 Hz was fixed to the right end of the water flume to form a wave with a controllable wave height and frequency (Figure 2a). A permeable slope with a slope of 1:4 was set on the left side of the sink to eliminate the influence of reflected waves (Figure 2a). The two side walls of the sink are made from transparent tempered glass to easily observe test phenomena and markings.


wave flume (14.0 m × 0.5 m × 1.3 m) (Figure 2) housed at the Environmental Geotechnical Laboratory **Table 1.** Soil sample properties and instrument parameters.

To verify the feasibility of the above two methods, a physical model test was carried out in the

*J. Mar. Sci. Eng.* **2020**, *8*, x FOR PEER REVIEW 4 of 12

**Figure 2.** Schematic diagram of the water flume structure and test device. (**a**) Top view of the test device; (**b**) side view of the simulated sand wave bed. **Figure 2.** Schematic diagram of the water flume structure and test device. (**a**) Top view of the test device; (**b**) side view of the simulated sand wave bed.

**Table 1.** Soil sample properties and instrument parameters. **Instrument Characteristic Parameters Sand Sample** Average particle diameter 0.25 mm Nonuniformity coefficient 1.47 Curvature coefficient 1.14 Buoyant unit weight 16.2 N / cm<sup>3</sup> AA400 Accuracy 1 mm Range 0.15 – 100 m Ultrasonic terrain scanner Accuracy 1 mm Range 0.1 – 2 m Pressure sensor Accuracy 0.5% Range 0 – 20 kPa Fiber optic pressure sensor Accuracy 1‰ F.S Range 0 – 30kN The traditional electrical pressure sensor is easily affected by its own thermal effect and poor linearity, while the optical fiber pressure sensor is small in size, highly sensitive and stable, and responds directly to pressure changes. Therefore, because the measurement performance of a pressure sensor directly determines the accuracy of the ocean observation depth [32], in this The traditional electrical pressure sensor is easily affected by its own thermal effect and poor linearity, while the optical fiber pressure sensor is small in size, highly sensitive and stable, and responds directly to pressure changes. Therefore, because the measurement performance of a pressure sensor directly determines the accuracy of the ocean observation depth [32], in this experiment, the optical fiber pressure sensor (Suzhou NanZee Sensing Technology Co., Ltd., Suzhou, China) was used to observe the total pressure level. The sensor is 100 mm × 100 mm × 19.2 mm in size, and the interior of it is designed as a "Seesaw" structure (Figure 3). The pressure was measured from the change in the strain wavelength (P1, P2) caused by the change in the force of the two fibers installed on the seesaw structure. With no stress, the strain wavelengths of the two fibers were: *P*<sup>1</sup> = 1538.22 nm and *P*<sup>2</sup> = 1546.303 nm. The pressure calculation formula is W = K*<sup>P</sup>* × (∆*P*<sup>1</sup> + ∆*P*2) where W is the weight of the overlying object, and ∆P<sup>1</sup> and ∆P<sup>2</sup> are the changes in the strain wavelength after being stressed. The NZS-FBG-A01 (M) multi-channel fiber grating sensor demodulation module (Suzhou NanZee Sensing Technology Co., Ltd., Suzhou, China) was used to collect and demodulate the data measured by the fiber sensor. It is a high-resolution Bragg grating sensor demodulation system and a high-precision spectrum analysis system. The resolution of the demodulation wavelength is 0.1 pm and the speed of demodulation is 1 Hz. The central wavelength, peak value and wavelength scanning reflection spectrum of the optical fiber pressure sensor can be output to the computer connected to the demodulation module in real-time through the USB cable. After using standard weights, increasing the number of weights step by step, and combining calculation formulas to calibrate the sensors in the test environment, parameter K<sup>P</sup> is 290.3 g/nm, and the linear equation is *W<sup>X</sup>* = 290.3 × (∆*P*1*<sup>X</sup>* + ∆*P*2*X*).

experiment, the optical fiber pressure sensor (Suzhou NanZee Sensing Technology Co., Ltd., China) was used to observe the total pressure level. The sensor is 100 mm × 100 mm × 19.2 mm in size, and the interior of it is designed as a "Seesaw " structure (Figure 3). The pressure was measured from the change in the strain wavelength (P1, P2) caused by the change in the force of the two fibers installed on the seesaw structure. With no stress, the strain wavelengths of the two fibers were: *P<sup>1</sup>* = 1538.22 nm and *P<sup>2</sup>* = 1546.303 nm. The pressure calculation formula is W = K × (∆<sup>1</sup> + ∆2) where W is the weight of the overlying object, and ∆P<sup>1</sup> and ∆P<sup>2</sup> are the changes in the strain wavelength after being stressed. The NZS-FBG-A01 (M) multi-channel fiber grating sensor demodulation module (Suzhou NanZee Sensing Technology Co., Ltd., China) was used to collect and demodulate the data measured Whether the height of the bottom pressure sensor can synchronously change with the height of the sea floor at the observation point is key to whether the BPRSS method can be used for observation. Therefore, a float with a density value between those of the sand bed and water was designed to carry the pressure sensor. Float spheres made from polyamide (PA) have a density (1.14 g/cm<sup>3</sup> ) slightly greater than that of seawater (1.10 g/cm<sup>3</sup> ). Because a dish-shaped object has good hydrodynamic features, to reduce measurement errors caused by the movement of the floating ball due to hydrodynamic forces, a dish-shaped floating ball was used in the test. As Figure 4 shows, the float has a diameter of 186 mm on the horizontal axis and a height of 93 mm on the vertical axis. In the middle of the upper structure of the float, a 16 mm diameter penetration hole is reserved. A smooth stainless steel rod is connected

by the fiber sensor. It is a high-resolution Bragg grating sensor demodulation system and a high-

(∆1 + ∆2).

to the metal base through the floating ball penetration hole to reduce the left and right sway caused by the wave as the floating ball moves up and down. The interior is hollow, and a bracket is reserved to mount the pressure sensor. There are four through holes with a diameter of 12 mm above and below the sphere to keep internal and external hydrostatic pressure levels consistent. reflection spectrum of the optical fiber pressure sensor can be output to the computer connected to the demodulation module in real-time through the USB cable. After using standard weights, increasing the number of weights step by step, and combining calculation formulas to calibrate the sensors in the test environment, parameter K<sup>P</sup> is 290.3 g / nm, and the linear equation is = 290.3 × (∆1 + ∆2). **Figure 3.** Fiber optic pressure sensor. (**a**) Appearance; (**b**) internal structure. Whether the height of the bottom pressure sensor can synchronously change with the height of the sea floor at the observation point is key to whether the BPRSS method can be used for observation. Therefore, a float with a density value between those of the sand bed and water was designed to carry

*J. Mar. Sci. Eng.* **2020**, *8*, x FOR PEER REVIEW 5 of 12

reflection spectrum of the optical fiber pressure sensor can be output to the computer connected to the demodulation module in real-time through the USB cable. After using standard weights, increasing the number of weights step by step, and combining calculation formulas to calibrate the sensors in the test environment, parameter K<sup>P</sup> is 290.3 g / nm, and the linear equation is = 290.3 ×

**Figure 3.** Fiber optic pressure sensor. (**a**) Appearance; (**b**) internal structure. **Figure 3.** Fiber optic pressure sensor. (**a**) Appearance; (**b**) internal structure. levels consistent.

stainless steel rod is connected to the metal base through the floating ball penetration hole to reduce the left and right sway caused by the wave as the floating ball moves up and down. The interior is **Figure 4.** Dish-shaped float. (**a**) Appearance; (**b**) internal structure. **Figure 4.** Dish-shaped float. (**a**) Appearance; (**b**) internal structure.

hollow, and a bracket is reserved to mount the pressure sensor. There are four through holes with a diameter of 12 mm above and below the sphere to keep internal and external hydrostatic pressure levels consistent. (**a**) (**b**) The test was applied to TPRFD and BPRSS groups, and observation points were set at the crest (A1, A2) and trough (B1, B2) (Figure 2) of each group to compare the applicability of the two methods at different positions. With the exception of the pressure sensor, the layout and test conditions of the instruments used in the two groups of tests remained the same. In this test, a hydrodynamic force was applied over two stages. First, waves with a frequency of 34 Hz and a height of 7.9 cm were applied for one hour, and then waves with a frequency of 50 Hz and a height of 12.0 cm were applied for 25 minutes (in the experiment without any measuring instrument in advance, through direct observation, we found that when the wave action in the second stage reached 25 min, the bed shape The test was applied to TPRFD and BPRSS groups, and observation points were set at the crest (A1, A2) and trough (B1, B2) (Figure 2) of each group to compare the applicability of the two methods at different positions. With the exception of the pressure sensor, the layout and test conditions of the instruments used in the two groups of tests remained the same. In this test, a hydrodynamic force was applied over two stages. First, waves with a frequency of 34 Hz and a height of 7.9 cm were applied for one hour, and then waves with a frequency of 50 Hz and a height of 12.0 cm were applied for 25 min (in the experiment without any measuring instrument in advance, through direct observation, we found that when the wave action in the second stage reached 25 min, the bed shape had reached a stable state). In addition, to evaluate the accuracy of the two methods, we applied echo ranging, which has been widely used in seabed deformation measurement [33,34], as a control group. A freestyle sonar altimeter (AA400, EofE Ultrasonics Co., Ltd., Goyang-si, Korea) and an ultrasonic terrain scanner were used for the echo ranging group (Table 1). The ultrasonic terrain scanner was used to collect bottom bed morphological data before and after each test, while the AA400 made real-time observations of the bottom bed height at the observation point.
