2 Key Lab of Port, Waterway and Sedimentation Engineering of MOT, Nanjing 210029, China
Andersen and Buhrman (2007) explored erosion characteristics of the inner slope and proposed the formulas of mean overtopping discharge and mean overflow thickness respectively in the case of coupling between storm surges and waves. Many scholars have carried out in-depth studies on roller-compacted concrete (RCC), articulated concrete block (ACB) and high-performance turf reinforced mat (HPTRM) as well as other facings, these new armor blocks are more stable (Hughes, 2008; Li et al., 2012; Pan et al., 2013). However, most scholars carried out physical model tests on the damage of storm surge and wave coupling to seawalls without consideration of the dynamic water level change process of storm surges, which is very one-sided. In the process of storm surges, it can be possible to accurately simulate actual hydrodynamic and wave conditions to provide a basis for further studies only by taking into overall consideration the interaction among storm surges, astronomical tides and waves via different mechanisms. Van der Gent et al. (2016) coupled the variable water level of storm surges with waves in the two-dimensional water tank and explored the erosion mechanism of seawalls in the case of coupling. It is worth noting that the storm surge level hydrograph used in the experiment is ladder-shaped rather than continuously varying. As shown by experimental results, relatively speaking, the scour pit profile was wider in the case of variable water level, and the scour pit depth bigger in the case of fixed water level; variable water level resulted in less seawall scour and siltation. Thus, it can be seen that the water level variation of storm surges plays an important role in siltation and scour.
The effect of storm surge on the seawall is mainly the levee overflowing and damage to the levee crown and backwall caused by the superposition of storm surge elevation and astronomical tide or flood. The process of storm surge is always accompanied by wave, strong wind and other physical factors, so most scholars consider wave factors when conducting physical model tests. There are only a few physical model tests with consideration of the damage of single storm surge elevation to the seawall. Nelsen (2014), through field observation and physical model test in the water channel, explored the erosion characteristics of seawalls under the levee overflowing of storm surge. Johnson et al. (2013) studied the instantaneous scour dynamic process and scour characteristics of seawall scour under the action of storm surge, and put forward the measures for effective scour prevention, thus providing assistance for engineers to design and repair the seawall defense system.
The damage of waves to coastal seawalls is mainly manifested in the following three forms: levee toe instability, external slope structure damage, levee crown and backwall damage (Lu et al., 2005; Huang and Lv, 2009). Overtopping is the main cause of levee crown and backwall damage. In order to determine the direct impact of overtopping on the levee crown and backwall, some scholars have carried out a series of physical model tests. Möller et al. (2003), through large-scale model test (no wave wall on the levee crown), analyzed and studied the process of damage to the backwall (made of different clay materials) caused by overtopping, concluding that: (1) the erosion and permeability damage of backwalls begins with the levee crown; (2) when the grass cover is fully developed, erosion damage is more dominant than permeability damage; (3) single overtopping has no obvious impact on permeability damage, and the impact of the sustained action of overtopping is more important. Steendam et al. (2010) systematically studied the formation of scour pits and the failure mechanism of earth dikes by conducting research on the parameters of overtopping water body on the levee body from both theoretical and experimental aspects. Chinnarasri et al. (2003) summarized the four processes of damage to the seawall by analyzing the process of damage of overtopping water flow to the seawall through laboratory tank experiment. Van der Meer et al. (2010) summarized a large number of physical model test results and found that the flow velocity of overtopping flow is an important parameter for determining whether erosion damage will occur to the backwall of seawall. Fan and Zhu (2008) and Zhu (2012) analyzed the modes of damage of water flow state and flow velocity of the levee crown and backwall to the levee crown and backwall after overtopping through two-dimensional physical experiments. Chen et al. (2016) conducted a series of two-dimensional physical model tests on the seawall backwall concrete panel, placed rockfill and rock riprap as well as other surface covers, and proposed the calculation formula of stable thickness of paved rockfill of the backwall under the action of irregular waves.2 EQUIPMENT AND METHOD 2.1 Equipment
The simulation was carried out in the long wave tank of State key laboratory of hydrology-water resource and hydraulic engineering. In order to simulate the combined effect of storm surges and waves, the tank was modified to simulate tidal level change by controlling the tailgate height to adjust the variation of water level. The schematic diagram of wave tank is shown in Fig. 1. The wave height measurement adopts the DS30 capacitive wave height meter, which collects and records the wave process data by computer, collecting box and corresponding software. The ZWS-40 intelligent water level trackers are used to measure dynamic water level.2.2 Method 2.2.1 The coupling of storm surge and wave
Firstly, relevant data of the project area should be collected, and numerical model calculation should be carried out if it is necessary to obtain the duration curves of storm surge water level and wave parameters (effective wave height Hs and mean wave period Tm) in the simulated project area. The Institute of Oceanology Chinese Academy of Sciences established the numerical model to provided wave and storm surge process data of Typhoon Winnie (No. 9711), which induced the most severe storm surge in Ningbo area within 100 years.
Figures 2-4 show the calculated variation procedures of the storm surge water level, the significant wave height and the mean wave period at the engineering site during Typhoon Winnie. The red box selection range in Figs. 2-4 is the simulation time period selected in the model test.
Then the storm surge water level and wave processes were simulated respectively in the water tank. The average error of the simulation of the storm surge water level process was controlled within +2 mm (model value). When simulating the wave process, the storm surge and wave processes should be discretized. It is assumed that water level and wave conditions are basically unchanged within each time interval Δt. Wave parameters (wave height and period) were calibrated at the water level corresponding to each time interval Δt, and the calibrated wave-making files of all the time intervals were spliced seamlessly to obtain the wave-making file continuously changing with the water level in the whole period of model test time. The mean errors between the measured and target values of significant wave height and mean wave period were controlled within 5%. Finally, the continuous change process of storm surge water level was superposed on the encrypted discretized wave process to realize the synchronous change of water level and wave through continuous tide generation and wave making by the wave maker and tide generating device, thus implementing the dynamic coupling simulation of storm surge and wave in the laboratory.
The simulation technology should be put into practice. The laboratory simulation process of superposition of waves on tidal level changes is shown in Fig. 5. The moving average method was adopted to the wave surface elevation data collected from the wave-height meter to obtain a smooth storm surge water level hydrograph. The average error of this water level hydrograph and the water level hydrograph measured by the water level tracker 2 at tailgate is -1.4 mm and 0.4 mm respectively (model value). The comparison of the target water level hydrograph with the simulated results obtained by the moving average method and the water level tracker 2 are shown in Fig. 6. The errors of the significant wave height and mean wave period of coupling simulation are shown in Table 1. The average error of the measured value and target value of wave height and wave period is within 5%, which meets the precision requirements. Therefore, this simulation technology can be applied to the simulation of coastal buildings under the co-action of waves and storm surges (or tides).2.2.2 Seawall cross section and model test design
The study seawall section was selected from Beilun District, Ningbo, Zhejiang Province, China (Fig. 7). The thickness of concrete panel on the road on the bank is 16 cm. The physical model test simulated the damage process of the combined action of storm surges, waves and tides on the typical seawall section in Ningbo. The geometric scale of the model was set at 1:16. The core material in seawall section is 10-100 kg block stone, which is simulated according to gravity similarity and considering seepage similarity.
Two physical model test cases are carried out: case 1 is the dynamic coupling action of storm surge and wave and case 2 is under the condition of a fixed water level combined with corresponding wave parameters. The fixed water level is 5.01 m, i.e. the maximum water level, and the corresponding significant wave height and mean wave period are 2.60 m and 9.81 s, respectively. In the model tests, the damage process of seawalls was observed.3 EXPERIMENTAL RESULT 3.1 Damage results of seawalls under the dynamic coupling of storm surge and wave
The water level continued to rise 160 to 184 min after the commencement of the test. With the wave impacting the concrete wave wall, some of it were broken, splashing out along with the anti-arc wave wall with tiny displacement. Within 184 to 376 min, the overtopping wave began to appear. As the overtopping discharge gradually increased and the nappe thickened, the waves continued to hit the levee crown, scouring the slope shoulder at the joint of the levee crown and backwall. At the 256th minute, the backwall concrete panel was lifted by the waves, and at the 268th minute, the concrete panel slipped about 32 cm. At the 280th minute, the concrete panel slipped off completely, and the waves began to wash away the exposed core stones, forming a scour pit. After 328 min, an obvious scour pit appeared, and afterwards the scour pit shape was shown in Fig. 8. The maximum scour depth was reached at the 348th minute and the maximum length of scour range was reached at the 360th minute.
Under the dynamic coupling of storm surge and wave, the wave wall moved backward, and the concrete panel of the backwall completely slipped off, forming a scour pit under the action of waves.
There are mainly two types of waveforms at the formation stage of the scour pit. The first waveform a generated a small amount of overtopping discharge; water flowed along the road on the bank until reaching the slope shoulder, and formed a vortex near the slope shoulder, scouring backwall stones. The second waveform b was characterized by a large amount of overtopping discharge generated, thick nappe, and very thick water body on the road on the bank and scoured stones under the road at the slope shoulder. At the later stage of the scour pit, the whirlpool gradually moved down, mainly with waveforms c and d, as shown in Fig. 9.3.2 Damage results of seawalls under the action of fixed water level superposed on corresponding waves
At the 44th minute, the concrete panel of the backwall began to tilt and slip off, resulting in misplacement after continuous scouring. At the 52nd minute, the concrete panel slipped off completely. When the concrete panel slipped off, the waves began to scour the exposed core stone, and the subsequent form is shown in Fig. 10. The maximum scour depth reached a balanced state at the 124th minute, and the maximum length of scouring range was reached at the 148th minute.
The fixed water level is 5.01 m, and the wave duration is equivalent to 3 h of the prototype. Under the continuous action of fixed water level waves, the concrete wave wall shifted backward, and the concrete panel of the backwall slipped off completely, forming a scour pit under the action of waves.3.3 Measurement results of overtopping discharge
The measurement results of overtopping discharge are shown in Table 2. The averaging window used in the calculation of mean overtopping discharge in the dynamic coupling test was defined within the period when overtopping can occur, the measured results of overtopping discharge under the dynamic coupling of storm surge and wave is 0.059 3 m3/(m·s). The overtopping discharge measured at the 5.01 m fixed water level and at the 4.11 m fixed water level is 0.121 4 m3/(m·s) and 0.008 7 m3/(m·s), respectively.
The measured results of overtopping discharge under the dynamic coupling of storm surge and wave are about 50% of the measured results of overtopping discharge at the fixed water level of 5.01 m. Therefore, the results of overtopping discharge measured by the traditional test method of constant water level tend to be conservative and will lead to the increase in the levee crown and wave wall crest elevation, thus increasing project costs.4 DISCUSSION
In terms of time, the failure time of the backwall at a fixed water level is 212 min earlier than that under the dynamic coupling of storm surge and wave. The time of complete slip-off (when the waves started to scour the core stone) of the backwall concrete panel at a fixed water level is 228 min earlier than that under the dynamic coupling of storm surge and wave. The arrival time of the maximum scour depth of scour pit at a fixed water level is 224 min earlier than that under the dynamic coupling of storm surge and wave. The arrival time of the maximum length of scour range of the scour pit at a fixed water level is 212 min earlier than under the dynamic coupling of storm surge and wave. The time nodes of the working condition 1 and the working condition 2 are shown in Table 3.
From the perspective of scope, the moving distance of the wave wall at a fixed water level is 0.024 m greater than that under the dynamic coupling of storm surge and wave. The maximum scour depth at a fixed water level is 0.208 m greater than that under the dynamic coupling of storm surge and wave. The length of scour range at a fixed water level is 0.8 m greater than that under the dynamic coupling of storm surge and wave. The comparison of the range of the working condition 1 and the working condition 2 is shown in Table 4. The comparison photos of the working condition 1 and the working condition 2 after the test are shown in Fig. 11.
Although the traditional fixed water level superposed on waves can more safely consider the damage to the wave wall and backwall, it cannot effectively reproduce the damage to the backwall under the dynamic coupling of storm surge and wave. The experimental results of the traditional test method of constant water level are more conservative than those under the dynamic coupling of storm surge and wave.5 CONCLUSION
In this paper, the continuous change process of storm surge water level was superposed on the encrypted discretized wave process, to realize the synchronous process of water level and wave through the continuous tide generation and wave making by the wave maker and tide generating device, thus realizing the dynamic coupling simulation of storm surge and wave in the laboratory. Then, according to the storm surge water level and wave change process data of Beilun District, Ningbo, during the 9 711 typhoon period, physical model tests of the typical seawall sections were carried out under the dynamic coupling of storm surge and wave as well as at a conventional fixed water level respectively, to observe and compare the damage process and overtopping discharge of different parts of the seawall, and explore the damage mechanism of the seawall. The main conclusions are shown as follows:
(1) For the typical seawall sections in Beilun district, the average error of water level simulation results processed by the sliding average method after coupling and of water level simulation results at tailgate is -1.4 mm and 0.4 mm (model value) respectively. The mean error of the measured value and target value of effective wave height and average period is less than 5%, which meets the precision requirement. The dynamic coupling simulation of storm surge and wave can be realized well by the synchronous operation of tide generating device and wave making machine.
(2) With regard to the wave wall and levee crown backwall, the failure time of the backwall, the time of complete slip-off of the backwall concrete panel, the arrival time of the maximum scour depth of the scour pit and the arrival time of the maximum length of scour range of the scour pit at a fixed water level are quite ahead of those under the dynamic coupling of storm surge and wave. The maximum scour length and maximum scour depth of the scour pit formed at a fixed water level are obviously greater than those under the dynamic coupling of storm surge and wave. Therefore, the test results obtained by the traditional method of constant water level are more conservative than those obtained under the dynamic coupling of storm surge and wave.
(3) With regard to the overtopping discharge, the measured results of overtopping discharge under the dynamic coupling of storm surge and wave are about 50% of the measured results of overtopping discharge at the fixed water level of 5.01 m. Therefore, the results of overtopping discharge measured by the traditional test method of constant water level tend to be conservative, and will lead to the increase in the levee crown and wave wall crest elevation, thus increasing project costs.6 DATA AVAILABILITY STATEMENT
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.
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