Experimental Study on Scouring and Silting Deformation of Artificial Beach Under Storm Surge—Wave Coupling

With the increasing construction of artificial beach in coastal areas, it is of practical significance to study the beach surface deformation of artificial beach profile. Previous studies only focus on a single wave dynamic factor, and it is difficult to predict the beach deformation of artificial beach profile under the storm surge—wave co-action. To solve this problem, the cross-section physical model test method was used to study the beach surface deformation of a typical artificial beach profile in Shuangdao Bay, Weihai, Shandong Province, after continuous wave actions till they stabilize. The characteristics of beach surface deformation under the conditions of constant water levels, ladder-shaped water level combined with corresponding wave elements and storm surge—wave co-action are compared and analyzed. A beach profile model which satisfies the theory of Bruun model is proposed. The test results show that the maximum scour depth of beach under storm surge—wave co-action is smaller and the scour range is obviously larger than that under the condition of constant water levels or ladder-shaped water level. The evaluation of the maximum scour depth by traditional model test tends to be conservative while the evaluation of the scour range is insufficient. The research results can provide scientific reference for designing artificial beaches.


Introduction
Natural beaches are difficult to form in some bays with good conditions due to the lack of sand sources or other reasons, thereby artificial beaches come into sight. The construction of artificial beach has always been a complex problem in coastal engineering. The natural beach profile is relatively stable, formed by the long-term interaction between coastal components and coastal dynamics. The artificial beach is more sensitive to environmental changes, and the new beach profile is difficult to achieve stability under the coastal dynamics. For the bay with better site selection, the scouring and silting deformation of the artificial beach is mainly caused by the transverse sediment transport which is an important engineering problem related to the stability of the beach profile.
As to the stability of artificial beach, Fenneman (1902) put forward the concept of beach equilibrium profile, considering that under the condition that waves and other hydrodynamic factors can significantly interact, an equilibrium beach profile could be formed. Bodge (1992) and Lee (1994) proposed the exponential and logarithmic dynamic analytical models of beach equilibrium profile respectively based on the edge wave theory and the analysis of Coriolis force effect.
In the early stage, the classification of beach profile was only based on the wave steepness (e.g. Iwagaki and Noda, 1962;Dong, 1981). Subsequently, the parameters such as median particle size, sediment bulk density and wave height were added to the criteria, but with different combinations. Most of them were still empirical or semi-empirical. In recent years, many researchers have studied the deformation of artificial beach under the action of waves by means of numerical simulation or physical model tests. Zhang (2014) used XBeach transverse profile evolution model to simulate the stability of different beach replenishment profiles and studied the design parameters that affect the stability of beach profiles in a beach restoration project. Huang et al. (2018) carried out an experimental study on the morphological changes of the artificial beach profile under different water levels and wave conditions, and calculated and compared the relatively stable profile with the balanced profile model. It is considered that the balanced beach profile could be formed when the wave was less affected by the structure. Zhu et al. (2018) explored the variation of beach surface with different gradations under the action of external wave force. Tan et al. (2019) have discussed the relationships between the scour position, scour degree and wave elements of single slope and multi-slope sand beach under the action of waves with different water levels and different return periods through physical model tests.
The above research only considers the influence of wave and other single dynamic factors, which is not consistent with the continuous variation of water level and wave in the actual storm surge process, and ignores the influence of the coupling effect of storm surge and wave on the surface deformation of artificial beach. Van Gent et al. (2017) carried out physical model tests on the seawall erosion mechanism considering water level change of storm surges in a wave flume. Although storm surge level hydrograph used in the experiment is ladder-shaped rather than continuously varying, it is shown by the model test results that the water level variation of storm surges plays an important role in siltation and scour on the front slope of seawall. Therefore, it is necessary to simulate actual variation process of storm surge and wave in a wave tank to consider the coupling effects of storm surges, astronomical tides and waves.
The storm surge-wave coupling action refers to the coupling action with the corresponding waves under the condition of continuously changing water level. In this paper, the physical model test was used to carry out the scouring and silting deformation tests of the typical artificial beach profile in the Shuangdao Bay, Shandong Province, under the action of constant water levels, ladder-shaped water level combined with corresponding wave elements, as well as the storm surge−wave co-action. The beach surface deformation was measured after continuous wave actions till stability. The characteristics of beach surface deformation under the conditions of constant water levels, ladder-shaped water level and the storm surge−wave co-action were compared and analyzed, and a beach profile model which satisfies the theory of Bruun model has been put forward.
2 Coupling simulation technique of waves and storm surges 2.1 Instruments and equipment Wave and tidal coupling simulation was carried out in the long wave tank of State key laboratory of hydrology-water resource and hydraulic engineering (see Fig. 1). This tank can produce waves, current and wind simultaneously. The tank, 175 m long, 1.2 m wide and 1.8 m deep, is equipped with a piston irregular wave generator produced by Nanjing Hydraulic Research Institute. The working section of the tank was divided into two halves along the width of 1.2 m (see Fig. 2), one half of the widths (0.6 m) was used to place the model section and conduct model test, and the other 0.6 m was used for diffusing the secondary reflection wave of the wave paddle.  In order to simulate the combined effect of storm surges and waves, the wave tank was modified to simulate tidal level change by controlling the tail gate height to adjust the variation of water level. The maximum range of water level variation is 35 cm (model value). The schematic diagram of wave tank is shown in Fig. 3. The storm surge measurement and control system are composed of the tail gate, electric motor, water level control system and water level tracker, as shown in Fig. 4. The detailed introduction of the coupling measurement and control system can be found in

Coupling simulation technique
First, the water level process was input in the computer to generate storm surge in the flume and the water level data of the control station was measured and compared with the given value, to obtain a difference Δh. The deviation Δh was made to approach zero by a controllable speed governor driving a DC servo motor to adjust the opening degree of the tail gate to control the variation of water level. The water level process was calibrated and the mean error of the simulated water level was controlled within 2 mm (model value).
When simulating the wave process, the storm surge and wave processes were discretized, i.e., water levels and waves were divided into several small segments. In each time segment, the water level and wave conditions were considered nearly constant, and wave parameters of different time segments were calibrated at the corresponding water levels. Then the calibrated wave generation file elements were connected to get the whole continuous wave generation file, in which wave parameters vary with the water level during the simulation period. In the process of calibration, wave height and period simulation results were measured and analyzed in real time by wave-height meter, and compared with the target value, and the mean error of the measured values of wave height and period and the target values was controlled within 5%.
Finally, the storm surge water level and wave process were simulated simultaneously. In the experiment, the wave-maker was used to produce the wave with the connected wave generation file, and meanwhile the tide generation system was utilized to adjust the water level according to the continuous water level change process, so as to realize the continuous and synchronous changes of water level and wave. In the process of coupling simulation, it is necessary to collect the wave element data of the whole process and analyze the accuracy. If it does not meet the accuracy requirements, it is necessary to re-calibrate and modify the wave generation file, re-collect the data and analyze again until the accuracy is satisfied.

Test section and wave elements
The study area is located in the Shuangdao Bay, Weihai, Shandong Province (see Fig. 5). The typical artificial beach section selected in the experiment is shown in Fig. 6. The slope of the beach section is 1:15, the thickness is 2.0 m, the bottom elevation is −5.0 m, the top elevation is +4.0 m, and the total width (slope section and beach shoulder section) is about 150 m. The Institute of Oceanography, Chinese Academy of Sciences has calculated the wave and storm surge process of Typhoon "Meihua" No. 1109, which has caused great dam-  SUN Tian-ting et al. China Ocean Eng., 2022, Vol. 36, No. 1, P. 65-75 age to the sea area of Shuangdao Bay in Weihai. In this paper, the strong dynamic period (10 h) of Typhoon "Meihua" is selected for simulation. During the test calibration, the wave and water level processes are divided into several segments at intervals of 20 minutes (see Fig. 7), so that the change of water level in this period is as small as possible to reduce the determination error. And the number of irregular waves is larger than 130, which meets the needs of wave eigenvalue analysis. The calibrated wave generation file (see Table 1) is re-written and seamlessly spliced according to the format required by the storm surge-wave coupling measurement and control system, and a complete wave generation file with continuous variation with water level in the whole period of storm surge is obtained, which is used to simulate the continuous variation of wave parameters with the water level during the storm surge.

Wave simulation
The wave is simulated according to the gravity similarity criterion, and the JONSWAP spectrum is used for the irregular wave spectrum and the spectral density function is: where α is a dimensionless constant, f p is the peak frequency, r is the peak parameter, set as 3.3, and σ denotes the peak shape parameters, σ = 0.07 when f ≤ f p , and σ = 0.09 when f > f p . The characteristic wave elements converted according to the model scale are input into the computer to generate wave-making signals and control the wave maker to generate corresponding irregular wave sequences. In the model test, the error between the simulated values of wave height and period and the target values is controlled within ±2%, and can be controlled within ±5% after coupling with the dynamic water level.
3.3 Sediment movement simulation 3.3.1 Similarity of beach slope F The relationship between sandy beach slope s and beach parameter is as follows: where, is the specific gravity of water, is the specific gravity of sand, is the median particle size of sand, is the wave height, and is the wavelength. By using the normal model, according to the similar slope of the beach, the relationship between the sediment particle size scale and the horizontal scale can be obtained as follows: is the scale of the parameter related to the specific gravity of sand.

Similarity of wave incipient velocity
According to Bagnold's formula of sediment incipient velocity under wave action: The relationship between sediment particle size scale and horizontal scale can be obtained as follows:

Similarity of erosion-deposition trend of beach profile in surf zone
According to the Hattori formula (Xu, 1988): λ ω the sediment deposition velocity scale can be derived: When the wave height scale is equal to the water depth scale , it can be re-written as: In the normal model, the geometric scale is equal to the water depth scale , that is, Since this study focuses on the stability of the beach profile in the nearshore area, the similarity of erosion-deposition trend of the beach profile in surf zone is particularly important. On the premise that the incipient velocity of waves is similar, the requirement of similarity of sediment settlement under wave conditions should be satisfied as far as possible.

Selection of model sand
In the design of model sand, the grain size of model sand with different bulk densities is calculated from the me-λ ω dian grain size of the beach bottom material according to the similarity of beach slope Eq. (4) and the similarity of sediment incipient velocity Eq. (6). Then, according to the similar requirements of erosion-deposition trend Eq. (10), the sediment deposition velocity scale is calculated, and the particle sizes corresponding to different-bulk-density sediment are calculated by Zhang's (1961) settling velocity formula. Finally, according to the comparison of the two calculation results, the type and particle size of the model sand are determined.
The settling velocity of sediment is calculated by Zhang' s (1961) ν where, is the kinematic viscosity coefficient of water. γ s The median sand particle size of the beach near Shuangdao Bay ranges from 0.24 mm to 0.36 mm, with an average of 0.30 mm. In this model, the coal dust with bulk density =1.36 g/cm 3 is selected as the model sand, and its dry bulk density is about 0.7 g/cm 3 . After comprehensive comparison, the median particle size of the model sand is selected as 0.26 mm. The test was conducted in accordance with the relevant provisions of "Wave Model Test Regulation (JTJ/T 234-2001)(Ministry of Transport of the People's Republic of China, 2001)". According to the selection of model sand, design water level, wave elements, test section and test equipment conditions and other factors, the geometric scale is taken as 1:25. The main scales of the model are shown in Table 2.

Test methods and test groups
Firstly, according to the storm surge-wave coupling simulation method proposed in this paper, the continuous storm surge water level variation process is superimposed with the wave process after encryption and discretization, and the wave-maker was used to produce the wave with the connected wave generation file, and meanwhile the tide generation system was utilized to adjust the water level, so as to real- ize the continuous and synchronous change of water level and wave. Then the artificial beach section is constructed. Before the test, the wavelet is used to make the sand surface dense, and then the constant water levels, laddershaped water level and storm surge−wave co-action tests are carried out. In order to ensure the reliability of the test results, each group of tests is repeated at least three times, and the average value of three times is taken as the test results. When there is a large difference in the three repeated tests, the number of repetitions shall be increased. The cross section of the beach was re-flattened in each experiment. The test groups are as follows.
(1) Constant water levels: under the conditions of 1.48 m water level (WH16), 1.14 m water level (WH22), 0.42 m water level (WH28) and corresponding wave combination, the cross-section form of the artificial beach is measured when the erosion and deposition deformation of the artificial beach is finally stabilized under the cumulative action of waves.
(2) Ladder-shaped water level: under the conditions of 1.48 m water level (WH16), 1.14 m water level (WH22), 0.42 m water level (WH28) and corresponding wave combination, the cross-section form of the artificial beach is measured when the erosion and deposition deformation of the artificial beach is finally stabilized under the cumulative action of waves. By considering that the wave action time of the middle water level is longer, the ratio of the action time of each water level is generalized to 1:2:1.
(3) Storm surge−wave co-action: under the condition of continuous change of storm surge water level superimposed with corresponding waves, when the cumulative action time of waves is equivalent to a storm surge process (10 hours), the cross-section form of artificial beach after erosion and deposition deformation is measured.

Constant water level
According to Wave Model Test Regulation (JTJ/T 234-2001) (Ministry of Transport of the People's Republic of China, 2001), the cross section changes of the beach in the experiment were measured at 15, 30 and 60 min after wave generation, and then at intervals of 1 h. Taking the test phenomenon of 1.48 m water level (WH16) as an example (Fig. 8), the beach profile has been basically stable after 6 h, and there is no obvious change before and after 10 h and 11 h, so the beach profile after 10 h-action is determined as the final dynamic stability profile.   Table 3 shows the test results for the sand accretion (sandbar position and sandbar height) and sand erosion (scouring range, maximum scour position, maximum scour depth and net erosion) after 6 h and 10 h testing.
The results show that under the action of 1.48 m water level and corresponding wave elements (WH16), the waves break after passing through the gentle slope of the beach and form an obvious sandbar near the breaking point; there is a large range of scouring behind the sandbar on the land side and obvious sediment accumulation in front of the beach shoulder. With the continuous action of waves, the sandbar moves offshore and the height increases slightly; the scour depth behind the sandbar continues to increase, and the sediment accumulation in front of the beach shoulder increases. Under the action of 1.14 m water level and corresponding wave elements (WH22), the test phenomenon is basically consistent with that of 1.48 m water level (WH16). With the decrease of water level, the breaking point and the sandbar move to the sea side, and the height of the sandbar decreases; there is a large range of scouring behind the sandbar to the land side, and the scouring range and depth decrease slightly; the sediment accumulation position in front of the beach shoulder moves slightly to the sea side. Under the action of 0.42 m water level and corresponding wave elements (WH28), the wave breaking point and sandbar continue to move to the sea side and the height of sandbar decreases obviously because the water level continues to decrease; the scouring range behind the sandbar decreases, the scour depth increases, and there is a certain range of scouring in front of the sandbar; the sediment accumulation position in front of the beach shoulder moves to the sea side, and the accumulation height increases obviously. For 1.48 m water level (WH16) and 1.14 m water level (WH22), there is little difference between their test results, and the wave breaking patterns are similar. During the first 6-hour testing, the beach erosion process is relatively faster while after 6 hours the increase in erosion process is relatively small or even absent. For the water level of 0.42 m (WH28), during the first 3 hours of testing, the beach erosion process is relatively faster while after 3 hours the increase in erosion process is relatively small.

Ladder-shaped water level
The results of the constant water level tests only consider the influence of single wave dynamic factor, which is not consistent with the variation of water level and wave in real storm surge process. Van Gent et al. (2017) has conducted preliminary exploration on the influence of water level changes on artificial beach, and the water level process used in the experiment was a three-stage ladder-shaped water level. Therefore, in order to study the influence of water level change on the deformation of artificial beach, refer to Van Gent et al. (2017) for the selected water level process, this paper selects the same cross-section form as that in the constant water level tests, and measures the cross-section form under the conditions of 1.48 m water level (WH16), 1.14 m water level (WH22) and 0.42 m water level (WH28) and the corresponding wave combination, after the artificial beach scouring and silting deformation and its final stability caused by accumulated wave actions. As the wave action time of the middle water level is longer, the ratio of the action time of each water level is generalized to 1:2:1. Fig. 10 shows the variation of the profiles of the artificial beach in time under the condition of ladder-shaped water level, and table 4 shows the test results of scouring range, maximum scour position, maximum scour depth and net erosion after 6 hours and 10 hours testing. Fig. 11 shows the resulting profiles after 6 hours and 10 hours testing under the condition of ladder-shaped water level, as well as the comparison with the resulting profiles under the condition of constant water levels (WH16, WH22, WH28) for the same time.
It can be seen from the figure that the deformation range of beach surface under the condition of ladder-shaped water level is much wider compared with that of the constant water levels. The scouring range is about 45% larger and the net erosion increases by about 9%. The reason is that under  the condition of ladder-shaped water level, the position of breaking wave point is different under different water levels. The accretion area that appeared during the high water level (WH16) got eroded in the following middle water level (WH22), and the accretion area in the middle water level got eroded in the following low water level (WH28), which leads to a wide area of scouring and the disappearance of accretion area without obvious sandbar. In addition, the maximum scour depth was about 20% lower than that for the three constant water level conditions because the scour area appeared in the former water level was silted up in the latter water level. which is consistent with the general law of Van Gent et al. (2017) test results.
In conclusion, compared with the constant water levels, the ladder-shaped water level leads to a wider range of scouring and silting deformation, but the silting height and scour depth are reduced. The change of storm surge water level plays an important role in the scour and deposition deformation of artificial beach, so it is necessary to further simulate the scour and deposition deformation of artificial beach in the process of actual storm surge and wave coupling.

Wave−storm surge co-action
The water level process used in the previous chapter is ladder-shaped, which is still different from the actual storm surge process. To study effects of continuous variations of water level and wave on the erosion and accretion of artificial beach in the actual storm surge process, the coupling simulation technique of storm surge and wave proposed in this paper is used to simulate and measure the cross-section form of artificial beach after erosion and deposition deformation when the cumulative action time of waves is equivalent to a storm surge process (10 hours). Fig. 12 shows the resulting profiles after 10-hour test under the condition of storm surge−wave co-action, as well as the comparison with the resulting profiles under the condition of ladder-shaped water level and constant water levels for the same time. Table 5 shows the test results of scouring range, maximum scour position, maximum scour depth and net erosion after 10 hours testing.
It can be seen from the figure that the deformation characteristics of beach surface under the coupling action of storm surge and wave are obviously different from those under the condition of constant water levels, which is similar to that under the condition of ladder-shaped water level, showing the characteristics of "large deformation range and small deformation degree". Fig. 12a shows that compared with the constant water levels, the scouring range increases obviously and is about 50% larger, while the maximum scour depth decreases by about 45.8%, and the maximum silting height decreases by about 28.8%. This is similar to the action mechanism of waves on sand beach under the condition of ladder-shaped water level. Since a continuous water level change process is used in the coupling, the positions of breaking wave point are different under different water levels, resulting in different degrees of scouring and silting deformation in different positions of the beach. The accretion or scour area that appeared in the former water level got eroded or silted up in the later water level, which leads to a decrease in the deformation degree of the formed silting or scouring area as well as the decrease of the maximum scour depth and leads to a wide area of scouring. At the same time, the accretion area near the sea side in front of the beach disappears and there is no obvious sandbar. Fig. 12b shows that compared with the ladder-shaped water level, the deformation characteristics of the two beach surfaces are similar. Under the coupling action of storm surges and waves, the range of beach deformation increases slightly, about 5.3%, the maximum scour depth decreases by about 30.8%, and the maximum siltation height decreases by about 8.9%. This is because the continuous water level changing process is adopted, which is gentler and more uniform, and the wave breaking points are distributed along the underwater part of the whole beach. The positions of scouring and silting deformation on the beach are more than those of the ladder-shaped water level, which leads to the further increase of the deformation range of the beach. At the same time, the action time of the wave action at each position tends to be average, and the action time at the same position decreases, resulting in a decrease in the degree of deformation compared with the ladder-shaped water level.
According to the coastal equilibrium profile model proposed by Bruun (1954), combined with the experimental results of this paper, the beach profiles of constant water  levels, ladder-shaped water level and storm surge−wave coaction are fitted. The fitting results are shown in Table 6. The Bruun beach profile model can be expressed as follows: f (x) x where, is the elevation of the bottom relative to the average horizontal plane, is the distance from the shoreline, and A and m are empirical coefficients.
The fitting results show that the shape of the beach profile formed under the five working conditions is close to that of the beach profile in nature, the empirical coefficient A=0.085−0.087, m=0.95, and the correlation coefficient is about 0.99, which accords with the power function theory of Bruun model.
In order to facilitate the practical application, this paper selects the empirical coefficient A=0.086, m=0.95, then the Bruun beach profile model can be expressed as: Fig. 13 shows the comparison of the deformation of the test beach surface under five working conditions with the fitting results of the Bruun model. The comparison results show that although the range of scouring and silting deformation, silting height and scouring depth are different, the shape of the beach profile formed under different working conditions is relatively similar, and the variation range of the beach profile formed by storm surge−wave co-action is the smallest, which also indicates that the beach surface erosion and deposition deformation tends to be uniformly distributed in a larger range under the action of storm surge−wave co-action.
To sum up, due to the water level change process adopted by the wave−storm surge co-action is more uniform and gentler, the degree of beach erosion tends to be uniformly distributed in a larger range. Compared with the constant water levels, the range of scouring and silting deformation caused by the storm surge−wave co-action is obviously increased, the siltation height and scour depth are decreased. And compared with the ladder-shaped water level, the range of scouring and silting deformation further increases, and the scour depth further decreases.

Conclusions and recommendations
In this paper, the cross-section physical model test method was used to measure the beach surface deformation of a typical artificial beach profile in the Shuangdao Bay, China after continuous wave actions till stablility. The characteristics of beach surface deformation under the conditions of constant water levels, ladder-shaped water level combined with corresponding wave elements and wave−storm surge co-action were compared and analyzed. The following conclusions are drawn.
(1) The maximum scour depth of the beach surface under the storm surge−wave co-action is smaller than that of constant water levels or the combination of ladder-shaped   water level and corresponding waves. The maximum scour depth is about 45.8% lower than that of constant water levels and 30.8% lower than that of ladder-shaped water level. The evaluation of the maximum scour depth by traditional test methods tends to be conservative.
(2) Since the water level change process adopted by the storm surge−wave co-action is more uniform and gentler, the scouring degree of the beach tends to be uniformly distributed in a wider range. The scouring range increases obviously, by about 50% compared with that of the steady water level and about 5.3% compared with that of the laddershaped water level. The traditional test method is insufficient to evaluate the scouring range.
(3) According to the theory of Bruun model, the beach profile model given in Eq. (13) can well represent the beach surface deformation under different conditions.