A sketch of the wave flume is shown in Fig. 2. The wave flume was approximately 14 m in length, 0.5 m in width and 0.7 m in depth. It is equipped with a piston-tape wave generator on the one end, and a 1:4 dissipating gravel beach on the other end. A glass-walled sediment tank (2.6 m (L)×0.6 m (H)×0.5 m (W)) embedded in the wave flume filled with sediment, the transparent sidewalls of the sediment tank provided convenience for us to observe the phenomenon of the sediment responses under wave action. Regular water waves were paraded from one side of the flume and disappeared when the front waves reach the dissipation system, and wave parameters can be changed by controlling the driving frequency (Jia et al., 2014; Zhang et al., 2018b).

The pore-water pressure measurements were performed via six pore-water pressure transducers (CYY2, China, 5 mm in diameter and 12 mm in length, with 1 Hz, continuous) which deployed along the central site of the sediment tank at six different depths, Z=7, 12, 20, 28, 36 and 44 cm, in which Z is the vertical distance measured downwards from the initial seabed surface. The spatial and temporal changes of suspended sediment concentration (SSC) in the water column were records via an Argus Surface Meter IV (ASM, Argus, Germany, with frequency 1 Hz, 10 min interval), ASM is a high-resolution SSC profiler and operates with optical backscatter infrared sensors (OBS) embedded in a stainless steel rod, the sensors are placed on an active board at a distance of 10 mm. The ASM records the reflections and the dynamic parameters that are created in the water column by solid particles moving in a multiphase current, and responds directly to SSC’s and thus may be used to identify process-driven variations in water turbidity. The conversion from signal reflectivity (R_s, FTU) to SSC values has been achieved using a calibration function defined in the laboratory prior to field deployment, further descriptions of the calibration methodology can be found in Guo et al. (2016). The signal reflectivity to suspended sediment concentration conversion formula was deduced via linear regression (Fig. 3). As R² was 0.955 3, which indicates that the conversion is reliable enough to estimate the SSC with accuracy.

The sediment used in the experiment was from the tidal flats of the subaqueous Huanghe River Delta. The sediment was silt with D₅₀=43.04 μm and the geometric standard deviation is ${\sigma _{\rm{g}}}({\rm{ = }}\sqrt {{{\rm{d}}_{{{84}}}}/{{{d}}_{{\rm{16}}}}} ){\rm{ = 1}}.{\rm{5}}$. The particle size distribution (PSD) is given in Fig. 4. The PSD curve was determined using the Rise-2002 mode laser Particle analyzer. The sediment properties are given in Table 1. In the table, γ is the specific weight of sediment and w is the water content. Other quantities are described in the table. Before the experiment, air-dried sediment was crushed and thoroughly mixed with water and homogenized to make saturated slurry, which was used as the initial seabed. In the sediment tank, the initial sediment depth was 62 cm. A week later, the seabed sediments were consolidation by drainage, and then the depth of seabed sediments was reduced to 60 cm. The properties of sediment for initial seabed were summarized in Table 1.

According to the distribution curves of background SSC and SSC under wave loading, the net re-suspended sediment concentration can be calculated, which represented the amount of sediment transferred from underneath the sediment bed into the water. The net re-suspended sediment (Q_net) per basal area water column was adopted as an index representing the variability net re-suspended sediment, which can be calculated by the following formula (stratified summation method):

The basic assumption of the stratified summation method is that SSC at the same elevation in the water flume can be represented by the reference concentration of the data from ASM, the concentration of this water layer is assumed to be horizontally uniform. Q_net denotes the quantity of re-suspended sediment within a unit basal area water column (kg/m²); i is the partitioning layer number in the water column; and h_i=1 cm represents the thickness of each layer (depends on the distance between sensors of ASM), and n= 31 (regardless of the effects of sea-bed interface changes and sea level fluctuations). C_neti=C_i–C_bi is the net re-suspended sediment concentration of each layer, the C_i and C_bi represent the instantaneous SSC and the background SSC of each layer.

Four designed wave conditions (with a wave height of 6, 10, 14 and 18 cm respectively) were successively loaded on the seabed until the SSC finally attain an equilibrium state. The wave parameters were summarized in Table 2. In the table, h is the depth of water, H is wave heights, T is the wave period and L is the wavelength, T_dw is the duration of wave action. In the test, liquefaction of sediment or not was discriminated by observing the oscillatory motion of the sediment. During the experiments, the ASM was used to measure the turbidity of the water in predetermined time intervals (Period of a single measurement: 10 s). The variation of pore water pressure is recorded by pore-water pressure transducers. The experimental phenomena including: (1) the time development of the sediment/water interface, (2) the time development of the liquefaction front, (3) the time development of the compaction front, and (4) the characteristics of the liquefied sediment oscillation were recorded by video camera.

Over the course of the experiments, typical photographs were arranged orderly in Fig. 5, in which the first (Fig. 5a) is a consolidation period during which the pore water and bubbles flow up to the seabed surface, resulting in the formation of micro-mud volcanoes. The wave column is clear due to the lack of wave loading; Fig. 5b is the response of seabed during the initial period of 6 cm wave action, during which no significant movement of sub-bottom sediments was detected, which indicates that there is no liquefaction in the seabed. Surface sediments moved along the sediment/water interface, and the water column gradually became too turbid to identify the interface. There was also no significant movement of sub-bottom sediments during the 10 cm, 14 cm wave action, but the more surface sediments move into the water column; Fig. 3c is the response of seabed during the period of 18 cm wave action, the seepage channels were observed and the sub-bottom fine particle migration up to the seabed surface. The experiments of Liu et al. (2017) and Xu et al. (2016) were also conducted in the same wave flume using similar Yellow River silts, and similar experimental phenomena were found in these experiments. Subsequently, a partial liquefaction zone formed in the shallow layers, the sediments began to oscillate horizontally along an arc-shaped sub-bottom sliding interface. Meanwhile, sediments were re-suspended again until a liquid of higher turbidity; and Fig. 5d is the typical stratification characteristics of seabed sediment after the termination of waves. The liquefaction front traveled downwards under the action of wave loading and the liquefied areas developed over time in both horizontal and vertical directions. Finally, the liquefaction front stopped at a certain depth, and then the compaction process began from the bottom of the liquefied zone, the compaction front moved upwards, compaction front also stopped at a certain depth (Maybe, the compaction front could arrive at the surface of the sediment, if the time is long enough, or the wave energy decreases). The superficial sediments, which located between compaction front and the sediment/water interface kept oscillating elliptically with waves. A fluid mud layer formed on the surface of the seabed after wave termination due to re-settled of re-suspended sediments in the water column.

In order to judge the occurrence of the liquefaction, the wave-induced pore pressure responses to waves at 12, 20, 36 and 44 cm below the initial sediment/water interface during the corresponding period are presented in Fig. 6a. However, no reliable results were obtained due to some unknown problems of the pore-water pressure transducers located at 7 and 28 cm below the initial sediment/water interface. During the period of 6, 10 and 14 cm wave actions, the pore pressure started to fluctuate and accumulate when the subsequent waves were switched on. After that, the accumulated pore pressure (excess pore pressure) dissipated with the duration of wave loading. There was no significant movement of sub-bottom sediments was detected. When t=330 min, the 18 cm waves were switched on and the then pore pressure built up in a short period to offset overlying effective stress, liquefies the seabed and dissipates over a longer time subsequently.

This wave-induced liquefaction process has been studied independently in similar experiments (e.g., Jia et al., 2014; Xu et al., 2016; Liu et al., 2017), in the present authors, the most representative phenomenon of seabed liquefaction in the wave flume is the elliptical motion of sediments with the wave. The “elliptical motion of sediments” as a sign of liquefaction is used herein. After sediment liquefaction, a liquefaction zone formed in the shallow layers and subsequently spreads downwards (Fig. 6b). In the initial stage, the liquefaction in depth expanded rapidly. After reaching 39 cm (the value is 27 cm in the experiment of Xu et al. (2016)), variation in liquefaction depth began to decrease. At t=650 min, the liquefaction front reached a limit liquefaction depth of 45 cm. After that, the latter process gradually progresses in the upward direction. The process resembles the self-weight consolidation of hydraulic fill although, which the waves continue during the process. Miyamoto et al. (2004) termed the process “solidification process” and Sumer et al. (2004) called it “compaction process”. The latter term is used herein, as it refers to compaction of sediment by waves, an expression frequently used in hydraulic/coastal engineering practice.

With the sediment liquefied, there are two distinct layers of sediment: one with a distinct “orbital motion” of sediment with waves (the top layer is in the liquefied state), and the other with no orbital motion at all (the bottom layer) which is in the solid-state with the interface between the two layers (the compaction front) moving gradually in the upward direction. With the wave action, the speed of upward movement of the compaction front was significantly less than the speed of downward movement of liquefaction front, and the compaction front stopped at 25 cm below the initial sediment/water interface, finally. At any time, the water column and the liquefied sediment also formed a two-layered system of liquids (of different density) (discussed later).

The response of SSC under wave actions is divided into five processes (as shown in Fig. 7). Stage Ⅰ: The consolidation period, no wave loading. The SSC of the water column was close to 0.5–0.7 g/L in this period, as shown in Fig. 5a, the water column was clear and transparent. Stage Ⅱ: The responses of SSC during the period of 6, 10, 14 and18 cm wave actions. Obviously, waves mobilize sediments on the bed, distribute them vertically in the water column to produce a net suspension of sediment grains. The SSC of the water column would finally attain an equilibrium state if the wave lasts long enough, such as the period of 10 cm wave loads. The re-suspended sediments formed a high-concentration layer, the thickness is less than 5 CMAB (centimeters above the bottom) and SSC < 2 g/L. The fluid mud layer (SSC > 10 g/L) with a thickness of about 1.0 cm was formed, and the thickness of it is more than 2.0 cm under the 18 cm wave loading. The sediments under water/sediment interface did not have absolute movement and only surface sediment erosion. Stage Ⅲ: The onset of liquefaction and the liquefied zone extended downward. At this stage, more sediments were suspended into the water column and constantly dissipated upwards along with the downward expansion of the liquefaction front. As a result, the thickness of the fluid rapidly extended to the whole water column. And a sharp increase was observed of the net re-suspended sediment (Q_net) per basal area water column after the onset of liquefaction. Stage Ⅳ: Compaction process, developed at the base of the liquefied sediment layer. The liquefaction front came to a standstill at a certain sediment depth. Under the further continuation of wave loads, the compaction began to develop. In the process of consolidation, the SSC and Q_net increased continuously and the SSC of water column exceeded the maximum range of the instrument. Stage Ⅴ: Re-settlement of suspended sediment without wave loads. At the end of the experiment, the wave load was stopped. Subsequently, the elliptical movement of shallow sediments stopped and the suspended sediments rapid settled.

As mentioned previously, the progressive evolution process of BBL in this experiment can be divided into five subphases according to the response of seabed sediment under wave actions. Consider sinusoidal wave trains propagate over a level bed. The passage of wave trains induces an oscillation in the fluid pressure acting on the sediment bed. The wave pressure oscillation causes excess pore pressure (including oscillatory component and residual component) to develop at a generic point in the sediment bed. When the effective stresses between the individual grains vanish because of the residual pore pressure buildup, sediment liquefaction occurs and the sediment mixture acts as a fluid.

The value of the residual pore pressure responses strongly depends on the dynamic wave pressure acting on the surface of the sediment bed. Under the action of 6, 10, 14 cm wave loadings, the value of residual pore pressure was less than the effective stress, and then residual pore pressure dissipated quickly. The sediment surface has settled by an amount S (S=1–2 cm, Fig. 7a) at time t<410 min in the course of wave loadings (part of S stems from the erosion of surface sediments). Since only wave loads were simulated in this wave flume (no unidirectional currents), the re-suspension sediments were attributed to the reciprocating wave orbital velocities before the seabed liquefaction. The experiments of Guo et al. (2016) and Zhang et al. (2018b) were also conducted in the same wave flume using similar Huanghe River silts, to evaluate the contribution of seabed liquefaction/fluidization to sediment resuspension. The results indicate that the re-suspension sediments before the seabed liquefaction is less than 50% of the total suspension under the model scales. In the present study, the results also indicated the amount of re-suspended sediments is limited before the seabed liquefaction, and only a thin high concentration layer formed the near-bed bottom. The vertical distribution of the SSC profile is shown in Fig. 8b₁ and Fig. 8b₂.

With the sediment liquefied, the interlocking of solid particles was loosed and translated fluid-like sediment. The water column and the liquefied sediment form a two-layer-fluid region (Z_L < 0 < H) (Fig. 8c₂). Following the onset of liquefaction, the liquefied sediment with a distinct “orbital motion” and the liquefied zone extends downwards. The range of BBL extended downward to the liquefaction front, meanwhile, the vertical distribution of re-suspended sediments in the water column expanded upward. As it has been referred before, it was liquefaction leading to the great increase of SSC. Zhang et al. (2018) pointed out the contribution of fluidization (the present authors called it “liquefaction”) is attributed to two physical mechanisms: (1) an attenuation of the erosion resistance of liquefied sediments in surface layers due to the disappearing of original cohesion and the uplifting effect resulting from upward seepage flows, and (2) seepage pumping of fines from the interior to the surface of liquefied seabed.

During the progressive liquefaction process, the visual observations indicate that there are also two-layer-sediment region (Fig. 8c₂). One is the completely liquefied sediment with an “orbital motion”, and the other is sub-liquefied sediment. Therefore, the behavior of the bed sediments changes from essentially liquid in the upper layer (as a part of the BBL) to essentially solid in the lower layer. Sumer et al. (2006) too described this phenomenon. The interface between the two-layer sediment region is called “liquefaction front”. When the liquefaction front extended downward to maximum depth, a transition layer in the lowermost part of the liquefied zone start developing, and the compaction will start developing. Now, the interface between the two-layer sediment region is called “compaction front”. The liquefied sediment in the transition layer was called the structured liquefied sediment with marked densification owing to the compaction during continued wave loading (Fig. 8c₂). The compaction front advanced upwards during the continued wave loading. Miyamoto et al. (2004) discussed the process of compaction with marked densification in liquefied sand during continued wave loading and attributed this phenomenon to shear-induced contracting of sand due to the wave loading. Xu et al. (2016) carried out similar flume experiments using similar Yellow River silts, the results showed that the penetration resistance of structured liquefied sediment was remarkably enhanced (Fig. 9). The range of BBL in sediments decreased as the completely liquefied sediment changed from essentially liquid to essentially solid with the compaction front advanced upwards. It is noted that the SSC of water column increased continuously (discussed later).

The SSC in the water column is an important index for the variation of BBL. The silt sediments from the Yellow River Estuary have demonstrated fast initiation and re-suspension characteristics, and moderate wave energy could cause bottom silt re-suspension (Wright et al., 1986). As mentioned previously, the sediments below water/sediment interface undergo erosion, liquefaction, and compaction owing to the water pressure above it, successively. The net re-suspended sediment (Q_net) per basal area water column and net re-suspended sediment increment (Q_ssi) which is the time derivative of Q_net are shown in Fig. 10. The initial re-suspended sediment increment generated in the erosion stage before the liquefaction was the re-suspended sediments from the surface sediment when the wave-induced shear stress reached the critical shear stress. There was a peak value of Q_ssi when the subsequent waves were switched on, such as a and b points in Fig. 10. With the buildup of excess pore pressure, an upward- directed pressure gradient is generated. This pressure gradient drove the water in the sediment upwards, which promoted the resuspension of sediments (Figs 10b-c). Zhang et al. (2017) putted forward a hypothesis of subbottom sediment pump action which argues that subsurface fine-grained sediments will be transported from the interior to the surface of a fluidized (or liquefied) seabed driven by the upward seepage flows resulting from the wave-induced nonuniform distribution of the pore pressure build up. The theoretical indicates that seabed liquefaction greatly promotes sediment resuspension. As shown in Fig. 10, another peak of Q_ssi occurred when the seabed liquefaction, and the Q_net continuously increased accompanying the reciprocating arc-shaped oscillation motion of part of the sediment bed. It can be explained using the conceptual model of sediment fluidization by Liu et al. (2013). During the compaction stage, the Q_net continuously increased, but the value of Q_ssi was smaller than which in the liquefaction stage.