(1)When the pressure head differences were negative, the pressure head recorded at the bed surface (Fig. 5, Position 2) was greater than the pressure head recorded below it (Fig. 5, Position 3). This means that the pressure gradient was directed downward from the bed surface to within the sediment media [Fig. 1(b)]. This additional force may increase the strength of the soil, reduce liquefaction risk, and is beyond the scope of this study.(2)When the pressure head difference between the two positions was positive but less than the liquefaction pressure heads determined either from Eq. (7) or from the laboratory tests, the pressure gradient was directed from within the sediment (Fig. 5, Position 3) to the bed surface (Fig. 5, Position 2) [Fig. 1(c)]. This acts similar to a buoyancy force lifting the sediment particles and may increase erodibility. While these values may be important for scour risk assessment, they were not the focus of this study.(3)When the excess pore-pressure head difference determined from the pressure sensors met or exceeded the liquefaction pressure head values, then the pressure head was large enough and directed in such a way as to cause the soil to liquefy (i.e., behave like a fluid rather than a granular solid) [Fig. 1(c)]. Pressure values in this range are the most critical as the shear stress required to mobilize or transport the sediment is significantly reduced (Shields 1936; Sakai et al. 1992; Mory et al. 2007). As can be seen from Figs. 11 and 12, both the high- and ebb tide at Cannon Beach in Yakutat, AK had instances when the laboratory liquefaction pressure head or the liquefaction pressure head determined from Eq. (7) were exceeded. Looking at the number of instances, the ebb tide (water depth of 0.63 m) showed more instances compared with the high tide (water depth of 1.3 m). This scenario may have an important role in sediment transportation and scour events and was the focus of this study.Figs. 13 and 14 show the results of the frequency-dependent pressure signal attenuation caused by the wave pressure signal propagating vertically through the porous media, with Fig. 13 representing the ebb tide and Fig. 14 representing the high tide, as calculated from the Yamamoto et al. (1978) model. The solid blue line is created by taking the FFT of two pressure signals and dividing the FFT of the bottom pressure sensor (P2, located at Position 3 in Fig. 5) by the FFT of the topmost pressure sensor (P1, Position 2 in Fig. 5) and then squaring. This ratio describes the amount of attenuation (or damping) of a pressure signal caused by a particular wave frequency. If there is no damping present in the bottom signal (P2), the ratio approaches 1. In both Figs. 13 and 14, there is a discrepancy between the Yamamoto et al. (1978) model and the field data at very low frequencies. This was most likely caused by the removal of 0 Hz effects during data processing (e.g., removal of pressure caused by the still water depth and the atmosphere).The Yamamoto et al. (1978) model had greater difficulty predicting the pore-pressure response (i.e., greater discrepancies between the model and field data) during the ebb tide as compared with the high tide. In Fig. 13, the model seemed to predict the ebb tide pressure dissipation behavior well for frequencies of 0.10 to 0.22 Hz. There was some underprediction of the model from 0.04 to 0.10 Hz and overprediction for frequencies greater than 0.24 Hz. Conversely, there was greater agreement between the model and the field excess pore-pressure dissipation data across essentially all frequencies during high tide (Fig. 14). While the model underpredicted the pressure dissipation in the high tide from 0.10 to 0.60 Hz, the magnitude of the difference was less than that of the ebb tide. The cause of the differences in accuracy between the ebb- and high tides is currently unknown but may be linked to gas content and still water depth (Yamamoto et al. 1978; Mory et al. 2007). Figs. 13 and 14 show that the ebb tide may experience increased excess pore-pressure attenuation, which may result in larger or more frequent liquefaction inducing excess pore-pressure differences, as seen in Figs. 11 and 12.DiscussionScour EquationsTable 8 presents the number of prediction iterations that met or exceeded the 1:1 line in the respective Figs. 7–10 for each equation. This corresponds to a horizontal line from Figs. 7–10 meeting or being to the right of the 1:1 line. A number less than 15 indicates that more than half of the prediction attempts by that equation resulted in an underprediction. The input ranges used in each equation for Table 8, and whether the ranges tested here were within the ranges for each equation, can be found in Table 3.Table 8. Instances of 1:1 line exceedance for each respective equationTable 8. Instances of 1:1 line exceedance for each respective equationEquationFroehlich (1988)Froehlich (1988) DesignHEC-18 (FHWA 2012)Sumer et al. (1992)Instances of 1:1 exceedance2123286The nature of these prediction equations is generally conservative and favors overprediction (FHWA 2005; Falcone and Stark 2016). By overpredicting the scour depth for a scenario, these equations have something similar to a built-in factor of safety. In this study, even the applied range of input parameters led to more accurate or even underpredicted scour hole depth estimates than would be expected from the conservative equations. Therefore, the specific effects of the Sumer and Fredsøe (2001) equation on the scour prediction range were not considered further since the equation does not correct underpredictions of current only cases (Fig. 9; blue points only extend the lower bound) and cannot be applied to wave only cases.Sources of discrepancy between the prediction models and field measurements include, but are not limited to, limited inundation time, complex flow geometry, armoring effects, refilling of the scour hole from ex situ sediments, in situ conditions exceeding the range tested here, momentary liquefaction, scour caused by breaking waves, additional scour from flood water returning to the ocean, and the effects of debris (Sumer and Fredsøe 2002; Nielsen et al. 2012; Borga et al. 2017; Kennedy et al. 2020).A limited inundation time should, in theory, cause an overprediction of the scour depth (Sumer and Fredsøe 2002). However, the focus of this study was the underprediction of the equations that can be seen in Figs. 7–10. Complex flow geometry resulting from infrastructure and flow debris could result in disagreement between measurements and predictions. The effect of these two processes on scour depth is not accounted for in the equations or quantifiable from the available data. The refilling of scour holes from ex situ sediments would result in overpredictions by the scour equations as the measured depths become shallower.The processes of armoring, winnowing, and the effects of grain-size distribution on the possible scour depth may also explain the under- and overprediction seen by the scour equations. However, the equations tested here do not account for any of these processes. Median grain size (d50) is generally the only geotechnical parameter taken into consideration by scour equations. However, the median grain size was not sufficient to adequately describe sediments with different grain-size distributions, armoring, or an indicator of winnowing (Lambe and Whitman 1969). Additionally, the data collected for this study were not sufficient to draw conclusions on the possible impacts of armoring, winnowing, or grain-size distribution.In situ conditions could have exceeded those used in this study, as discussed previously. The range of input parameters taken from in situ measurements attempted to prevent this; however, it is possible that these parameters varied greatly throughout Mexico Beach, FL, and some parameters did not have measurements. The measurements were performed during a rapid reconnaissance mission and did not include the placement of sensors during the hurricane by the authors. In the future, sensor deployments prior to hurricane arrival would be desired. However, the acquisition of, for example, all input parameters needed for this study during hurricane conditions would still be challenged by accurate prediction of inundation zones, structures at risk, equipment failure during storm conditions, and the risk of damage to equipment and to personnel associated with the deployment. Therefore, a reasonable range of input parameters was chosen to be applied to scour prediction equations that required only a limited number of additional assumptions on more complex input parameters in this study. For example, equations 3.12, 3.13, 3.22, 3.23 and others in Sumer and Fredsøe (2002) and equations in studies by Vanoni (2014) and Borga et al. (2017) would possibly prove more accurate, but they would add uncertainty in the form of additional parameters not seen in Table 2 (e.g., boundary layer thickness, consideration of armoring) in this study. While it is acknowledged that the ranges of input parameters (over accurate measurements) applied in this study prohibited the accurate prediction of a specific scour depth, it did indicate a risk for underprediction, representing an unfavorable risk for the respective structures. The reader is also referred to the sensitivity analysis.Scour could have been deepened as flood water returned back to the ocean. This would have exacerbated any existing scour from intense return flow and would have caused underpredictions of the scour equations. Yeh and Mason (2014) studied the drawdown period of a tsunami and its effects on excess pore pressures and scour. They observed that severe scour can occur as a result of thin swift currents forming during the drawdown period eroding weak spots (Yeh and Mason 2014). Additionally, they found that during the drawdown period, momentary liquefaction occurred as a result of a rapid reduction of excess pore water pressure. This momentary liquefaction resulted in what Yeh and Mason (2014) termed “enhanced scour” (scour beyond what is expected from ordinary flows). However, no measurements on flood flows receding or excess pore pressures are available for the Mexico Beach, FL, area (Kennedy et al. 2020), and thus, no conclusions could be drawn on the impacts of the observed scour.The analysis of scour equations thus far has ignored the role of breaking waves on the scour depth. While the calculations for breaker depth mentioned previously indicated that wave heights up to the significant wave height of 2 m in 3.5 m of water were not breaking, waves larger than this value or waves in different water depths would most likely have experienced breaking as wave height and water depth changed over the duration of the storm. Furthermore, the equations used for scour prediction did not take into consideration the difference in scour mechanisms due to breaking waves as compared with nonbreaking waves (Bijker and De Bruyn 1988; Carreiras et al. 2000; Nielsen et al. 2012). Nielsen et al. (2012) describe a particular distance between a pile and where a wave breaks that results in a significant scour depth. With the rapidly changing water depth and wave conditions during Hurricane Michael, coupled with the lack of in situ measurements of these parameters, it is possible that the piles used in this study experienced waves that broke at the distance described by Nielsen et al. (2012), leading to an increased scour depth.Carreiras et al. (2000) and Nielsen et al. (2012) provide easy to use first approximations of scour depth as a function of pile diameter based on their laboratory experiments. Carreiras et al. (2000) reported a maximum scour depth equal to 1.04D and Nielsen et al. (2012) reported a maximum scour depth equal to 0.6D. Comparing the pile diameters with the respective scour depth from Table 1, it can be seen that four piles (the bottom four with scour depths of 0.24, 0.26, 0.28, and 0.30 m) had a scour depth that ranged from 0.8D to 1.03D. It is possible that breaking waves resulted in at least four scour depths listed in Table 1. Based on the data collected in this study and the two approximations provided by Carreiras et al. (2000) and Nielsen et al. (2012), it is unlikely that breaking waves alone explain all the observed underpredictions.Momentary liquefaction from waves is another possible source of underprediction of the scour equations tested (Sakai et al. 1992; Mory et al. 2007; Yeh and Mason 2014; Stark 2017). The scour equations that accounted for wave interactions did not account for momentary liquefaction (Sumer and Fredsøe 2002). While without further testing it is difficult to say what accounts for the disagreement between predictions and measurements at the observed sites, the observed occurrences of underprediction are concerning and call for additional investigations. In this study, the possibility of momentary liquefaction enhancing scour was then further investigated based on laboratory testing and field recordings under nostorm conditions at a site with similar soil conditions.Sensitivity AnalysisOf the parameters tested, wave period and flow velocity were the only parameters without any in situ measurements. Kennedy et al. (2020) indicated that reported high-water marks may be conservative and could have been exceeded during Hurricane Michael. This could be a source of underprediction, as a deeper water depth will yield larger scour holes from the equations used here. No in situ measurements of wave period were found, but an estimate was calculated as 14.6 s using Young (2003). The range of wave periods tested noticeably exceeds the wave periods tested in the Sumer et al. (1992) and Sumer and Fredsøe (2001) equations by a factor of ∼10. The difficulty arises in the dichotomy between choosing a wave period within the ranges tested by the equations (1.2–4.5 s) or choosing a range that better represents the possible wave periods that the piles are exposed to in storm conditions (1–30 s, Munk 1950). Furthermore, the maximum current velocity (5.9 m/s) used for the predictive equation was an estimation based on a shallow water wave assumption as well as an assumption on the maximum water depth (3.5 m) (Dean and Dalrymple 1991). As the water depth changes, assuming shallow water wave conditions persist, the maximum current velocity will also increase, according to the square root of water depth times gravity. It should also be noted that Matsutomi et al. (2011) proposed an additional constant to be multiplied to the shallow water relationship between velocity and water depth. This value ranges between 0.6 and 1.2 depending on the difference in water depth at the front and back of an inundated structure. While Matsutomi et al. (2011) studied the effects of a tsunami, not a hurricane, inundating a structure larger than a pile with a difference in water depth across the structure, it may be possible that a similar effect may enhance the flow around piles. This could result in larger current velocities than those given by the shallow water relationship (i.e., maximum current velocity larger than 5.9 m/s for a water depth of 3.5 m), this would increase the upward bound of predicted scour than what is shown here.Regardless, underestimating either of these parameters may lead to inaccuracies in the scour equations used here. A significantly higher flow velocity will ultimately result in deeper scour depths. An increase in wave period leads to an increase in the KC number, which may not strictly increase the scour depth as the wave scours out a larger area compared with a smaller KC number (Sumer and Fredsøe 2002). This may indicate that uncertainty in either of these parameters could be a source of underprediction.Pore Pressure and LiquefactionConsidering the grain-size distribution, median grain size, Cu and Cc values, sediments from Cannon Beach, Yakutat, AK, and Mexico Beach, FL, were similar for the purpose of this study. Both sediments contained a negligible amount of fine grains (grains smaller than 0.075 mm) and may have had permeabilities of similar magnitude. The largest difference between these two sediments was the specific gravity with the Cannon Beach, AK, sediment being 1.1 times larger than the Mexico Beach, FL, sediment. This would imply that for similar sediment conditions, the Cannon Beach, AK, sediment would require a larger excess pore-pressure difference to induce liquefaction (Mory et al. 2007).Figs. 11 and 12 show that the excess pore-pressure head differences that occurred at Cannon Beach, AK, were sufficiently large to overcome the liquefaction criteria determined by the laboratory experiments for the Mexico Beach, FL, sediments and the Mory et al. (2007) equation using the Mexico Beach, FL, and Cannon Beach, AK, sediments. The wave heights and water depths for the Cannon Beach, AK, data (0.58–0.83 m, 0.63–1.3 m, respectively) were smaller than the maximum values reported by in situ measurements at Mexico Beach, FL, from Hurricane Michael (2 m, 3.5 m, respectively) (Kennedy et al. 2020; USGS 2020). In addition to the less energetic conditions of the Cannon Beach, AK, sediment, the Mexico Beach, FL, sediment surrounding the piles tested in this study were significantly farther away from the shoreline (∼100–350 m). The Mexico Beach, FL, sediments were, in all likelihood, drier and looser before their inundation than the Cannon Beach, AK, sediments. This implies a larger gas content and porosity for the Mexico Beach, FL, sediments than the Cannon Beach, AK, sediments prior to the Mexico Beach, FL, sediment inundation.From these differences in sediment conditions, it could be said that the Mexico Beach, FL, sediment would have an increased risk of liquefaction compared with the Cannon Beach, AK, sediment (Yamamoto et al. 1978; Sakai et al. 1992; Mory et al. 2007). Since Cannon Beach, AK, had possible liquefaction events under less energetic conditions than the Mexico Beach, FL, sediment, it is a feasible hypothesis that the more at risk of liquefaction Mexico Beach, FL, sediment experienced liquefaction events under the more energetic Hurricane Michael conditions. Furthermore, liquefaction may occur more often in normally emerged locations far from the shoreline when rapidly inundated compared with normally submerged sediments due to the emerged location’s looser (high porosity) and drier (high gas content) sediments (Yamamoto et al. 1978; Sakai et al. 1992; Mory et al. 2007).Figs. 11 and 12 show that more liquefaction events occurred during the ebb- rather than the high tide. The larger amount of attenuation found in the ebb- compared with the high tide (Figs. 13 and 14) may imply that the risk of liquefaction at ebb tide is greater, resulting in more liquefaction events. A more attenuated signal implies a larger magnitude in the excess pore-pressure gradient, thus increasing the risk of momentary liquefaction (Yamamoto et al. 1978; Sakai et al. 1992; Mory et al. 2007). The increased attenuation in Fig. 13 and larger amount of liquefaction events for the ebb tide data (Figs. 11 and 12) may be a result of the changes in gas content from high- to ebb tide as previously discussed (Yamamoto et al. 1978; Mory et al. 2007). Furthermore, waves may have become steeper during the ebb tide. This would change the appearance of the wave crest and trough and thus have an impact on the development of excess pore-pressure gradients (Stark 2017).ConclusionThe depth of scour holes at 30 piles caused by Hurricane Michael was measured in inundated areas at Mexico Beach, FL. The observed scour hole depths were compared against the results of five prediction equations. It should be highlighted that the scour holes were located inland [100–350 m from coastline; see in Fig. 2(d)] in areas inundated during Hurricane Michael, while the scour prediction equations were developed for riverine (Froehlich 1988; FHWA 2012) and offshore environments (Sumer et al. 1992; Sumer and Fredsøe 2002). Soil samples at Mexico Beach, FL, were collected and tested in the laboratory to characterize the sediment and to determine the excess pore-pressure head difference required to liquefy the soil. This was then compared with the theoretical liquefaction pressure given by Mory et al. (2007). The possibility of occurrence of these excess pore-pressure gradients was assessed using field data collected in Yakutat, AK, during moderate wave conditions (wave heights of 0.58–0.83 m in water depths of 0.63–1.3 m). Finally, the pore-pressure dissipation model as presented by Yamamoto et al. (1978) was compared with field data to observe the wave-induced excess pore-pressure attenuation behavior during different phases of the tide. The first goal of this study was to test common scour prediction equations for the special scenario of scour under hurricane inundation of onshore areas in the case of Mexico Beach, FL, during Hurricane Michael. The second goal was to investigate the feasibility of momentary liquefaction as a mechanism enhancing scour and thus as a possible explanation for some of the observed underprediction of scour. The following conclusions can be drawn.The equations were generally able to provide predicted scour depths that are equal to or greater than the measured scour depth (Figs. 7–10). However, in 42 of the total 120 (35%) prediction iterations (Table 8), the predicted scour depths were smaller than the observed scour depths, representing an underprediction and undesired risk. Momentary liquefaction was found to be one possible contributor to and explanation for this discrepancy. Other explanations include, but are not limited to, unknown soil and hydrodynamic conditions or that are outside the range of a specific equation, breaking waves, complex flow geometry, the refilling of scour holes after their development, and other physical processes that are not accounted for by the equations.From a combination of laboratory liquefaction tests and field data, it appears possible that momentary liquefaction occurred and enhanced local scour in inundated areas during Hurricane Michael. Rapid inundation time may have left the soil with an above average gas content, which may have increased the likelihood of momentary liquefaction (Yamamoto et al. 1978; Sakai et al. 1992; Mory et al. 2007). The field data from Yakutat, AK, suggest that the difference in excess pore-pressure head between two sediment layers (with sediment properties characteristic of Yakutat, AK, as well as Mexico Beach, FL) caused by the troughs of ordinary- and infragravity waves was large enough to cause momentary liquefaction. Additionally, the data showed that there were more instances of momentary liquefaction during shallow water conditions (0.68 m water depth). This supports the premise that momentary liquefaction during inundation and storm conditions could have exacerbated the effects of scour and possibly contributed to the development and depth of onshore scour holes during Hurricane Michael in Mexico Beach, FL.The scale of this study, the difficulty in predicting hurricane landfall, and the risks associated with deploying sensors in hurricane conditions prevented a wide range of scour prediction equations and their respective parameters being tested. The results of this study represent a first examination of the processes and other factors contributing to scour formation around onshore-located round and square piles due to hurricane-induced inundation. The possibility of momentary liquefaction as a likely source of the discrepancy between measured scour holes and predictions of scour from existing equations was considered. Future and larger scale studies should consider a wider range of equations (e.g., slender piles, pile groups, around structures) and the necessary measurements for the respective input parameters (e.g., wave period, boundary layer thickness, the refilling of scour holes). Additionally, to tackle the uncertainties of scour enhancement by return flow (e.g., Yeh and Mason 2014) or inundation velocities (e.g., Matsutomi et al. 2011), focus should be on the directionality of debris to determine whether they were deposited by return or inundating flows.References Albatal, A., N. Stark, and B. 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