Explaining the Flood Behavior for the Bridge Collapse Sites

Abstract

Given the increasing intensity and frequency of flood events, and the casualties and cost associated with bridge collapse events, explaining the flood behavior for the collapse sites would be of great necessity. In this study, annual peak flows of two hundred and five watersheds, associated with two hundred and ninety-seven collapse sites, are analyzed. Generalized Extreme Value distribution together with other statistical analyses are used to derive and analyze the shape parameters of the distributions which represent the extremeness of flood events. Random forest mechanism is employed in order to identify the predictor variables (and the associated importance levels) for the shape parameters. Peak flows are also classified in order to find the extremes and the associated return periods. The results indicate that most of the bridge collapse sites across different physiographic regions, i.e., Appalachian Highland, Central Lowland, Coastal Plain, and Interior Highlands, exhibit common characteristics such as (a) variation of important predictor variables, (b) human interference, (c) extremeness of flood events similar to the regions with hydrologic heterogeneity, and (d) frequent occurrence of extreme flows. These results indicate a commonality in flood behavior, as stems from specific settings, for the collapse sites studied. The findings instigate the revisiting of the bridge design practices and guidelines and provide some basis to assess the risk of future collapse.

1. Introduction

Floods and other hydraulic events are perceived to be the most common causes of total or partial bridge collapse in the United States (U.S.) [1]. About 62.23% of overwater bridge collapses correspond to hydraulic events [1], with an annual hydraulic collapse frequency of approximately 1/5000 [1,2]. Probable hydraulic effects causing bridge collapses include scour, hydrodynamic horizontal loads applied on the piers, hydrodynamic loads applied on the superstructure (i.e., deck), debris jam, and/or a combination of these effects. The topics of scouring [1,3,4,5] and hydrodynamic horizontal loads (on piers) [6,7] have been studied extensively, whereas hydrodynamic loads on the superstructure are being studied more recently [8,9]. Although several studies exist focusing on the effects of debris jam [10,11,12,13,14,15,16], it is one of the most challenging topics under investigation by the hydraulic engineering community. Given that all of these hydraulic effects can be induced and exaggerated by floods, investigating flood events are of particular concern with the increasing intensity and frequency of recent floods in the U.S. It is noted that scour—particularly scour during floods—alone has been estimated to cause the collapse of 20–100 bridges per year in the U.S. [1,3,4]. More frequent or intense flooding is linked with climate and land use change [17]; the associated high risk is linked with direct and indirect costs, casualties, and user delays [1,3,4,18]. The 2021 American Society of Civil Engineers (ASCE) Report Card noted that a $22.7 billion annual investment is needed to substantially improve the current bridge conditions [19].

In response to reducing collapse risk due to floods, engineers primarily aim at determining the magnitude and frequency of design floods. Methods commonly used for estimating the return period of a flood event include block maxima approaches, in which a series of annual peak flows is used to define an extreme value distribution. The generalized extreme value distribution (GEV) is a widely used model for extreme events [20]. The major benefit of the GEV model is its ability to fit highly skewed data since it combines three distributions: Gumbel, Frechet, and Weibull [20]. The GEV distribution has three parameters, namely, the location and scale parameters which are mostly related to the magnitude of flow [21], and the shape parameter that determines the behavior (or shape) of the tail of the distribution [21].

Although it is obvious that flood behavior and/or flood hazard depends on the climate, soil, topography, and other watershed conditions, the specific attributes which can be used as predictors for flood behavior are not apparent. Whereas there exists a plethora of studies on site specific flood hazard, there is a knowledge gap in relation to finding the exact relationships among flood behavior and regional attributes. Regional study and/or large-sample catchment hydrology is a common practice in relation to the 2003–2012 initiative of the hydrological community for predictions in ungauged basins [22]. In particular, such approach is called regionalization of parameters using regression algorithms [22]. The large spatial scale is considered an advantage for hydrologic studies in that it includes more diverse basins; therefore, statistical characterizations would be more complete and generalizable in their extrapolation ability. Whereas local study provides more refined, site-specific analysis, their uses are limited because of their limited extrapolation ability. The regional-based approach is also in advantage since the comparison study can be conducted to identify the similarities and differences among different regions within a country or across countries, and to interpret the findings in terms of underlying climate–watershed–soil–topography–human controls [22].

Many hydraulic studies have also drawn attention to the regional scale [23,24,25,26,27], particularly in the presence of human intervention in the water system [23] for assessing the risk of the bridge collapse. There is an emphasis on physiographic settings when assessing bridge–stream intersections since the risk issues/events are intrinsically different for different physiographic regions [27]. Designing bridge scour countermeasures ignoring the regional scale hydrology sometimes results in continuous local maintenance of the structure [23]. For instance, debris jam is often caused by factors acting at a larger scale and addressing such a problem requires consideration of a large spatial scale [23]. In fact, assessing channel instability in relation to both regional and local scales is recommended by the Federal Highway Administration [27].

The goal of the study is to explain flood behavior for 297 bridge collapse sites in relation to the shape parameters of the GEV distribution within a regional context. To attain the goal, three objectives are identified: (1) to derive shape parameters of GEV distribution using annual peak flow data, (2) to identify predictor variables for the shape parameter in relation to specific physiographic regions and all regions combined, and (3) to identify extreme flows with associated return periods. The values of shape parameters would reveal the overall extremeness of the flood events. The predictor variables within the regional context would help to identify important hydrological signatures in relation to the extremeness of the flood events. Finally, the identification of extreme flows with return periods would help to identify the uniqueness of the flood events for the collapse sites, if any. The results can reveal any anomaly and/or trend in the behavior of peak floods for the bridge collapse sites and can support the understanding of the mechanism behind the generation of collapse-inducing floods. Since analyzing peak flow distribution parameters is not a common practice in bridge design procedures, such regional analysis can provide preliminary data to assess future collapse risk, as it can be highlighted that the flood event occurrence should be expected within a specific context. Concerning the bridge collapse sites, the findings of the present study are also original in comparison to previous studies in which the shape parameters were examined.

2. Methods

2.1. Selection of Sites

The New York State Department of Transportation (NYSDOT) bridge failure database is used here to identify 297 bridge collapse sites (Figure 1). NYSDOT is the only U.S.-wide database of bridge collapses. The recorded information includes the NYSDOT failure database ID, identifier in the National Bridge Inventory (NBI), failure cause, the location of the collapsed bridge, the feature (or stream) under the bridge, the year of construction, the date or year of collapse, the bridge material and structure type, the type of collapse (total or partial), the number of casualties related to the collapse, and other comments. The NYSDOT bridge failure database includes information based on available information, that is, searches of journalism databases and surveys of other DOTs. An overpresentation of collapsed bridges in a certain region/state, therefore, does not imply comparatively more collapse events; rather, it only implies the availability of the specific collapse information in that region [28]. In the current study, the selection of hydraulic collapse sites from the NYSDOT database is guided by the availability of the required information at the recorded collapse sites. The selected bridges were located in Appalachian Highland (140 sites), Coastal Plain (47 sites), Central Lowland (42 sites), Interior Highlands (54 sites), Pacific Mountain (8 sites), and Rocky Mountain (8 sites). The selection criteria are discussed in detail below:

• Existence of a stream gauge listed in the U.S. Geological Survey (USGS) National Water Information System Database at the bridge location, near the bridge location (on the same tributary of the river or on a different tributary), or at a further distance (not the same tributary, but on the same river or within the same watershed).

• Availability of climate, soil, topography, watershed, and human interference data in relation to the USGS stations in the Geospatial Attributes of Gages for Evaluating Streamflow, version II (GAGES II) database.
• Bridges were apparently collapsed (complete or partial collapse) due to hydraulic effects including scour, debris, and hydraulic pressure/load on the piers and the superstructure. Each hydraulic effect and/or a combination of them could result in the washout of a bridge, which is the case for a couple of bridges. Some collapses are caused by specific flood and hurricane events as reported by NYSDOT. Whereas hydraulic effects are exaggerated during floods and hurricane events, hurricanes are much more complex, multifaceted natural hazards. Hurricanes can cause additional rainfall, extreme waves, and storm surge. There are in-depth studies that focus on the estimation of hurricane-induced hydrodynamic effects on structures [29,30,31,32,33]. Both for bridges [29,30] and buildings [31,32,33], it is proven that storm surges and waves, induced by hurricanes, can exert large uplift pressures/forces and smaller horizontal forces leading to potential collapse. With the presence of debris, the effect of any hydraulic event can become more severe. The effects of debris include large, short-duration horizontal impact forces on piers [10,11], both horizontal and uplift forces at different locations of the bridge superstructure [12], and long-duration damming effects both on the pier [13,14,15] as well as on the bridge superstructure [16]. Debris jams can also significantly increase the collapse risk, particularly in three specific ways: (i) increasing the drag force exerted by the flow [34], (ii) substantially increasing the upstream flood levels [35,36], and (iii) exacerbating the scour [14]. In fact, the accumulation of debris at piers is being acknowledged as a key mechanism of affecting the interaction between bridges, rivers, and floods [14], and contribute to more than one-third of bridge collapses in the United States [13].

Retrieved information of the selected bridge collapse sites (with associated USGS stations) can be found at https://github.com/fahmidah/Shape-Parameter-Bridge-Collapse-Sites/tree/main/List%20of%20Collapse%20Sites (accessed on 10 March 2022).

2.2. Shape Parameters

Shape parameters are retrieved for the GEV distribution using the extRemes R package. Annual peak flow data, retrieved from the United States Geological Survey (USGS), are used to fit with the GEV distribution. The cumulative distribution function of the GEV distribution is given by the following equation [37,38,39,40,41].

$$F\left(x/\theta \right)=exp\left(-{\left(1+k\left(x-\mu \right)/\sigma \right)}^{\pm 1/k}\right),\theta =\left(\mu ,\sigma ,k\right),\sigma >o$$

Here, μ is the location parameter, σ is the scale parameter, and k is the shape parameter. The shape parameter is of critical significance in that it represents the type of distribution: Gumbel (shape parameter = 0), Frechet or heavy tail (shape parameter > 0), and Weibull (shape parameter < 0) for fitting to block maxima series of data. Therefore, the shape parameter is related to how extreme the floods are. The higher values of k result in heavier tails.

2.3. Predictor Variables

The variables used in the current work are retrieved from the “GAGES II dataset” [42]. The dataset provides geospatial data and classifications for a total of 9322 stream gages maintained by USGS. The GAGES II dataset consists of gages that have had either 20+ complete years (not necessarily continuous) of discharge records since 1950 or are currently active. The geospatial data include watershed characteristics compiled from national data sources, including environmental features (e.g., climate—including precipitation, geology, soils, topography) and anthropogenic influences (e.g., land use, road density, or presence of dams). The dataset also includes comments from local USGS Water Science Centers, based on Annual Data Reports, pertinent to hydrologic modifications and influences. The dataset and associated detail description are available to the public at https://water.usgs.gov/lookup/getspatial?gagesII_Sept2011 (accessed on 29 August 2022). For the current study, specific variables are retained which are continuous, have physical meaning, and are not related to each other in an obvious way. For instance, ‘DDENS_2009’ and ‘pre1990_DDENS’ refer to dam density currently and pre-1990, respectively; both data are continuous and have physical meaning. However, they are related to each other; therefore, only the most updated data, ‘DDENS_2009’, is included in the analysis. There are a total of 40 distinct variables selected for the current study, as shown below:

• 15 variables related to climate: watershed average of annual number of days of measurable precipitation, watershed average of mean day of the year of last freeze, watershed average of monthly maximum number of days of measurable precipitation, mean annual precipitation (cm) for the watershed, watershed average of mean day of the year of first freeze, watershed average of minimum monthly air temperature (degrees C), average annual air temperature for the watershed (degrees C), mean annual potential evapotranspiration, standard deviation of maximum monthly air temperature, watershed average of maximum monthly air temperature, precipitation seasonality index of how much annual precipitation falls seasonally, watershed average of monthly minimum number of days of measurable precipitation, standard deviation of minimum monthly air temperature (degrees C), watershed average relative humidity (percent), and snow percent of total precipitation estimate.
• 7 variables related to watershed: fragmentation index of “undeveloped” land in the watershed, watershed percent “planted/cultivated” (agriculture), watershed percent “forest”, watershed percent “developed” (urban), watershed drainage area (sq km), watershed compactness ratio, density (per square km) of lakes/ponds, and reservoir water bodies.
• 6 variables related to soil: average value for the range of available water capacity for the soil layer, average value of sand content (percentage), average value of silt content (percentage), average value of clay content (percentage), average value of bulk density (grams per cubic centimeter), and average permeability (inches/hour).
• 5 variables related to topography: mean watershed elevation (meters), standard deviation of elevation (meters) across the watershed, aspect “north”, aspect “east, and mean watershed slope (percent).
• 3 variables related to population infrastructure: watershed percent impervious surfaces, population density in the watershed, and road density (km of roads per watershed square km).
• 4 variables related to dams: dam density, dam storage in watershed (normal storage), dam storage in watershed (NID storage), and major dam density.

A brief summary of the predictor variables used in the study is provided in Appendix A. The summary includes variable names, descriptions, types, units, time period, extent of data, data processing method, the scale of source data, and source of data.

For the selected variables, the random forests mechanism [43] is used to derive physiography-based important levels. Pacific Mountain and Rocky Mountain System were excluded from the physiography-based study because of the low number of sites. The methodology is then also implemented considering all the collapse sites together across different physiographic regions in the U.S. Random forests is a machine learning algorithm of increasing interest because of its excellent predictive performance [43]. Because of its ability to find important predictor variables, the mechanism has been used in geoscience [44,45], and in hydrology, particularly, to interpret the characteristics and relationships among different hydrological signatures [46,47]. In the current study, the random forests algorithm is used for regression [48], and the estimation of the importance levels [48,49] of different predictor variables, that is, the contribution of each input variable in predicting the response within a regional context. A negative importance level means that inclusion of the predictor variable results in a decrease in the performance of the algorithm. Positive values indicate a positive contribution to the prediction of the algorithm. The randomForest R package [50,51] is used to implement the algorithm. The algorithm requires little tuning, and its performance is very good when using the default parameters, i.e., the number of trees, the maximum number of terminal nodes of the trees, and the minimum size of terminal nodes. R scripts used for the analysis can be retrieved from https://github.com/fahmidah/Shape-Parameter-Bridge-Collapse-Sites/blob/main/Random%20Forest/Analysis (accessed on 10 March 2022).

2.4. Classification of Peak Flows

This study employs Jiang’s classification scheme [52] to categorize annual peak flows into heavy tail and light tail flows. Heavy tail flow implies that flows in the heavy tail increase more than the exponential order as compared to the flows in the light tail, and such high flows are expected to be with higher return periods. With Jiang’s classification scheme [52], the minimum heavy tail flow would be identified. To retrieve the return periods of minimum and maximum heavy tail flows, the annual peak flow data are fitted with GEV distribution, and the task is performed by implementing the extRemes R package.

3. Results

3.1. Shape Parameters

For physiographic regions studied, as shown in Figure 2, shape parameters do present fairly normal distributions (p-value of the Shapiro-Wilk normality test > 0.05). The extremeness of the flood behavior is quite similar across the study regions, as evident by the similar shape parameter values (mean and median). In fact, the median value of the shape parameter (

Table 1. Descriptive statistics of the shape parameter values for the bridge collapse sites.

Physiographic Region	Range	Mean	Median	Standard Deviation	Kurtosis	Shapiro-Wilk Normality Test
Appalachian Highland	−0.21–0.61	0.21	0.20	0.19	2.58	0.16
Central Lowland	−0.31–0.74	0.20	0.19	0.25	2.96	0.65
Interior Highland	−0.11–0.43	0.18	0.17	0.14	2.43	0.53
Coastal Plain	−0.32–0.63	0.18	0.2	0.21	3.28	0.64
All Sites	−0.32–0.74	0.20	0.19	0.19	3.02	0.85

) within each physiographic region is close to the median value of 0.19 as obtained for the watersheds with a diversity of climate types [43]. The site with the largest shape parameter value (0.74) is located within Central Lowland (USGS station #6108000) (Table 1), which implies a higher likelihood of obtaining extreme flows at this specific location. Here, the heavy tail flows are defined as extreme flows since they increase more than the exponential order as compared to the flows in the light tail. Sites within Coastal Plain experience much broader fluctuations (e.g., three or more standard deviations from the mean) in peak flows; such finding is evident by the value of the kurtosis (>3) in Table 1. A distribution is said to be leptokurtic when the kurtosis is greater than 3, implying that there is a greater potential for extreme fluctuations in the observed values. Coastal areas typically experience various kinds of flooding caused by high tides, heavy rain, storm surge, and high waves. Extreme coastal hazards (i.e., hurricanes) do not occur frequently, but when they do occur, they have a dominant effect on the rainfall and the level of flooding. Such unique characteristics of the coastal area might explain the broader fluctuation in the peak flow values. All the shape parameters’ values for 205 stations can be retrieved from https://github.com/fahmidah/Shape-Parameter-Bridge-Collapse-Sites/tree/main/Shape%20Parameters (accessed on 10 March 2022).

3.2. Predictor Variables

Among the six types of predictor variables, climate variables are found in a greater number across all regions (Figure 3). Predictor variables with associated importance levels for each physiographic region and all sites combined are provided in Appendix B.

For Appalachian Highland, there are a total of 36 predictor variables (with positive importance levels) identified: climate (13), watershed (7), soils (6), topography (3), dams (4), and population infrastructure (3) (Figure 4, see also Appendix B).

For Interior Highlands, 29 predictor variables (with positive importance levels) are identified: climate (10), soils (6), watershed (4), dams (4), population infrastructure (3), and topography (2) (Figure 5, see also Appendix B).

In total, 32 predictor variables (with positive importance levels) are identified for Central Lowland: climate (13), watershed (5), soils (4), topography (4), dams (3), and population infrastructure (3) (Figure 6, see also Appendix B).

For Coastal Plain, 32 predictor variables (with positive importance levels) are identified: climate (13), watershed (6), soils (6), dams (3), population infrastructure (3), and topography (1) (Figure 7, see also Appendix B).

When considering all sites together, 39 predictor variables (with positive importance levels) are identified: climate (15), topography (5), soils (6), population infrastructure (3), dams (3), and watershed (7) (Figure 8, see also Appendix B).

Considering the importance levels, certain climate variables are found to be most important for Appalachian Highland; 9 out of 10 variables (ranking between 1 to 10) are climate variables (

Table 2. Types of most important (ranking 1 to 10) predictor variables across different physiographic regions. Description of predictor variables is provided in Appendix A.

Ranking	Appalachian Highland	Interior Highlands	Coastal Plain	Central Lowland	All Sites
1	WDMIN_BASIN	FST32F_BASIN	AWCAVE	ELEV_MEAN_M_BASIN	WD_BASIN
2	WD_BASIN	LST32F_BASIN	SANDAVE	PDEN_2000_BLOCK	LST32F_BASIN
3	WDMAX_BASIN	DDENS_2009	PERMAVE	IMPNLCD06	WDMAX_BASIN
4	SLOPE_PCT	BDAVE	PLANTNLCD06	DEVNLCD06	PPTAVG_BASIN
5	T_MIN_BASIN	T_MIN_BASIN	SILTAVE	T_MAXSTD_BASIN	FST32F_BASIN
6	T_AVG_BASIN	STOR_NID_2009	PRECIP_SEAS_IND	LST32F_BASIN	ELEV_MEAN_M_BASIN
7	LST32F_BASIN	T_AVG_BASIN	LST32F_BASIN	ROADS_KM_SQ_KM	RH_BASIN
8	T_MAX_BASIN	STOR_NOR_2009	PPTAVG_BASIN	RH_BASIN	T_MIN_BASIN
9	SNOW_PCT_PRECIP	PET	ELEV_MEAN_M_BASIN	ELEV_STD_M_BASIN	T_AVG_BASIN
10	PET	CLAYAVE	ROADS_KM_SQ_KM	FST32F_BASIN	PET
		Climate		Watershed
		Soils		Dams
		Population Infrastructure		Topography

). For Interior Highlands, certain climate, dam, and soil variables are found to be most important (Table 2). Finding dam properties as the important predictor variables (third, sixth, eighth) (Table 2) might be noted here specifically as it suggests the apparent importance of human interference within the watershed. The importance of human interference is also apparent within Central Lowland with the rankings of certain variables: population density (second), percentage of impervious area (third), percentage of developed area in the watershed (fourth), and road density (seventh) (Table 2). Certain topography, population infrastructure, and climate variables are also found to be most important for Central Lowland (Table 2). For Coastal Plain, certain soil and climate variables are found to be the most important (Table 2). The findings, considering all sites together, are quite similar to the Appalachian Highland; 9 out of 10 important variables are found to be climate type (Table 2).

Among 40 distinct variables, 10 predictor variables are found common across all regions (

Table 3. Common predictor variables across all study regions. Description of predictor variables is provided in Appendix A.

Variables	Variable Type	Important (Ranking between 1 to 10) Regions
LST32F_BASIN	Climate	All regions
T_MIN_BASIN	Climate	Appalachian Highland, Interior Highlands
T_AVG_BASIN	Climate	Appalachian Highland, Interior Highlands
SNOW_PCT_PRECIP	Climate	Appalachian Highland
FST32F_BASIN	Climate	Interior Highlands
T_MINSTD_BASIN	Climate	NA
CLAYAVE	Soils	Interior Highlands
SANDAVE	Soils	Coastal Plain
ROADS_KM_SQ_KM	Population Infrastructure	Central Lowland, Coastal Plain
FRAGUN_BASIN	Watershed	NA

); climate (6), soil (2), population infrastructure (1), and watershed (1). Each of the common variables is found to be important for one or more than one physiographic region (Table 3), except for the variables ‘T_MIN_STD_BASIN’, and ‘FRAGUN_BASIN’. Only one common variable, ‘LST32F_BASIN’, is found to be important (ranking between 1 to 10) for all regions (Table 3).

When comparing important (ranking between 1 to 10) variables common to more than one region, comparatively higher importance levels are obtained for certain regions (Figure 9, Figure 10, Figure 11, Figure 12 and Figure 13). For instance, for common soil variables (ranking 1 to 10), relatively higher important levels are retrieved for Coastal Plain except for ‘BDAVE’ (Figure 10). For common topography variables (ranking 1 to 10), comparatively higher importance levels are retrieved for Central Lowland (Figure 11). On the other hand, for common topography and watershed variables (ranking 1 to 10), Interior Highlands have the least importance levels (Figure 11 and Figure 12). Higher importance levels imply higher predictability of the flood behavior for Central Lowland and Coastal Plain while considering certain variables as predictors. Since the system has higher predictability, accurate forecasts based on current observations (predictor variables with higher importance levels) would be comparatively easier.

3.3. Heavy Tail Flows

Most of the USGS stations (172 out of 195) associated with the collapse sites are found to be exhibiting a ‘heavy tail’ distribution (Figure 14,

Table 4. Return periods and associated information for heavy tail flows of the bridge collapse sites across different regions.

Physiographic Region	# of Sites with Heavy Tail Flows (Total Sites)	# of Sites with Different Return Periods (Years)				Minimum/Maximum Return Periods (Years)	Mean/Median	Kurtosis
		<50 Years	50–100 Years	100–500 Years	>500 Years
Appalachian Highland	100 (111)	80	9	10	1	3/897	45.58/13.57	47.0
Central Lowland	23 (26)	18	1	4		2/465	55.37/10.12	10.41
Coastal Plain	28 (33)	22	1	5		2/213	45.38/14.81	2.05
Interior Highlands	21 (25)	15	3	2	1	1/627	75/18.41	9.30

) for peak flows, that is, the shape parameter values of the GEV distributions are greater than zero.

Heavy tail flows are expected to be with higher return periods. However, for most of the sites, heavy tail flows exhibit lower return periods (Figure 15, Table 4). The minimum return periods range from 1 to 3 years considering all regions (Table 4). In fact, the median values for the return periods are found to be less than 50 years for each of the physiographic regions studied (Table 4). Within these regions, heavy tail flows occur more frequently than expected. There are also a few collapse sites within each region, for which no heavy tail flow occurred yet. Such results imply that at these specific sites, bridges collapsed at flows with lower return periods, particularly, less than 50 years. On the other hand, the maximum return periods for the heavy tail flows range from 213 to about 897 years (Table 4). Comparing all regions, the likelihood of having extremes with higher return periods (outliers) is greater for Appalachian Highland as implied by the larger kurtosis value of 47 (Table 4). The calculated return periods for the heavy tail flows (for 205 USGS stations) can be retrieved from https://github.com/fahmidah/Shape-Parameter-Bridge-Collapse-Sites/tree/main/Return%20Periods (accessed on 10 March 2022).

4. Discussion

The key findings are discussed in detail here.

• The normal distribution of shape parameters does not imply climate variables as the most important predictor variables. Some studies suggest that the shape parameter depends on climate indexes, while other attributes of the catchments are less important [46,53,54,55]. With such attributes, the GEV shape parameter is most preferably modeled by a normal distribution with a common mean across all sites [46,53,56,57,58]. However, it is also claimed that this may be a result of an insufficient summary of the catchment attributes by the implemented indexes [59]. For the current study, the retrieved values of shape parameters do agree with recent studies [59,60,61,62] in that the values follow a fairly normal distribution within each physiographic region. However, for the study sites, the distinct association with climate variables is not evident except for Appalachian Highland.
• There is a variation in the types of important predictor variables across all study regions. Although there is an over-representation of climate variables, important predictors (ranking 1 to 10) include more than one type across all regions: climate and topography for Appalachian Highland; climate, dam, and soil for Interior Highlands; topography, population, and climate for Central Lowland; and soil and climate for Coastal Plain. In fact, the median value of the shape parameters obtained for each region is very close to the median value of 0.19, as obtained for the sites with hydrological heterogeneity [46]. Such a result implies that the flood behavior (or extremeness) within each specific region is similar to the flood behavior (or extremeness) within the region of hydrological heterogeneity.
• Predictor variables associated with human interference are important. For all regions, ‘population infrastructure’ and ‘dams’ variables are obtained as the predictor variables. For Interior Highlands, Coastal Plain, and Central Lowland, the importance of human interference is apparent with higher importance levels (ranking between 1 to 10) as compared to other predictor variables. It is well-established that human interference, particularly the presence of dams, can cause and/or exacerbate flood events. Dam break-generated floods can be much more catastrophic than typical riverine floods since dam break generates significant impulsive loads, which can exceed the drag of typical riverine floods by up to 270% [63]. Dam break-generated floods also generate different patterns of vertical forces and moments, which would lead to different probabilities of collapse and different failure modes as compared to riverine floods [63]. Emergency releases of water down spillways can also cause far greater and more sudden floods downstream as compared to the natural riverine floods [64]. The loss of natural sponges for floodwaters, such as deforestation, removal of scrub, and/or drained-out wetlands, caused by building dams, can result in a completely different hydrological regime, and can also increase the risk of extreme floods [64]. In the current study, the peak flows of 29 sites are affected by possible dam breaks as noted by USGS. The reconnaissance studies throughout the mid-west also revealed that the widespread human disturbance together with easily erodible soils has produced thousands of miles of highly unstable streams [27,65]. Therefore, it can be argued that human interference, for instance, through dams, is an important parameter at a watershed and/or regional scale, given the unique flood generation mechanism within such a context.
• Return periods of heavy tail flows vary from very low to very high. For the collapse sites studied, there exists a wide variation of return periods for the heavy tail flows. However, there is a persistence of lower return periods, as low as 1 to 3 years, which implies that the heavy tail flows occur more frequently than expected at the bridge collapse sites. Such a finding is in accordance with a recent study of the bridge collapse sites in the U.S. where the prevalence of collapse-inducing floods with lower return periods has become evident [28]. In fact, certain physiographic settings do possess plausible conditions for which flows with lower return periods can induce collapse [66,67]. For instance, within physiographic regions, namely, Central Lowland, Intermontane, Great Plains, Appalachian Highland, and Coastal Plain, unique conditions such as irregular channel shifting, high erosion at bed and bank, debris jam, backwater from bays, and/or intensive human interventions are exhibited [27,65]. Regions with such intrinsic risk conditions would not have the resiliency to flow with lower return periods as would have been expected. Extreme flows with higher return periods would have catastrophic effects within such settings. The study results do also indicate the occurrence of extreme flows with return periods as high as 213 to 897 years at a few sites within each region studied. Such findings instigate revisiting the guidelines specifying the use of a “100-year flood” (flood with an annual probability of exceedance of 1%) for modern interstate bridges receiving federal funding [68]. Typically, for design purposes, i.e., calculation of expected scour and hydraulic loads, engineers would consider the magnitude of a single design flood. One single, characteristic flood, such as a 100-year flood, is also frequently used in collapse risk studies [1]. Given that the collapse can be induced by heavy tail flows with both low and high return periods, in relation to certain physiographic settings, bridge design should be modeled over a range of possible collapse-inducing flows. Risk studies should also consider all plausible collapse-inducing floods in relation to certain regional conditions.

Summary

Whereas climate, soil, topography, and watershed attributes are common in flood hazard indexing, recent studies suggest that the shape parameter of the flood distribution mostly depends on climate indexes, while other attributes of the catchments are less important [46,53,54,55]. The association of the shape parameter mostly with climate variables implies that certain climate variables are the most important predictors of flood behavior. The current study results are novel in that they suggest that other variables, including soil, topography, watershed, and human interference, are more important than climate variables in certain physiographic settings, at least for the collapse sites considered. Widespread human interference at a regional scale is also evident in the bridge collapse sites, particularly within Interior Highlands, Coastal Plain, and Central Lowland. Another key finding is that the collapse sites within each physiographic region exhibit a. similar extremeness of flood as within the region of hydrologic heterogeneity. The extremeness of floods is also implied by the frequent occurrence of heavy tail flows within each region. All of these key findings, within a regional context, should be considered in failure modes and effect analysis for assessing collapse risk at a local scale, which could be an area for further research. Here, it should be noted that failure modes and effects analysis for a large dataset of bridge collapse sites are not feasible because of the unavailability of the required information. The NYDOT failure database does not include any information about the failed component or the failure mode for the collapse events. Such information might be available at the state-based DOT (Department of Transportation); however, they are not available to the public. Nonetheless, if an association can be established among regional variables, bridge characteristics, and local conditions in relation to specific failure modes, it can lead to a robust risk assessment framework for the bridge structures. In addition, hydrologic variables, such as the 40 variables selected in the current study, are typically analyzed at a regional and/or watershed scale, whereas hydraulic parameters, such as flood level, bridge type, etc., are considered at a more refined local scale. Some parameters, such as debris jams, are investigated both at the regional and local scales. Integration of these two spatial scales requires extensive research and, therefore, could be a topic of future studies.

5. Conclusions

In the study, analysis of shape parameters, retrieved from the GEV distribution of annual peak flows, are performed for 205 USGS watersheds (or stations) associated with 297 bridge collapse sites across different physiographic regions. Annual peak flows are also analyzed in relation to the heavy tail flows and their return periods. Certain unique findings become apparent for all of the collapse sites in relation to each physiographic region (Appalachian Highland, Central Lowland, Interior Highlands, and Coastal Plain): (a) variation of the most important predictor variables, (b) apparent importance of human interference, (c) flood extremeness similar to the region with hydrologic heterogeneity, and (d) frequent occurrence of extreme peak flows. Such findings necessitate revisiting bridge design and bridge collapse risk study in relation to not only the magnitude and frequency of floods but also the behavior of the floods as stemming from specific physiographic settings.