PIAHSProceedings of the International Association of Hydrological SciencesPIAHSProc. IAHS2199-899XCopernicus PublicationsGöttingen, Germany10.5194/piahs-373-143-2016Vehicles instability criteria for flood risk assessment of a street networkArrighiChiarachiara.arrighi@dicea.unifi.ithttps://orcid.org/0000-0002-8096-7435HuybrechtsNicolasOuahsineAbdellatifChasséPatrickOumeraciHocineCastelliFabiohttps://orcid.org/0000-0003-0304-0289Department of Civil and Environmental Engineering, University of
Florence, Florence, ItalyLaboratoire Roberval, Sorbonne Universités, Université de
Technologie de Compiègne, CNRS, Centre de Recherches de Royallieu,
Compiègne Cedex, FranceCEREMA-DTecEMF, Margny Lès Compiègne, FranceTU Brauschweig, Leicthweiss Institute for Hydraulic Engineering and
Water Resources, Braunschweig, GermanyChiara Arrighi (chiara.arrighi@dicea.unifi.it)12May2016373143146This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://piahs.copernicus.org/articles/373/143/2016/piahs-373-143-2016.htmlThe full text article is available as a PDF file from https://piahs.copernicus.org/articles/373/143/2016/piahs-373-143-2016.pdf
The mutual interaction between floods and human activity is a
process, which has been evolving over history and has shaped flood risk
pathways. In developed countries, many events have illustrated that the
majority of the fatalities during a flood occurs in a vehicle, which is
considered as a safe shelter but it may turn into a trap for several
combinations of water depth and velocity. Thus, driving a car in floodwaters
is recognized as the most crucial aggravating factor for people safety. On
the other hand, the entrainment of vehicles may locally cause obstructions
to the flow and induce the collapse of infrastructures. Flood risk to
vehicles can be defined as the combination of the probability of a vehicle
of being swept away (i.e. the hazard) and the actual traffic/parking
density, i.e. the vulnerability. Hazard for vehicles can be assessed through
the spatial identification and mapping of the critical conditions for
vehicles incipient motion. This analysis requires a flood map with
information on water depth and velocity and consistent instability criteria
accounting for flood and vehicles characteristics. Vulnerability is
evaluated thanks to the road network and traffic data. Therefore, vehicles
flood risk mapping can support people's education and management practices
in order to reduce the casualties. In this work, a flood hazard
classification for vehicles is introduced and an application to a real case
study is presented and discussed.
Introduction
According to global statistics, in the last decade floods affected the
largest number of people with respect to other natural hazards (EM-DAT,
2012). In developed countries the majority of fatalities occurs in vehicles
(Jonkman and Kelman, 2005; Maples and Tiefenbacher, 2009; Fitzgerald et al.,
2010; Kellar and Schmidlin, 2012). On one hand, vehicles can become unstable
by losing traction even for very low water depths, or they become buoyant,
so that they are swept away by floodwaters and possibly produce a debris. On
the other hand, several fatalities occur for inappropriate high-risk
behaviours, like driving in flooded streets. These are the reasons why
vehicles are usually recognized as one of the most aggravating factors in
urban floodings (Rodriguez et al., 2006; Franklin et al., 2014). Although the problem of vehicle
mobilization is so crucial, only a few experimental investigation on the
incipient motion conditions of small-scale vehicle models have been carried
out so far (Shu et al., 2011, Xia et al., 2011, 2014). The
experimental data on vehicles instability, expressed as pairs of water depth
and velocity, are affected by a large scatter, which depends on the
different characteristics (i.e. weight, shape, height of the planform) of
the considered vehicle model.
Moreover, the different contribution of the hydrodynamic forces and the
influence of flow regime on the mechanism of the onset of motion has been
numerically studied by Arrighi et al. (2015).
The aim of the work is to introduce hazard criteria for vehicles at rest in
flooded streets easily applicable to inundation maps, which account for both
flood and vehicles characteristics, in order to overcome the scatter of
existing experimental data.
Dimensionless instability diagram for flooded vehicles
Incipient motion for sliding occurs when the drag force exerted by the water
just exceeds the friction force, which is the product of the friction
coefficient μ and immersed weight of the car (Eq. 1). The onset of
motion by sliding of a vehicle is modeled using the geometric scheme shown
in Fig. 1a. The flow direction has an orientation β with
respect to the longitudinal axis of the car and the bed slope is assumed
null, the wheels are considered as locked.
12ρCDU2AD>μρcgHV-hclL-ρgH-hclL-12ρCLU2AL
where ρ is the water density, ρc is the car density, U is
the mean flow velocity, H is the water depth, HV is the height of the
vehicle, hc is the height of the planform, g is the acceleration of
gravity, l and L are the car width and length and CD and CL are the
drag and lift coefficients (official IS of units). The reference areas for
drag (AD) and lift (AL) forces are the projection of the full area
of the car normal to the flow (Eq. 2) and the planform (Eq. 3) which are
respectively
AD=(l⋅cosβ+L⋅sinβ)⋅(HV-hc)AL=L⋅l
The manipulation of Eq. (1) here modified to account for any given flow
orientation after Arrighi et al. (2015) yields a relation between the
square of Froude number U2gH and a dimensionless group of
variables which is called mobility parameter θVθV=2LHV-hc⋅α⋅ρc⋅HV-hcρ⋅H-hc-1α=ll⋅cosβ+L⋅sinβ
where the first term is a shape factor, α accounts for the angle of
flow incidence and the latter accounts for the immersed weight of the car.
Sketch of the car geometry and definition of the mobility
parameter (a), definition of hazard criterion (b) and dimensionless
instability diagram for flooded vehicles with identification of the critical
threshold (c) (experimental data by Shu et al., 2011; Xia et al., 2011, 2014).
The mobility parameter has been calculated for three experimental datasets
(Shu et al., 2011, Xia et al., 2011, 2014) including seven
different car models and densities and three model scales (1 : 14, 1 : 18,
1 : 43). The values of the calculated mobility parameter θV
plotted against Froude number identify a unique threshold of incipient
motion (Fig. 1c), which separates safe conditions (above the
curve) from dangerous conditions (below the curve) where the vehicle
mobilization is likely to occur. Thus, a hazard criterion can be defined as
the ratio between the critical threshold θVcr and the mobility
parameter θV for a predefined reference vehicle and flow regime
(i.e. water depth and velocity of an inundation map) as shown in Fig. 1b.
The case study of Ajaccio (France)
The study area considered to show the application of the vehicles hazard
criterion derived from the mobility parameter, is the Les Cannes district in
Ajaccio, situated in southwestern Corse (France). The flood simulation has
been carried out with TELEMAC-2D (Galland et al., 1991) solving the shallow
water equations over an unstructured grid of triangular elements. The
results have been provided by CEREMA (Centre d'études et d'Expertise sur
les Risques, l'Environment, la Mobilité et l'Aménagement) and are
described in detail in a project report for the Direction Départementale
de l'Equipment Corse du Sud (Sogreah, 2006).
The Cannes district is located downstream of three small catchments
(Arbitrone, Moulins Blancs and Arbajola), whose streams are culverted in the
urbanized area up to the gulf (Fig. 2, top). The cadastral map 1 : 5000 has
been used to extract the built footprint and a detailed topographic survey
has been carried out to measure the terrain elevation (max 30 m a.s.l.). The
mesh is composed of 10 511 nodes and 18 486 elements, with edge size ranging
from 0.5 to 25 m in the sea.
Although the area is not densely urbanized, it hosts two educational
facilities and some commercial activities and it is connected to the port
area through an important traffic artery along the coastline, the Cours Jean
Nicoli.
Benchmark inundation events date back to 23 January 2003 and 25–26 November
1990 and allowed the validation of the numerical model (Sogreah, 2006).
The maximum water depth reached in the Cannes district for the simulated 100
years scenario is about 2 m (Fig. 2, top) and the maximum velocity is
above 3.0 m s-1. The dark blue area at the bottom of the top panel in Fig. 2
represents the sea level used as a southern boundary condition. The hazard
level is calculated for a Ford Focus and β=90∘ (i.e. a
medium size passenger vehicle oriented normally to the flow) combining in
each computational cell, for each time step, the variables obtained during
the simulation (i.e. water depth and velocity). Figure 2 (bottom) shows the
extraction of the maximum value of the vehicle hazard over the simulation
time. The colour scale goes from 0.25 (green colour, very low hazard) up to
1.5 (dark violet, very high hazard). Red areas are those likely to be prone
to incipient motion of vehicles (high hazard) and violet areas can be
considered as extremely dangerous for parked vehicles since the hazard level
is higher than one. Moreover, since many open areas are used as car parking
for the commercial areas, it is likely that vehicles can be swept away by
floodwaters for a similar scenario.
Conclusions
The mobility parameter allows defining hazard criteria capable of accounting
for both flood and vehicles characteristics. The hazard map here presented
can be drawn for different probability scenarios and can be used to assess
the risk for vehicles if the parking/traffic density is accounted for. From
this preliminary test, the main traffic artery shows very high hazard levels
for the simulated 100 years flood and can be significantly affected in case
of event.
Flood depth map for the simulated 100 years scenario (top) and
temporal maximum of the hazard for vehicles with identification of
vulnerable buildings and main traffic artery (bottom).
The available visual documentation of the 2003 flood event demonstrate that
vehicles mobilization occurred in the area. The presence of the schools is a
further traffic-attractor during several time slots and represents a
vulnerability factor. In order to prevent people's fatalities, hazard maps
for vehicles can be adopted to implement non-structural flood risk
mitigation measures (i.e. people education, traffic management) or emergency
actions (roads closure).
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