An approach to the modelling of stability of waste containers during urban flooding

Before the solid waste is dumped in landfills, the collection process for large Spanish cities starts from a regular collection of household waste municipal service which is carried out through street containers. When an urban flood occurs those containers may lose their stability, thereby allowing debris (i.e., solid waste contained) and leachate to escape from the container and contaminate the flood water. Moreover, once a container loses its stability it can further constrict a narrow street and increase flooding, thereby creating a closed basin with no outlet for runoff and exacerbating the effects of flooding. Therefore, the waste containers stability when exposed to flooding is definitely an environmental, safety and health concern to be addressed. In this research stability functions for waste containers exposed to urban floods have been derived. These thresholds have been employed to analyse the containers' potential behaviour during floods in Barcelona. In order to validate the model a historical rainfall has been modelled and low‐return‐period design storms (i.e., 1, 5, and 10 years) have been used to assess the containers vulnerability against floods for frequent rainfall events. Once the number of potentially unstable containers has been estimated, an adaptation measure has been proposed in order to increase the resilience of waste sector against urban floods in Barcelona.


Introduction 31
Cities around the world, can be affected by floods. However, urban floods may have different 32 sources and are called riverine flood, when the main river bed exceeds its capacity; stormwater 33 flood, when the conveyance capacity of the urban drainage system is exceeded; or coastal flood, 34 when the seawater causes the flooding. Only stormwater floods may affect any city, even if 35 neither is a coastal city nor have a nearby river to be overflowed (Zbigniew W. et al., 2014;Patra 36 et al., 2016).

37
Stormwater flooding occurs because the "exceedance flow" is generated on the urban 38 surface. For this reason, the design of drainage systems should consider the dual drainage concept 39 (Djordjevic et al., 1999;Schmitt et al., 2004;Nanía et al., 2015;Russo et al. 2015), through which 40 certain amount of runoff is assumed to flow on the streets because only a portion of runoff can be 41 conveyed by the sewer system. The term pluvial flooding is sometimes used synonymously with 42 stormwater flooding, or sometimes used to denote urban flooding where there is no sewer network 43 or the network is already at full capacity (Butler and Davies, 2011). When accepting the dual 44 drainage concept, the consequences of this flow on the streets must be analysed by ensuring firstly 45 a high level of safety for pedestrians (Martínez-Gomariz et al. 2016) but also minimizing the 46 direct and indirect economic damages. Therefore, a comprehensive flood risk assessment must be conducted in order to implement adaptation measures if necessary. 4 the 'technical fix' approach, such as landfill gas collection and utilization, and upstream measures, 85 particularly reduction, reuse, recycling and composting. Solid waste management, often a 86 neglected aspect of urban management, is a problem in both developed and developing countries 87 (Sam, 2002) and there are reasons (Lamond et al., 2012)

93
Only a few studies focused on the impacts caused by climate change on waste sector 94 (Zimmerman et al., 2010;Winne et al., 2012;USAID, 2012USAID, , 2014USAID, , 2015. By assuming more 95 intense rainfall events, potential impacts on solid waste management are described, such as:

100
As stated, the main research effort regarding climate change-related impacts of solid 101 waste sector is focused on offering mitigation measures and strategies in order to reduce the waste 102 greenhouse gases emissions. However, no research studies addressed the reverse problem: how exacerbating the effects of flooding. This hazard is greatest upstream of culverts, bridges, or other 115 places where debris can collect. On the other hand, inlets and sewers can become clogged with 116 solid waste if it comes out of the container after it loses stability, thereby worsening the drainage 117 system and contributing to exacerbate the flood impacts. Consequently, the waste containers 118 stability when exposed to flooding is definitely an environmental, safety and health concern to be 119 addressed.

120
The main cascading effects due to containers' instabilities may be listed as follows: 121  Traffic disruption: Traffic may be disrupted not just while flood is occurring 122 but also after the event when these containers that were washed away may be left 123 on roads. 124  Waste collection disruption: After a flood event, the waste collection may be 125 disrupted if containers were moved from their original location. The municipal 126 workers have to relocate them and even collect their content in case it came out 127 from the container after losing the stability.

128
 Potential sewer blockages: Potential fractions coming out from the container 129 may block sewers and thereby adversely affect the drainage efficiency.

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 Increased likelihood of cascading effects due to flooding: If containers, moved 6 with the description of the types of containers and which kind of fractions they may contain is 139 presented first. Afterwards, a comprehensive study of the forces acting on a flooded container, 140 the different modes of instabilities and the derivation of the formula for the stability threshold 141 (i.e. the velocity and water depth combinations which lead to the containers instability) is 142 conducted. Finally, these obtained stability thresholds are employed to analyse the potential 143 behaviour of containers against floods in Barcelona caused by historical and low-return-period 144 design storms (i.e. 2, 5 and 10 years). Adaptation measures in order to improve the resilience of 145 waste sector against urban floods in Barcelona will be proposed based on the results of the case 146 study of the stability of containers exposed to flooding.

Waste and recycling collection service by containers in 148
Barcelona 149

Description of waste and recycling Barcelona municipal service 150
Barcelona has an extensive municipal service for a daily collection of household and commercial 151 waste to provide waste collection to citizens and ensure a clean and healthy public space. This 152 service is carried out through street containers, door to door bags collection service, pneumatic 153 collection boxes and bins for collection in shops. Waste which cannot be placed in conventional 154 containers is delivered to Green Dots. Citizens also have special services regarding waste 155 collection, such as old furniture and clothes, dead animals, debris bags gardening waste, 156 fibrocement or asbestos. 7 Barcelona opts for a recycling collection including five different fraction-types of 164 containers. There are containers for each one of them located citywide in order to make waste 165 management easier: waste, organic, paper and cardboard, packaging, and glass. All citizens have 166 recycling collection containers located less than 100 meters from their home. 167

175
Due to the less percentage of rear and underground loading-type containers when 176 comparing with lateral and bilateral type (Figure 2), only the former have been taken into 177 account in this study, which is an 87% of the total number of containers.

179
The positioning of the containers in the city is as follows: these are placed in groups of 180 4 or 5, one per type of fraction to be collected, and their position on the streets is established 181 either by painting enclosed areas on the ground or by defining their area with plastic yellow 182 pieces, which are used also as guides to place the containers on it (Figure 4). That is the reason 183 for the containers to have a hollow along their base, to place the yellow guides on it. These 184 hollows, as will be explained later, contribute to a better stability against the buoyancy.

185
In order to analyse the containers stability, an important parameter is their weight, which can vary 186 greatly depending on their filling degree and the type of contained fraction. Moreover, when it 187 comes to different fractions inside the containers the concept of bulk density has to be presented.

188
In contrast to density, bulk density is only used in cases where the particles or chunks of matter 8 are loosely packed with space for air within. Therefore, bulk density is not an intrinsic property

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In Table 2

3.
Containers stability when exposed to flooding 209

Forces and torques acting on a flooded container 210
Two types of forces and torques may be considered in order to analyse the stability of such urban 211 elements exposed to flooding, those due to the water flow (i.e. hydrodynamic forces) and those 212 due to the container contact with the ground (Figure 6). Focusing firstly on hydrodynamic forces, 9 drag force ( ) and vertical pushing force ( ) are the ones that may affect the container stability.
where is the water density, is the water velocity, is the drag coefficient, which depends 216 on Reynolds number and the shape of the container (i.e. rectangular prism), and is the projected 217 area of the submerged container part perpendicular to the flow direction. The other hydrodynamic 218 force is the vertical pushing force ( ) which is the combination of the lift force ( ) and the 219 buoyancy force ( ) (Martínez-Gomariz et al., 2017). A container is expected to lose its stability 220 for low or zero (i.e. hydrostatic conditions) once the water depth reaches the buoyancy depth, 221 therefore, for simplicity, only buoyancy force, even for hydrodynamic conditions, is considered Where is the displaced container volume, 1 and 2 are the container width and 226 depth respectively, is the specific weight of water, and is the water depth.

227
Nevertheless, the container is expected to become buoyant for low water depths, thus the 228 contribution of the containers bottom hollows on reducing buoyancy will likely be significant.

229
For this reason, these hollows ( Figure 8) have been considered by deriving a function ( ℎ ( )) 230 ( Figure 9) to determine the water-filled hollows volume ( ℎ1 (lateral and bilateral) and ℎ2 231 (lateral)) for both types of containers (i.e. lateral and bilateral loading). This volume will be taken 232 off the one assumed as completely solid (3); consequently, the displaced volume will be obtained 233 based on the expression (4). Once the water depth reaches the hollows depths ( ℎi), this volume 234 ( ℎimax) remains constant ( Figure 9).

235
On the other hand, gravitational and frictional forces will act as stabilizing forces in this 236 system of forces. The first, gravitational force ( ), depends on the container weight ( ( , )), 237 which in turn depends on their unladed weight ( ), the container filling ( ), and the type of 238 fraction that it contains ( ) as described in section 2.2. Accordingly, gravitational force can be 239 obtained as indicated in expression (5).

241
However, the gravitational force stabilization will be countered by the vertical pushing 242 force action, to some extent, depending on the water depth. Therefore, the so-called effective 243 weight ( ) may join the action of both forces ( = − ), so that the resulting will 244 determine the vertical force stabilization.

245
Previous statements only are true in case the container is located on a flat ground, thereby 246 considering only vertical component for the normal ground reaction ( ). Consequently, the 247 frictional force ( ) may be obtained according to the expression (6).

248
where is the friction coefficient between container and ground. 249

Modes of instabilities 250
Different modes of instability may occur when a container is flooded ( Figure 10). In case 251 of stagnant water only buoyancy may act on the flooded container, and it will occur when the 252 buoyancy force reaches the gravitational one. On the other hand, hydrodynamic instabilities may 253 occur also, by either combining effects or acting isolated. Sliding instabilities will occur when the 254 drag force exceeds the frictional one, and toppling will take place in case of container rotation 255 from one corner of its base. In reality, both instabilities will likely occur together, when after 256 sliding the container may be blocked by an object located on the ground and is toppled. The yellow guides placed on the ground (Figure 4) to define the container placing area and also to fix 258 the location of the containers themselves, could be a reason for container toppling. Regarding this 259 yellow plastic pieces, it has to be considered that could be supportive in terms of stability in 260 certain situations. However, the less favourable conditions have been taken into account in this 261 study, thus the guides effect has been neglected herein. 262

Buoyancy 263
Critical or buoyant water depth can be obtained by establishing the equilibrium condition 264 for buoyancy (7). It can be seen also as the water depth for which the previously defined container 265 effective weight ( ) becomes zero.

266
Based on this equilibrium condition, and on the buoyancy force expression (8), a critical 267 or buoyant water depth may be derived (9).
By applying expression (8), all critical water depths, for the different types of container 269 with their respective characteristics (  (10), (11), (12) and (13) where are the different horizontal forces acting on the flooded container.

286
Equilibrium condition for toppling where 0 are the torques produced on the flooded container from the depicted pivoted point (O 288 in Figure 6), is the torque due to the drag force ( ), and is the torque due to the effective 289 weight ( ). Note that a uniform distribution of the contained fraction is assumed, so that the 290 downwards gravitational force direction will be coincident in a same vertical with the upwards 291 buoyancy force direction.

13
The threshold function (i.e. a relationship between flow velocity and water depth) for 293 each mode of instability has been derived also for two flow directions, parallel to L1 and L2, which 294 considers different areas for drag force to act on. Therefore, four threshold functions have been 295 obtained as indicated in the expressions (13a,b) and (14a,b) given in Figure 11.

296
The two unknown parameters are the roughness coefficient ( ) and the drag coefficient

Historical real stormwater flood in Barcelona (30/07/2011) 360
On 30 th of July 2011 a heavy rainfall event occurred which caused a major flood in 361 Barcelona. The cumulative rainfall was 30.4 mm in one hour, the maximum rainfall intensity in 362 20 minutes was 105.9 mm/h (corresponding to a return period of 8 years approximately), and a 363 maximum rainfall intensity in 5 minutes was 140.4 mm/h (corresponding to a return period of 2 364 years approximately). This rainfall event was the one employed to validate the CORFU model 365 and its spatial distribution was taken into account by considering rainfall data recorded from 11 366 rain gauges across Barcelona.

367
The output of this model (i.e. water depths and velocities in each grid cell) has been 368 employed in this section in order to study the potentially unstable containers within the flooded 369 area. In this case, according to the 2D surface extent of the CORFU model, only 10,455 containers 370 out of 23,141 (45%) have been studied. In a way, the flood (i.e. CORFU model output) caused by the 30 th of July 2011 event has been thus employed as validation of the proposed stability criteria 372 for solid waste containers.

373
Three scenarios have been studied: containers empty, 50% filled and full, and the 374 distribution of these containers potentially unstable are shown in Figure 14.

375
In Table 4

Floods related to different design storms (T= 1, 10 and 50 years) 389
Design storms of 1, 10 and 50 years return period, 155 minutes duration, and 5 minutes funded RESCCUE project. In this occasion, same procedure as previously described (using 396 CORFU) has been followed, although a more extended area, which covers almost the whole Barcelona city, has been studied. It means 17,836 containers, out of 23,141 (77%) in Barcelona, 398 placed within the model domain and whose stability has been assessed.

399
Since 2016 fixation pieces (Figure 16a) started to be installed in order to ensure the 400 stability of containers when observed that only their own weight could cause their instability in 401 steep streets. The number of installed pieces is 147 so far, but 574 more are planned to be installed 402 in the short term. However, these pieces may be used also to ensure stability of containers located 403 in flat or low-slope areas (Figure 16b), which may be potentially unstable when an urban flood 404 occurs. Therefore, these already-fixed containers are not potentially unstable due to floodwater 405 and hence have been removed from the analysed ones.

406
In Figure 17 maps with the potentially unstable containers are shown, for the considered 407 scenarios (i.e. empty, half-full, and completely full) and return periods that caused containers' 408 instabilities (i.e. 10 and 50 years). Moreover, in Table 5

Adaptation measures proposed 417
Based on these findings, in order to increase the resilience of waste sector against urban 418 floods caused by a 10 years return period rainfall in Barcelona for an empty containers scenario, 419 1,668 fixation pieces would be necessary to be installed. It has to be noted that a couple of pieces 420 are needed to be installed per group of containers (Figure 16a), thus 2 pieces have been taken into 421 account per each group location where at least one potentially unstable container can be found. It 422 would mean an estimated investment of 151,788 € (91€/piece). The purpose of these pieces will be to ensure the containers' stability due to floodwaters in flat areas, and due to their own weight 424 in steep streets.

Conclusions 426
According to the collection process for large Spanish cities (e.g. Barcelona city), before 427 the solid waste is dumped in landfills its management starts from a regular collection of household 428 waste municipal service which is carried out through street containers. When an urban flood 429 occurs those containers may lose their stability, thereby allowing debris (i.e. solid waste 430 contained) and leachate to escape from the container and contaminate floodwaters. As the waste 431 containers stability when exposed to flooding is definitely an environmental, safety and health 432 concern, this research has been focused on assessing how vulnerable against common urban flood 433 these containers are in Barcelona. Moreover, some cascading effects may be caused when 434 containers instabilities occur: traffic disruption, waste collection disruption, potential sewer 435 blockages, and increase likelihood of cascading effects due to flooding.

436
The methodology proposed here is the study of the stability of the containers when 437 exposed to urban floods, which the Barcelona City Council has distributed across the city to 438 provide waste collection to citizens. In order to do this, three main stages were carried out: 1)