Conceptual overview

The conceptual steps and considerations required to develop a tephra clean-up model for municipal authorities are outlined in Fig. 3. The three aspects necessary to assess the tephra clean-up operations for response and recovery are: the quantity of material to collect, transport, and dispose; cost of operations; and duration of operations.

Fig. 3 Framework of tephra clean-up model. See text for explanations. Dotted lines indicate suggested options Full size image

Determining quantity of tephra for removal

To determine the quantity (volume) of tephra to be removed from an urban environment following deposition, it is necessary to firstly determine the total quantity of tephra deposited in the urban area, typically using an isopach map. Secondly, the proportion of this tephra to be removed must be determined, as it is unlikely that the total volume of tephra will be completely removed (Hayes et al. 2015). Hayes et al. (2015) compiled a catalogue of tephra clean-up operations in urban environments from around the world, which indicates an increasing proportion of a tephra deposit is removed as deposit thickness increases. Land-use of an urban area exposed to tephra deposition also influences how much tephra is collected (e.g., from a recreational park compared to a high-density commercial area). Accordingly, identifying thickness thresholds as a function of impacted land use is important to include in any tephra clean up model (Table 1). For example, mitigating impacts on transportation networks will be a primary focus when responding to a tephra fall to ensure functioning routes for evacuation and movement of responding agencies. Because road traction reductions occur at thicknesses as low as 1 mm, and road markings are obscured at thicknesses as low as 0.5 mm (Blong 1984; Magill et al. 2013; Blake et al. 2016), clean-up operations on roads are often initiated at thicknesses between 0.5 and 1 mm (Hayes et al. 2015). In comparison, at these small thicknesses, private property owners (homes and businesses) often self-manage clean-up (Hayes et al. 2015).

Table 1 Generic and Auckland specific clean-up response thresholds for tephra clean-up operations (adapted from Hayes et al. 2015). See text for details on Auckland thresholds Full size table

Where tephra deposits are sufficiently thick and widespread, municipal/emergency management, volunteer and sometimes commercial resources are required to aid clean-up of urban areas; such concerted responses have been documented in areas impacted by 20–30 mm of tephra in Guatemala City (Wardman et al. 2012), 150–170 mm in Villa la Angostura, Argentina (Wilson et al. 2013; Craig et al. 2016), and 40 mm in Bariloche, Argentina (Wilson et al. 2013). Typically, a concerted response is initiated at around 10 mm thickness of tephra.

Clean up thresholds for urban green spaces tend to be different from residential and commercial land-uses. Data from Hayes et al. (2015) indicate that deposits >50 mm in thickness need to be removed from vegetated areas, as this thickness is too great for natural incorporation into the soil within reasonable timeframes. If tephra is not removed it can lead to tephra remobilisation, inhibit use of the surface (e.g., recreation activities), and potentially kill the buried vegetation (Craig et al. 2016). Hayes et al. (2015) proposed tephra accumulation thresholds for when different clean-up responses and methods are initiated (Table 1).

Community tolerance to ashy conditions will vary depending on local contextual factors such as the recurrence of tephra fall, environmental conditions (e.g., dry and windy conditions that exacerbate tephra remobilisation; Wilson et al. 2011; Reckziegel et al. 2016), socio-economic factors (e.g., reliance on tourism trade), environmental and public health standards, impacts to critical services, and the ability of property owners to self-manage clean-up (Hayes et al. 2015). Response thresholds are best developed in collaboration with the community, with an understanding of the available balance of official and community resources (Hayes et al. 2015).

Considerations for cost and duration of clean-up operations

Hayes et al. (2015) found that there is considerable variability in the duration and cost of tephra clean-up operations between different communities that have conducted clean-up operations. Thus, it is not possible to use hazard-intensity metrics (e.g., volume or thickness) alone to estimate cost and duration. Therefore, we outline key phases of work that must be conducted as part of best-practice tephra clean-up operations; we do this here to estimate clean-up operation duration and cost (detailed in the following subsections). The following information is required to determine the cost and duration for clean-up operations:

quantity of tephra to be collected and transported to disposal sites;

methods of clean-up (e.g., sweeper truck or dump truck);

the locations of where tephra is loaded onto trucks;

locations of disposal sites;

transport routes from and to disposal site; and

collection (including manual labour), loading and transportation resources (e.g., trucks, street sweepers, paid and volunteer labour).

The methods of clean-up should be considered as part of assessing duration and cost because the most efficient method of clean-up will vary with tephra thickness. For example, global experience suggests that for urban areas with tephra deposition of 1–10 mm the use of street sweeper trucks is most likely to be utilised (Hayes et al. 2015). With greater thicknesses (>10 mm) some combination of manual labour, heavy machinery, and dump trucks is more efficient to remove the bulk of the material, with a potential final street sweeping operation to remove the fine residue, if necessary (Hayes et al. 2015).

For efficient organisation of clean-up operations, urban areas are often partitioned into smaller zones where clean-up activities are conducted simultaneously by crews assigned to that sector (Labelle et al. 2002; Hayes et al. 2015). For example, partitioning of urban areas is commonly used to model snow removal operations where specific disposal sites are assigned to a sector (Cook and Alprin 1976; Campbell and Langevin 1995; Labelle et al. 2002; Perrier et al. 2006a; b). Although tephra differs from snow in that it will not melt away, this approach to clean-up operations suits modelling of tephra clean-up.

Disposal sites are an integral aspect of tephra clean-up operations as they provide a permanent site for containment of tephra deposits (Hayes et al. 2015). Hence, potential tephra disposal sites will also need to be identified. Ideally, these sites will have adequate capacity for the tephra volume requiring disposal, access for large trucks and machinery, and be as close as reasonably possible to clean-up areas. Provisions should also be made to ensure the disposal site has low susceptibility to erosion and leaching into groundwater (Dolan et al. 2003). Typical locations used for tephra disposal include existing waste landfills, old quarries, and empty fields (Hayes et al. 2015). If more than one disposal site is to be utilised it will be necessary to assign optimal disposal sites to sectors (e.g., neighbourhoods) to manage volumes and traffic congestion.

Modelling duration of clean-up using dump trucks

Here we present a series of equations for clean-up duration where dump trucks are used to transport bulk quantities of tephra to disposal sites, adapted from work by Peurifoy and Schexnayder (2002) based on civil works projects. Variables are listed and defined in Table 2.

Table 2 Model parameters and definitions Full size table

Clean-up generally requires the following phases of work to occur (Hayes et al. 2015):

1. Tephra removed from property and placed at roadside 2. Tephra piled at a pickup point by heavy machinery 3. Trucks loaded with tephra at pickup point 4. Truck travels to disposal site and unloads tephra 5. Truck returns to a pickup point to reload.

Practically, phases 1–2 can occur constantly throughout the process. Therefore, with respect to duration, our model only considers phases 3–5 under the assumption that pickup points will be replenished while trucks are travelling to and from disposal sites.

The time it takes to complete clean-up operations depends on the number of trips to move material to disposal sites and how long each trip takes to complete, following an initial delay while material is moved from clean-up site to pick-up sites. The number of truck trips will depend on the volume capacity of the trucks within the fleet. The duration of each truck trip depends on the time to load trucks, haul tephra from pickup points to disposal sites, unload tephra at disposal sites, and then return to a pickup point to be reloaded.

In Eqs. 1 to 3 we conceptually outline the process of how to assess clean-up duration based on a single dump truck. Then in Eqs. 4 and 5 we demonstrate how to apply this conceptual process to a fleet of trucks. Truck loading time depends on the required number of bucket swings (B s ) from a loader to fill a truck (Fig. 4), which depends on the capacity of the bucket on the loader and capacity of the truck being loaded:

Fig. 4 a Start of bucket cycle, b end of bucket cycle (Photo: Josh Hayes) Full size image

$$ {B}_s = {T}_v/{B}_v $$ (1)

where B s = Bucket swings, T v = Truck volume (m3), and B v = Bucket volume (m3).

In practice, it is inefficient to underload a bucket (scoop up less than a full bucket) to match the exact volumetric capacity of a truck (Peurifoy and Schexnayder 2002). This means that B s is an integer, which can either be rounded down (fewer bucket loads and less tephra per truck) or rounded up (excess spills off the truck). Here, B s is rounded up to ensure full trucks are used. Peurifoy and Schexnayder (2002) suggest loading time can then be determined as per Eq. 2:

$$ {L}_t = {B}_sx\ {B}_c $$ (2)

where L t = loading time, B s = Bucket swings, and B c = Bucket cycle time (time to collect a load and dump it in a truck).

Truck cycle time (T c ) is the time it takes for a truck to complete a clean-up cycle: (1) load, (2) travel to disposal, (3) queuing at the disposal site, (4) unload, and (5) return to the pick-up point for the next cycle. Truck cycle time can be estimated based on Eq. 3 (adapted from Peurifoy and Schexnayder 2002). Queuing times are dependent on operational capacity of disposal sites (number of trucks a disposal site can accept per hour or day):

$$ {T}_c = {L}_t + \left({H}_tx2\right) + {Q}_t + {U}_t $$ (3)

where T c = Truck cycle time, L t = Loading time, H = Hauling time, Q t = queuing time, and U t = Unloading time. We apply a doubling factor to H t to consider the return journey.

Equation 3 applies to the duration for a single truck to complete a clean-up cycle. However, in reality, clean-up operations utilise fleets of trucks of varying types and sizes. Thus, we now adapt this conceptual equation of a single truck to consider characteristics of the entire truck fleet. One of these characteristics is the fleet hauling capacity, which is the volume of material the entire fleet could carry in a single clean-up cycle (i.e., summed volumetric capacity of every truck in the fleet). The other important characteristic is the fleet hauling time. This is the hauling time it would take the fleet to travel from every pick-up point to the designated disposal site. In this model, we assume all truck types travel at the same speed (depending on road speed restrictions). Therefore, fleet hauling time is calculated using Eq. 4:

$$ {\mathrm{F}}_{\mathrm{t}} = \left(\sum {\mathrm{P}}_{\mathrm{t}}\right)/{\mathrm{N}}_{\mathrm{t}} $$ (4)

where F t = fleet hauling time, P t = time from a pickup point to a disposal site, and N t = number of trucks within the fleet. Clean-up operation duration can then be estimated by accounting for the hours per day that transportation of material would be done:

$$ \mathrm{T} = \left(\left({\mathrm{F}}_{\mathrm{t}}\mathrm{x}\ 2\right) + {\mathrm{F}}_{\mathrm{c}}\mathrm{x}\ \left({\mathrm{L}}_{\mathrm{t}} + {\mathrm{U}}_{\mathrm{t}}\right)\right)/{\mathrm{H}}_{\mathrm{d}} $$ (5)

where T = Clean-up duration (days), Fc = Fleet cycles (Fleet hauling capacity/volume to transport), and h d = Hours per day transportation works occurs.

Street sweepers

Similar to dump trucks, street sweepers have a maximum volumetric capacity with which they can collect material. However, they collect material by sweeping across a surface and not from specific pick-up points. Therefore, the duration for clean-up using street sweepers requires an adjusted equation to account for this (Eq. 6).

$$ \mathrm{T} = {\mathrm{D}}_{\mathrm{km}}/{\mathrm{D}}_{\mathrm{d}} $$ (6)

where D km = distance of road lanes required to be cleaned, and D d = distance of road lanes a sweeping fleet can clean per day. To solve this equation, the following are required: (1) total length of road requiring cleaning, (2) number of sweeper trucks, (3) speed of sweeping, and (4) efficiency of sweeping.

The total volume of road requiring cleaning is determined by exposure analysis of road length within the <10 mm tephra zone. We assume that a sweeper is able to clean the width of a single lane of road. To determine the cumulative distance of road cleaned per hour, the length of road lanes a single sweeper truck can clean per hour is multiplied by the number of sweeper trucks available for clean-up operations:

$$ {\mathrm{D}}_{\mathrm{d}} = {\mathrm{L}}_{\mathrm{r}}\mathrm{x}\ {\mathrm{n}}_{\mathrm{s}} $$ (7)

where L r = Length of road that one sweeper truck can clean per hour (km/h), and n s = number of sweepers available for clean-up activity.

To determine L r , the truck speed while sweeping is required. It is also important to consider time spent travelling to and from disposal sites as this will influence the total time a sweeper truck spends sweeping per day. Additionally, experiences of street sweeping operations to remove tephra from roads suggest roads will need multiple cleanings due to the inefficiencies of sweeper trucks in removing fine-grained tephra, and potential remobilisation of tephra (Blong 1984; Hayes et al. 2015). This inefficiency will need to be factored into the length of road that is cleaned per day. Therefore:

$$ {\mathrm{L}}_{\mathrm{r}} = {\mathrm{H}}_{\mathrm{d}}\mathrm{x}\ \left(\left({\mathrm{S}}_{\mathrm{V}}\mathrm{x}\ \left({1\ \hbox{--}\ \mathrm{H}}_{\mathrm{f}}\right)\right)/\mathrm{E}\right) $$ (8)

where S v = speed of a sweeper truck (km/h), H f = fraction of each hour spent travelling to and from disposal sites, and E = Efficiency factor (how many times a sweeper would need to pass over a surface to remove all tephra).

Clean-up operation cost

Hayes et al. (2015) found that there is a poor correlation between clean-up operation cost and tephra accumulation, and therefore cost relationships as a function of discrete tephra fall are not appropriate for use in this analysis. To illustrate how to incorporate costs into the model we use tephra clean-up costs specifically estimated for Auckland by Johnston et al. (2001) and adjusted for inflation to 2015 New Zealand dollars (Reserve Bank of New Zealand 2016a). This equates to approximately 45 cents per m3 per km to disposal sites for transportation. The cost of disposal is estimated at $4 per m3. We use these values as a proxy for total clean-up cost to municipal authorities and discuss the uncertainties associated with these values in more detail in the section entitled: “Uncertainties relating to clean-up costs”. We use both of Johnston et al. (2001)’s rates to consider clean-up costs (Eq. 9):

$$ \mathrm{Clean}\hbox{-} \mathrm{up}\ \mathrm{cost} = \left(\$0.45\ \mathrm{x}\ \mathrm{V}\ \mathrm{x}\ \mathrm{D}\right) + \$4\ \mathrm{x}\ \mathrm{V} $$ (9)

where V = Volume of tephra removed in cubic metres, and D = Kilometres to a disposal site.