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Incorporating the effect of weather in construction scheduling and management with sine wave curves: application in the United Kingdom Article
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BallesterosPérez, P., Smith, S. T., LloydPapworth, J. G. and Cooke, P. (2018) Incorporating the effect of weather in construction scheduling and management with sine wave curves: application in the United Kingdom. Construction Management and Economics, 36 (12). pp. 666682. ISSN 01446193 doi: https://doi.org/10.1080/01446193.2018.1478109 Available at http://centaur.reading.ac.uk/74639/
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Incorporating the effect of weather in constructionscheduling and management with sine wavecurves: application in the United Kingdom
Pablo Ballesteros-Pérez, Stefán Thor Smith, Josephine Gwen Lloyd-Papworth& Peter Cooke
To cite this article: Pablo Ballesteros-Pérez, Stefán Thor Smith, Josephine Gwen Lloyd-Papworth & Peter Cooke (2018): Incorporating the effect of weather in construction scheduling andmanagement with sine wave curves: application in the United Kingdom, Construction Managementand Economics
To link to this article: https://doi.org/10.1080/01446193.2018.1478109
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Incorporating the effect of weather in construction scheduling andmanagement with sine wave curves: application in the United Kingdom
Pablo Ballesteros-P�ereza , Stef�an Thor Smithb , Josephine Gwen Lloyd-Papworthb and Peter Cookeb
aSchool of Architecture, Building and Civil Engineering, Loughborough University, Loughborough, UK; bSchool of the BuiltEnvironment, Whiteknights, Reading, UK
ABSTRACTThe impact of (adverse) weather is a common cause of delays, legal claims and economic lossesin construction projects. Research has recently been carried out aimed at incorporating theeffect of weather in project planning; but these studies have focussed on either a narrow set ofweather variables, or a very limited range of construction activities or projects. A method forprocessing a country’s historical weather data into a set of weather delay maps for some repre-sentative standard construction activities is proposed. Namely, sine curves are used to associatedaily combinations of weather variables to delay and provide coefficients for expected productiv-ity losses. A complete case study comprising the construction of these maps and the associatedsine waves for the UK is presented along with an example of their use in building constructionplanning. Findings of this study indicate that UK weather extends project durations by an aver-age of 21%. However, using climatological data derived from weather observations when plan-ning could lead to average reductions in project durations of 16%, with proportional reductionsin indirect and overhead costs.
ARTICLE HISTORYReceived 15 December 2017Accepted 11 May 2018
KEYWORDSWeather; climate;construction; schedule;project delay
Introduction
Many construction projects fail to meet their initiallyplanned completion dates. This is a common phenom-enon in many countries and affects almost all kinds ofconstruction works (Alaghbari et al. 2007, Mahamidet al. 2012, G€und€uz et al. 2013, Ruqaishi andBashir 2015).
Lateness (understanding ‘late’ as missing the origin-ally agreed completion date between the contractorand the project owner) has repercussions for almostall stakeholders (Thorpe and Karan 2008). From thepublic or private project owner’s perspective, latedelivery of a project means delaying the start of anasset’s operation. This in turn might mean missing abusiness opportunity, losing a competitive advantage,delaying a return on investment, and ultimately reduc-ing profits (Trauner et al. 2009, Głuszak and Les€niak2015). From the contractors’ perspective, late comple-tion might involve contractual penalties and alsoblocks reallocation of resources for longer periods, lim-its the resources’ productive capacity, and generallyincreases the contractor’s indirect and overhead costs
(Jang et al. 2008, Hamzah et al. 2011). From the sub-contractors’ perspective, late projects generally makeresource planning suboptimal as projections forresource demand are inaccurate and thus it is morelikely that resource overlaps between multiple projectswill occur (Shahin et al. 2011). From the end users’perspective, late delivery of projects almost alwayscauses some discomfort and disappointment, particu-larly if users live nearby and/or are affected by theconstruction works (Mezher and Tawil 1998).
In some cases, lateness can have certain positiveoutcomes. For example, activity costs can be reducedto some extent when a longer time span allows formore efficient allocation of resources. However, thebenefits of these ‘intentional’ delays are almostentirely realized by the contractors, and other stake-holders merely experience the negative outcomes.
Among common causes of project delays, weather isconsistently rated as one of the most frequent andharmful (Assaf and Al-Hejji 2006, AlSehaimi and Koskela2008, Orangi et al. 2011, Mentis 2015). Weather canimpact construction projects in multiple ways: by
CONTACT Pablo Ballesteros-P�erez [email protected] School of Architecture, Building and Civil Engineering, Loughborough University,LE11 3TU Loughborough, UK
Supplemental data for this article can be accessed here.
� 2018 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed,or built upon in any way.
CONSTRUCTION MANAGEMENT AND ECONOMICShttps://doi.org/10.1080/01446193.2018.1478109
decreasing productivity and sometimes halting con-struction (Rogalska et al. 2006); by ruining unprotectedand exposed constructed elements (El-Rayes andMoselhi 2001), by disrupting communications and/orblocking access to site locations (Alarc�on et al. 2005), tocite but a few. Moreover, weather-related claims are afrequent source of dispute between contractors andproject owners (Moselhi and El-Rayes 2002, Nguyenet al. 2010). It is not unusual that in the absence ofagreement, unsettled claims can escalate into legal dis-putes and protracted litigation causing suspension ofwork for a longer period than the original abnormalweather episode itself (e.g. Finke 1990, Kumaraswamy1997, Yogeswaran et al. 1998).
When categorizing the impact of weather, it is com-mon to differentiate between foreseeable and unfore-seeable weather (Tian and De Wilde 2011), as well asextreme and non-extreme (but generally combined)weather events (Jung et al. 2016).
Foreseeable weather is generally considered toencompass extreme adverse weather events that canimpact the execution or exploitation of infrastructureunless precautionary measures are taken. Takingaccount of foreseeable weather is more frequently prac-tised during the construction phase of special projectssuch as long, exposed bridges or high-rise buildings(Tanijiri et al. 1997, Jung et al. 2016). These types ofprojects normally have large budgets, and thus theyare more likely to have resources for monitoring howand when on-site weather will cause changes to sched-uled activities. Developments in sub-seasonal and sea-sonal weather forecasting have shown early promisetoo, but forecasts of acceptable quality still just span amaximum 10-d window (White et al. 2017).
However, despite advances in forecasting, there willalways be an inherent uncertainty in a chaotic systemsuch as the weather, which makes it difficult to alwaysprovide accurate forecasts. This is particularly truewhen considering extremes related to climate change(Sato et al. 2017).
Furthermore, whilst there are some constructionactivities that require forecast information for makinggood short-term decisions (e.g. whether to pour con-crete today or tomorrow, or whether high winds willprevent work in exposed environments or at height),most resource-related operational decisions, and cer-tainly all project planning, have to be undertakenanticipating weather beyond what current forecastingmethods can predict. People (workers) have high man-oeuvrability, but generally not the equipment, machin-ery, vehicles and special supplies that they employ.This is why this piece of research considers the applic-ability of climatology data drawn from historical
weather information as opposed to simple weatherforecasts. This does not mean, however, that theimportance of relevant and sometimes crucial short-term weather forecasting is not acknowledged.
The main aim of this paper is to propose anew approach for processing historical weather infor-mation from a construction-relevant perspective.Combinations of weather variables and intensities thataffect the execution of construction activities havebeen analyzed and processed into a series of maps forconstruction managers.
From now on, this paper is structured as follows: theLiterature review section includes an overview of themost relevant pieces of research proposing models ofthe interaction between weather and constructionproductivity. The Materials and methods section pro-vides a comprehensive step-by-step description of themethod proposed. Namely, in this section, the proposedmodel is first outlined; then how all the necessary wea-ther data were extracted and processed; and, finally,how most weather variability can be captured by andreduced to sine wave curves. Next, the Case study sec-tion describes the application of the proposed methodto the construction of a reinforced concrete building inthe UK. The Discussion section provides further analysesand insights for both the case study considered andalternative potential applications. The Conclusions sec-tion summarises and highlights the contributions of thispaper to both the scientific community and the con-struction practitioners. Finally, the Supplemental onlinematerial contains all the calculations, weather maps (themain research outputs generated in this study), as wellas some programmable spreadsheets that allow perfor-ming weather-aware project scheduling calculations.
Literature review
General meteorological and climate research coveringforecasting or retrospective analysis is significant andwill not be reviewed here. Instead, the focus will beon two main areas. The first comprises the most recentmodels that have integrated the effect of weather inthe planning and/or execution of construction works.The second is the particular combinations of weathervariables and intensities that can produce significantimpacts with regard to the execution of representativeand frequent construction activities.
Overview of weather models forconstruction projects
Research on how weather impacts the execution ofconstruction projects is plentiful. However, only
2 P. BALLESTEROS-P�EREZ ET AL.
recently have quantitative models been developed formeasuring the degree to which weather phenomenacan cause a productivity decrease. A comprehensivesample of these quantitative models is summarizedin Table 1.
Table 1 is first organized by type of construction pro-ject (first column) and second by chronological order ofpublication (second column). It can clearly be seen thatalmost all works have been published in the last 10years, and that building projects in particular have
attracted the most attention. Furthermore, only onework proposes a forecasting model that uses live wea-ther data retrieved from nearby stations to inform deci-sions regarding which construction activities toundertake in the short term. The remainder of the workscontaining forecasting models simply employs historicalweather data. This suggests that there is a belief amongconstruction researchers (or perhaps a lack of multidis-ciplinary input) that historical weather at nearbylocations will be probabilistically or deterministically
Table 1. Sample of relevant research papers on the effect of weather on construction projects.
Project type Publication year Reference Weather data sourceForecasting
model Activities analyzed Weather agents
Buildings 1999 Thomas et al. (1999) Historical (past) data No Steel structure deliveryand erection activities
Temperatureand snow
2008 Jang et al. (2008) Short-term(live) forecasts
Yes Generic Temperature andprecipitation
2008 Thorpe andKaran (2008)
Historical (past) data No Clearing and grubbing,excavation, founda-tions, structural erec-tion, floors, interiors,roofs and HVAC
Temperature, snow,humidity andprecipitation
2010 David et al. (2010) Historical (past) data Yes Generic Solar radiation, tem-perature, humid-ity, wind
2013 Dytczak et al. (2013) Historical (past) data No Generic Temperatureand wind
2013 Marzouk andHamdy (2013)
Historical (past) data Yes Formwork Precipitation andtemperature
2014 Shan andGoodrum (2014)
Historical (past) data Yes Steel structure Temperatureand humidity
2014 Gonz�alez et al. (2014) Historical (past) data No RC structures and fin-ishing’s (e.g. partitionwalls, windows,and doors)
Not specified
2016 Jung et al. (2016) Historical (past) data Yes Genericþ core wall, steelframe, deck plate, RC,curtain wall
Solar radiation, tem-perature, wind andprecipitation
2016 Li et al. (2016) Historical (past) data No Steel reinforced bars (Hot) temperature2017 Ballesteros-P�erez et al.
(2017a, 2017b)Historical (past) data Yes Earthworks, formworks,
concrete, steelworks,scaffolding, outdoorpaintings andasphalt pavements
Temperature, precipi-tation, wind andelectrical storms
Highways 2001 El-Rayes andMoselhi (2001)
Historical (past) data Yes Earthworks, basecourses, drainagelayers and paving
Precipitation
2010 Apipattanaviset al. (2010)
Historical (past) data Yes Concrete and asphaltpaving, structures,excavationsand grading
Precipitation, air andsoil temperatureand wind
2013 Chinowskyet al. (2013)
Historical (past) data Yes Generic Temperature andprecipitation
Pipelines 2011 Shahin et al. (2011) Historical (past) data Yes Clearing and grading,trenching, bedding,pipe-fusing, laying-in,hydro testing, com-paction andbackfilling
Air and soil tempera-ture, wind, humid-ity andprecipitation
2012 Duffy et al. (2012) Historical (past) data Yes Grading, stringing, bend-ing, welding, trench-ing, coating, backfill,clean-up
Temperature, wind,and precipitation
Tunnelling 2014 Shahin et al. (2014) Historical (past) data Yes All tunnelling process,hoisting and muckcar cleaning
Air and soil tempera-ture and wind
Bridges 2015 Ballesteros-P�erezet al. (2015)
Historical (past) data Yes Earthworks, formworks,concrete andasphalt pavements
Temperature, precipi-tation, wind andelectrical storms
CONSTRUCTION MANAGEMENT AND ECONOMICS 3
repeated to some extent in subsequent years. It is alsoa common practice to use synthetically generated wea-ther series for informing management decisions.
However, it is necessary to point out that Table 1only includes studies with construction-oriented fore-casting models. As mentioned previously, forecastingmodels in pure meteorology and other applied fieldshave not been considered here. The impact of weatheron each field of application can help to identify therelevant weather variables, and ultimately demonstratesthe value of better forecasting. Most construction proj-ects, however, generally involve many disparate activ-ities each of which is susceptible to differentcombinations of weather variables and intensities.
To date, most studies have focussed on very narrowsets of activities (last but one column in Table 1) and/or have considered a limited number of weather varia-bles (last column). This generally constitutes a neces-sary simplification due to the difficulty of obtaininglocal (representative) data for a sufficient number ofweather variables and from a sufficient number oflocations. Moreover, the data available must also besufficiently consistent (not much data missing), fine-grained (daily, hourly) and from a sufficient number ofprevious years to be useful.
The method proposed later can be considered acontinuation of Ballesteros-P�erez et al.’s (2015, 2017b)research. As can be seen in Table 1, their models havealready been adapted to two different types of proj-ects (buildings and bridges), and have considered avaried and representative set of activities common tomany construction projects (earthworks, formworks,concrete, steelworks, scaffolding, outdoor paintingsand asphalt pavements). These models are of particu-lar interest because they are two of the few coveringextensive geographical areas (almost the whole ofChile and Spain, respectively), which means they canbe used as general country-wide planning tools bygovernments and contractors alike.
However, the proposed method extends the scopeof previous research in this area. Most previous studies(including those of Ballesteros-P�erez et al.) haverequired the use of either probabilistic or time seriescurves with many parameters or points. Some havealso been developed to work with long series of dis-crete registers for modelling local weather. In contrast,the method proposed here only requires simple sinewave curves with only one, two or three parametersdepending on the level of accuracy required. This is asignificant advantage as the simplicity of the devel-oped expressions means most construction managerswill easily be able to use them in practice, with hardlyany mathematical expertise.
In the next section, the selection of weather varia-bles considered in this study will be justified as well astheir relationship with a representative set of cross-project construction activities.
Combinations of weather variables affectingconstruction activities
The weather involves the confluence of multiple phe-nomena (wind, rain, heat, etc.) that quite often do notinvolve a clear correlation of occurrence with eachother (Ballesteros-P�erez et al. 2017b). Studies analysingthe seasonal variability of combinations of weatheragents are quite scarce (Kim and Augenbroe 2012).However, it is precisely this weather variability (sea-sonal or not) that makes anticipating how weather willaffect construction work difficult.
In this study, it is assumed that the impact of wea-ther can be represented in a project schedule viaactivity duration extensions and, in some cases costincreases, and that weather-aware construction sched-ules can be useful tools for helping construction man-agers make better decisions.
The first stage is thus deciding which combinationsof weather variables and intensities determine whethercertain construction activities can be performed. Theimpact of a particular set of weather variables andintensities on an activity can be very different depend-ing on the: construction technologies employed,equipment used, materials involved and/or proceduresadopted; how exposed the construction site is; howpersistently (consistently and/or repetitively) the wea-ther is classed as unusual; what is considered the aver-age (or normal) weather in the particular region (orcountry). However, it is still possible to choose a com-bination of weather variables that, under some com-mon conditions (e.g. same country, similarconstruction technologies, materials and constructionpractices), can be considered as ‘relatively repre-sentative’ of the regional/industry standard. This studywill consider the thresholds for the weather variablesdescribed in Table 2 as precluding the stated construc-tion activities.
As noted, the combination of weather variables inTable 2 might not be appropriate for many countriesor contexts. However, it is considered sufficiently rep-resentative for the UK which is where the proposedmethod will be applied later. Similar combinations ofweather variables have also been considered recentlyby other authors (Ballesteros-P�erez et al. 2017a, 2017b)for both Spain and the UK.
By way of explanation for the values chosen, earth-work activities are more difficult to execute when the
4 P. BALLESTEROS-P�EREZ ET AL.
ground is partially or totally frozen (Shahin et al. 2011,2014) or when too much water causes a slope tobecome partially unstable (NCHRP 1978, El-Rayes andMoselhi 2001).
Concerning activities involving concrete, the min-imum temperature must not drop below 0 �C before ithas hardened, otherwise it will microfracture(American Concrete Institute 1985). The temperaturemust also not rise above 40 �C and/or the wind speedexceed 30 knots, or the concrete will dry out too fastwhen curing (American Concrete Institute 1985). Inaddition, the amount of extra water coming from rain,snow or hail must be small (e.g. 10mm), otherwise thewater/cement ratio will vary affecting the concrete’sfinal strength and durability (NCHRP 1978, AmericanConcrete Institute 1985).
Formwork and Scaffolding activities are affected in asimilar manner by the weather. In particular, their exe-cution is unsafe during electrical storms (due to therisk of electrocution) (Rogalska et al. 2006) and highwinds (Nguyen et al. 2010, Marzouk and Hamdy 2013).
Steelwork activities are also sensitive to electricalstorms and high winds (Irizarry et al. 2005), but inaddition are affected by extremely high and lowtemperatures (Thomas et al. 1999) and excessiveamounts of rain (particularly welding) (Thorpe andKaran 2008).
Outdoor painting activities can be difficult to exe-cute when it is raining, snowing or hailing as when thepaint is still fresh, extra water can decrease the effect-iveness of the primer and/or lead to colour changes(Ballesteros-P�erez et al. 2015). Water-based paints canalso lose their adherence if they freeze when drying. Inaddition, painting in windy areas is risky as paintingequipment, like buckets, can be blown over or fallonto lower levels (Nguyen et al. 2010).
Finally, asphalt pavements are very susceptible tothe addition of small quantities of water (in the formof rain, snow or hail) (El-Rayes and Moselhi 2001,Apipattanavis et al. 2010), and to extremely high andlow temperatures (NCHRP 1978).
Materials and methods
Method outline
This section will describe a method for processing his-torical weather information from a construction-relevant perspective. The weather data employed islimited to inland stations, because the latter normallyregister more weather variables than at sea. Themethod involves three main stages.
The first stage involves gathering and analysing his-torical daily weather data from as many weather sta-tions as possible. By ‘analysing’, we mean calculatingthe percentage of each day considered ‘workable’ inprevious years, where workable implies that none ofthe weather variables exceeded the threshold valuesin Table 2 such that the completion of an activitywould be prevented. More specifically, the analysisinvolves calculating percentages of workable days forevery single day of the year (1–365), for each of thesix construction activities [e.g. earthworks (E), concrete(C), formworks/scaffolding (F), steelworks (S), outdoorpaintings (O) and asphalt pavements (P)].
The second stage involves fitting sine wave curvesto the data for the percentage of workable days for alldays of the year. Each type of activity and weather sta-tion require one sine wave curve, and then all of theparameters from the various sine wave curves for aparticular activity can be represented on contourmaps. These maps allow easy interpolation of thevalues of the sine wave parameters for a particular sitewhen no weather stations are located nearby.
Finally, the third stage involves applying the neces-sary location-specific sine wave data to a constructionschedule so that time (and cost) extensions can beanticipated. In this latter stage, it will be assumed, asin almost all previous models, that past weather andclimate patterns will be repeated to some extent inthe upcoming years for a given location.
The next two subsections include detailed descriptionsof the first and second stages, respectively. The followingsection (Case study) will describe stage three, i.e. theapplication of the weather model to a project schedule.
Table 2. Weather variables and thresholds assumed to cause non-working days.Weather variable (daily value) Earthworks (E) Concrete (C) Formworks/scaffolding (F) Steelworks (S) Outdoor paintings (O) Asphalt pavements (P)
Minimum temperature �0 �C 3 3Mean temperature �0 �C 3 3 3Maximum temperature �40 �C 3 3 3
Precipitation �1mm 3 3Precipitation �10mm 3 3Precipitation �30mm 3
Hail precipitation 3 3Snow precipitation 3 3Electrical storm 3 3
Wind gusts �30 knots 3 3 3 3
CONSTRUCTION MANAGEMENT AND ECONOMICS 5
Analysis of UK weather data
This subsection will detail and exemplify how calcula-tion of the number of workable days was performedfor the UK (England, Wales, Scotland and NorthernIreland) for the six generic types of construction activ-ities described in Table 2.
First, daily weather data were retrieved from the UKMet Office (2018) databases, particularly from theMIDAS dataset. Data were extracted from only thoseweather stations with daily registers of maximum, min-imum and mean temperature, rainfall and maximumwind gust, as well as snow, hail and thunder flags.Additionally, only weather stations that started register-ing these variables between 1986 and 1996 wereselected for the sake of representativeness. Thirty yearsare the standard adopted by the World MeteorologicalOrganization for analysing climatic patterns. However,we resorted to a minimum of 20 years coverage toincrease the number of stations from 40 to 102, andbecause Vose and Menne (2004) proved that 20 yearswere quite likely to be beyond what is necessary forcapturing interannual variability for construction works.In any case, even departing with 20–30 years nominally,in most cases, the meteorological equipment at eachstation had either malfunctioned and/or required peri-odic maintenance resulting in blank periods in the data.
Therefore, 102 stations were eventually consideredfrom across the UK spanning 20–30 years, but withoccasional (normally minor) data blank periods. Thelocations of these stations are shown in Figure 1where they are marked using the UK Met Office (2018)codes from the MIDAS dataset.
It is worth highlighting that whenever at least oneweather variable was not registered for a given day,that day was completely ruled out for that weather sta-tion. The reason for this was to avoid optimistic biaswhen assessing whether the day was workable (a day ismore likely to be workable when fewer variables thatmight cause a day to be non-workable are considered).
The final cutoff criterion was whether the data froma given weather station for a particular type of con-struction activity had at least three complete registersfor a given day (all weather variables registered) for atleast half of the days (not necessarily consecutive) ofthe year. This filter ruled out two complete weatherstation registers from the initial 102, but also up to48% of the weather stations for outdoor painting andasphalt pavement activities.
Nevertheless, with a minimum of 52 stations’ histor-ical registers per activity, there was a considerableamount of data to be processed. The number of wea-ther stations included was much larger than in most of
the studies listed in Table 1, and generally many morecomplete years of data (around 23 on average per wea-ther station) were analyzed. Complete calculations areavailable on the first Supplemental Online Materialspreadsheet file for all stations and activity types.
The next step involved calculating the climaticreduction coefficients (CRC). A CRC, as defined byBallesteros-P�erez et al. (2015), represents the percent-age of each day in past years that was considered work-able. This means that none of the relevant weathervariables exceeded their threshold values from Table 2for a given activity and weather station. Hence, thevalue of the CRC corresponds to the percentage, orper-unit value, representing the probability of a daybeing workable for a particular type of activity. A repre-sentative sample of CRC calculations for different wea-ther stations and activity types (E, C, F, S, O and P) isshown in Figure 2. All CRC values can be found byactivity type for all weather stations in the last six tabsof the same Supplemental Online Material spreadsheet.
Along with the CRC data (black lines) in Figure 2,two smooth curve fits are shown: a sixth-degree poly-nomial (seven parameters) in blue, and a sine wavecurve (up to three parameters) in red. As can be seen,both curves fit the data similarly, meaning the sinewave curve represents a good fit with the CRC dataeven with substantially fewer parameters. Later, theloss of precision after having resorted to sine waveexpressions will also be examined.
Reduction of weather variability to sine waves
As exemplified in Figure 2, sine wave expressions werefitted to all weather stations’ CRC data for all types ofconstruction activities. Sine waves, in this case, aremathematical expressions whose equations andparameters are of the form:
y ¼ CRC ¼ K þ A � cos�2pfðx=365� uÞ� (1)
where:CRC: climatic reduction coefficients: (E, C, F, S, O and
P). Percentage of workable days for each day ofthe year (x).
x: day of the year (days 1–365). In leap years, the29th February is considered as x¼ 59.5.
K: vertical shift (in per unit). Approximately corre-sponds to the geometric mean of the annualCRC values.
A: amplitude (in per unit). Approximately correspondsto the maximum positive and negative averageoscillation of the CRC values with respect to K.
f: frequency. This was set at 1 so that 365 d corre-sponded to one complete oscillation.
6 P. BALLESTEROS-P�EREZ ET AL.
u: phase shift (in per unit). Corresponds to the dayof the year (but expressed in per unit) whenthe sine wave reaches its maximum value(optimum weather conditions). This is truebecause expression (1) has been built using a
cosine, instead of a sine. However, unlessmultiple waves are compared, cosine waves arealso named sine waves. We will follow the sameterminology here and refer to expression (1) as asine wave then.
Figure 1. Locations of weather stations used for the analysis.
CONSTRUCTION MANAGEMENT AND ECONOMICS 7
R² = 0.53
R² = 0.52
0.00.10.20.30.40.50.60.70.80.91.0
0 30 60 90 120 150 180 210 240 270 300 330 360
Earthworks (830 Reading University)
R² = 0.70
R² = 0.70
0.00.10.20.30.40.50.60.70.80.91.0
0 30 60 90 120 150 180 210 240 270 300 330 360
Concrete (1572 Guernsey: Airport)
R² = 0.73
R² = 0.74
0.00.10.20.30.40.50.60.70.80.91.0
0 30 60 90 120 150 180 210 240 270 300 330 360
Formworks/Scaffolding (1180 Bala)
R² = 0.79
R² = 0.81
0.00.10.20.30.40.50.60.70.80.91.0
0 30 60 90 120 150 180 210 240 270 300 330 360
Steelworks (18974 Tiree)
R² = 0.58
R² = 0.63
0.00.10.20.30.40.50.60.70.80.91.0
0 30 60 90 120 150 180 210 240 270 300 330 360
Outdoor pain�ngs (605 Brize Norton)
R² = 0.67
R² = 0.71
0.00.10.20.30.40.50.60.70.80.91.0
0 30 60 90 120 150 180 210 240 270 300 330 360
Asphalt Pavements (886 Lyneham)
Figure 2. Examples of average daily CRC calculations for all construction activities.
8 P. BALLESTEROS-P�EREZ ET AL.
Hence, each sine wave curve has three free parame-ters (K, A and u). The values of these parameters wereobtained by minimizing the least squares betweeneach sine wave curve and its respective CRC data foreach CRC data series (i.e. for each weather station andconstruction activity type).
A summary of the final (K, A and u) parameter val-ues can be found on the second tab of theSupplemental Online Material spreadsheet mentionedabove. Details of the errors associated with the sinewave expressions can be found in the first tab of thesame file. Errors between the CRC and the sixth-degree polynomial fits are also available for the caseswhere there were enough data.
However, a series of K, A and u values are notnecessarily immediately useful unless the constructionsite is geographically close to one of the weather sta-tions. Therefore, a series of maps for each sine waveparameter and type of activity was developed. Anexample set of maps for the three parameters (K, A,and u) corresponding to formworks/scaffolding activ-ities is shown in Figure 3.
These contour maps were created with Surfer v.14VR
(Golden software, CO, USA) from gridded data byimplementing a Kriging interpolation method. Thisinterpolation method was invented in the 1950s by theSouth African geologist Danie G. Krige for predictingdistribution of minerals. However, it was mathematic-ally formalized by the French engineer GeorgesMatheron in the 1960s (Matheron 1969). For statisti-cians, the Kriging interpolation method is also knownas Gaussian process regression. This as it is a method ofinterpolation for which the interpolated values aremodelled by a Gaussian process governed by prior co-variances. With only mild conditions on the priors,Kriging interpolation gives the best linear unbiased pre-diction of intermediate values, which is why thismethod was used here. Maps for the other five activ-ities are included in the PDF file in the SupplementalOnline Material.
Furthermore, one of the main aims of this studywas to develop a series of expressions that were notjust as representative as possible, but also as simple aspossible. Therefore, after obtaining the original K, Aand u values for all weather stations and type of activ-ity, the values were represented by type of construc-tion activity graphically as shown in Figure 4. Theintention was to determine whether the amplitude Aand/or the phase shift u could be expressed as a func-tion of the vertical shift K in order to reduce the num-ber of parameters in Equation (1) and obtain thesimplest expressions possible.
Quite surprisingly, the amplitude A exhibited adegree of correlation with K. This is probably due tosome common boundary conditions for the twoparameters. For example, when K has its lowest (K¼ 0)or highest (K¼ 1) value, A must equal zero (A¼ 0) asthere is no oscillation possible. Similarly, A is expectedto approach its maximum value when K is approxi-mately equal to 0.5. Overall, this means that a single-parameter quadratic expression crossing the points(K¼ 0, A¼ 0) and (K¼ 1, A¼ 0) should model the cor-relation between the two variables. That quadraticexpression corresponds to A¼ ai(K – K
2), and the best-fit values for ai for the six types of activities are repre-sented on the left hand of Figure 4.
In contrast, there was little correlation between Kand u; this was because u does not vary significantlywith K or the station location. This can be checkedeasily as the value of u lies within a relatively narrowvertical band. Hence, it is possible to assume with littleerror, that u is a constant for each type of activity. Thetwo values of this constant (for earthworks and for allother activities) are given on the right side of Figure 4.
To summarise, the original three-parameter (3-p)sine wave expression can be reduced most of the timeto a 2-p, or even a 1-p expression, by assuming that Kis the only free parameter. In other words, A can bereplaced by a quadratic expression which is a functionof K (A¼ ai(K – K
2)) and u can be assumed tobe constant.
The remaining step involves checking whether the3-p, 2-p and 1-p sine wave approximations generatesufficiently small errors in comparison to the originalCRC data series. Details of the calculations can befound at the bottom of the second tab in theSupplemental Online Material spreadsheet and aresummarized in Table 3.
Table 3 contains the mean squared errors (MSE),mean absolute errors (MAE) and mean absolute per-centage errors (MAPE) for the three sine wave approxi-mations for each type of construction activity. It alsoincludes the average squared, absolute and percent-age deviations between neighbour CRC points fromconsecutive days which reflects the small scale vari-ability or jaggedness of the CRC curves. It can not onlybe seen from the data in Table 3 that the errors forthe 2-p and 1-p sine waves are not significantly largerthan the errors for the 3-p versions, but also that theerrors remain below the deviations between neigh-bour points. This means that the simplified 2-p and1-p sine waves closely reflect the CRC curves almostall of the time, and are not too dissimilar to the 3-psine waves.
CONSTRUCTION MANAGEMENT AND ECONOMICS 9
Figure 3. Example maps for vertical shift K (bottom), amplitude A (middle) and phase shift u (top) for formworks/scaffoldingactivities in the UK.
10 P. BALLESTEROS-P�EREZ ET AL.
Finally, from the average R2 values from all weatherstations by type of construction activity (see the Excelspreadsheet with summary of all regression calculationsin the Supplemental Online material), it can be claimedthat overall, the proposed sine waves capture between28% (at worst, for earthworks) and 79% (at best, forconcrete) of the average weather variability, and this isaccomplished with reasonably simple mathematicalexpressions suitable for use by construction managersduring project planning. The final stage is to imple-ment the developed expressions in a real project,which is the purpose of the next section.
Case study
An example of how the sine waves can be used duringconstruction scheduling is contained in this section. Theschedule proposed here represents the construction of
a fictitious simplified three-storey reinforced concretebuilding. It consists of 24 activities arranged underthree work packages, as shown in Figure 5.
Figure 5 represents a weather-unaware schedule, ora schedule in which the activity durations have beencalculated without considering the potential impact ofthe weather. The schedule represented in Figure 5, likethe following schedules calculated later, has all beengenerated assuming unlimited resources. The way thisweather-unaware schedule can be transformed into aweather-aware schedule is relatively simple.
The first step consists of identifying which type ofactivity (E, C, F, S, O or P) each schedule activity resem-bles the most. These allocations are represented by thedifferent coloured bars in Figure 5. Activities with greybars are not weather-sensitive (because they are exe-cuted indoors, for instance) and for which the durationwill not change when the weather is considered.
Table 3. Errors in CRC estimates.Data Error E C F S O P Average
3-p sine waves (K, A and u are free) MSE 0.004 0.017 0.012 0.016 0.017 0.017 0.01MAE 0.050 0.076 0.083 0.095 0.096 0.097 0.08MAPE 0.058 0.140 0.124 0.148 0.276 0.261 0.17
2-p sine waves (K and A are free, u¼ constant) MSE 0.005 0.010 0.013 0.017 0.017 0.017 0.01MAE 0.051 0.077 0.084 0.096 0.097 0.098 0.08MAPE 0.058 0.143 0.126 0.150 0.278 0.263 0.17
1-p sine waves (K free, A¼ f(K) and u¼ constant) MSE 0.005 0.010 0.013 0.017 0.018 0.018 0.01MAE 0.052 0.080 0.086 0.098 0.100 0.100 0.09MAPE 0.059 0.146 0.128 0.151 0.285 0.268 0.17
Deviations between neighbour data points (consecutive CRC values) MSE 0.006 0.012 0.018 0.023 0.023 0.024 0.02MAE 0.057 0.084 0.098 0.108 0.112 0.114 0.10MAPE 0.067 0.168 0.157 0.184 0.337 0.322 0.21
A=ai(K-K2)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ampl
itude
(A)
Ver�cal Shi� (K)
(K, A)
φE = 0.465
φC,F,S,O, P= 0.537
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Phas
e sh
i� (φ
)
Ver�cal Shi� (K)
(K, φ)
Earthworks (E) Concrete (C) Formworks/Scaffolding (F) Steelworks (S) Outdoor pain�ngs (O) Asphalt Pavements (P)
ai values:aC = 1.157aS = 0.886aF = 0.787aE = 0.719aP = 0.640aO = 0.574
Figure 4. Plots of K, A and u values with regression expressions assumed.
CONSTRUCTION MANAGEMENT AND ECONOMICS 11
The second step involves calculating how muchlonger each weather-sensitive activity will take to com-plete once the effect of the weather is included. Forthis, the corresponding sine wave expression for eachactivity is required. The choice of sine wave expressiondepends on the type of activity (E, C, F, S, O or P) andthe location. The appropriate values of K, A and u foreach sine wave can be obtained from maps like theones described in Figure 3, or via an automated (andfar quicker) process from a grid data file using theactivity (or project location) coordinates. Grid valuesfor all three parameters for the six types of construc-tion activities can also be found in the third tab of theSupplemental Online Material spreadsheet.
The third and final step comprises taking both the(one, two or three) parameters for each sine wavecurve and the start date of each activity and addingup the CRC values from the sine wave expression as x(the day of the year) increases. Variable x thus takes itsfirst value from the activity start date and continues toincrease until the sum of the generated CRC values isequal to the original activity duration. This is equiva-lent to considering that the sum of the fractions ofproductivity on consecutive days will equal the origin-ally defined duration of the activity (the one calculatedassuming that all days would be 100% workable). Thelast day for which variable x is added to the sum willcorrespond to the finish date of the new (weather-aware) activity duration. This process can be repeatedfor all project activities in chronological order of theirstart dates until all the activity durations havebeen revised.
Having defined the calculation process, the totalduration of the building project can be found taking
into consideration the weather. This has been done forall major cities in the UK in order to find out how sig-nificant, but also how different, the impact of the wea-ther can be in different locations.
It is initially worth noting that the original (weather-unaware) project duration was 186 d, which is a littlemore than 6 months. In the analysis, working days areconsidered to be Monday to Friday only, but the totalduration calculated includes Saturdays and Sundays.No extra holidays have been considered.
The reason why this specific project configurationhas been adopted is because it represents the mostchallenging situation for the 3-p, 2-p and 1-p sinewave approximations. Half-year projects are generallythe ones that experience the (proportionally) greatestweather-related variability; longer projects can offsetthis variability through summer and winter. Moreover,including non-working days (in this case Saturdaysand Sundays) means there are bigger deviations pos-sible in project duration estimates with the 1-p, 2-pand 3-p sine waves as every 5 d, two more are added.The predicted project durations are shown in Figure 6.
Interpretations of Figure 6 are manifold so only themost important will be highlighted here. First, it isnecessary to state using the 3-p sine waves and theactual series of CRC values produced exactly the sameestimated project durations for all cities and for allproject start dates. This is not necessarily a surpriseand the differences between these approaches mayonly be noticeable if the initial project duration is ofthe order of a few days, instead of a few months.
The duration estimates calculated using the 3-p sinewaves indicate that the weather is likely to cause anextension to the original (weather-unaware) 186-d
Group WBS Ac�vi�es Dura�on Predecessor
1.1 Site marking 1 - Earthworks (E)1.2 Excava�ons 6 1.1FS Earthworks (E)1.3 Lean concrete 1 1.2FS Concrete (C)1.4 Reinforcing steel (founda�ons) 10 1.3FS Steelworks (S)1.5 Formworks (founda�ons) 8 1.4SS+50% Formworks/Scaffolding (F)1.6 Concrete (founda�ons) 2 1.5FS Concrete (C)1.7 Reinforcing steel (structure) 40 1.6FS Steelworks (T)1.8 Formworks (structure) 30 1.7SS+25% Formworks/Scaffolding (F)1.9 Concrete (structure) 22 1.8SS+33.3% Concrete (C)
SF9.102fooR01.1 Formworks/Scaffolding (F)SF9.101gnidloffacS11.1 Formworks/Scaffolding (F)
2.1 Outdoor paint coa�ng 20 1.11SS+50% Outdoor pain�ngs (O)SF9.103gniretsalP2.2
2.3 Par��ons and cladding 30 1.9FS2.4 Doors and windows install. 20 2.3FS2.5 Indoor paint coa�ng 30 2.3SS+33.3%2.6 Suspended ceilings 30 2.5SS+33.3%
%3.33+SS6.203sroolF7.2%05+SS7.202sgnidloM8.2
2.9 Other minor finishings 20 2.8SS+20%
3.1 Electrical works 20 2.7SS+33.3%3.2 Furnishing and fixture install. 20 2.7SS+33.3%3.3 Plumbing domiciliary works 50 1.3FS3.4 Street pavements reconstruc�o 5 3.3FS Asphalt Pavements (P)
Jul-18
Stru
ctur
al w
orks
Fini
shin
gsIn
stal
lat.
Jan-18 Feb-18 Mar-18 Apr-18 May-18 Jun-18
Figure 5. Construction schedule for a simplified three-storey reinforced concrete building.
12 P. BALLESTEROS-P�EREZ ET AL.
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CONSTRUCTION MANAGEMENT AND ECONOMICS 13
project duration by an average of 21.6%. However, thisduration increase may be as large as 38.3%, or as smallas 5.7%, depending on the start date. Therefore, if a pro-ject schedule was managed weather-wise (e.g. by care-fully choosing the best project start date), averageproject durations could be reduced by21.6–5.7%¼ 15.9%. Analogously, time proportional costs,like indirect and overhead costs, could also be reduced.
With the 2-p sine wave approximations, it can beseen that deviations in predicted project durations arealmost always below 1 d (see the first three columnsof the 2-p Sine Waves Absolute Errors). Identifying theoptimum and worst project start days with regard tominimizing and maximizing project duration also onaverage remain below 1 week (see last two columnsof the 2-p Sine Waves Absolute Errors). This is a verygood approximation considering the simplicity of the2-p expression being used to model an entire yearday-by-day. Moreover, these predicted errors are thegreatest over the year, and for the remainder of theyear, deviations are much smaller.
In contrast, the 1-p sine wave curves produce signifi-cantly poorer approximations. This being said, averageproject duration errors remain below 3 d on average(see first columns of the 1-p Sine Waves Absolute Errors)which is in reality small and an upper bound. Projectslonger than 6 months and/or those without non-workingdays will generally have less error. The shortest and lon-gest project duration estimates, as well as their associ-ated start dates err on average by less than 2 and 3weeks, respectively (see the second and third columnsof the 1-p Sine Waves Absolute Errors). In practice, thesewould not be considered bad estimates, especially asthey come from such simple expressions with just oneparameter. Moreover, similarly to the 2-p sine wave esti-mates, the errors quoted represent the largest possibleerrors and with longer projects or different project startdates, they are significantly reduced.
Discussion
The case study above shows how the sine waves pro-posed can be used with a straightforward approach tocalculate individual activity and total project durations.Clearly, the possibility of calculating how long eachactivity will last depending on the start date and thelocation opens the door for further operationalresearch applications. For example, it would be pos-sible to analyse (a) how best to reduce project dura-tions and costs when multiple projects have to beexecuted and their order can be modified; (b) howbest to arrange non-critical activities to minimise
durations and/or costs; and (c) how to select the bestproject location if that was a feasible option.
The proposed sine waves can also be applied witha stochastic approach instead of the discrete approachused in the case study here. In this case, each CRCdaily value would be either 0 (workable day) or 1(non-workable day), where the probability of the valuebeing 0 or 1 would depend on the CRC calculated bythe sine wave expression for each day. The CRC dataseries represent proportions of workable days from thepast, but they can also be understood as ‘probabilities’of a day being workable. This means that Monte Carlosimulations can be very easily implemented and usedto calculate, through multiple iterations, a wide rangeof (probabilistic) project durations. This application,despite very interesting, goes beyond the aim of thispaper, but, for the sake of promoting further research,a programmable spreadsheet has been included asSupplemental Online material which performs theMonte Carlo simulations described above.
Furthermore, the sine waves can also be employedin weather-aware schedules for calculating correspond-ing weather-unaware activity durations. This kind offorensic analysis would be of interest when dealingwith weather-related claims. In this case, the actualactivity durations (from the as-built schedule) havenecessarily already been affected by the weather.Therefore, calculating the CRC values for each activityand adding them up from the actual activity start dateuntil its finish date are all that is needed. Later, if anextended analysis is required, it would be possible tosubmit the calculated (weather-unaware) activity dura-tions to Monte Carlo simulations. These simulationswould provide the probabilistic project durationscurve, from which it would be possible to determinethe percentile to which the actual (as-built) scheduleduration corresponded. This percentile would indicatewhether some form of time and/or cost compensationwould be appropriate, helping to mediate negotiationsbetween contractors and clients. Again, despite givingmore details about this application exceeds the aim ofthis paper, another programmable spreadsheet thatperforms ‘forensic’ weather scheduling analyses hasbeen appended as Supplemental Online material.
Finally, although the sine wave method proposedmay prove useful in many applications, it should bepointed out that it does have some limitations, even dis-advantages. Regarding disadvantages, any project man-ager who is aware of the Parkinson’s law (project workexpands to fill all the available time) will know thatallowing for increased activity durations (due to weatheror anything else) might lead to lower productivity levels.This productivity decrease might be caused by resources
14 P. BALLESTEROS-P�EREZ ET AL.
being more relaxed (on believing that they have moretime than needed) or even by intentionally delaying theactual start dates due to the Student’s syndrome (delayto start working on a task until it becomes reallyurgent). A nice case explaining how pervasive these twophenomena can be for project progress can be found inVanhoucke (2012, p. 188–189).
Then, the method proposed here anticipates longeractivity durations, but that does not mean the resour-ces will have extra time to work on them. They willhave exactly the original planned time (because theywill not be able to work during some days due toadverse weather conditions). It is the project manag-er’s responsibility to raise awareness on this issue andhandle the resources as effectively as possible.Otherwise, further delays will occur.
However, concerning the proposed method limita-tions, the curves require data from as many weatherstations as possible for improved accuracy and tomake up for data sets that are not sufficient quality.This is not a problem in a country like the UK whereweather stations are widespread and the data avail-able spans many years. However, it could be an issuein other countries where there are significantly fewerand/or newer stations.
Moreover, the sine waves correspond to weatherand thus workability at ground level (measurementstaken at a height of 10 m). This means that for tallstructures and/or for projects executed at sea, thecurves may not be representative at all. Similarly, forprojects located in very unusual and/or isolatedregions where the climate is significantly differentfrom nearby areas, the proposed sine wave curvesmay prove unrepresentative too.
However, there are many applications where theproposed sine waves will be more than sufficient, par-ticularly as they are based on extremely simple math-ematical expressions and allow for highly customisablecombinations of weather variables.
A last cautionary note must be given before pro-ceeding to the Conclusions section. On developing thecase study, only deterministic scheduling analyses havebeen implemented. It is well known that, due to theMerge event bias1 being neglected, deterministicschedules tend to underestimate the project duration(Ballesteros-P�erez 2017). Stochastic analysis has beenintentionally not considered here for the sake of com-paring homogeneous scheduling results (an original sin-gle weather-unaware deterministic schedule versus theremaining weather-aware, but also deterministic, sched-ules). This has allowed us to gauge the relative durationincreases that are to be expected when introducing theweather factor. But also avoiding other sources of
potential bias like activity duration variability present inthe original weather-unaware schedule. Finally, the casestudy developed consisted of a schedule with very fewactivities in parallel. This made the potential projectduration underestimations a very minor cause of con-cern in this occasion. For future scheduling analyses,though, Monte Carlo simulations like the ones that canbe performed in the spreadsheets included asSupplemental Online material, are recommended.
Conclusions
Construction projects involve multiple weather-sensitiveactivities that frequently cause significant project delaysand economic losses for both contractors and projectowners. A significant proportion of infrastructure-relatedactivities (from construction to operation and mainten-ance) are highly weather-sensitive, as they are mostlyperformed outdoors. This weather sensitivity, however,varies according to the nature of each activity, as wellas the location and season in which they are carriedout. Furthermore, different activities are susceptible todifferent combinations of weather variables (e.g. tem-perature, rain and wind) and their intensities.
Quantitative research on the influence of weatheron construction productivity is scarce, predominantlyless than 10 years old, and focuses mostly on buildingconstruction. Therefore, the main aim of this paperwas to propose a method that allows constructionindustry professionals to plan in the medium- andlong-term (beyond 2 weeks) considering the seasonalvariation of weather. The method proposed is not lim-ited to a small number of weather variables, nor tosmall geographical areas, and allows for many types ofproject activities to be considered.
The major contribution of this research is the devel-opment of a series of sine wave expressions that modelquite closely the average probability of a day beingworkable for a particular type of activity. The curves alsoallow a planner to anticipate how much longer a projectactivity will take to complete as a consequence of theweather. The proposed calculations can cover all days ofthe year, and by selecting appropriate combinations ofweather variables, can be defined for different types ofactivities and projects. Moreover, the expressions can beimplemented with either one, two or three parametersdepending on the degree of accuracy required.
Most construction projects comprise hundreds(sometimes thousands) of weather-sensitive activitieswhich interact through a precedence network (e.g. cer-tain activities must be completed before others canstart). Ascertaining the weather sensitivity of a wholeproject requires combining the weather’s impact on
CONSTRUCTION MANAGEMENT AND ECONOMICS 15
multiple activities and determining the ensuing effecton the overall project duration.
In this paper, six frequent and standard constructionactivities were defined and the weather variable combi-nations and intensities commonly accepted as prevent-ing them from being executed were justified. Using datafrom 102 weather stations and applying the relevantconstraints, sine wave expressions corresponding to thesix types of construction activities were calculated.
A case study involving the construction of a rein-forced concrete building was used to demonstratehow these sine waves can be applied in the predictionof project durations. The findings from the case studyindicate that UK weather can extend building projectdurations, on average by 21%. Furthermore, planningto minimise potential weather-related delays can leadto average project duration reductions of 16%, withassociated indirect and overhead cost reductions.
Finally, some limitations and further applications ofthe proposed sine wave expressions were discussed.Among these applications, the use of the sine wavesfor stochastic weather-aware scheduling and in dealingobjectively with weather-related claims is the most rele-vant. However, it is likely that many other applicationsof this research will be found in the future. Finally, tofacilitate use of the model, the majority of the dataanalysis, results (contour maps of the UK), and pro-grammable spreadsheets for performing both determin-istic and stochastic project scheduling calculations haveall been included as Supplemental Online Material.
Note
1. Actually, the merge event bias is nothing but a specialcase of Jensen’s inequality. This, as the maximum ofthe average durations of multiple activities which areperformed in parallel is always equal to or lower thanthe average duration of the maximum of suchactivity durations.
Acknowledgement
Weather data were supplied by the UK Met Office (MIDASdata set).
Disclosure statement
No potential conflict of interest was reported by the authors.
Funding
This work was supported by the CIOB Bowen Jenkins LegacyResearch Fund under [Grant number BLJ2016/BJL.01]; andNERC with the Environmental Risks to InfrastructureInnovation Programme under [Grant number NE/R008876/1].
ORCID
Pablo Ballesteros-P�erez http://orcid.org/0000-0002-4629-9664Stef�an Thor Smith http://orcid.org/0000-0002-5053-4639
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