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Research Article Monte Carlo Simulation to Evaluate Mould Growth in Walls: The Effect of Insulation, Orientation, and Finishing Coating Ricardo M. S. F. Almeida 1,2 and Eva Barreira 2 1 Department of Civil Engineering, School of Technology and Management, Polytechnic Institute of Viseu, Campus Polit´ecnico de Repeses, 3504-510 Viseu, Portugal 2 CONSTRUCT-LFC, Faculdade de Engenharia (FEUP), Universidade do Porto, Rua Dr. Roberto Frias s/n, 4200-465 Porto, Portugal Correspondence should be addressed to Ricardo M. S. F. Almeida; [email protected] Received 29 March 2018; Accepted 5 July 2018; Published 1 August 2018 Academic Editor: Arnaud Perrot Copyright © 2018 Ricardo M. S. F. Almeida and Eva Barreira. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Mould growth can have severe consequences both on the health of occupants and on constructions’ durability. Mould growth is a very complex process that depends on many factors such as temperature and relative humidity, presence of nutrients, and exposure time. Several mould prediction models, which allow estimating mould growth in building components and performing risk analysis, are available in the literature, such as the updated VTT model or the Biohygrothermal model. A Portuguese typical wall configuration was used for a sensitivity analysis. e importance of insulation (with and without insulation), orientation (north and south), and finishing coating (gypsum-based rendering, medium density fibreboard (mdf), and untreated wood) for the mould growth phenomenon was tested using both the updated VTTmodel and the Biohygrothermal model. A total of 12 case studies were investigated. e influence of indoor climate was evaluated by simulating 200 scenarios previously generated using the Monte Carlo method. Each of the scenarios has been applied to the 12 case studies, and 2400 hygrothermal simulations were carried out. Initially, the case studies were simulated using WUFI 1D since both mould growth models require the superficial temperature and relative humidity as input. Simulations were carried out for a one-year period. e updated VTTmodel produced results (mould index—M) ranging between 0.4 (gypsum-based rendering, insulated, and south oriented wall) and 5.9 (untreated wood, noninsulated, and north oriented wall) and the Biohygrothermal model (mould growth) between 10.1 and 406.4mm for the same case studies. Despite that the effect of the orientation of the wall could be identified, the importance of insulation and nature of substrate was more evident. Although the two models produced overall comparable results, some differences could be found, creating the opportunity to discuss their strengths and weaknesses as well as their sensitivity to the input parameters. 1. Introduction Mould growth is a very common problem in dwellings and has been steadily increasing in the last decades due to the growing concerns about energy efficiency of buildings. In fact, higher airtightness of the envelopes and lower venti- lation rates provide favourable conditions to enable mould growth. On the other hand, new materials used as interior coatings may also increase the problem [1]. Several studies performed by the scientific community pointed that mould growth affects not only the durability and performance of the materials but has also a main impact on the health and well-being of occupants. Respiratory infections, asthma, allergies, and cough are reported by several authors as respiratory diseases related to inhalation of mould spores. Coating detachment, materials deterio- ration, and decrease of thermal, hygric, and mechanical performance are the most common drawbacks of mould growth from the building point of view [1–4]. Although more than 100,000 mould species can be found in nature, only about 200 occur inside buildings. In dwellings, the transmission by air is the one that plays a relevant role on the health of occupants. Critical concentrations in rooms have been defined, although the information available in different Hindawi Advances in Civil Engineering Volume 2018, Article ID 8532167, 12 pages https://doi.org/10.1155/2018/8532167

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Page 1: Monte Carlo Simulation to Evaluate Mould Growth in Walls ...Monte Carlo Simulation to Evaluate Mould Growth in Walls: The Effect of Insulation, Orientation, and Finishing Coating Ricardo

Research ArticleMonte Carlo Simulation to Evaluate Mould Growth in Walls: TheEffect of Insulation, Orientation, and Finishing Coating

Ricardo M. S. F. Almeida 1,2 and Eva Barreira 2

1Department of Civil Engineering, School of Technology and Management, Polytechnic Institute of Viseu,Campus Politecnico de Repeses, 3504-510 Viseu, Portugal2CONSTRUCT-LFC, Faculdade de Engenharia (FEUP), Universidade do Porto, Rua Dr. Roberto Frias s/n,4200-465 Porto, Portugal

Correspondence should be addressed to Ricardo M. S. F. Almeida; [email protected]

Received 29 March 2018; Accepted 5 July 2018; Published 1 August 2018

Academic Editor: Arnaud Perrot

Copyright © 2018 Ricardo M. S. F. Almeida and Eva Barreira. )is is an open access article distributed under the CreativeCommons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided theoriginal work is properly cited.

Mould growth can have severe consequences both on the health of occupants and on constructions’ durability. Mould growth isa very complex process that depends on many factors such as temperature and relative humidity, presence of nutrients, andexposure time. Several mould prediction models, which allow estimating mould growth in building components and performingrisk analysis, are available in the literature, such as the updated VTTmodel or the Biohygrothermal model. A Portuguese typicalwall configuration was used for a sensitivity analysis. )e importance of insulation (with and without insulation), orientation(north and south), and finishing coating (gypsum-based rendering, medium density fibreboard (mdf), and untreated wood) forthe mould growth phenomenon was tested using both the updated VTTmodel and the Biohygrothermal model. A total of 12 casestudies were investigated. )e influence of indoor climate was evaluated by simulating 200 scenarios previously generated usingthe Monte Carlo method. Each of the scenarios has been applied to the 12 case studies, and 2400 hygrothermal simulations werecarried out. Initially, the case studies were simulated using WUFI 1D since both mould growth models require the superficialtemperature and relative humidity as input. Simulations were carried out for a one-year period.)e updated VTTmodel producedresults (mould index—M) ranging between 0.4 (gypsum-based rendering, insulated, and south oriented wall) and 5.9 (untreatedwood, noninsulated, and north oriented wall) and the Biohygrothermal model (mould growth) between 10.1 and 406.4mm for thesame case studies. Despite that the effect of the orientation of the wall could be identified, the importance of insulation and natureof substrate was more evident. Although the two models produced overall comparable results, some differences could be found,creating the opportunity to discuss their strengths and weaknesses as well as their sensitivity to the input parameters.

1. Introduction

Mould growth is a very common problem in dwellings andhas been steadily increasing in the last decades due to thegrowing concerns about energy efficiency of buildings. Infact, higher airtightness of the envelopes and lower venti-lation rates provide favourable conditions to enable mouldgrowth. On the other hand, new materials used as interiorcoatings may also increase the problem [1].

Several studies performed by the scientific communitypointed that mould growth affects not only the durabilityand performance of the materials but has also a main impact

on the health and well-being of occupants. Respiratoryinfections, asthma, allergies, and cough are reported byseveral authors as respiratory diseases related to inhalationof mould spores. Coating detachment, materials deterio-ration, and decrease of thermal, hygric, and mechanicalperformance are the most common drawbacks of mouldgrowth from the building point of view [1–4].

Although more than 100,000 mould species can be foundin nature, only about 200 occur inside buildings. In dwellings,the transmission by air is the one that plays a relevant role onthe health of occupants. Critical concentrations in rooms havebeen defined, although the information available in different

HindawiAdvances in Civil EngineeringVolume 2018, Article ID 8532167, 12 pageshttps://doi.org/10.1155/2018/8532167

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legal directives/guidelines often differs among them. In ad-dition, no accurate and widely applicable information existsabout which concentrations do represent a hazard to health[2]. According to the World Health Organization (WHO),pathogenic and toxic mould species are not acceptable in-doors and a maximum concentration of 150CFU/m3 ofa mixture of not very common different mould spores isconsidered to be acceptable, and if mould belongs to commonspecies that usually occur in the outside air, a maximumconcentration of 500CFU/m3 is satisfactory [5].

For mould growth to occur, certain conditions are re-quired. Although these conditions depend on the species, itis possible to generally state that temperature, relative hu-midity (and the combination of these two), the existence ofnutrients and oxygen, and exposure time play a major role inmould development [1, 2, 6]. Krus et al. pointed otherparameters that also influence mould growth, like pH value,light, surface roughness, and biotic interactions [7].

In the last decades, several models have been developedin order to assess mould growth in buildings [1, 2, 4, 6–13].)ese models are very interesting tools as their correctapplication can help prevent damage in buildings. However,it is important a deep knowledge of the models in order tounderstand their strengths and limitations and to learn howto interpret their results.

)e VTT model [11] was developed in the TechnicalResearch Centre of Finland (VTT) by Hukka and Viitanen.It is an empirical model based on visual findings of mouldgrowth in pine and spruce sapwood under controlledconditions (laboratory tests). )is model quantifies themould growth through a mould index (M) that varies from0 (no growth) to 6 (visually detected coverage 100%). Inorder to apply this model to other materials rather thanwood, new tests were performed in collaboration betweenVTTand the Tampere University of Technology (TUT), andthe mould index was related with other substrates in theupdated VTT model also called the Finnish mould growthmodel. Temperature and relative humidity of the surface,together with the exposure time and the surface charac-teristics, are the key input parameters considered by themodel. )e complete formulation of the model can be foundin [11, 14, 15].

To classify the materials, the model establishes fourmould growth sensitivity classes: (a) very sensitive, whichincludes pine sapwood; (b) sensitive, which includes gluedwooden boards, PUR with paper surface and spruce; (c)medium resistant, which includes concrete (aerated andcellular concrete), glass wool, and polyester wool; and (d)resistant, which includes PUR polished surface. )e modelalso considers a decrease function in the mould index, whenrelative humidity and/or temperature are unfavourable formould growth, as a function of materials characteristics [14].

)e Biohygrothermal model was developed by Sedlbaueret al. [7, 16, 17] based on the isopleth system proposed bySedlbauer [2]. )e model allows calculating the moisturebalance in a spore considering transient boundary condi-tions comprising temperature and relative humidity of thesurface. Biological growth is directly dependent not only onthe hygrothermal boundary conditions but also on the

substrate. For that reason, four different substrate classes areconsidered: (a) Class 0, which corresponds to the optimalbiologic culture medium; (b) Class I, which includes bi-ologically recyclable building materials like wall paper, paperfacings on gypsum board, building materials made of bi-ologically degradable raw materials, and materials for per-manent caulking; (c) Class II, which includes buildingmaterials with porous structure such as renderings, mineralbuilding materials, and certain wood species as well asinsulation material not covered by I; and (d) Class III, whichcorresponds to building materials that are neither bio-degradable nor contain any nutrients and for which noisopleth system was developed as it is considered that mouldgrowth is not possible on their surface [17]. )e model alsoincludes an additional Class K that was created to differ-entiate mould species pointed as critical to health consid-ering the optimum culture medium [18].

According to the Biohygrothermal model, if the courseof the moisture content within a spore, which depends onambient relative humidity, achieves the critical water con-tent inside the spore, which depends on temperature andmoisture retention curve for each substrate, mould growthwill begin.)e growth is expressed in millimetres and, in thebeginning of the simulation, it describes the increase of themycel length. However, this model allows continuousgrowth as long as there are suitable boundary conditionsand, with ongoing growth, unrealistic values of severalhundred millimetres can be reached. )erefore, these valuescan only be regarded for a comparative assessment of therisk of mould development, but not as a realistic growth [19].

Some studies about the comparison of these two modelsare available in the literature [19–24]. Both models traducethe influence on mould development of surface temperature,relative humidity, and substrate, but while in the updatedVTT model, a decrease in the mould index exists underunfavourable conditions, in the Biohygrothermal modelgrowth is assumed equal to zero in those circumstances. Onthe other hand, updated VTTmodel limits mould index toa climate specific maximum value, while the Bio-hygrothermal model allows continuous growth as long asthere are suitable boundary conditions. Although theiroutputs are different (mould index (−) for the updated VTTmodel and mould growth (mm) for the Biohygrothermalmodel), a correlation between them was proposed based onhygrothermal calculations [19].

)ese models have recently been applied in mould riskevaluation. )e risk of mould growth when adding interiorthermal insulation to a log wall in a cold climate wasanalysed by Alev and Kalamees [25]. Almeida and Barreira[26] selected critical locations of a gymnasium envelope andmonitored superficial temperature and relative humidityduring 4 months. )e results were used as inputs forcomparing the mould growth models. Gradeci et al. [27]proposed a probabilistic-based methodology to assess theperformance of façade constructions against mould growth.)e methodology takes into account uncertainties related tothe biological phenomenon, the climate exposure, and thematerial properties and integrates several mould growthmodels in a combined outcome.

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Although there are existing studies that use and comparethe updated VTT and the Biohygrothermal models, no de-tailed information exists about their application to Medi-terranean countries. In fact, in southern European countries,not only the exterior climate has specific particularities butalso the interior climate is much more dependent on exteriorconditions as no heating habits exist and “adventitiousventilation” is a common strategy. )e main objective of thispaper is to present the results of a sensitivity analysis toevaluate mould risk in a wall, using a probabilistic approachbased on Monte Carlo simulation.

2. Methodology

In this work, a sensitivity analysis of the updated VTT andthe Biohygrothermal models was made. )ree parameterswere assessed, coating material, orientation, and the exis-tence of a layer with thermal insulation characteristics,resulting in 12 cases analysed (3 coatings, 2 orientations, andexistence or not of thermal insulation). )e main aim of theanalysis was to evaluate the influence of these three pa-rameters on mould growth. Additionally, a comparisonbetween the results produced by each model was attempted.

)e coating materials were selected according to themost common Portuguese construction practices and takinginto account the substrate classes in the Biohygrothermalmodel (Classes I and II) and the sensitivity classes in theupdated VTTmodel (very sensitive, sensitive, and mediumresistant), in order to obtain at least one material repre-sentative of each group. Table 1 describes the sensitivity classand type of substrate in which each coating material isincluded.

Surface hygrothermal conditions are also fundamentalfor mould growth. )ese conditions depend essentially on

the interior climate, whose variability is highly dependent onthe actions and behaviours of the users [28, 29]. In this work,a probabilistic approach was used to evaluate the effect ofindoor climate (air temperature and relative humidity). )ebase case for the interior climate was established in accor-dance with the typical fluctuation of the interior air tem-perature and relative humidity on a Portuguese dwelling(black line in Figure 1).

After defining a base case, the Monte Carlo method wasused to generate 200 new scenarios (Figure 1) assuminga normal distribution for the air temperature and relativehumidity and a standard deviation of 20%. )e Latin hy-percube sampling (LHS) algorithm was selected for thenumber generation because it provides good convergence ofparameter space when compared to the simple randomsampling. Each of the scenarios was then applied to the 12case studies (wall configurations), and a total of 2400 one-dimensional hygrothermal simulations were carried outusing WUFI 1D, since both mould growth models requirethe superficial temperature and relative humidity as input.)e simulations were carried out for a one-year period.Figure 2 presents schematically the methodology that wasused and the cases Id.

)e exterior climate was the one of Porto (Portugal),generated by the commercial software Meteonorm in anhourly base [30] (Table 2). Table 3 presents the materials’main properties used in the hygrothermal simulations,where e is the layer thickness (m), c is the bulk density(kg/m3), ξ is the porosity (m3/m3), Cdry is the specificheat capacity of the dry material (J/kg·K), λdry is thethermal conductivity of the dry material (W/m·K), and µ isthe water vapour diffusion resistance factor (−). A sche-matic representation of the wall section can be found inFigure 3.

Table 1: Selected materials and their classification according to the updated VTT and biohygrothermal models.

Material Sensitivity class (updated VTT model) Substrate class (Biohygrothermal model)Gypsum-based rendering (M1) Medium resistant IIMedium density fibreboard (mdf) (M2) Sensitive IUntreated wood (M3) Very sensitive I

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Figure 1: Typical fluctuation of the interior air (black line) and indoor climates used in the hygrothermal simulations: (a) temperature; (b)relative humidity.

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3. Hygrothermal Simulations

)e first step of this research was simulating the interiorsuperficial temperature and relative humidity for the 2400scenarios. As an example, Figure 4 shows the results of thehygrothermal simulation for the scenario M1_NI_N usingthe base case as indoor climate (black line in Figure 1).Figure 5 synthesizes the results for the entire dataset, in-cluding the average, maximum, and minimum values.

Results reveal that the presence of an insulation layer isthe most important factor as a clear difference between I andNI cases can be observed. As expected, NI cases presentlower temperature and higher relative humidity (differencesof 1°C and 5%, approximately). Moreover, a larger variabilitycan be found in NI cases, confirmed by an average coefficientof variation of 13.8% and 15.9% in temperature results, for Iand NI cases, respectively, and of 10.3% and 12.5% in therelative humidity results.

In the I scenarios, the effect of finishing coating andorientation is almost imperceptible. On the contrary, in the

NI cases, the effect of the finishing coating is more obvious inthe north oriented scenarios.

4. Results

4.1. VTTModel. Figure 6 shows the maximum mould indexobtained for each case study considering only the base caseas indoor climate. Although only slight differences in thesuperficial hygrothermal conditions were found among thedataset, the application of the VTT model exposed a com-pletely different scenario as the mould index ranged from 0.4(M1_I_S) to 5.9 (M3_NI_N). )ese differences justifieda detailed sensitivity analysis to establish the relative im-portance of each parameter under this study: finishingcoating material, insulation layer, and orientation (Figure 7).Only the base case as indoor climate was considered in thisanalyses.

Figure 7(a) highlights the effect of the finishing materialusing the north oriented, noninsulated set-up as example.)e maximum mould index was 2.98, 4.41, and 5.86 for the

Finishing coating

Gypsum-based rendering (M1)Medium density fiberboard (mdf) (M2)

Untreated wood (M3)

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#01: M1_I_N #04: M1_I_S #07: M1_NI_N #10: M1_NI_S#02: M2_I_N #05: M2_I_S #08: M2_NI_N #11: M2_NI_S#03: M3_I_N #06: M3_I_S #09: M3_NI_N #12: M3_NI_S

Monte Carlo simulation200 indoor climates

Figure 2: Methodology and cases Id.

Table 2: Porto climate (generated by Meteonorm 6.0).

Climatic parameter Annual average Annual accumulatedTemperature 14.8°C —Relative humidity 78% —Global radiation emitted by the sun 343W/m2 —Wind velocity 2.6m/s —Wind direction (north: 0°; east: 90°; south: 180°; west: 270°) 195° —Rain — 779mm

Table 3: Material properties used in the hygrothermal simulations.

Material e (m) c (kg/m3) ξ (m3/m3) Cdry (J/kg·K) λdry (W/m·K) µ (−)Exterior rendering 0.02 1219 0.3 850 0.25 10.8Concrete 0.2 2200 0.18 850 1.6 92XPS (extruded polystyrene insulation) 0.06 30 0.95 1500 0.04 50Gypsum-based rendering (M1) 0.015 850 0.65 850 0.2 8.3Medium density fibreboard (mdf) (M2) 0.015 508 0.66 1700 0.12 15Untreated wood (M3) 0.02 550 0.66 1700 0.18 70

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Figure 3: Schematic representation of the wall section.

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Figure 5: Average, maximum, and minimum for the entire dataset: (a) temperature; (b) relative humidity.

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gypsum-based rendering, the medium density �breboard(mdf), and the untreated wood, respectively. For the threematerials, the maximum mould index occurred approxi-mately in the same instant, around 2600 hours. Figure 7(b)uses the north oriented set-up with the gypsum-basedrendering, to expose the e�ect of the insulation layer. Asigni�cant di�erence between the two cases can be observedas the maximummould index increases from 0.54 up to 2.98.Furthermore, a time lag between themaximum values is nowdistinguishable. �e maximummould index in the insulatedcase occurs around the 3400 hours, but when there is no

insulation, it occurs about 1000 hours before. Finally, inFigure 7(c), it can be con�rmed that orientation is the lessimportant parameter. In the gypsum-based rendering,noninsulated set-up, the maximum mould index variesbetween 2.63 and 2.98. As expected, the higher value occursin the north oriented case due to the lower incident solarradiation. Despite the small di�erence in the maximummould index value, a time lag between the instants is alsovisible in this scenario as in the south oriented, it occurs atthe 3350 hours, approximately, and about 1000 hours afterthe north oriented.

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Figure 6: Maximum mould index, considering the base case as indoor climate.

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Figure 7: VTTmodel: sensitivity analysis (base case as indoor climate): (a) �nishing coating material; (b) insulation layer; (c) orientation.

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)e introduction of variability in indoor climate hasconfirmed the importance of this parameter in the evalu-ation of the risk of mould growth. Figure 8 shows, as

a cumulative percentage, the results of the maximum valueof the mould index obtained in the 2400 simulations, sep-arately for the 12 case studies. In Figure 8(a) are the cases

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Figure 9: Maximum mould growth, considering the base case as indoor climate.

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Figure 10: Biohygrothermal model: sensitivity analysis (base case as indoor climate): (a) finishing coating material; (b) insulation layer; (c)orientation.

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with an insulation layer, while in Figure 8(b) are the oneswithout insulation.

In addition to the already known importance of thesensitivity class of the coating material, it is observed that incases with insulation layer, the importance of the variability ofthe interior climate is more evident. In fact, in the caseswithout thermal insulation, the value of the mould index hasa much lower dispersion, that is, the introduction of the layerreduces the impact of the exterior climate, thus maximizingthe importance of the indoor climate. It is also worth notingthat the cases with an untreated wood coating and withoutinsulation layer are clearly limited by the model itself (M� 6).

4.2. Biohygrothermal Model (Wufi Bio). )e Bio-hygrothermal model was applied to the entire dataset using

Wufi Bio, and the maximum growth was used as thecomparison output. )e same approach used in the VTTmodel was applied and Figure 9 shows the maximum growthfor the 12 case studies considering only the base case asindoor climate. Once again, large differences between thedifferent case studies can be observed. )e lower mouldgrowth value occurred in theM1_I_S case (10.1mm) and thehighest in the M3_NI_N case (406.4mm). )ese results arein line with the ones obtained with the VTT model, whichalso pointed out these two cases as the extreme scenarios.Figure 10 depicts the results of the sensitivity analysis.

)e effect of the finishing coating material is shown inFigure 10(a) using, once again, the north oriented, non-insulated set-up as an example case. )e maximum mouldgrowth was 255.7mm, 325.0mm, and 406.4mm for thegypsum-based rendering, the medium density fibreboard

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Figure 11: Maximum value of mould growth cumulative relative frequency: (a) case studies with insulation layer; (b) case studies withoutinsulation layer.

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(mdf) and the untreated wood, respectively. Since theBiohygrothermal model does not include a decrease factorto take into account unfavourable growth conditions, thefirst instant in which the maximum mould growth valueoccurred was used as the “time indicator.” In this way,only slight differences can be found between the cases asin the three, the instant was at 5800 hours, approximately.Figure 10(b) uses the north oriented set-up, with gypsum-based rendering, to expose the large differences found in themould growth due to the presence of an insulation layer.)e maximum mould growth decreases from 255.7mm inthe noninsulated case to 19.4mm in the insulated one.Furthermore, this value is reached earlier in the insulatedcase (4000 hours). Compared with the VTT model, theBiohygrothermal model is more sensitive to the effect oforientation as exposed in Figure 10(c).)emaximummouldgrowth was 163.2mm in the south oriented and 255.7mm inthe north one. Both occurred around the same instant.

)e importance of variability of the indoor climate isshown in Figure 11, where the cumulative percentage of themaximum value of mould growth obtained in the 2400simulations is depicted, separately for the 12 case studies. InFigure 11(a) are the cases with an insulation layer, while inFigure 11(b) are the ones without insulation.

In this model, unlike the VTT model, the dispersion ofthe distribution is not much affected by the presence of theinsulation layer. Using as example case the untreated wood(the material with the highest risk of mould growth), it isverified that for both north and south oriented cases, 80% ofthe maximum values (percentiles between 0.1 and 0.9) arewithin a range of about 100mm. For the remaining casestudies, an equivalent range is observed.

4.3. Discussion. )e results previously presented showedsome agreement between the twomodels as both pointed thesame cases as the extreme scenarios. Nevertheless, some

differences were also identified such as the highest sensitivityto wall orientation found in the Biohygrothermal model andthe more evident effect of the variability of indoor climate inthe VTT model. Figure 12 illustrates the relationship be-tween maximummould index and maximummould growthin the entire dataset (2400 simulations). )e agreementbetween the two models was already tested and reported byprevious researchers, suggesting the use of a BETfunction tomathematically describe this relationship [19–21]. In thiswork, in addition to the previously mentioned BETfunction,two approximations were tested: a third degree polynomialfunction and an exponential function. )e attained co-efficient of determination was 0.66 and 0.59, respectively.Although better than the BET function, these coefficientsindicate that these functions seem unsuitable to describe therelationship.

Analyzing the results, it is possible to verify that the BETfunction tends to overestimate the mould growth value whenthe mould index is high. In addition, this function presentsamore interesting performance in the case studies without theinsulation layer. )e two approximation functions presentedin this research (polynomial and exponential), for the samevalues of mould index, suggest lower values of mould growth.One should also stress that the high number of results withmaximum mould index (M� 6) may overestimate the im-portance of these points and thus bias the functions.

Interesting findings can be drawn if one compares theinstants at which the maximum mould index and themaximum mould growth occur as illustrated in Figure 13.)e main conclusion is that the maximum value occursearlier when the VTT model is used. )is is an obviousconsequence of the reduction function included in themodel to take into account unfavourable hygrothermalconditions, while in the Biohygrothermal model, the mouldgrowth function can only increase or be stable.

Additionally, clear patterns can be identified on theresults of the VTTmodel. In the noninsulated cases, besides

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Figure 12: Mould growth versus mould index (2400 simulations).

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the evident effect of the finishing material, a time lag due toorientation can also be observed. )e south oriented sce-narios reached the maximum mould index, approximately,800 hours after the corresponding north oriented cases. )issituation disappears when the insulation layer is added. Amore random configuration can be observed in the results ofthe Biohygrothermal model. Nevertheless, a trend for anearlier maximum mould growth in the insulated scenarioscan be pointed out.

5. Conclusions

In this study, the importance of insulation (with and withoutinsulation), orientation (north and south), and finishingcoating (gypsum-based rendering, medium density fibre-board (mdf), and untreated wood) for the mould growthphenomenon was tested using the two most well-knownmodels to assess mould growth: updated VTT and Bio-hygrothermal. Taking into account the importance of in-terior climate in the phenomenon and due to its highlyvariable nature in Mediterranean countries, a probabilisticapproach based on Monte Carlo simulation was alsoimplemented. A typical external wall configuration was usedas the case study. From the results, the following mainfindings can be stated:

(i) Although only slight differences among the datasetwere found in the superficial hygrothermal condi-tions, the application of the updated VTT andBiohygrothermal models exposed great differencesbetween the simulated scenarios (mould indexranged from 0.4 to 5.9 and mould growth rangedfrom 10.1mm to 406.4mm).

(ii) From the three parameters that were assessed, thethermal insulation is the more relevant (relativedifferences are on average 78%), followed by thecoatingmaterials (relative differences are on averagearound 57%) and, finally, the orientation (relativedifferences are on average around 18%). )e Bio-hygrothermal model is more sensitive to the effect of

orientation than the updated VTT model (relativedifferences are, on average, 11% for the updatedVTT model and 25% for the Biohygrothermalmodel).

(iii) )e importance of the variability of indoor climatewas confirmed by the results of the Monte Carlosimulation. In the VTT model, in cases with insu-lation layer, the importance of this variability wasmore evident. )is finding was not so obvious in theBiohygrothermal model.

(iv) An agreement between the two models (mouldindex versus mould growth) was searched. Apolynomial and an exponential function were testedto approximate the results of the 2400 simulations,and a coefficient of determination of 0.66 and 0.59,respectively, was attained.

(v) )e maximum mould index (updated VTTmodel)occurs earlier than the maximum mould growth(Biohygrothermal model). Maximum mould indexoccurs on average at 2900 hours and maximummould growth occurs on average at 5155 hours.)isis a consequence of the reduction function includedin the updated VTT model to take into accountunfavourable hygrothermal conditions that are notconsidered in the Biohygrothermal model.

(vi) Clear patterns can be identified on the results of theVTTmodel when analysing the instants at which themaximum mould index occur. On the contrary,a more random configuration can be observed in theresults of the Biohygrothermal model.

)e future research will include the use of real data tocompare the results provided by the two models and assesswhich one is the most interesting for modelling mouldgrowth in the Mediterranean climate.

Data Availability

)e data are available on request from the correspondingauthor. )e datasets generated during and/or analysed

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Figure 13: Comparison of the results calculated by both models.

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during the current study are available from the corre-sponding author on reasonable request. )e large amount ofdata justifies this option.

Conflicts of Interest

)e authors declare that they have no conflicts of interest.

Acknowledgments

)is work was financially supported by Project POCI-01-0145-FEDER-007457–CONSTRUCT–Institute of R&D inStructures and Construction funded by FEDER fundsthrough COMPETE2020–Programa Operacional Com-petitividade e Internacionalização (POCI).

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