Research in Building Physics and Building Engineering – Fazio, Ge, Rao & Desmarais (eds)© 2006 Taylor & Francis Group, London, ISBN 0-415-41675-2

Hygrothermal simulation of masonry under atmospheric excitation

H. Janssen & J. Carmeliet1

Laboratory for Building Physics, Katholieke Universiteit Leuven, Belgium1also at: Building Physics Group, Technical University Eindhoven, the Netherlands

ABSTRACT: This paper demonstrates that the homogenizability condition is not fulfilled for a macro-heterogeneous material like masonry. Homogenization can thus not be applied to reduce the size-problem ofnumerical simulation of moisture and heat transfer in masonry under atmospheric excitation. Instead, it willbe verified that the internal redistribution of moisture – presumed to result from the spatial variation of thewind-driven rain exposure over a facade – is negligible, and that the hygrothermal response of a masonry facadecan hence accurately be determined by ‘sampling’.

1 INTRODUCTION

Until recently the Glaser method counted as the stan-dard calculation tool for evaluating the hygrothermalbehavior of building components, but its restrictions –stationary, no liquid transfer, no air transfer, … –render it only rarely reliably applicable. Presently theuse of numerical simulation models for moisture andheat transfer becomes increasingly common. Recently,hygrothermal simulation has been applied for the eval-uation of: the hygric and thermal performance ofnew building components (Scheffler & Grunewald,2002); the risk on algae formation and mould growth(Sedlbauer, 2002); the effect of rain buffering on theoccurrence of runoff on brick facades (Janssen et al.2002) ; the influence of moisture buffering on theinterior relative humidity (Simonson et al., 2002), … .

Hygrothermal simulation of masonry – or gener-ally: a macro-heterogeneous material layer – currentlyremains challenging though. Without simplifications,the spatial discretisation of every brick and joint yieldsvery large systems of equations, which are expen-sive to solve. A possible solution is homogenization,which replaces the heterogeneous material layer withan ‘equivalent homogeneous’material, this way allevi-ating the need for discretisation of all different materialblocks. This paper will show that the homogenizabilitycondition (Auriault, 1991) is not met for masonry how-ever. Instead, a sampling approach will be introducedand verified.

Hygrothermal simulation of masonry is moreovercomplicated by the behavior of the interface betweenbrick and joint, a bonding layer with its own specificcharacteristics (Brocken, 1998), an aspect which willonly be summarily addressed in this paper.

The research discussed in this paper forms partof a large research project on damage to built struc-tures due to mechanical or hygrothermal loading.The paper hence focuses on ‘modern’ masonry, con-structed according to the state of the art. Horizontalflashings are presumed present at the bottom of thefacade, avoiding capillary moisture rise from thefoundation. Atmospheric excitation (vapour exchangeand wind-driven rain) can thus be assumed the pri-mary hygric boundary condition for the facade. Thepaper moreover concentrates on the problem of themacro-heterogeneity, for which it will be demonstratedthat the homogenization approach is not applicable.Instead, ‘sampling’ is introduced as the simplify-ing approach to make hygrothermal simulations ofmasonry under atmospheric excitation possible.

2 MODELS AND MATERIALS

2.1 Hygrothermal simulation model

All simulations in this paper are performed with thehygrothermal simulation model presented by Janssenet al. (2005). This model solves the partial differentialequations describing the moisture and heat transfer inbuilding components by use of a finite-element spatialand an implicit temporal discretisation, with an explicitcorrection for mass and energy conservation. A com-plete implementation of the atmospheric phenomena –precipitation, convection, radiation, … – is includedto supply the atmospheric hygrothermal boundaryconditions. To facilitate large-scale multi-dimensionalhygrothermal simulations, much attention was paidto the numerical optimization of the solution scheme(Janssen & Carmeliet, 2005).

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Figure 1. Moisture retention curve w(pc) (a) and total hydraulic permeability K(pc) (b) for ceramic brick and cement mortar,where w = volumetric moisture content; K = total hydraulic permeability; and pc = capillary pressure.

2.2 Hygrothermal material properties

The hygrothermal material properties for the ceramicbrick and cement mortar, as used in the simulations,stem from a commercially available fired-clay brick,and a laboratory prepared mortar. The ceramic brickhas a bulk density of 2005 kg/m3 and an open poros-ity of 24%. The mortar is composed from 68% sand(by mass), 15% Portland cement, 17% water, yieldinga water/cement factor of 1.15. The resulting mortarhas a bulk density of 1850 kg/m3 and an open porosityof 28%. The main hygric properties (moisture reten-tion curve, total hydraulic permeability) of these twomaterials are shown in Figure 1.

These hygric properties result in capillary absorp-tion coefficients of respectively 0.14 and 0.11 kg/m2s0.5,indicating that especially the mortar is quite sorptive.It is assumed that the properties of mortar, while deter-mined for a non-bonded material, remain valid for thedescription of the bonded material of the joints.

3 ATMOSPHERIC EXCITATION OF MASONRY

3.1 Problem statement

The numerical simulation of moisture and heat transferin building components under atmospheric excitationis inherently demanding: it necessitates the numeri-cal solution of highly non-linear transfer equationsdriven by strongly variable – temporally and spatially –boundary conditions. The non-linearity of the trans-fer equations is clearly illustrated by Figure 1: thestorage and transfer properties depend on the capil-lary pressure. The exterior climate – the moisture andheat exchange between atmosphere and component –evidently varies over time. The hygrothermal loadsare furthermore also spatially variable: particularly

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Figure 2. Distribution of the wind-driven rain coefficientsover a facade of a cubic 10 × 10 × 10 m3 building for windsperpendicular to the facade.

the catchment of wind-driven rain is not uniformlydistributed over a facade.

Figure 2 portrays the variation of the wind-drivenrain coefficient over the facade of a low-rise buildingfor winds perpendicular to the facade. This wind-driven rain coefficient is the proportionality in therelation between the wind-driven rain index – prod-uct of reference wind speed and rain intensity througha horizontal plane – and the wind-driven rain inten-sity on a facade. It is clear that the top corners receiveabout three times as much rain as the bottom centre.

Hygrothermal simulation of masonry under atmo-spheric excitation suffers from an additional complex-ity: the macro-heterogeneous structure of masonry.Without simplification, discretisation of every brickand mortar joint is required, leading to an extremely

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a. b. c.

1.5 mm 1.5 mm 2.5 mm

Figure 3. Discretised representation of Savionnières limestone: the dark grey material represents the ooliths, the light greymaterial the calcite cement (a), simulation of free water uptake into mesoscale model of Savonnières: the bottom is broughtin contact with water (b), microscopic image (with fluorescent light) of free uptake of a low-viscous colored epoxy resin (c)(Roels, 2000).

fine mesh over the facade plane. A homogeneousfacade on the other hand would tolerate a rougher dis-cretisation. Such refined discretisation is impossibleto solve with presently available computers though:simplification is thus required.

3.2 Homogenization approach

In the homogenization approach, abstraction is madeof the precise heterogeneous structure of the mate-rial, by replacing it with an ‘equivalent homoge-neous’ material. Such an homogeneous material doesnot require fine discretisation of different materialblocks, and thus contributes to the feasibility of thesimulations.

Most research on the homogenization of mois-ture transfer in porous media originates from soilphysics where regularly large soil domains with sev-eral heterogeneities are studied. To specify only afew, publications vary from theoretical (Auriault,1991) to phenomological (Zhu and Mohanty, 2002).Homogenization in the building physical researchfield was introduced by Roels (2000).

Roels (2000) determined the macroscopic perme-ability of a French limestone with heterogeneities onthe mesoscale from detailed simulations of the mate-rial on that scale. The studied Savonnières limestoneis composed of spherical ooliths, glued together by acalcite cement. An abstract depiction of the structureis shown in Figure 3a. Due to the large differences inthe moisture capacity and permeability of both mate-rials, and their specific connectivity, straightforwarddetermination of macroscopic permeabilities provedinaccurate. Mesoscale simulations of the storage andtransfer of moisture were executed instead, whichallowed developing equivalent homogeneous moisturetransfer properties. Figure 3b illustrates the moisturefront during a free water uptake simulation, whileFigure 3c shows the measurement of an analogous freeuptake of a low-viscous epoxy resin.

Both simulation and measurement show that,despite the material’s heterogeneous nature, the freewater uptake still gives fairly one-dimensional mois-ture fronts on the depicted mesoscale. These obser-vations imply that the represented material samplecan be assumed a ‘representative elementary vol-ume’ (REV), with dimensions much smaller than theinvolved macroscale dimensions of building parts.

The condition for homogenizability is hence satis-fied (Auriault, 1991): ‘the macroscopic domain mustcontain a (very) large number of heterogeneities, andthe characteristic lengths of these must be limited, sothat there exists a representative elementary volumeof the medium, small in comparison to its macro-scopic volume’. The sub-millimeter heterogeneities ofSavonnières satisfy this condition, for most realisticmacroscopic thicknesses of the material.

Such separation of scales is impossible though for amacro-heterogeneous material like masonry. The sim-ulation and measurements of free water uptake in abrick-mortar sample depicted in Figure 4, point outthat no one-dimensional moisture fronts develop andthat no REV, with dimensions much smaller than themacroscale, can hence be obtained: hygrothermal sim-ulation of masonry under atmospheric excitation isthus not homogenizable.

3.3 Sampling approach

The primary complexity of the hygrothermal simula-tion of masonry under atmospheric excitation residesin the shear size of the problem. The relatively smallsize of the bricks and mortar joints, together withthe spatial distribution of the atmospheric bound-ary conditions, creates a giant system of equations,which is moreover to be solved iteratively for tran-sient boundary conditions. This problem statementthough implicitly assumes that the spatial distribu-tion of wind-driven rain – and, accordingly, all othermoisture and heat exchanges between atmosphere and

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30 mm30 mm 35 mm 35 mm

d.c.a. b .

Figure 4. Discretised representation of a brick-mortar sample: the dark grey material represents the mortar, the light greymaterial the brick (a), simulation of free water uptake into brick-mortar sample: the bottom is brought in contact with water;status after 5 minutes (b), X-ray radiographic images of free water uptake, status after 5 minutes (c) and 1 hour (d). Pleasenote that the simulations and measurements are performed on different materials. Particularly the mortar properties differ: theabsorption coefficients for the simulated and measured mortar are respectively 0.11 and 0.03 kg/m2s0.5.

Figure 5. Periodic unit of a single-layer masonry facade.

facade – gives rise to important moisture and heattransfers between different locations on the facade.Nullification of this assumption would however allowapplication of the ‘sampling’approach: instead of sim-ulating the masonry facade as a totality, the hygrother-mal behavior of the facade could be characterized fromsimulations of small(er) subsections of masonry. In thelimit, the latter could be brought down to the periodicunit of masonry, as illustrated in Figure 5.

3.3.1 Simulation studyIn order to corroborate the sampling approach, large-and small-scale hygrothermal simulations of masonryunder atmospheric excitation are compared. Sincelarge-scale three-dimensional hygrothermal simula-tions are still not feasible with nowadays computersor numerical methods, simulations have been limitedto two dimensions.

Large-scale simulations are performed for 9 three-meter high vertical segments of the 10 × 10 m2 facadeof Figure 2: segments span between 2.2–5.2 m, 4.6–7.6 m, 7.0–10.0 m height, located at the side edge, at2.5 m from the side edge, and at the center line of thefacade. Each three-meter high segment consists of 50bricks and mortar joints.

All small-scale simulations are limited to the two-dimensional periodic cell of masonry (½ brick and½ mortar joint), located at different heights in theformerly specified vertical segments: the small-scalesimulations hence sample the large-scale geometry.

Only the exterior layer of the cavity wall masonryfacade is simulated: the insulation layer constitutes ahygric and thermal break making the hygric and ther-mal capacity of the inner leaf negligible for this analy-sis. Insulation and inner leaf are modeled with surfacetransfer coefficients of 10−10 s/m and 0.7 W/m2K (anearly vapour tight insulated structure). The bricks aretaken 5 cm high and 9 cm thick, the mortar joints 1 cmhigh. A grid refinement analysis points out that thesmall-scale geometry can be accurately simulated with198 nodes. This results in 17523 required nodes for thelarge-scale simulations though. Two year-intervals aresimulated from which the first is assumed transitional.Hourly design reference year climate values for Essen(Germany) are applied. Interior temperature and rela-tive humidity are kept at 20◦C and 50%, as the inves-tigation does not focus on interior climate influences.

As long as the masonry’s exterior surface remainsunsaturated, the moisture transfers in the componentare in equilibrium with the moisture exchanges at thesurface of the component. If the exterior surface attains

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Figure 6. Comparison of hourly moisture contents for the large- and small-scale simulation, for the average moisture contentsin brick and mortar.

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Figure 7. Distribution of moisture content differences between large- and small-scale simulation, for the average moisturecontents in brick and mortar, and for the surface moisture contents at the middle of the exterior surfaces of brick and of mortar.

saturation though, not all the supplied moisture canbe absorbed: the overload drains as surface runoff.Presently all runoff is assumed to disappear from thesystem, and does thus not form a moisture source forunderlying locations on the facade. The analysis herefocuses on internal, and not external redistribution ofmoisture and heat.

3.3.2 Comparison of resultsTo confirm the validity of the sampling approach,the moisture contents resulting from the large- andsmall-scale simulations are compared. The compari-son here is limited to a location at 9.52 m high on thefacade’s centre line. As can be noticed in Figure 2,this central upper region has the largest gradients inwind-driven rain exposure, and should thus yield thelargest internal moisture redistributions in the facade.

These should moreover be most visible at this highlocation, since moisture should drain from here tolower locations. A comparison for other locationsyields similar conclusions.

Figure 6 gives hourly values of the average mois-ture contents, in the brick and in the mortar joint. Forreasons of clarity, the values for the last four monthsonly are represented in the figure.

It is clear that the redistributions of moisturebetween different locations on the facade with dif-ferent wind-driven rain exposure are not significant:Figure 6 plainly indicates that deviations between thelarge- and the small-scale simulations of masonry arenegligible.A more in depth representation of the differ-ences is shown in Figure 7, which depicts a distributionof the large-scale/small-scale differences for the aver-age and surface moisture contents. Figure 7 illustrates

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that more than 90% of the deviations remain below1 kg/m3, more than 95% lower than 2 kg/m3. Less than5% of the deviations are larger, and such are due to aslight time-shift rather than a big internal redistribu-tion of moisture, as can be observed in Figure 6. Itcan thus be concluded that the sampling approach issufficiently accurate for masonry.

3.3.3 ConclusionsBased on a simulation study it was demonstrated thatthe spatial variation of the wind-driven rain does notyield any significant internal moisture redistribution ina single-layer masonry facade. The analysis involveda quite common ceramic brick, and a quite sorptivecement mortar. The application of a less sorptive mor-tar – or implementation of an interface resistancebetween brick and mortar joint – would only add tothe resistance against redistribution and thus yield thesame conclusions. While the study was limited to oneset of material and climate data, both are assumedsuitably arbitrary to allow generalization.

One important aspect has however been neglectedin this analysis: surface redistribution by runoff overthe exterior surface of the component. If such runoffis frequent or intensive, its influence on the moisturetransfer in the complete facade can not be neglected.The presented sampling approach preserves its valuethough: sampling can be applied for all periods of timewhere no runoff occurs, whereas a whole-facade sim-ulation must be executed during times of runoff. Thiskind of simulation is however something of the future,since such capacity is not yet provided by the currentcomputers or numerical methods.

4 CONCLUSIONS

The numerical simulation of moisture and heat transferin building components under atmospheric excitationis inherently demanding: it requires the numericalsolution of highly non-linear transfer equations drivenby strongly variable – temporally and spatially –boundary conditions. The hygrothermal simulation ofmasonry besides suffers from that material’s macro-heterogeneous structure: discretisation of every brickand mortar joint yields a fine mesh over the facadeplane, whereas a homogeneous material would toleratea rougher discretisation.

This paper shows that a macro-heterogeneous mate-rial, like masonry, does not allow homogenization,since no suitable ‘representative elementary volume’can be determined.

Instead this paper verifies that the spatial varia-tion of the wind-driven rain exposure over the facadeof a building does not result in any important mois-ture redistributions in the facade itself. Such impliesthat the hygrothermal response of masonry facadescan be accurately determined by simulation of smaller

subsections of the masonry, hence ‘sampling’the com-plete facade. In the limit, such subsections can bebrought down to the periodic unit of masonry.

While runoff – or moisture redistribution over thesurface of the facade – was not included in the sim-ulation, it was motivated that the sampling approachretains its applicability for such simulations.

ACKNOWLEDGEMENT

This paper results from the IWT 03175 SBOproject ‘Structural damage due to dynamic excita-tions: a multi-disciplinary approach’, funded by IWTVlaanderen (Institute for Promotion of Innovation byScience and Technology in Flanders). This financialsupport is gratefully acknowledged.

REFERENCES

Auriault, J.L. 1991. Heterogeneous medium. Is an equivalentmacroscopic description possible? International Journalof Engineering Science 29: 785–795.

Brocken, H.J.P. 1998. Moisture transport in brick masonry:the grey area between bricks. PhD thesis, TechnicalUniversity Eindhoven, Netherlands.

Janssen, H., Desadeleer, W., Blocken, B. & Carmeliet, J.2004. Rain penetration through thin layer mortar brickfacades with open vertical joints. Proceedings of the“13thInternational Brick and Block Masonry Conference”,Amsterdam, The Netherlands, July 4–7 2004.

Janssen, H., Blocken, B. & Carmeliet, C. 2005; Con-servative modeling of the moisture and heat transferin building components under atmospheric excitation.International Journal of Heat and Mass Transfer submit-ted for publication.

Janssen, H. & Carmeliet, C. 2005. Numerical optimizationof the simulation of moisture and heat transfer in buildingcomponents under atmospheric excitation. InternationalJournal of for Computational Methods in Engineeringsubmitted for publication.

Roels, S. 2002; Modelling unsaturated moisture transport inheterogeneous limestone. PhD thesis, Katholieke Univer-siteit Leuven.

Scheffler, G. & Grunewald, J. 2002. Interior capillary-active thermal insulation: a material development study.Building Research Journal 50: 153–168.

Sedlbauer, K. 2002. Prediction of mould growth byhygrothermal calculation. Journal of Thermal Envelopeand Building Science 25: 321–336.

Simonson, C.J., Salonvaara, M. & Ojanen, T. 2002. Heat andmass transfer between indoor air and a permeable andhygroscopic building envelope: part II – verificationand numerical studies. Journal of Thermal Envelope andBuilding Science 28: 161–185.

Zhu, J. & Mohanty, B.P. 2002. Upscaling of soilhydraulic properties for steady-state evaporation andinfiltration. Water Resources Research 39, 1178, doi:10.1029/2002WR001831.

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