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Building and Environment 85 (2015) 160e172

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Building and Environment

journal homepage: www.elsevier .com/locate/bui ldenv

Hygric properties of porous building materials: Analysis ofmeasurement repeatability and reproducibility

Chi Feng a, b, *, Hans Janssen b, Ya Feng c, Qinglin Meng d

a Institute of Building Environment and Energy Efficiency, China Academy of Building Research, Beijing 100013, PR Chinab KU Leuven, Department of Civil Engineering, Building Physics Section, Kasteelpark Arenberg 40, 3000 Leuven, Belgiumc China Southwest Architectural Design and Research Institute Corp. LTD, Chengdu 610041, PR Chinad Building Environment and Energy Laboratory, State Key Laboratory of Subtropical Building Science, South China University of Technology, Wushan,Guangzhou 510641, PR China

a r t i c l e i n f o

Article history:Received 20 October 2014Received in revised form28 November 2014Accepted 29 November 2014Available online 9 December 2014

Keywords:Porous building materialsHygric propertiesError analysisRepeatability and reproducibility

* Corresponding author. Institute of Building EnviroChina Academy of Building Research, Beijing 1013240305046.

E-mail address: fengchi860602@gmail.com (C. Fen

http://dx.doi.org/10.1016/j.buildenv.2014.11.0360360-1323/© 2014 Elsevier Ltd. All rights reserved.

a b s t r a c t

Material properties are crucial input parameters for the analysis of heat, air and moisture transferphenomena in built environment. However, many round robin tests reveal that the measurements onmaterial properties e especially hygric properties e have poor reproducibility. Thus the measurementand data analysis methods should be questioned, and the currently available databases for materialproperties are not perfectly reliable.

In this paper we aim at analyzing the material errors, repeatability errors, between-lab errors andreproducibility errors involved in the determination of hygric properties of porous building materials.The same materials as those used in the EC HAMSTAD project e autoclaved aerated concrete, calciumsilicate board and ceramic brick e are chosen as target materials in our tests to facilitate error analysis.Static gravimetric tests, cup tests, capillary absorption tests, vacuum saturation tests and pressure platetests have been repeated three times under repeatability conditions. Then the experimental results areanalyzed in combination with the EC HAMSTAD report to calculate various errors. Results show thatdifferent materials have different heterogeneity errors, which can hardly be avoided. Moreover, ingeneral these tests have excellent repeatability, indicating that under proper control the tests themselvesare trustworthy. However, the large between-lab errors and the subsequent poor reproducibilitydemonstrate that in different labs the experimental procedures, condition controls, as well as dataprocessing methods can deviate significantly. As a result, stricter and more detailed instructions areneeded to improve the reproducibility of the tests for determining the hygric properties of porousbuilding materials.

© 2014 Elsevier Ltd. All rights reserved.

1. Introduction

1.1. Background

Moisture transfer is one of the most classic topics in buildingphysics. Many issues, such as indoor air quality [1e3], the servicelife of building components [4e6], and the energy efficiency ofbuildings [1,3,7,8] are all closely related to moisture transferprocesses.

nment and Energy Efficiency,0013, PR China. Tel.: þ86

g).

To analyze moisture related phenomena, the hygric propertiesof materials are indispensable input parameters. Large scale cam-paigns aiming at the determination of the hygric properties ofporous building materialse such as EC HAMSTAD [9], IEA Annex 24[10] and ASHRAE Research Project 1018-RP [11] e started out abouttwo decades ago and have obtained encouraging achievements.Relatively complete databases have been established in westerncountries.

Unfortunately, these databases are not flawless. One of the mostchallenging dilemmas is the fact that the test results of the samematerial can be quite dissimilar in different labs, as revealed bymany round robin tests. For instance, in the EC HAMSTAD project,six labs participated in the round robin tests for various materialproperties of autoclaved aerated concrete (AAC), calcium silicate

C. Feng et al. / Building and Environment 85 (2015) 160e172 161

board (CS), and ceramic brick (CB). The outcomes demonstratedthat non-negligible deviations exist between the results fromdifferent labs, especially for the actual hygric properties [9].Another case in point is the IEA Annex 41 project. In its Subtask 2,14participating labs measured the hygroscopic properties e sorptionisotherms and vapor permeabilities e of uncoated and coatedgypsum board. Again the results from different labs showedimpressive divergences [12].

The poor reproducibility of hygric properties exerts a negativeimpact on both scientific research and engineering practice, as itposes a threat to the reliability of any heat-air-moisture (HAM)analysis. For instance, to reliably predict a drying process, sorptionisotherms and vapor permeabilities should be determined within5% and 20% uncertainties, respectively [11]. These requirements,however, can hardly be fulfilled in view of the currently poorreproducibility in measurements. Worse still, a drying process is arelatively simple issue, implying that other more complicated HAMprocesses may require even more accuracy in material properties.

The problem of unsatisfactory reproducibility may have variousroots, such as materials' heterogeneity, test methods' inherentuncertainty, variant faculty and facilities, as well as differences inexperimental procedures and data analysis methods. A better un-derstanding of these errors is needed in order to identify the keyproblem and formulate solutions to it. Before articulating the ob-jectives of the paper, we first shortly introduce the error analysisused in this paper.

1.2. Basics for error analysis

Errors exist in all measurements, as no test is perfectly reliable.Accuracy describes the reliability of measured results, and it coverstwo aspects e trueness and precision. Trueness represents thecloseness between the average result and the true or acceptedreference value, and it is often expressed in terms of bias. Precisionstands for the agreement between multiple test results, and it isoften expressed in terms of standard deviation [14]. Trueness andprecision can be distinguished with the help of Fig. 1. Obviously,trueness relates to systematic errors (esystematic), while precisiondescribes random errors (erandom).

More often than not, trueness can only be estimated because thetrue value is often unavailable, unless a generally accepted refer-ence value has been prescribed. Consequently, there are not manystudies about trueness. On the contrary, precision is much morefrequently analyzed, since it involves only measured results. It isinfluenced bymany factors. First and foremost, the heterogeneity ofmaterials should be taken into account. Some materials e such asCS e are well known for their homogeneity. So the results fromduplicate CS samples in the same test can be very close to eachother. Other materials e such as CB e are not so homogeneous,leading to greater differences.

Fig. 1. Basic concepts for error

Besides the errors rooted in the materials' heterogeneity, thereare some other influence factors that should be considered. Ac-cording to the ISO 5725 standard [14], these factors include:

a) the operator;b) the equipment used;c) the calibration of the equipment;d) the environment (temperature, RH…);e) the time elapsed between measurements.

While not being mentioned in the standard, we assume that

f) the overall experimental procedure plays an important roleas well.

If the same samples are used and all factors from a) to f) remainunchanged in replicate tests (a short period of time applies to factore)), then these test conditions are defined as repeatability condi-tions and the standard deviation of the results is defined as therepeatability error (erepeatability). If the same samples are used but allthese factors are different, then reproducibility conditions andreproducibility error (ereproducibility) are obtained accordingly [14].Obviously, reproducibility and repeatability are two extremes ofprecision.

The round robin tests carried out in various labse such as the ECHAMSTAD [9] and IEA Annex 41 [12]mentioned abovee are perfectexamples related to reproducibility, except that the materials'heterogeneity is normally not included in reproducibility but un-avoidable in such round robin tests, because usually differentsamples are used by different labs. Repeatability, on the other hand,has not received much attention. One of the key reasons may bethat tests on hygric properties are extremely time consuming, andreplicate tests under repeatability conditions are even moreexhausting.

With (explicit or implicit) knowledge on systematic and randomerrors, we can express a measurement result as:

x ¼ xtrue=ref þ esystematic þ erandom (1)

where x is a measured value and xtrue/ref the true or reference value.esystematic cannot be determined easily, and it is not our primary

concern in this study. For more insight into erandom, we can developit further, as is illustrated in Fig. 1:

erandom ¼ ematerial þ ewithin þ ebetween (2)

where ematerial is the error caused bymaterials' heterogeneity, ewithin

the random error caused within a lab (such as the influence oftemperature and RH fluctuations of ambient air on the staticgravimetric test for sorption isotherms), and ebetween the between-

analysis (Ref. [13] for a)).

C. Feng et al. / Building and Environment 85 (2015) 160e172162

lab error (such as the influence of different average RHs of ambientair in different labs on the weighing results).

ebetween can be calculated from the results in round robin tests bycomparing the results of individual labs and the overall results.ematerial cannot be obtained directly. However, under repeatabilityconditions no material error is involved, and ewithin is exactly ere-peatability. Then by comparing the errors from duplicate samples anderepeatability we can derive ematerial. After knowing erepeatability andebetween, ereproducibility can be easily calculated because it is simply acombination of them [14]. Clearly, ereproducibility is always greaterthan erepeatability.

So far we have briefly introduced the basic concepts in erroranalysis. The detailed calculation methods for various errors will bediscussed in Section 2.3.

1.3. Objectives

This paper aims at investigating the errors in the determinationof hygric properties of porous building materials, especially therepeatability and reproducibility errors. Previously, a lot of researchwork with insightful interpretations has been reported to analyzethe results from round robin tests [15e19]. It has been revealed thatthe hygric properties measured on the same material but indifferent labs can vary significantly. However, without informationon material and repeatability errors, it is impossible to tell whetherthese great discrepancies between different labs stem frombetween-lab errors or within-lab deviations. The significance ofthis research is that, based on the combination of repeatability tests(our own) and reproducibility tests (EC HAMSTAD), all types oferrors e material errors, between-lab errors, repeatability errorsand reproducibility errorse involved in the determination of hygricproperties are quantitatively distinguished for the first time.

In the following sections, we will:

a) introduce the experimental methods for performing ourrepeatability tests, as well as the statistical methods foridentifying various errors (Section 2);

b) present our experimental results, and calculate material andrepeatability errors (Section 3);

c) analyze reproducibility errors by combining our own resultsand the EC HAMSTAD report (Section 4);

d) summarize our findings and draw final conclusions (Section5).

2. Materials and methods

The same porous building materials as those used in the ECHAMSTAD project e autoclaved aerated concrete (AAC), calciumsilicate board (CS), as well as ceramic brick (CB) e are chosen astarget materials in our tests. This choice facilitates our furtheranalysis for all sorts of errors, because the results in the EC HAM-STAD report can hence be cited.

In the following parts of this section, we will first explain ourarrangements of various tests for determining different hygricproperties. Then the differences of basic properties for materialcharacterization are analyzed in order to compare the materialsused by us and in the EC HAMSTAD project. Finally the detailedcalculation methods for identifying various errors are described.

2.1. Experimental arrangement

Five classic tests e namely static gravimetric tests, cup tests,capillary absorption tests, vacuum saturation tests and pressureplate tests (Fig. 2)e have been repeated 3 times under repeatabilityconditions. All masses are determined with balances reading

0.001 g (for static gravimetric tests, capillary absorption tests,vacuum saturation tests and pressure plate tests) or 0.01 g (for cuptests). All samples' dimensions are measured with calipers reading0.01 mm.

To determine the dry mass, all samples are dried in a ventilatedoven supplied with dry air at 70 �C for at least 7 days. When 3successive weighing results at intervals of at least 48 h show a non-monotonous evolution with a relative standard deviation below0.1%, we assume that the samples have been thoroughly dried. Theaverage of these 3 weighing results is taken as the dry mass. Thedrying and weighing methods adopted here are detailedlydescribed and validated in Refs. [20e22].

2.1.1. Static gravimetric testsStatic gravimetric tests are performed to obtain the equilibrium

moisture content (u, kg/kg) for adsorption isotherms based on theISO 12571 standard [23] and our previous research [22]. Fourdifferent saturated salt solutions e LiCl, Mg(NO3)2, KCl and K2SO4 e

are used to maintain stable RHs in desiccators, which are 11%, 53%,84% and 97%, respectively (at 25 �C). In each desiccator, 5 previouslydried samples of each material (size: 5 cm � 5 cm � 1 cm) are putinside for adsorption tests. The criterion for equilibrium is the sameas that used in dry mass determination.

When one test is over, all samples are dried in the oven againand then put back to their original desiccators for another test. Theaverage temperature in the desiccators during 3 replicate tests is25.7 ± 1.0 �C, 25.8 ± 1.0 �C and 26.2 ± 1.0 �C, respectively. Suchlimited differences in temperature can be neglected.

2.1.2. Cup testsCup tests are performed to determine the vapor permeability (d,

kg/msPa) of thesematerials. The ISO 12572 standard [24] is applied,as the EC HAMSTAD project did. However, modifications on cupsare made in our tests. Samples are sealed on detachable non-permeable lids to glass cups so that they can be recycled to fulfillrepeatability conditions: the same samples should be used duringall replicate tests.

Similarly, saturated salt solutions are used to control the RH. Fordry cup tests, LiCl and Mg(NO3)2 are used to sustain a RH pair of11%e53%, while for wet cup tests, Mg(NO3)2 and K2SO4 are used forRH 53%e97%. Samples are cut into sizes of 10 cm in diameter and4 cm in thickness (AAC and CS), or 8 cm in diameter and 2 cm inthickness (CB). For both dry cup and wet cup tests, 3 duplicatesamples of each material are used. Sealed samples with lids arevacuum dried at room temperature first (the paraffin sealant meltsat raised temperature) and afterward pre-conditioned for 2 weeksat RH 11% and 53% for dry cup and wet cup tests, respectively. Thetests are stopped when 7 successive weighing results at intervals ofat least 3 days give excellent linear fitting results (R2 > 0.99).

After one test, samples with lids are vacuum dried, pre-conditioned and put back to their original conditions to startanother replicate test. The average temperature during 3 replicatetests is 25.7 ± 1.0 �C, 25.7 ± 1.0 �C and 25.8 ± 1.0 �C respectively, andcan be considered the same.

2.1.3. Capillary absorption testsCapillary absorption tests are carried out for the capillary ab-

sorption coefficient (Acap, kg/m2s0.5) and capillary saturated mois-ture content (wcap, kg/m3) according to the ISO 15148 standard [25].Samples are cut into the same bottom size (8 cm � 4 cm) butdifferent heights (6 cm, 15 cm and 12 cm for AAC, CS and CB,respectively). For each material, 5 duplicate samples are used. Theyare wrapped with plastic cling film on all surfaces except for thebottom to minimize evaporation. But to facilitate air evacuation,two small holes are left at the top. To avoid capillary uptake

Fig. 2. Tests conducted for determining hygric properties.

C. Feng et al. / Building and Environment 85 (2015) 160e172 163

between the sample and the wrap, the bottom 1 cm of the lateralsides is left unwrapped.

Before the tests, oven dried samples are cooled down in adesiccator with desiccant at room temperature, and are then placedinto a shallow water basin with a metal support for 1-D free wateruptake. They are regularly taken out of the water for mass deter-mination. The tests are finished after obtaining at least 5 points forthe 2nd stage.

After the test, samples are dried in the oven for another replicatetest. The water temperature during 3 replicate tests fluctuates at22.5 ± 0.5 �C (about 2 �C lower than the temperature of ambient airbecause of evaporation), and is considered stable.

2.1.4. Vacuum saturation testsVacuum saturation tests are done based on the ASTM C1699

standard [26] to determine open porosity (F, %) and bulk density(rbulk, kg/m3). Samples are cut into the same size of5 cm � 5 cm � 1 cm. For each material, 5 duplicate samples areused.

During each test, initially oven-dried samples are first placed ina vacuum desiccator at below 20 mbar air pressure for 4 h toevacuate all air from their open pores. Then distilled water isallowed in gradually, until the water level is 5 cm above the sam-ples' top. After that the pressure of the whole system is returned tonormal. 7 days later samples are taken out of the water andweighed underwater and in the air.

After all these processes, samples are dried in the oven foranother replicate test. The average water temperature during 3replicate tests is 24.4 ± 0.5 �C, 24.3 ± 0.5 �C and 24.4 ± 0.5 �C,respectively, and is considered the same.

It should be noted here that vacuum saturation tests can provideopen porosity, vacuum saturated moisture content, bulk densityandmatrix density. Although open porosity is not a hygric property,it is proportional to vacuum saturated moisture content (the coef-ficient is water density). Thus we take open porosity here instead ofvacuum saturated moisture content. Moreover, bulk density isneither a hygric property. It is, however, one of the most importantmaterial properties. So we also include it here. Last but not least,matrix density can be calculated from open porosity and bulkdensity, but it is seldomly used in practice. Thus it is not analyzed inthis paper.

2.1.5. Pressure plate testsPressure plate tests are carried out to determine the equilibrium

moisture content (u, kg/kg) for the water retention curves accord-ing to the ISO 11274 standard [27]. Samples of all three materialshave the same size of 5 cm � 5 cm � 1 cm, and 3 duplicate samplesare used to represent each material. During the tests, samples arepre-conditioned to capillary saturation and then placed on thesame pre-saturated ceramic plate in the pressure pot. Pre-saturatedcellulose film is used as the separating material between thesamples and the kaolin layer. Due to the limited time and therequired repeatability conditions, we apply only one pressure(3 bar) instead of a series of sequential pressures. After 7 dayssamples are taken out of the system and weighed.

After each test, samples are dried in the oven and then pre-conditioned to capillary saturated state. Then the same experi-mental process described above is repeated. The temperature ofambient air in the room changes between 22 �C and 25 �C during 3replicate tests. The influence of these temperature fluctuations isassumed negligible.

2.2. Material differences

Further below, we will combine results from our own repeat-ability tests and EC HAMSTAD's reproducibility tests. For this to bepermitted, our and EC HAMSTAD's materials need to be sufficientlysimilar. The materials used by us and in the EC HAMSTAD projectare of same kind, but not necessarily identical. To verify that thesetwo sets of experimental results are compatible with each other, wecompare the basic properties for material characterization [9] byevaluating the differences in their respective mean values via in-dependent T-tests [28]. The mean values of the two groups of re-sults are statistically the same if the calculated significance (a) isgreater than a certain level (0.05 in this paper), otherwise they arestatistically different. The average values of the various propertiesand the statistical results are summarized in Table 1.

Clearly, for AAC all these characteristic properties are statisti-cally the same. So we assume the AAC used by us and in the ECHAMSTAD project is very similar. For CS, although 3 out of 5properties are statistically different, the differences are still negli-gibly small in many cases, and we accept the assumption of ma-terial similarity, too. For CB this assumption is not perfectly valid,

Table 1Comparison of the materials used by us and in the EC HAMSTAD project.

Material property AAC CS CB

Ours HSa a Ours HS a Ours HS a

rbulk(kg/m3) 462.4 452.7 0.231 259.8 267.1 <0.001 2081.7 2014.4 <0.001F(%) 82.5 81.2 0.126 90.1 89.1 0.052 20.9 23.5 <0.001Acap(kg/m2s0.5) 0.027 0.032 0.156 1.06 1.21 0.005 0.052 0.149 <0.001wcap(kg/m3) 301.1 287.9 0.495 752.1 801.7 0.001 107.6 144.6 <0.001m(from dry cup tests) 8.54 7.89 0.514 2.12 3.49 0.155 23.02 14.44 0.096

a The EC HAMSTAD project is short as HS in this table.

C. Feng et al. / Building and Environment 85 (2015) 160e172164

since almost all the characteristic properties are statisticallydifferent. However, results from CB still provide useful informationand act as valuable references.

2.3. Detailed error calculation methods

The most important errors for our analysis in this paper areematerial, erepeatability and ereproducibility. These will be expressed asrelative standard deviations rsmaterial, rsrepeatability and rsreproducibility,respectively. In this section we will explain how to calculate them.

To facilitate later analysis, let's denote the test result of sample iin test j in lab k as xki;j, where i, j and k range as follows:

i2½1;p�; j2½1; q�; k2½1; r� (3)

In these, p, q and r respectively represent the number of sam-ples, tests and labs. Be aware that the number of samples and tests

Fig. 3. Calculation process for mater

is not necessarily the same for all labs. Moreover, some key pointsin our expressions should be explained here:

a) Average, standard deviation and relative standard deviation areexpressed as e, s and rs, respectively;

b) The letter in the bracket indicates towhich factor the calculationis performed. For instance, the letter j in the bracket of xx1i;j ðjÞmeans the average result is taken for replicate tests (j);

c) If more than one letter is in the bracket, then their order cor-responds to the order of calculations. For instance, i comesbefore k in rs

xki;1ði; kÞ, implying that we calculate the average

result of duplicate samples (i) first, and calculate the relativestandard deviation for all labs (k) next.

2.3.1. The calculation methods for rsmaterial and rsrepeatabilityTo calculate rsmaterial and rsrepeatability, only results obtained under

repeatability conditions are needed. Thus we just refer to the

ial error and repeatability error.

Fig. 4. Calculation process for reproducibility error.

Fig. 5. Repeatability of static gravimetric tests for u (5 duplicate AAC samples for eachRH).

C. Feng et al. / Building and Environment 85 (2015) 160e172 165

results from our repeatability tests at this moment. Since only onelab is involved here (r ¼ k ¼ 1), all the results can be expressed asx1i;j.

The detailed calculation process is illustrated in Fig. 3. The firststep is to obtain the relative standard deviation of each sample(rsx1i;j ðjÞ) over replicate tests through Eq. (4)e(6). Then rsrepeatabilitycan be derived by taking average for all samples (Eq. (7)). The nextstep is to calculate the relative standard deviation of all results(rsx1i;j ði; jÞ) through Eq. (8)e(10). Finally rsmaterial can be achieved byremoving rsrepeatability from rsx1i;j ði; jÞ according to Eq. (11).

In our case for repeatability study, r¼ k¼ 1, q¼ 3 and p¼ 3 (cuptests and pressure plate tests) or 5 (static gravimetric tests, capillaryabsorption tests and vacuum saturation tests).

2.3.2. The calculation methods for rsreproducibility and other errorsUnlike rsmaterial and rsrepeatability, to obtain rsreproducibility we need

the results under both repeatability conditions and reproducibilityconditions. The analysis of the results from repeatability tests hasalready been introduced before, and here we concentrate onanalyzing results from reproducibility tests.

Since repeatability tests are hardly included in round robin tests(such as in the EC HAMSTAD project, whose results are going to beanalyzed in combination with our repeatability tests for deriving

rsreproducibility), the repetition number is fixed as q ¼ j ¼ 1. Conse-quently, the test result of the sample i in lab k can be denoted as xki;1.It should however be noted that the numbers of duplicate samplesare not necessarily the same in different labs.

Fig. 6. Repeatability of cup tests for d (3 duplicate AAC samples for each condition).

Fig. 7. Repeatability of capillary absorption tests (5 duplicate AAC samples).

C. Feng et al. / Building and Environment 85 (2015) 160e172166

Comparatively, the calculation process for rsreproducibility is morecomplicated, as illustrated in Fig. 4. First, we have to calculate the

average result of all duplicate samples in a single lab (xki;1ðiÞ) andtheir relative standard deviation (rsxki;1 ðiÞ) through Eq. (12)e(14).

Then we are able to obtain the relative standard deviation of xki;1ðiÞfor all labs through Eq. (15)e(17), as well as the average rsxki;1 ðiÞ of alllabs through Eq. (18). The next step is to derive between-lab error

rsbetween by removing rsxki;1 ði; kÞ from rsxki;1

ði; kÞ according to Eq. (19).

Finally, we can combine rsrepeatability and rsbetween to get rsreproducibilitybased on Eq. (20) [14].

Fig. 8. Repeatability of vacuum saturati

It is worth mentioning that in this paper we express errors interms of relative standard deviations rather than standard de-viations. This doesn't influence the calculation, but is advantageousfor comparison [29].

For the EC HAMSTAD project, q ¼ j ¼ 1 while r ¼ 5 or 6 (InTable 3, if all labs’ results are used, then r ¼ 6. Otherwise it is 5.). pvaries from 2 to 26 according to different materials, labs and tests.

3. Material and repeatability errors

In this sectionwewill analyze the experimental results obtainedfrom our replicate tests under repeatability conditions.

on tests (5 duplicate AAC samples).

Fig. 9. Repeatability of pressure plate tests for u at 3 bar (3 duplicate AAC samplesfrom capillary saturation).

C. Feng et al. / Building and Environment 85 (2015) 160e172 167

As a first step, we take AAC as an example to illustrate the resultsobtained from static gravimetric tests, cup tests, capillary absorp-tion tests, vacuum saturation tests and pressure plate tests,respectively (Figs. 5e9). In all these figures, test results fromreplicate tests are represented in different colors. The CS and CBsamples show similar tendencies as the AAC samples in these tests,and their results are not shown here.

From the figures above, we can easily tell that the repeatabilityof all these tests is generally very good. As a further step, we derivematerial errors (rsmaterial) and repeatability errors (rsrepeatability)based on the methods described in Section 2.3. The calculated re-sults are summarized in Table 2. It should be noted here thatoccasionallyrsx1i;j ðj; iÞ � rsx1i;j ði; jÞ, indicating that the errors caused bymaterials’ heterogeneity are clouded by repeatability errors so thatthey cannot be distinguished. In that case, no rsmaterial is provided inTable 2.

As is clearly reflected in Table 2, rsrepeatability is generally verylimited when compared with rsmaterial. To finalize our analysis inthis section and to have a better understanding of rsrepeatability, wemake analysis from one test to another.

3.1. Static gravimetric tests

The u of CB is less than 0.1% kg/kg even at a RH of 90%. For suchweakly hygroscopic materials the results determined by static

Table 2Material and repeatability errors (%).

Test Property Material rsmaterial rsrepeatability

Static gravimetric tests u(RH 11%) AAC 2.17 1.85CS 5.80 2.69CB e 105.39

u(RH 53%) AAC 2.43 2.81CS 3.86 1.49CB 16.12 8.87

u(RH 84%) AAC e 11.74CS e 18.19CB 13.52 10.34

u(RH 97%) AAC e 11.87CS e 11.03CB 16.57 6.51

Cup tests d(RH 11%e53%) AAC 5.88 6.02CS e 1.87CB 16.70 1.62

d(RH 53%e97%) AAC 4.02 1.29CS 1.24 2.82CB 17.08 3.74

gravimetric measurements are of limited reliability. So we mainlyfocus on the results from AAC and CS samples.

For both AAC and CS, rsmaterial is very small throughout thewhole RH range and can be neglected in most cases. However,although CS is famous for its homogeneity, in Table 2 the rsmaterial

for CS is bigger than the rsmaterial for AAC. This may be because CShas lower u than AAC at the same RH. Moreover, in our tests CSsamples have smaller dry mass (the same sample size but smallerbulk density). Bringing two factors together, it is understandablethat the mass change for CS samples in static gravimetric tests isless discernable, leading to larger rsmaterial. This phenomenonfurthermore implies that the static gravimetric test may not beperfect for moderate hygroscopic materials with small densitiesbecause of limited balance resolution (not to mention weakly hy-groscopic materials such as CB). Although this shortcoming can bepartly overcome by increasing samples’ size, the time needed forreaching equilibrium also increases as a side effect, calling for acompromise [22].

Interestingly, rsrepeatability depends on RH. When the RH isbelow 80%, rsrepeatability is very limited (less than 3%). However,when the RH rises above 80%, rsrepeatability rockets dramatically.This can be attributed to the fact that normally sorption curvesrise slowly during low and intermediate RH ranges, but soar inthe high RH range. In the replicate tests, it is impossible tomaintain the RH in the desiccator at exactly the same value (a1%e2% RH fluctuation is unavoidable). Such RH fluctuationsinevitably exert an influence on u. Due to different sensitivities indifferent RH ranges, the repeatability shows the RH dependenttendency.

3.2. Cup tests

CS samples enjoy extremely low rsmaterial. This is mainly becauseof the well-known homogeneity of CS, and its large d also plays arole. The rsmaterial for AAC is slightly larger because of greater het-erogeneity and smaller d, but the errors are still negligible. Moreimportantly, the small rsmaterial also confirms that samples’ sealingis very good in our experimental setup. Otherwise leakage shouldhave obviously increased rsmaterial.

A closer look reveals that rsrepeatability changes a bit accordingto different conditions. However, the largest value is merely 6% e

a very limited level. This proves that cup tests themselves arestable, and the experimental conditions can be controlled verywell.

Test Property Material rsmaterial rsrepeatability

Capillary absorption tests Acap AAC 7.06 8.24CS 0.40 1.61CB 15.24 2.13

wcap AAC 3.75 1.58CS 0.67 0.11CB 4.26 0.32

Vacuum saturation tests rbulk AAC 0.93 0.44CS 0.23 0.26CB 0.91 0.06

F AAC 0.09 0.38CS e 0.17CB 4.08 0.19

Pressure plate tests u(3 bar) AAC 2.15 0.40CS e 4.13CB 17.12 25.75

C. Feng et al. / Building and Environment 85 (2015) 160e172168

3.3. Capillary absorption tests

CS samples again show very limited rsmaterial. On the contrary, CBsamples show the largest rsmaterial, especially for Acap. This may bebecause of the commonly observed internal defects of CB, whichmay influence the speed of capillary absorption.

Similarly, rsrepeatability is always negligibly small, whichever Acap

or wcap is concerned. This is, of course, because material hetero-geneity is not involved in Ref. rsrepeatability. And again, it has beenproven that under proper control and handling, it is capable ofobtaining consistent results from capillary absorption tests.

3.4. Vacuum saturation tests

We find the smallest rsmaterial and rsrepeatability in all tests,whatever the nature of the errors. This is because vacuum satura-tion tests are very reliable e the test procedures are explicitlydefined, and no significant influence factor e such as temperature,weighing, data processing and pressure e exists.

3.5. Pressure plate tests

We recall our experience that pressure plate tests are verydifficult to perform, albeit that the test method is quite mature insoil science [30,31]. The keys are the hydraulic contact and airtightness in the system. However, once the requirements are

Table 3Errors of tests for hygric properties (%).

Test Property Material

Static gravimetric tests u (RH 11%) AACCSCB

u(RH 53% for us and 33% for HSa) AACCSCB

u(RH 84% for us and 80% for HS) AACCSCB

u (RH 97%) AACCSCB

Cup tests d(RH 11%e53% for us and 0%e50% for HS) AACCSCB

d(RH 53%e97% for us and 53%e86% for HS) AACCSCB

d(RH 53%e97% for us and 86%e94% for HS) AACCSCB

Capillary absorption tests Acap AACCSCB

wcap AACCSCB

Vacuum saturation tests rbulk AACCSCB

F AACCSCB

Pressure plate tests u(3 bar for us and 3.16 bar for HS) AACCSCB

a The EC HAMSTAD project is short as HS in this table.b TNO, CTU, TUD and UE stand for TNO Building and Construction Research (the Nether

(Germany) and University of Edinburgh (UK), respectively.

fulfilled, tests results become very stable for AAC and CS, as is re-flected in Table 2. For CB the scatters are large, but this should bemainly attributed to its very limited equilibrium moisture content(less than one tenth of AAC and CS).

We have now analyzed our experimental results by derivingrsmaterial and rsrepeatability directly from the replicate tests underrepeatability conditions. It can be concluded here that rsrepeatability isclose to or in the same order of magnitude as rsmaterial, indicatingthat these test methods are reliable and are capable of producingclose results in any single lab. The availability of rsrepeatability formsan indispensable foundation for obtaining rsreproducibility in the nextsection, where we will combine our test results together with thereported results from the EC HAMSTAD project for deeper analysis.

4. Reproducibility errors

By combining the results from our own measurements (dis-cussed in the previous section) and from the EC HAMSTAD project[9], we are able to obtain all sorts of errors concerning the deter-mination of hygric properties. The detailed errors are in listedTable 3. In this section, we will focus on the reproducibility errors(rsreproducibility) involved in round robin tests.

The test temperature during our measurements is very close tothat in the EC HAMSTAD project. Thus we assume the influence oftemperature on our analysis is negligible. Moreover, when addi-tional tests are reported in the EC HAMSTAD project, these results

From our tests From EC HAMSTAD project

rsmaterial rsrepeatability rsbetween rsreproducibility Original results discardedb

2.17 1.85 38.80 38.845.80 2.69 e e TNO

e 105.39 Unavailable (not tested)2.43 2.81 23.32 23.493.86 1.49 31.38 31.42

16.12 8.87 e e TNOe 11.74 22.57 25.44e 18.19 31.38 36.2713.52 10.34 e e

e 11.87 23.95 26.73e 11.03 43.22 44.6116.57 6.51 Unavailable (not tested)5.88 6.02 17.82 18.81

e 1.87 39.59 39.6316.70 1.62 45.28 45.314.02 1.29 20.68 20.721.24 2.82 47.60 47.68

17.08 3.74 42.96 43.124.02 1.29 e e CTU1.24 2.82 41.67 41.77

17.08 3.74 e e TUD7.06 8.24 e e

0.40 1.61 3.79 4.12 CTU15.24 2.13 14.43 14.583.75 1.58 10.38 10.500.67 0.11 2.52 2.52 CTU4.26 0.32 6.90 6.910.93 0.44 e e

0.23 0.26 0.50 0.56 CTU0.91 0.06 0.49 0.490.09 0.38 1.84 1.88

e 0.17 0.82 0.834.08 0.19 e e

2.15 0.40 Unavailable (not tested)e 4.13 0.50 4.1617.12 25.75 40.82 48.26 UE

lands), Czech Technical University (Czech Republic), Technical University of Dresden

Fig. 10. Various errors of static gravimetric tests for u.

C. Feng et al. / Building and Environment 85 (2015) 160e172 169

(instead of the results from original tests) are used for calculations.Last but not least, while the results from the EC HAMSTAD reportare used for the analysis of a specific property, the most dubiousone (the average value from a lab) is sometimes discarded ac-cording to the Grubbs's test (a ¼ 0.05) [32]. This is because suchoutliers are largely due to problematic handling in the measure-ments, and should be avoided. These discarded results are indicatedin Table 3.

During the calculation, sometimes rsxki;1 ði; kÞ is greater than

rsxki;1

ði; kÞ, thus rsbetween (and subsequently rsreproducibility) cannot be

calculated. In addition, the rsreproducibility of CB in static gravimetrictests at RH 11% and 97%, as well as the rsreproducibility of AAC inpressure plate tests at 3 bar are also unavailable, because thesemeasurements are not performed in the EC HAMSTAD project.

For a better understanding of the magnitude of rsreproducibility, weput rsmaterial, rsrepeatability, as well as rsreproducibility together, as illus-trated in Figs. 10e14 for various tests.

As can be clearly seen from figures above, rsreproducibility is ingeneral impressively great, reflecting that there are conspicuousdifferences in experimental handling and/or data processing invarious labs. Worse still, these discrepancies are even greater thanthe commonly assumed errors of material properties for sensitivityanalysis [33e35], indicating that the influence of inputting data onHAM analysis results might be underestimated previously.

Before continuing with the discussion of these tests, an impor-tant remark must be considered. The results from repeatabilityerrors are obviously dependent on the handling process. In ourtests we take special care to the measurements, thus the repeat-ability errors are under good control. However, even in case of lesscareful handling, the general tendency that repeatability errors arerelatively negligible should remain valid. Moreover, as is alreadyexplained in Section 1.2, repeatability and reproducibility errors are

two extremes of precision. Thus we can expect that if factors b) to f)listed in Section 1.2 remain the same but operators are different(the common practice in many labs), the errors should be in-between. By training operators systematically, the errors can bereduced.

4.1. Static gravimetric tests

As already explained, we just focus on hygroscopic materials eAAC and CS e for this test. At all RHs rsmaterial is negligibly small, sothere is no need for us to worry about it too much. Interestingly,unlike the RH dependent rsrepeatability, rsreproducibility just fluctuatesmoderately throughout the whole RH range. The reasons are mul-tiple. Besides the RH control in desiccators, one of themost possiblereasons may be the dry mass determination. Although in the ECHAMSTAD project the same oven temperature is prescribed, theRHs in the ovens (with different air supply) and ambient environ-ment, as well as the weighing methods may differ, causing signif-icant between-lab dry mass differences [20].

Another important influence happens during the weighing pro-cess for moist samples. Whenever samples are taken out of desic-cators, themoisture transfer with ambient air will occur, exerting animpact on the results. Thus weighing protocols do matter a lot, andnecessary measures should be taken [20]. The RH in desiccators isalso disturbed after opening, needing hours for recovery. Accordingto our experience, 3e7 days are the optimumobservation frequency,consistent with other publications on this issue [36].

4.2. Cup tests

In our measurements, dry cup and wet cup tests are carried outat RH 11%e53% and 53%e97%, respectively. In the EC HAMSTADproject, dry cup tests are at RH 0%e50%, while wet cup tests have

C. Feng et al. / Building and Environment 85 (2015) 160e172170

two sets of RH pairs: 53%e86% and 86%e94%. Although the RHsettings are not exactly the same, results from our measurementsand from the EC HAMSTAD report should still be comparable.

On average, the rsreproducibility of cup tests is almost one orderlarger than the corresponding rsmaterial and rsrepeatability, whateverthe test condition is. The poor rsreproducibility reveals huge deviationsbetween different labs. Since no complicated measurements ordata processing procedures are involved, the experimental set upshould be blamed. Cup shapes and sizes, air layer thicknesses,sample dimensions, sealing, as well as RH controls are not uniformamong participants. These all inevitably cause discrepancies. Of all

Fig. 11. Various errors of cup tests for d.

these factors, the impact from sealing must be taken into specialaccount. As has already been proved, different sealants and sealingmethods give rise to different leakage conditions, and may finallylead to conspicuous variations between labs [16]. Another crucialfactor is the RH deviation. For instance, one of the wet cup RHsettings in EC HAMSTAD is 86%e94%, meaning an 8% RH difference.However, according to our experimental experience, a 1%e2% RHdeviation from the reference RH (such as the values in the ISO12571:2000(E) standard [23]) is not unusual. Consequently anoverall 3%e4% RH uncertainty is entirely possible, and a 30% oreven 50% relative difference in the calculation of d may subse-quently occur in this case.

4.3. Capillary absorption tests

In capillary absorption tests 3 issues may play an important rolein determining rsreproducibility: handling, temperature control anddata processing. For handling, the initial moisture content will in-fluence Acap according to our experience. Moreover, the cling filmwrapped on the surfaces of samples may have an impact on wcap.Last but not least, the timing for weighing samples is obviouslygoing to exert an influence on both Acap and wcap. For temperaturecontrol, the actually water temperature may differ due to differentevaporation rates (corresponding to the experimental setup),although the ambient temperature is prescribed as 23 ± 1 �C in theEC HAMSTAD project. Temperature influences water's surfacetension and viscosity, and therefore changes Acap. This is predictedby the well known Lucas-Washburn equation [37,38]. For dataprocessing, this mainly affects AAC, which doesn't display a cleardistinction between the first and second absorption stage. Thus thechoice for effective data and the later calculations can be versatile,enlarging differences between labs.

4.4. Vacuum saturation tests

Unlike other tests, the rsreproducibility for both rbulk and F is, at lessthan 2%, amazingly satisfactory. The extraordinary rsreproducibilityreveals the possibility of obtaining uniform test results underreproducibility conditions, and gives us desired confidence.

4.5. Pressure plate tests

The rsrepeatability and rsreproducibility of pressure plate tests are veryclose to each other. This implies that the major contributor to rsre-producibility is rsrepeatability. For CS both sorts of errors are less than 5%and can be neglected. However, for CB the over 20% rsrepeatability andrsreproducibility must be considered seriously. This makes us doubtwhether the pressure plate test is suitable for all materials.

To sum up, rsreproducibility of tests for hygric properties is generallymuch greater than rsrepeatability. This reveals that between differentlabs impressive discrepancies lie in test procedures and/or dataanalysis method. It is of urgent need to specify more details forthese tests. As a preferable way, operators should be trainedsystematically.

5. Conclusions

This paper studies different errors involved in the determinationof hygric properties of autoclaved aerated concrete, calcium silicateboard and ceramic brick. Static gravimetric tests, cup tests, capillaryabsorption tests, vacuum saturation tests and pressure plate testshave been repeated under repeatability conditions for 3 times.Profound error analysis is performed by combining our results andthe results from the EC HAMSTAD project, where round robin tests

Fig. 12. Various errors of capillary absorption tests.

Fig. 13. Various errors of vacuum saturation tests.

C. Feng et al. / Building and Environment 85 (2015) 160e172 171

are carried out in 6 labs. For the first time, various sorts of errors areanalyzed quantitatively.

Specifically, several important conclusions have been reached:

a) Errors from materials' heterogeneity vary according to differenttests and conditions;

b) These tests have very good overall repeatability, indicating thatunder proper control tests themselves are reliable;

c) The large between-lab errors, as well as the consequent poorreproducibility, demonstrate that in different labs the

Fig. 14. Various errors of pressure plate tests for u.

experimental procedures, condition controls and data analysismay differ significantly, calling for stricter and more detailedprescriptions (especially for the static gravimetric test, cup testand pressure plate test).

Acknowledgments

This project is supported by National Natural Science Founda-tion of China (No. 51278478). The authors express sincere thanks toPatricia Elsen, Willem Bertels and Filip Vandenberghe in KU Leuvenfor their help in carrying out the experiments.

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Nomenclature (the most important symbols)

ematerial: material errorserepeatability: repeatability errorsebetween: between-lab errorsereproducibility: reproducibility errorserandom: random errorsesystematic: systematic errorsx: measured valuextrue/ref: true or reference valuexki;j : test result of sample i in test j in lab ka: statistical significancersmaterial: relative standard deviation for material errorsrsrepeatability: relative standard deviation for repeatability errorsrsbetween: relative standard deviation for between-lab errorsrsreproducibility: relative standard deviation for reproducibility errorsrbulk: bulk densityF: open porosityAcap: capillary absorption coefficientwcap: capillary saturated moisture contentd: vapor permeabilityu: equilibrium moisture content