experimental investigation of the variability of concrete durability properties.pdf

8/11/2019 Experimental investigation of the variability of concrete durability properties.pdf

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support of Vinci Construction France. Two construction sites wheretwo concretes were prepared continuously during at least 12 monthsregularly provided specimens to the various participants for the exe-cution of their tests: works for the south tunnel in Highway A86 (con-struction site A1) and for a viaduct near Compigne (north of Paris

construction site A2).The rst specimen denoted A1-1 was cast on 6th March 2007 at

the tunnel construction site ( Table 1 ), and then specimens were pre-

pared and provided with a frequency of about 1 week. The concretewas a C50/60 (characteristic compressive strength at 28 days)containing Portland cement (CEM I) and y-ashes used for the con-struction of the slab separating the two lanes from the tunnel of High-way A86 ( Table 1 ). The concrete was prepared using the concreteplant on site by the site workers. Forty batches were made on this

rst construction site. The last specimen was cast on the 31st March2008. In fact, for each date, 15 specimens (cylinders with a diameterof 113 mm and a height of 226 mm; note that these shape and di-mensions are accepted by the European standards EN 12390 andthe French version of the ENV 206-1) were produced and dispatchedto the 7 laboratories participating in the project.

At the second construction site a concrete C40/50 was producedcontaining CEM III cement which was used for the construction of the supports (foundations, piles) of the viaduct of Compiegne(Table 1 ). The rst specimens (A2-1) were produced the 6th of No-vember 2007 at the viaduct construction site. The concrete was alsoprepared by the site workers using a ready mix concrete. However,from batch A2-21 on, due to work constraints another compositioncorresponding to the same concrete quality was used to improvethe concrete workability (denoted A2/2). Finally, forty batches wereproduced, each composed of 14 specimens dispatched to the 7 labora-tories involved. The last batch was produced the 21st of January 2009.

It must be added here that allthe specimens used in this project wereprepared on the two sites by the site workers simultaneously to the fab-rication of theslabs and supports of the construction sites A1 and A2, re-spectively. In theauthors'mind, theconcretespecimensarethenmade of realcrete and are believed to be more or less representative of the ma-terials that can be encountered within the considered structures. None-theless it must be kept in mind that the variability obtained in thisstudy might just be a rough estimateof thevariability of thecorrespond-ing structural elements because the impact of some worksite features(for instance presence of reinforcement, structural element dimensionsand height of chute) could not be reproduced using small specimens.

3. Experimental results

3.1. Compressive and tensile strengths

This part of the research aims at proposing a characterization of the mechanical behavior of each studied batch by standard tests todetermine the tensile strength (by a splitting test), and also the com-pressive strength and Young's modulus (through a compression test).The tests were performed at LMT of the Ecole Normale Suprieure deCachan. For each batch, a cylindrical 113226 mm specimen is de-voted to compression test, while the splitting test is performed on acylindrical specimen of 113 mm in diameter and 170 mm in height(the upper part of the specimen is used for porosity and pulse velocitymeasurements).

For the compression test, the specimen is mechanically grindedbefore being placed in press. The specimen is equipped with an ex-tensometer (three LVDTs positioned at 120 attached to a metalring, which is xed on the concrete specimen by set screws) to mea-sure the longitudinal strain of the specimen during the loading phaseassumed to be elastic, between 5 and 30% of the failure load in com-pression. Three cycles of loading and unloading are performed inthe elastic behavior region of the concrete, with a loading rate of 5 kN/s (the rate is the same for unloading). Young's modulus is deter-mined by linear regression on ve points placed on the curve corre-sponding to the third unloading, according to the protocol proposedby [2]. Then, after removing the extensometer, the specimen is loadeduntil failure.

Table 2 and Figs. 1 to 3 present an overview of the results derivedfrom the mechanical tests (mean value, standard deviation, coef -cient of variation 1 and number of specimens tested). It can be ob-served that the compressive strength is much higher than expectedaccording to the compressive strength class and to the achievedvalues of compressive strength at 28 days (measured on site). Thisis due to the fact that the specimens were tested after 1 year of curingin saturated lime water resulting in a higher hydration degree whichimproves the strength. The magnitude of the coef cient of variation issimilar for the compressive and tensile strengths: around 10%. How-ever, the variability observed for Young's modulus is signi cantlylower (between 5 and 7%).

The magnitude of the coef cient of variation is similar to whatMirza et al. [3] and Chmielewski & Konokpa [4] have observed forthe variability of the compressive strength for monitored concrete(produced with great care), but their strengths were lower thanthose of the APPLET project materials. For high-performance con-crete, having a compressive strength that is similar to that observedwithin this study, the variability observed by Torrenti [5] and Cussighet al. [6] is approximately two times lower than it is here.

Simultaneously, the compressive strengthswere also measured onsite at age of 28 days. The specimens used were fabricated and kept inthe same way as the ones that were sent to the involved laboratories.The tests were performed by Vinci Construction France using thesame test conditions as detailed above. 116 specimens were testedfor the construction site A1 and 114 for the construction site A2(that is to say three different specimens from the same batch were

tested at the same time except for some batches for which only twospecimens were used). The results obtained for the variability arevery similar to the previous ones ( Table 3 and Fig. 4).

3.2. Chloride migration

Non-steady state migration tests have been performed at LMDC(Toulouse University) in order to measure the chloride migration co-ef cient. For the two selected construction sites, an overview of theresults will be presented in the following sections.

The principle of the test method is described in the standard NTBuild 492 [7]. The specimens were kept in water until the start of

Table 1Concrete mixes (per m 3 of concrete).

Site A1 A2/1 A2/2

Cement C CEM I 52.5 350 kg CEM III /A 52.5 L LH 355 kgAdditions A Fly ash 80 kg Calcareous ller 50 kgWater W 177 L 176 L 193 L W/C 0.51 0.50 0.54

Table 2Mechanical tests for 3 concrete mix designs: mean values, coef cient of variation andnumber of specimens tested for the compressive ( f c ) and tensile ( f t ) strengths andYoung's modulus ( E ).

Site Number f c [MPa] f t [MPa] E [GPa]

Mean COV (%) Mean COV (%) Mean COV (%)

A1 40 83.8 10.5 4.9 13.2 46.8 6.2A2-1 20 75.6 11.3 5.1 9.7 40.8 7.0A2-2 20 68.2 9.0 4.8 9.3 40.8 5.4

1 The coef cient of variation (COV) is de ned as the ratio of the standard deviation

to the mean value. It is an indicator of the dataset dispersion.

22 A. At-Mokhtar et al. / Cement and Concrete Research 45 (2013) 21 36
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the test. The experiments were performed for similar maturity of eachspecimen in the same series in order not to introduce on the resultsthe effect of the evolution of the concrete. Due to the equipmentsand the constraints of organizing this extensive signi cant experi-mental campaign, experiments were launched at an age of 3 monthsfor the A1 series and an age of 12 months for A2. Furthermore, itshould be noted that logistic problems were encountered: somedeadlines were not respected and in these situations, the test wasnot conducted. Consequently, on the 40 initially planned, only 30specimens from the A1 series and 31 from the A2 series were tested.

At the date of test, the specimen is then prepared. Once out of thestorage room, specimens are cut to retain only a cylinder 113 mm of 50 mm height. The test specimen is taken from the central part of thespecimen by cutting the top 50 mm from the free surface. The con-crete surface closest to the latter is then exposed to chlorides ( Fig. 5).

The specimen is then introduced in a rubber sleeve, and afterclamping, sealing is ensured by a silicone sealant line. At rst a leak-

age test is performed to detect any failure. The extending part of thesleeve is used as downstream compartment while the cell migration(a plastic box which receives the sleeve) corresponds to the upstreamcompartment. The upper compartment contains the catholyte solu-tion, i.e. a solution of 10% sodium chloride by mass (about 110 g/l)

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45 50 55 60 65 70 75 80 85 90 95 100 105 110

F r e q u e n c y

Compressive strength (MPa)

a) A1

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25%

35 40 45 50 55 60 65 70 75 80 85 90 95 100

F r e q u e n c y

Compressive strength (MPa)

b) A2

Fig. 1. Distribution of the compressive strength measured in laboratory (LMT) after1 year curing.

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30%

35%

2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5

F r e q u e n c y

Tensile strength (MPa)

a) A1

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45%

2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0

F r e q u e n c y

Tensile strength (MPa)

b) A2

Fig. 2. Distribution of the tensile strength measured in laboratory (LMT) after 1 year

curing.

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37 39 41 43 45 47 49 51 53 55

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Elastic modulus (GPa)

a) A1

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31 33 35 37 39 41 43 45 47 49

F r e q u e n c y

Elastic modulus (GPa)

b) A2

Fig. 3. Distribution of the elastic modulus measured in laboratory (LMT) after 1 yearcuring.

Table 3Compressive strength measured on site by Vinci Construction France: number of tests(Nb), mean value and coef cient of variation (COV).

Site Nb f c [MPa]

Mean COV (%)

A1 40 58.2 7.3%A2-1 20 57.8 11.1%A2-2 20 52.6 11.1%



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whereas the downstream compartment is lled with the anolyte so-lution, 0.3 M sodium hydroxide. These solutions are stored in theconditioned test room at 20 C. In each compartment an electrode isimmersed, which is externally connected through a voltage sourceso that the cathode, immersed in the chloride solution, is connectedto the negative pole and the anode, placed in the extending part of the sleeve, is connected to the positive pole. An initial voltage of 30 V is applied to the specimen. This voltage is then adjusted toachieve a duration test of 24 h depending on the magnitude of thecurrent owing through the cell as a result of the initial voltage of 30 V. The correction is proposed in the standard NT Build 492 [7].For A1 specimens, for the entire series the voltage used for the testis 35 V whereas 50 V is applied for the entire A2 series.

After 24 h, the specimen is removed to be split in two pieces. Sil-ver nitrate AgNO 3 is then sprayed onto the freshly fractured concretesurface. The white precipitate of silver chloride appears after 10 minrevealing the achieved chloride penetration front. At the concretesurface where chlorides are not present silver nitrate will not precip-itate but will quickly oxidize and then turn black after a few hours.The chloride penetration depth in concrete xd is then measuredusing a slide caliper using an interval of 10 mm to obtain 7 measured

depths. To avoid edge effects, a distance of 10 mm is discarded ateach edge. Moreover, if the front ahead of a measuring point is obvi-ously blocked by an aggregate particle, then the associated measureddepth is rejected. Then the migration coef cient Dnssm (non steadystate migration) (m 2 /s) is calculated using the following formula:

Dnssm 0 : 0239 273 T L

U 2 t xd 0 : 0238 ffiffiffiffiffiffi273 T LxdU 2r ! 1

where U is the magnitude of the applied voltage (V), T the tempera-ture in the anolyte solution (C), L the thickness of the specimen(mm), xd the average value of the chloride penetration depth (mm)and t the test duration (h). All the results are shown in Fig. 6 whichshow the migration coef cient obtained for the specimens from theA1 series.

Themeasured valuesvaryarounda mean value of 4.12 10 12 m 2/s.Thepotential resistance against chloride ingress is then high. This canbeeasily explained by theformulation of thisC50/60 concretewhere y ashwasused, which is knownto signi cantly reduce thediffusion coef cient[8]. The minimum value observed is 3.1110 12 m 2/s and the maxi-mum amounts to 5.5910 12 m 2/s which corresponds to a ratio of 1.8. The difference may seem relevant but basically corresponds to a di-vergence in concrete porosity of about 1.5% if the migration coef cientsare estimated from basic models [9]. The standard deviation is equal to0.5310 12 m 2/s; this corresponds to a coef cient of variation of 12.4% (Table 4 ).

For the A2 series the experiments could not be conducted on spec-imens A2-12 to A2-20. The migration experiments have been re-sumed from A2-21, which corresponds to the modi ed mix designof the A2 series. The mean migration coef cients determined for thecomplete A2 series is 2.5310 12 m 2 /s with a standard deviation of 0.5510 12 m 2/s corresponding to a coef cient of variation of 21.9%. Compared to the concrete of the A1 series, the resistance of this concrete against chloride ingress is signi cantly higher. The aver-age value is even smaller however for this A2 series concrete speci-mens were tested at a later age, i.e. 1 year instead of 3 months forA1. The second concrete (A2) would certainly achieve more modest

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3 7 4 0 4 3 4 6 4 9 5 2 5 5 5 8 6 1 6 4 6 7 7 0 7 3 7 6

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Compressive strength at 28 days (MPa)

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3 4 3 7 4 0 4 3 4 6 4 9 5 2 5 5 5 8 6 1 6 4 6 7 7 0 7 3 7 6 7 9

F r e q u e n c y


b) A2 site

a) A1 site

Fig. 4. Distribution of the compressive strength (at 28 days) measured on site by VinciConstruction France.

Free surface

50 mm

110 mm

50 mmExposed surface

Fig. 5. Specimen preparation for the chloride migration test.

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2.61 3.11 3.61 4.10 4.60 5.10 5.59 6.09

F r e q u e n c y

D nssm (x10 -12 m2 /s)

Fig. 6. Histogram of the migration coef cient from the A1 series.



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results at a younger age because of the slow hydrationkineticsfor thistype of cement containing blast furnace slag.

In the same way as for the A1 series, all these results may begrouped in a histogram. In contrast, as A2 series contains two mix de-sign formulations, the results must be treated in two subsets. In addi-tion, the rst formulation contains only 11 results, whereas thehistogram of the second formulation of this A2 re ects 20 experimen-tal values ( Fig. 7). The mean migration coef cient of the second for-mulation of the A2 series amounts to 2.45 10 12 m 2/s with astandard deviation of 0.47 10 12 m 2 /s, which corresponds to a coef-

cient of variation of 19.4% ( Table 4 ). It should be noted that themean value and coef cient of variation are lower for the second for-mulation of the A2 series. This corresponds to observations on site(higher variability of the workability for A2-1) that has decided theVinci Company to modify the formulation.

The variability is higher than for the A1 series since the coef cientof variation increases from 12.4% to 19.5% (and even larger if A2-1consider is considered).

3.3. Water vapor desorption isotherm

Water vapor sorption desorption isotherms tests were performedat the LaSIE at La Rochelle University [10]. This test characterizeswater content in a porous medium as a function of relative humidityat equilibrium state. It expresses the relationship between the watercontent of the material and relative humidity (RH) of the surroundingair for different moisture conditions de ned by a RH ranging from0 to 100%.

The method undertaken in this study for the assessment of de-sorption isotherms is based on gravimetric measurements [11,12] .Specimens were placed in containers under isothermal condition(231 C). The relative humidity of the ambient air is regulatedusing saturated salt solutions. For each of the following moisturestages: RH=90.4%, 75.5%, 53.5%, 33%, 12% and 3%, a regular monitor-ing of the mass of each specimen in time was performed until equilib-rium was obtained characterized by a negligible variation of relative

mass. The weighing of specimens was performed inside the containeras to result into the least disturbance of the relative humidity duringmeasurements. The equilibrium is assumed to be achieved if thehereafter criterion is satis ed:

m t m t 24h m t 24h

0 : 005 % 2

where m(t ) is the mass measured at the moment t and m(t +24 h) isthe measured mass 24 h later.The test started with specimens which were initially saturated. To

achieve thesaturation, theadoptedprocedure consists in storingthe cy-lindrical specimens 113226 mm under water 1 day after mixingduring at least 4 months. Besides, this procedure promotes a high de-gree of hydration of cement. At the age of 3 months, these specimenswere sawn in disks of 113 mm diameter and 50.5 mm thickness. Inthese disks a 4 mm diameter hole was drilled allowing mass measure-ments to be made inside the controlled RH environment with an accu-racy of 0.001 g. At construction site A1, 3 specimens 113 226 mm perbatch were used and in the case of construction site A2, only the rstconcrete composition (i.e. A2-1) was studied with 3 specimens perbatch and overall, 180 specimens were studied.

Fig. 8 shows the isothermal desorption curves for compositions A1and A2-1. The water contents at equilibrium for the different RH levelswere calculated on the basis of dry mass measured at the equilibriumstate for 3% RH. The so-obtained desorption isotherms belong to typeIV according to the IUPAC classi cation [13]. These are characterizedbytwoin ectionswhichare often observed forsuch a material [12]. De-sorption is thus multi-molecular with capillary condensation over abroad interval, which highlights a pore size distribution with severalmodes (i.e. with several in ections points). For a given RH, concretemixture A2-1 has higher average water content, especially for RH levelsabove 50%. This is ratherconsistentwith themixproportions since mix-ture A2-1 has a higher initial water content than mixture A1.

Table 5 gives the average water content values calculated at equi-librium with the different tested humidity environments and the cor-responding standard deviations and coef cients of variation. Thecoef cient of variation for 3 specimens from a single batch is approx-imately equal to 10% for RH levels between 100 and 33% and equal to20% for RH=12%. The coef cients of variation determined over thecomplete construction period (given in Table 5 ) are higher than thecoef cients of variation for a single batch. The observed dispersionis not only due to the randomness of test measurements, but alsodue to variability of material properties under site conditions [14]. Itshould be recalled that mixtures were made in real ready-mix con-crete plants.

As shown in Fig. 9, the statistical distributions of the water con-tents at equilibrium can be adequately modeled by normal probabili-ty density functions. The parameter values of the normal probability

Table 4Migration coef cient: number of tests (Nb), mean value and coef cient of variation(COV).

Site Nb Dnssm [10 12 m 2 /s]

Mean COV (%)

A1 30 2.53 12.4%A2-1 11 2.67 25.4%A2-2 20 2.45 19.4%

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35%

40%

1.38 1.81 2.24 2.68 3.11 3.54 3.97

F r e q u e n c y

D nssm (x10 -12 m 2 /s)

Fig. 7. Histogram of the migration coef cient for the A2-2 series.

0

1

2

3

4

5

6

0 20 40 60 80 100

W a t e r c o n t e n

t ( % )

Relative humidity (%)

A1

A2-1

Fig. 8. Average isothermal desorption curves for mixtures A1 and A2-1.



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density functions determined through regression analysis are given inTable 5 .

3.4. Carbonation

The carbonation tests were performed at the CERIB and at theLaSIE (University of La Rochelle). For more details, the reader is re-ferred to [15]. From each construction site (A1 and A2), cylindricalspecimens, 113 mm in diameter and 226 mm in height were sampledfrom different batches. On site A1, 1 specimen per batch was sampledfrom the last 10 batches. On site A2, 3 specimens per batch weretaken from 40 subsequent batches. After water curing during atleast 28 days, each specimen was sawn at mid-height in order to ob-tain a disk, 113 mm in diameter and 50 mm in height.

The protocol of the accelerated carbonation test is described in theFrench Standard XP P18-458. Concrete disks were rst oven-dried at45 5 C during 14 days. After this treatment, the lateral side of thedisks was covered by adhesive aluminum in order to ensure an axialCO2 diffusion during the carbonation test. The disks were then placedin a chamber containing 505% CO 2 at 202 C and 65% RH. After28 days in this environment, the concrete disks were split into twoparts. A pH indicator solution, i.e. phenolphthalein, was sprayed onthe obtained cross sections in order to determine carbonation

depth. The reported carbonation depth is the mean value of 24 mea-sured depths per disk.

Table 6 gives an overview of the results of the accelerated carbon-ation tests. The average carbonation depth of A1 concrete is less thanthat of A2 concretes. This can be attributed to the difference in bindertype used in the concrete mixtures: slag substitution is known to en-hance carbonation [16,17] . A signi cant difference can also be ob-served between the two mixtures from construction site A2. Thisdifference might be explained by a higher connectivity of the porestructure induced by the air-entraining effect of the plasticizer usedfor the second mixture A2-2.

Thevariability of the resultsis rather high. Fig. 10 shows the statisti-cal distribution of the carbonation depth in the case of construction siteA2. The distribution can be reasonably described by a normal probabil-ity density function (cf. Section 4.2 ).

3.5. Electrical resistivity

The electrical resistivity of concrete is generally a parameter mea-sured on concrete structures to assess the probability of reinforcementcorrosion. However, because of its dependency on the porosity of thematerial [18], developmentshave been made for theassessment of con-crete transfer properties [19 21]. It appears increasingly as a durabilityindicator [18,22] .

The investigations done within the APPLET program, aim atassessing the reliability of resistivity measurements for concretesproperties, by performing tests on 113226 mm cylindrical speci-mens using the resistivity cell technique in the laboratory. It consistsin introducing an electrical current of known magnitude in a concretespecimen and measuring the potential difference thus generated be-tween two sensors on the opposite specimen faces. Preliminary in-vestigations have been done to study the in uence of conditioningparameters on electrical resistivity measurements. Finally, a light pro-cess has been de ned to store specimens before resistivity measure-ment in the laboratory [23].

The measurements have been performed at I2M in UniversityBordeaux1 (specimens having an age of 3 months, after continuoussubmersion in water) and at LMT (specimens of 1 year, after contin-uous submersion in a saturated lime solution), according to a proto-

col de ned to distinguish different levels of variability [23]. Therepeatability and reproducibility of laboratory measurement havebeen evaluated for each specimen; the variability of the materialwithin a batch (2 batches consisting of 20 specimens each are stud-ied), andthe variabilityof thematerial during a year of casting (2 for-mulations studied from 40 specimens of test) are determined.

It is observed ( Fig. 11) that concrete A1 presents different rangesaccording to the laboratory: between 111 and 236 m for 90 daysold concrete, and between 282 and 431 m for 1 year-old concrete.This difference can essentially be attributed to the aging, as was al-ready observed on concretes containing y ash [24].

Table 5Water vapor desorption isotherm: average values, standard deviations (Std dev.) andcoef cients of variations (COV) of water contents at equilibrium (throughout the con-struction period).

Concrete RH 12% 33% 53.5% 75.5% 90.4% 100%

A1 Mean (%) 0.2 0.8 1.9 2.8 3.2 4.3Std dev. (%) 0.09 0.13 0.27 0.27 0.26 0.33COV (%) 45 16 14 10 8 8

A2-1 Mean (%) 0.2 1.0 2.6 3.6 3.9 4.9

Std dev. (%) 0.08 0.17 0.18 0.31 0.35 0.39COV (%) 40 17 7 9 9 8

Fig. 9. Statistical distribution of water contents at equilibrium for A1 (a) and A2-1 (b) concretes.

Table 6Mean value, standard deviation and coef cient of variation of the carbonated depth.

Carbonation depth A1 A2-1 A2-2 A2

Mean value (mm) 4.3 7.6 12.6 10.1Standard deviation (mm) 1.6 2.6 1.5 3.3COV 37% 35% 12% 33%



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Concrete A2 ( Fig. 12) does not present this difference despite theage difference and although the cement contains a signi cant amountof slag. It is noted that both databases express a similar behavior evenif measurements on 1 year old concrete show an expected light in-crease in resistivity. However, for the distribution tail (towards thehigh resistivity values) the measured values range from 266 to570 m at an age of 90 days, and from 324 to 898 m at an age of 1 year. These results show the dif culty to compare concretes usingtheir resistivity values. Electrical resistivity is a parameter which isvery much in uenced by the conditions during measurements (satu-ration degree of the specimen, temperature, the nature of the satura-tion uid). An overview of the variability assessment for bothconcretes is given in Table 7 .

Variability linked to measurements is the repeatability (whichcharacterizes the equipment), and the reproducibility (which also es-timates the noise due to the protocol). Whatever the concrete andlaboratory are, it is concluded that these variabilities are good. Theyare indeed less than 2% and underline that in laboratory the measure-ment results are accurate. The variability within a batch (Vb) is gen-erally less than 5% (except for one year old concrete A1 whichremains however less than 8%). The variability between batches(VB) is determined to be less than 20% (except for the one year oldconcrete A2 which reaches 29.6%, but this can be explained by themodi cation of the mix design during the construction period).

Whatever thelaboratory or thesetof specimens considered, thevar-iability is always ranked consistently: r b R b Vbb VB. The values of r andR being low, variability Vb and VB are therefore only representative of the material variability. So, it is surprising to observe a relatively largerange, for materials the engineer considers to be homogeneous andidentical. These measurements show: (1) within a batch there are

signi cant differences between specimens; (2) for a single concretecast regularly during 1 year, variability is less than 20%.

The differences observed between laboratories emphasize the im-portance of measurement conditions. Only measurements performedunder controlled conditions, regardless of the type of the specimen,shouldbe considered. Anychangein theconditioning (for instance tem-perature, saturation or age) in uences the resistivity values measured.

Resistivity measurements have also been done on a wall on site,made of A1 concrete, at an age of 28 days. On site value of reproduc-ibility is slightly higher than for the laboratory measurements (4.8%).

These results illustrate that the conditions of on-site measure-ments are less controlled. Even though this study is not suf cient tolink the variability of the concrete specimens to the concrete structur-al elements, it is however observed that on-site measurement andlaboratory techniques are consistent [23].

3.6. Porosity

3.6.1. Experimental setupFor the A1 construction site, specimens are denoted A1-x where x

is the batch number (from 1 to 40). For the A2 construction site, as 2different concrete mixes were studied (20 weeks for the rst mix,then 20 weeks for the second), the specimens are denoted A2-y-x,where y is the mix number (1 or 2) and x the batch number (speci-men numbers range from A2-1-1 to A2-1-20, then A2-2-21 toA2-2-40). The determination of porosity is studied through cylindri-cal specimens (diameter: 113 mm height: about 50 mm) sawnfrom the bottom part of the bigger cylindrical molded specimens.This study was performed at the LMT. In particular, these testsaimed at analyzing the variability with respect to the batch number(one batch per week); that is to say the temporal variability of agiven concrete.

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F r e q u e n c y

Carbonation depth (mm)

A2-1

A2-2

Fig. 10. Statistical distribution of the accelerated carbonation depths throughout thecomplete construction period (site A2).

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30%35%

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Resistivity ( m)

I2M (Univ. Bordeaux)LMT (ENS Cachan) a) A1

Fig. 11. Resistivity distribution for concrete A1 (the specimens used at I2M were

90 days old whereas the age was 1 year at LMT).

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Resistivity ( m)

I2M (Univ. Bordeaux)LMT (ENS Cachan)

b) A2

Fig. 12. Resistivity distribution for concrete A2 (the specimens used at I2M were90 days old whereas the age was 1 year at LMT).

Table 7Electrical resistivity ( m): variability observed in laboratory.

Organism/laboratory I2M LMT I2M LMT

Concrete A1 A1 A2 A2Device used Resistivity

cellResistivitycell

Resistivitycell

Resistivitycell

Mean value 166.8 352.5 391.2 461.7Mean repeatability r 0.005 0.007

Mean reproducibility R 0.015 0.006 0.012 0.007Variabili ty wi thin a batch * Vb 0 .023 0.076 0.036 0.035Variabili tybetween batches VB 0.176 0.114 0.182 0.296Age at measurements 90 days 1 year 90 days 1 year

* 590 days * at eachterm

* 436 days * at eachterm

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Secondly, the variability of porosity inside a given concrete batchis also studied. Additional cylindrical molded specimens of batchA1-13 and A2-1-1 are cast. The porosity is determined on small cylin-drical specimens (diameter: 37 mm height: about 74 mm) coredfrom those cylindrical molded specimens. A total of 39 specimensare cored from batch A1-13, and 6 from batch A2-1-1. This studywas performed in the LML (Lille 1 University).

Such small diameter (37 mm) or small height (50 mm) was cho-

sen to limit the duration of the drying process and the needed timefor the experimentation. The specimens, until testing, were alwayskept immersed in lime saturated water at 20 2 C for at least6 months (12 months for specimens used for temporal variability)to ensure a suf cient maturity and a very limited evolution of the mi-crostructure. These storage conditions tend also to saturate the po-rous network of the material.

In order to achieve a full water saturation state, AFPC-AFREM pro-tocol [25] recommends maintaining an underpressure of 25 millibarsfor 4 h and then to place the specimens under water (with the sameunderpressure) for 20 h. Tests conducted at LMT highlight that forsuch specimens kept under water during a long period, the effect of low underpressure (25 millibars) on water saturation will be negligi-ble on water saturation. Therefore, specimens used by LMT were onlysaturated during the immersion in lime-saturated water.

The same conclusions were drawn at LML. The additional satura-tion protocol is adapted from recommendations of AFPC-AFREM[25], mainly by increasing the saturation time with underpressure.Specimens were placed in a hermetically closed box with a slightunderpressure of 300 millibars and achievement of the saturation isassumed to be achieved when the mass variation is less than 0.1%per week. In both cases, the mass change due to this saturationunder vacuum is negligible (mass change in 3 weeks amounts toonly 0.15%), and considering specimens to be completely water satu-rated after at least 6 months of continuous immersion appears to bevalid. This mass at saturation is noted msat . Then, the volume of thespecimens is determined through a hydrostatic weighing (massmhydro ).

Finally, specimens are stored in an oven until mass equilibrium(change in mass less than 0.1% per week). The specimens used forthe so-called temporal variability are dried in an oven at 105 Cuntil mass equilibrium as recommended in the AFPC-AFREM protocol[25]. The protocol is adapted for LML tests. The drying is conducted at60 C until equilibrium, then the temperature is increased to 90 Cand then to 105 C to study the effect of the drying temperature onexperimental variability. The mass at a dried state (at a temperatureT ) is noted moven-T . The porosity at the temperature T is called (T )and can be determined as follows (Eq. (3) ).

T msat moven T msat mhydro

: 3

3.6.2. ResultsFig. 13 presents the distribution of porosity for the 40 specimens

(directly dried at 105 C) received from the A1 construction site,from batch 1 to 40. This allows studying temporal variability of thesame concrete mix for several batches. In the same way, Fig. 14shows the distribution of porosity for the A2-1 mix (batch 1 to 20)and Fig. 15 for the A2-2 mix (batch 21 to 40), measured by direct dry-ing at 105 C. The average porosity, standard deviation and coef cientof variation are recapitulated in Table 8 .

The porosity of A1 concrete is lower than for A2 concretes, as thecomposition and designed strengths are clearly different. The coef -cient of variation for A1 and A2-1 mixes appears to be two timeshigher than for A2-2 (7.92% and 9% versus3.96%). This could be partly

explained by the low sensitivity of the A2-2 concrete to the small

changes in composition (due to the gap between theoretical andreal formulation).

Secondly, the study aims at quantifying more precisely the vari-ability inside one particular batch (batches A1-13 and A2-1-1).Fig. 16 presents the distribution of porosity on the 39 specimensfrom the batch A1-13 dried at 60 C ( Fig. 16a), then 90 C(Fig. 16b) and nally 105 C ( Fig. 16c). The values of average poros-ity, standard deviation, coef cient of variation and minimum andmaximum values are summed up in Table 9 . The effect of tempera-ture on porosity is clearly seen with an increase of the measuredporosity from 10.1% to 11.5% between 60 and 105 C, but the statis-tical dispersion remains identical for the 3 tested temperatures. Therole of drying temperature on statistical dispersion is, as a conse-quence, negligible. Table 10 is the analog of Table 9 but now forthe 6 specimens from the A2-1-1 batch. The same tendency is con-

rmed for specimens from the A2-1-1 batch, even if variability islower (3.5% versus 6.44% at 60 C). This could be attributed to alower material variability.

Eventually, a last comparison between the protocol of LMT (directdrying at 105 C) and LML (stepwise drying at 105 C) can be maderegarding the porosity of A1-13 batch. It appears that the measuredporosity is not the same (12.4% by LMT on 1 specimen, average of 11.5% by LML on 39 specimens). However, as the values of porosityon the 39 specimens range from 9.7 to 13.6%, it cannot be concludedthat porosity is actually different. Moreover, additional tests havebeen performed at the LML to check the effect on porosity of stepwiseor direct drying at 105 C. Porosity is always higher when specimensare immediately dried at 105 C rather than in steps at 60, 90 andthen 105 C (porosity of 12.2% by direct drying at 105 C versus

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Fig. 13. Porosity distribution of A1 specimens (from batch 1 to 40) immediately driedat 105 C. The line is the tted normal probability density function. Note that in thiscase, the normal probability density function does not t well the results.

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Fig. 14. Porosity distribution of A2-1 specimens (from batch 1 to 20) immediatelydried

at 105 C. The line is the tted normal probability density function.



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11.5%) [26] . As a consequence, it seems that the two protocols used bythe LML or LMT can provide a reliable characterization of porosity andits variability, provided that the drying method is clearly mentioned.

3.7. Leaching

The characterization of concrete variability in relation to leachingwas performed at LMT and will be described in the following section.Other complementary experiments were also conducted simulta-neously at CEA to check the in uence of temperature and test condi-tions. These tests are not described in this article. For more details, thereader is referred to [27,28] .

The measurements performed in LMT within the APPLET projectare accelerated tests using ammonium nitrate solution [29]. After astorage of about 1 year in lime saturated water, the specimens are im-mersed in a 6 mol/L concentrated NH 4NO3 solution. The specimensare immersed in the ammonium nitrate solution 8 by 8, every8 weeks. For safety reasons, the containers with the aggressive solu-tion and the specimens are kept outside the laboratory, and thussubjected to temperature variations. Therefore, a pH and temperatureprobe is placed in the container, so as to register once an hour the pHand temperature values in the ammonium nitrate solution. If the pHof the solution reaches the threshold value of 8.8, the ammonium ni-trate solution of the container is renewed.

Before immersion in the ammonium nitrate solution, the speci-mens had been sandblasted to remove a thin layer of calcite formedon the specimen surface during the storage phase, which mightslow down or prevent the degradation of the specimens. The degra-dation depths are measured at 4 experimental terms for each speci-men: 4, 8, 14 and 30 weeks. For each experimental time interval,the specimens are taken from the containers, and a slice is sawn, onwhich the degradation depth is revealed with phenolphthalein. The

thickness of the slice is adapted to the experimental interval (the lon-ger the specimen has been immersed in ammonium nitrate solution,the larger the slice). The rest of the concrete specimen is then placedback in the ammonium nitrate solution container. Phenolphthalein is

a pH indicator through colorimetric reaction: the sound part of theconcrete has a highly basic pH so that the phenolphthalein turns

pink, whereas the degraded area has a pH below the colorimetricthreshold of the phenolphthalein, and therefore remains gray. Actual-ly, it seems that the degradation depth revealed with phenolphtha-lein is not exactly the position of the portlandite dissolution front

Table 8Statistical data on porosity versus concrete mix.

Concrete mix A1 A2-1 A2-2

Average 12.9% 14.4% 14.1%Standard deviation 1.02% 1.29% 0.56%Coef cient of variation 7.92% 9.00% 3.96%Minimum 11.1% 12.7% 12.9%Maximum 14.4% 18.2% 15%

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a) Specimens A1-13Drying at 60C

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c) Specimens A1-13Drying at 60, 90 then

105C

Fig. 16. Porositydistributionof A1-13driedat: (a)60 C,(b) then90 C and(c) ultimately105 C. The line is the tted normal probability density function.

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Fig. 15. Porosity distribution of A2-2 specimens (from batch 21 to 40) immediatelydried at 105 C. The line is the tted normal probability density function.

Table 9Statistical data on porosity versus drying temperature (39 specimens of batch A1-13).

Drying temperature 60 C 90 C 105 C

Average 10.1% 10.9% 11.5%Standard deviation 0.65% 0.69% 0.75%Coef cient of variation 6.44% 6.35% 6.49%Minimum 8.5% 9.2% 9.7%Maximum 11.8% 12.8% 13.6%



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[30], but the ratio between both is not completely acknowledged;this is the reason why in this study for practical reasons thedegradation depth is considered to be equal to the one revealed byphenolphthalein. In Fig. 17 one can observe the degradation depthsrevealed with phenolphthalein for the 4 experimental terms on thevery same specimen.

For every experimental test interval, each specimen is scanned toobtain a digital image of the sawnslice of concrete after spraying withphenolphthalein. The degradation depth is then numerically evaluat-ed over about a hundred radiuses. For these measurements, specialcare has been taken to avoid the in uence of aggregates particles:the degradation has been measured on mortar exclusively. The aver-age coef cient of variation of the degradation depth measured on aconcrete specimen (about a hundred values) is 13% at 28 days, 12%at 56 days, 10% at 98 days and nally 8% at 210 days. This decreasingcoef cient of variation is partly explainable by the fact that the radiusof the sound concrete decreases with time, therefore the perimeterfor the measurement of the degradation depth decreases as well.

In Table 10 , for every concrete mix and each experimental test in-terval (4, 8, 14 and 30 weeks), a comparison is made between the av-erage degraded depth, the coef cient of variation as well as thenumberof considered specimens. It can be noted that the degradationseems to be faster for the concrete of the second construction sitethan for the rst one. However, all specimens do not undergo thesame temperature history during the leaching test (since the speci-mens are immersed in the ammonium nitrate solution at rate of 8 specimens every 8 weeks). Therefore, the variability observed onthe degradation depths, and presented in Table 11 , includes the in u-ence of temperature variations and, thus, is not considered represen-tative of the variability of the material ( Fig. 18).

In order to eliminate the in uence of temperature in the interpre-tation of the accelerated leaching tests, so as to assess the materialvariability, two modeling approaches have been proposed. The rstapproach is a global macroscopic modeling based on the hypothesisthat the leaching kinetics are proportional to the square root of timeand thus that theprocess is thermo-activated. This means that an Arrhe-nius law can be applied on the slope of the linear function giving thedegradation depth with regard to the square root of time (Eq. (4) ).The basic idea of this approach is to determine, from the degradationdepthsmeasured at the four experimental intervals for every specimen,one scalar parameter representative of the kinetics of the degradationbut independent from the temperature variations experienced by the

specimen during the test. This scalar parameter is denoted k0 in Eq. (4)See [27] for more details.

e t ; T k T ffiffit p k0 exp E ART ffiffit p : 4

The second approach is presented in more detail in de Larrard et al.[31]: it is a simpli ed model for calcium leaching under variable tem-perature in order to simulate the tests performed within the APPLETproject. This approach is based on the mass balance equation for calci-um (Eq. (5) ) [32,33] , under the assumption of a local instantaneouschemical equilibrium, and combined with thermo-activation laws forthe diffusion process and the local equilibrium of calcium. It appearsthat among the input parameters of this model, the most in uentialon the leaching kinetics are theporosity and thecoef cient of tortuos-ity coef cient , which is a macroscopic parameter to model the in u-ence of coarse aggregates on the kinetics of diffusion through theporous material [34]. This tortuosity coef cient, although not directlymeasurable by experiments, is nevertheless identi able by inverseanalysis. The main difference between and the parameter k0 of theglobal thermo-activation of the leaching process is that isbyde nitionindependent from both temperature and porosity.

t

C Ca div D0ek grad C Ca h i

S Ca t 5

Table 12 summarizes the variability that has been observed for thematerials studied within the APPLET program through the acceleratedleaching test. In this table one may consider the mean value and coef-

cient of variation for the material porosity , the coef cient andthe parameter of the global thermo-activation of the leaching processk0. It appears that the tortuosity is signi cantly lower for the rst con-crete formulation (site A1) indicating slower degradation kinetics,but for the two formulations of the second site, the coef cient has ex-actly the same mean value, and only the variability decreases (whichwas the objective sought by the readjustment of the concrete formu-lation). This equality between the two formulations of the secondconstruction operation could not be foreseen through the degrada-tion depths ( Table 11 ) or the parameter k0 (Table 12 ). This differencein the mean values for k0 (whereas the mean values for are identi-cal) may be interpreted as the in uence of the porosity, which is a

Table 10Statistical data on porosity versus drying temperature (6 specimens of batch A2-1).

Drying temperature 60 C 90 C 105 C

Average 12.1% 12.9% 13.4%Standard deviation 0.43% 0.46% 0.47%Coef cient of variation 3.50% 3.57% 3.54%

28 days 56 days 98 days 210 days

Fig. 17. Degradation depths observed on the same specimen (batch 38 of A1 concrete) at the 4 experimental time intervals of the ammonium nitrate leaching test.

Table 11Degradation depths observed in the accelerated leaching test: number of specimenstested (Nb), mean value and coef cient of variation.

28 days 56 days 96 days 210 days

Site Nb Mean COV Mean COV Mean COV Mean COV

A1 40 4.2 20.8% 6.3 19.4% 8.8 16.8% 14.6 10.1%A2-1 20 4.6 10.9% 7.0 8.1% 9.8 8.0% 15.9 8.1%A2-2 20 6.0 12.0% 10.2 12.7% 12.8 9.9% 17.0 9.8%



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highly important parameter on the kinetics of degradation, and thatthis is integrated in parameter k0 but not in the coef cient of tortuos-ity coef cient (Figs. 19 20).

3.8. Permeability

The gas permeability of the concrete produced at the rst con-struction site (A1 site) was characterized at CEA using a Hasslercell: this is a constant head permeameter which is very similar tothe well-known Cembureau device [35]. The specimens to be usedwith this device are cylindrical with a diameter equal to 40 mm,and their height can range from a few centimeters up to about ten.The device can be used to apply an inlet pressure up to 5 MPa(50 atm). The gas ow rate is measured after percolation throughthe specimen using a bubble ow-meter. The percolation of the gasthrough the specimen is ensured using an impervious thick casing(neoprene) and a containment pressure up to 6 MPa (60 atm). Notethat the latter is independent of the inlet pressure. This device has

been used at the CEA for more than 10 years for gas permeabilitymeasurements [36 38]. The difference between the Cembureau andHassler cells was investigated in another program: the two apparatusshowed very similar results [39].

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Degraded depth aty 210 days (mm)

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A2-2

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Fig. 18. Degraded depth distribution at 96 days (accelerated degradation using ammo-nium nitrate).

Table 12Measured and identi ed variability of the porosity , the coef cient of tortuosity coef-

cient and the parameter k0 of global thermo-activation of the leaching process.

Porosity Tortuosity Kineticsk0 [mm/d 0.5 ]

Nb Average COV Average COV Average COV

A1 40 12.9% 7.9% 0.134 15.1% 6.82 5.6%A2-1 20 14.4% 9.0% 0.173 24.5% 8.17 16.2%A2-2 20 14.1% 4.0% 0.173 17.5% 7.25 8.3%

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Fig. 19. Tortuosity distribution (using ammonium nitrate).

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Fig. 20. Accelerated degradation kinetics distribution (using ammonium nitrate). The

solid lines are guides for the eyes only (normal probability density function).



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The specimens to be tested (40 mm) were obtained by coringthe large specimens (113226 mm) cast at the rst constructionsite (A1). Both ends of each cored specimen (40226 mm) weresawn off and discarded. The remaining part was then cut to yieldthree specimens (4060 mm, cf. Fig. 21). A maximal number of nine specimens could be obtained from each 113 mm specimen.According to our experience in concrete permeability measure-ments, these dimensions (40 60 mm) are suf cientto ensure rep-

resentative and homogeneous results. Note that the large specimens(113226 mm) were kept under water (with lime at 20 C) for11 months before use as to ensure optimal hydration and preventcarbonation.

Before the permeability characterization, the specimens werecompletelydriedat105 C(thatistosayuntilconstantweight)accordingtotherecommendations [25,35] .Thispre-treatmentisknowntoinducedegradation of thehardenedcement paste hydrates.Yet it appeared asthe best compromise between representativeness, drying complexityand duration. From a practical point of view, the complete drying wasachieved inless than 1 month.After thedrying,the specimenswereletto cool down in an air-conditionedroom at 20 C 1 C in a desiccatorabovesilicagel(inordertopreventanywateringress).

After this pretreatment thepermeability tests were performed usingnitrogen (pure at 99.995%) in an air-conditionedroom(20 C 1 C) inwhich thespecimenswere in thermal equilibrium. Themeasurement of the gas ow rate at the outlet (after percolation through the specimen)and when the steady state was reached (constant ow-rate) allowedthe evaluation of the effective permeability K e [m 2] [40]. The intrinsicpermeability was then estimated using the approach proposed byKlinkenberg [40,41] . The latter allows the estimation of the impact of the gas slippage phenomenon on the measured effective permeabilityK e: in practice the effective permeability K e is a linear function of the in-trinsic permeability K [m2] and the inverse of the test average pressureP [Pa]:

K e K 1 P 6

where is the Klinkenberg coef cient [Pa] which accounts for the gasslippage. From a practical point of view at least three injection steps(typically 0.15, 0.30 and 0.60 MPa) were used to estimate the intrinsicpermeability K . A unique value of the con nement pressure was usedfor all the tests: 1.5 MPa. One 113 mm specimen per batch was usedand the rst nine batches collected from the rst construction site(A1) were characterized (a total of 75 tests were performed). The re-sults are presented in Fig. 21. The open symbols and horizontal errorbars stand for the results of each cored specimen and the averagevalue of each batch, respectively.

The concrete intrinsic permeability was found to be ranging be-tween 2.4 10 17 and 9.810 17 m 2 with an average value equal

to 5.610 17 m 2 (by averaging the average values for all the ninebatches). This is in good agreement with the results obtained by[37] using the same preconditioning procedure and a similar concrete(CEM I, w/c=0.43): 6.610 17 m 2. The standard deviation is equalto 1.210 17 m 2 ; which gives a coef cient of variation equal to22%. This value is of the same order of magnitude than for the othertransport properties investigated in this study ( Fig. 22).

The results emphasize the signi cant variability which can be en-

countered within a 113 mm specimen: for instance for batch 5, thepermeability was found to vary by a factor of 2. This variability is veryunusual with regard to our experience in permeability measurementsof laboratory concretes. It is believed that the specimens manufactur-ing on site by the site workers in industrial conditions (time con-straints, large concrete volume to be placed) did result in thedecrease of the concrete placement quality compared to laboratoryfabrication [42,43] . This point was supported by the presence of large air voids (about one centimeter large) within the specimenswhich could be occasionally detected during the coring operations.These voids are also believed to contribute to the permeability in-crease [44].

Note that the intrinsic variability of the test itself was estimated; apermeability test was repeated ten times using the same specimen(after a test the specimen was removed from the permeameter, leftin a desiccator for at least one day and then tested again). The mea-surements standard deviation was equal to 0.17 10 17 m 2 (for anaverage value equal to 4.110 17 m 2). The coef cient of variationis about 4%, which is far less than the variability observed. For clarity,in Fig. 22 the uncertainty related to the test corresponds to the sym-bol height.

Simultaneously, experiments were conducted at LML: permeabili-ty was measured using cylindrical specimens (diameter: 37 mm

height: about 74 mm) cored from bigger molded specimens of theA1 construction site (batch A1-13). The specimens, until testing,were always kept immersed in lime saturated water at 202 C. Per-meability was measured by gas (argon) percolation in a triaxial cellon small specimens dried in oven at 90 C or at 90 then at 105 Cuntil mass equilibrium. The choice of argon as a percolating gas isdue to its inert behavior with cement, allowing an adequate measureof the material permeability. The whole experimental permeabilitymeasurement device is composed of a triaxial cell that allows the ap-plication of a con ning pressure on the specimen through oil injec-tion. The specimen is equipped with a drainage disk (stainless steelwith holes and lines ensuring a one-dimensional homogenous gas

ow at the surface of the specimen) at each end. The specimen isthen placed in the bottom section of the cell where the gas pressurePi will be applied. A drainage head, to allow owing of gas to the ex-terior of the cell (atmospheric pressure Pf) after the percolationthrough the specimen, is placed on the upper part of the specimen.

2 2 0 m m

110 mm 40

6 0

Fig. 21. Preparation of the specimens for the gas permeability measurements.

0

2

4

6

8

10

12

0 1 2 3 4 5 6 7 8 9 10Batch number

I n t r i n s i c p e r m e a

b i l i t y

( x 1 0 - 1

7 ) [ m ]

Fig. 22. Intrinsic permeability (using nitrogen) of the rst nine batches (constructionsite A1). Each circle corresponds to an experimental value obtained using a cored spec-

imen. The horizontal bar stands for the mean value for each batch.



13/16

Then a protective jacket is put around the specimen and the drainagedevices to isolate the specimen where gas ows from con ning oil in-gress. A sketch of this permeability cell is presented in Fig. 23.

The measurement procedure and determination of permeability isperformed as follows. Once the specimen is in the triaxial cell, con n-ing pressure is increased and kept constant to 4 MPa. Then, the gas isinjected at a pressure of about 2 MPa, and the downstream pressureP f is in equilibrium with atmospheric pressure (0 MPa in relativepressure). This injection is directly done by the reducing valve of the gas bottle, which also feeds a buffer circuit. This phase is pursueduntil a permanent gas ow inside the specimen is achieved. This isdetected by a stabilization of the injection pressure P i. At this mo-ment, the reducing valve is closed, and only the buffer circuit providesgas to the specimen. As a consequence, a drop of pressure appearssince gas continues to ow through the specimen. The permeabilityis deduced from the time t needed to get a given change P of theinjection pressure. This decrease of injection pressure should remainlow to ensure the quasi-permanent ow hypothesis. The volume of the buffer circuit V is known by preliminary tests, and with the per-fect gas hypothesis, the effective permeability K e is calculated using:

K e 2 g Q mLP mS P 2m P 2 f

7

where g is the gas viscosity, L the height of the specimen, S its crosssection and P m the medium pressure given by:

P m P iP 2 : 8

Q m is the medium ow, which under isothermal conditions is:

Q m

V P

P mt :

9

The measured permeability K e is an effective permeability (and

not an intrinsic) being dependent on injection pressure due to theKlinkenberg effect. However, for an injection pressure of 2 MPa, thiseffect is negligible, as con rmed by additional tests. A re ned descrip-tion of permeability devices can be found in [45]. For our tests, P is0.025 MPa, the injection pressure varies around 2 MPa (between2.02 and 2.24 MPa). The permeability is determined on 6 specimensfrom batch A1-13, dried at 90 C, and values are presented inTable 13 . The permeability of each specimen is measured two timesto evaluate the immediate repeatability (between two measure-ments, the specimen remains in the cell under con ning pressure,the reducing valve is opened until a permanent gas ow inside the

specimen is achieved and nally the second measure is performed).

3 additional specimens from the same batch are rstly dried at90 C until mass equilibrium, then at 105 C, and their permeabilityis determined. Table 14 gives an overview of the statistical data of these specimens. The statistical dispersion, as for porosity, has thesame order of magnitude at both 90 and 105 C (around 11 12%),and thus the effect of temperature on variability remains negligible.

4. Analysis/discussion

4.1. Construction sites comparison

Table 15 summarizes all the coef cients of variation obtained forall the experiments concerning the two construction sites. Thechangeof mix design during the production at site A2 could be seen on sev-eral physical parameters, however not on the mechanical ones. If the entire production of site A2 is considered, except for the chloridemigration, the coef cients of variation are very similar between sitesA1 and A2. For the chloride migration, there may be an effect of slagon this speci c phenomenon.

4.2. Probability density tting

In order to perform lifetime simulations related to durability onthe basis of reliability approach, it is necessary to characterize the var-iability of the model parameters by their appropriate probability den-sity function according to the observed statistical distribution. Thesedensity functions can be used as initial or prior estimates for the stud-ies where no data are available. They could be updated, for exampleusing Bayesian techniques, when eld data will be available by mon-itoring or speci c investigation of a structure.

To determine the most appropriate probability density functionthat best represents the statistical distribution of the experimentaldata, an approach by the maximum likelihood estimator (MLE) wasused by Oxand [46,47] . This technique helps to determine amongthe various probability functions tested the one that has the mostimportant likelihood, i.e. the one that is best able to represent thedistribution of observations. The suitability of the experimental dis-tribution to the chosen function has not been achieved through anadequacy test (Kolmogorov Smirnov non-parametric test for the

equality of continuous, one-dimensional probability distributionsfor example) but by simple visual veri cation considering the smallamount of data sometimes available.

A fairly wide range of probability density functions has been test-ed (12 probability density functions, see Appendix A ) to test their ad-equacy with respect to the MLE principle even if generally, some of

Fig. 23. Sketch of the triaxial cell for permeability measurements at LML.

Table 13Permeability after drying at 90 C (batch A1-13).

Specimen Permeability (10 17 m 2)

1st run 2nd run

19-3 2.83 2.8119-5 2.97 2.9938-2 2.62 2.6138-3 2.25

38-4 2.91 2.8838-5 3.24 3.24

Table 14Statistical data on permeability for dried specimens at 90 C or at 90 and then 105 C(batch A1-13).

Specimennumber

Average permeability(10 17 m 2 )

Standard deviation(10 17 m 2)

Coef cient of variation

90 C 6 2.80 0.34 12.1%105 C 3 4.40 0.49 11.1%



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them are rarely used to describe physical parameters in civil engi-neering. The various parameters studied during the experimentalcampaign were sometimes obtained by different tests and techniques(e.g. the compressive strengthof concretewasdetermined by the exper-imental device of the contractor and in different research laboratories;permeability was determined using two different procedures). Table 16summarizes the different probability functions tested and those thatare proposed to represent the intrinsic and measurement variability of the different parameters studied during the experimental campaign.

The adequacy procedure based on the maximum likelihood esti-mator was applied to samples of varying size. The results wereinterpreted taking into account a rather small number of data for aprecise statistical study (depending on the parameter studied, thedata processed varied generally between 20 and 40). This may ex-plain the fact that for many parameters, several probability functionsseem relatively close without being able to have clear preference forone or the other. For some parameters, due to a very small numberof tests carried out, all the available data has been used to t the sta-tistical distribution even if some of them came from different speci-mens (this was done for the chloride migration coef cient Dnssm forexample, see Fig. 25).

From a practical point of view, and from the perspective of usingthese results in the context of reliability analysis for the engineer, itmay be wise to use classical probability functions with parametersthat are easy to estimate rather than others that are more dif cultto simulate. In this sense, the lognormal distribution has oftenappeared as one of the most appropriate, together with the gamma,extreme and normal distributions. Figs. 24 to 25 illustrate a compari-son between experimental and theoretical probability densities anddistribution functions for various parameters.

5. Conclusion

One of the main objectives of the APPLET project (work group 1)was to characterize concretes variability for the assessment of reinforced concrete structures durability. In practice, a quantitativeinsight of concretes variability was obtained through durability testsand indicators. Forty sets of concrete specimens were taken fromtwo different construction sites over a period of 1 year and sent tothe different project partners to have different characterization testsperformed. The specimens were prepared on the two constructionsites by the site workers: the authors then believed that the resultsobtained were representative of the variability of the two concreteformulations prepared in industrial conditions. Nevertheless, thereader must keep in mind that the variability of the concrete formu-lations might not fully representative of the variability that can beexpected for the structural elements concrete: the latter might behigher.

The results obtained do however constitute a unique dataset of re-liable and consistent experimental data that can be used to estimatethe variability of concrete properties within existing structures.Fitting using suitable probability density functions allows these datato be used as inputs for probabilistic approaches. From a practicalpoint of view, one could select from the database the parametersthat are relevant for his study in terms of physics and chemistry butalso sensitivity: depending on the considered phenomena and the as-sociated modeling some parameters with low variability may have apronounced in uence on the outcome and vice versa. For example,in the approach of Muigai et al. [48] describing reinforcementchloride-induced corrosion, one should select the chloride migrationcoef cient as the relevant parameter.

Table 15Coef cients of variation of all the tests.

Test Laboratory A1 A2/1 A2/2 A2

Compressive strength Vinci 7.3% 11.1% 11.1% 12%Compressive strength LMT 10.5% 11.3% 11.1% 12%Tensile strength LMT 13.3% 9.7% 9.3% 9.9%Young modulus LMT 6.2% 8.2% 5.4% 7%Chloride migration LMDC 12.4% 25.4% 19.4% 21.9%Water content at

RH=53.5%

LaSIE 14% 7% Not

available

Not

availableCarbonation depth CERIB and

LaSIE37% 35% 12% 33%

Resistivity I2M 17.9% 15.6% 17.2% 18.5%Porosity LMT 7.9% 9% 4% 7%Degraded depth after

210 days of leachingLMT 10.1% 8.1% 9.8% 9.5%

Permeability CEA 22% Notavailable

Notavailable

Notavailable

Table 16Summary of the adequacy of the probability density functions tested.

Durability indicator/test Proposed distribution laws Other distribution available

Compressive strength Lognormal, normal, extreme Birnbaum Sanders, Weibull, Gamma, RicePermeability Lognormal, gamma Normal, Weibull, Log-logistic, NakagamiResistivity Lognormal, gamma Normal, Weibull, Log-logistic, NakagamiDensity Extreme, Weibull Logistic, Log-logisticPorosity Lognormal, gamma Birnbaum Sanders, Log-logisticLeaching Normal, lognormal Birnbaum Sanders, Extreme, Weibull, RiceTensile strength Lognormal, gamma Birnbaum Sanders, Weibull, Rice, NakagamiYoung's modulus Lognormal, gamma Birnbaum Sanders, Logistic, Log-logisticCarbonation depth Weibull, normal RiceChloride migration coef cient Lognormal Birnbaum Sanders, GammaPoisson's coef cient Lognormal, gamma Birnbaum Sanders

0%

5%

10%

15%

20%

25%

30%

35%

4 0 4 3 4 6 4 9 5 2 5 5 5 8 6 1 6 4 6 7 7 0 7 3 7 6 7 9

F r e q u e n c y


Exp.

Weibul

Extreme

Fig. 24. Experimental (cf. Fig. 4) and theoretical probability densities and distributionfunctions for the compressive strength of A1 concrete at 28 days (sample size: 116).

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