Research ArticleInvestigation on the Sulfuric Acid Corrosion Mechanism forConcrete in Soaking Environment
Hongguang Min 123 and Zhigang Song 3
1Guangdong Provincial Key Laboratory of Durability for Marine Civil Engineering College of Civil EngineeringShenzhen University 3688 Nanhai Avenue Shenzhen 518060 China2Shenzhen Graduate School Harbin Institute of Technology Shenzhen 518055 China3Faculty of Civil Engineering and Mechanics Kunming University of Science and Technology 727 South Jingming RoadKunming 650500 China
Correspondence should be addressed to Hongguang Min minhongguang163com
Received 23 January 2018 Accepted 31 March 2018 Published 7 May 2018
Academic Editor Estokova Adriana
Copyright copy 2018 Hongguang Min and Zhigang Song )is is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in anymedium provided the original work isproperly cited
)is paper chooses the apparent diffusion coefficient for OHminus (hydroxyl ion) for concrete as an index to evaluate the corrosiondegree of concrete subjected to sulfuric acid Based on the reaction boundary layer theory a sulfuric acid corrosion model forconcrete was established and verified through experiments )e experiment design and data processing of sulfuric acid corrosiontests for concrete were carried out using uniform test design and nonparametric regression Effects of water-cement ratio and pHvalue are presented on the sulfuric acid corrosion mechanism for concrete Test results show that when the pH value was 250 thesulfuric acid corrosion degree of concrete was the most serious )e boundary layer effect always existed in the sulfuric acidcorrosion for concrete and the corrosion process included rapid and stable corrosion stages)e apparent diffusion coefficient forOHminus for concrete increased with the decrease of pH value and the increase of water-cement ratio and cement proportion
1 Introduction
Aggressive sulfuric acid is mainly derived from acid rainindustrial environment and sewage treatment systems[1ndash4] further the physical and chemical reactions betweenaggressive sulfuric acid and cement hydration products areprimary reasons for durability failure of concrete structures[5] For example the pH value of inner concrete decreases ina sulfuric acid corrosion environment which leads to thedestruction of the passive film on the surface of rein-forcement steel bars followed by severe steel bar corrosionPrevious studies have shown that water-cement ratio pHvalue type and proportion of cement coarse aggregatecontent mineral admixture and other factors have im-portant effects on the sulfuric acid corrosion mechanism forconcrete [6ndash13] In fact these factors will affect the porestructures of concrete and the change of pore structures willsignificantly affect the transport performance of concrete
[14ndash17] which results in a decline in concrete resistance tosulfuric acid corrosion Being different from the mechanismof sulfate attack on concrete [11 12 18 19] the sulfuric acidcorrosion mechanism for concrete is the result of a com-bined action of dissolved corrosion caused by hydrogen ion(H+) and expanded corrosion caused by SO4
2minus (sulfate ion)[20] )is finding led Bohm et al [21] to propose a movingboundary diffusion model which can be used to predictsulfide corrosion rate for concrete Bohm et al [21] alsostudied the influencing factors of sulfuric acid corrosion rateBased on this Bohm et al [22] and Jahani et al [23] pre-dicted sulfuric acid corrosion rate and corrosion layerthickness for concrete and cement mortar through applyingthe moving boundary diffusion model [21] which were alsoverified by experiments Overall the sulfuric acid corrosionmechanism for concrete is complicated)is mechanism hasbeen studied by different researchers from different aspectshowever differences between these research results still
HindawiAdvances in Materials Science and EngineeringVolume 2018 Article ID 3258123 10 pageshttpsdoiorg10115520183258123
exist erefore the prediction model for concrete corrosiondue to sulfuric acid needs to be further studied
Based on the theory of reaction boundary layer thispaper presents a sulfuric acid corrosion model for concretecombined with the authorsrsquo previous research results [24]us the apparent diusion coecient of OHminus (hydroxylion) for concrete was analyzed and the correspondingtheoretical formula was also put forward Long-term soakingtests for concrete subjected to sulfuric acid corrosion werecarried out for 150 days through applying uniform designand nonparametric regression is studyrsquos observations onthe eects of water-cement ratio and pH value on concretesulfuric acid corrosionmechanism led to an apparent diusioncoecient for OHminus for concrete At length the sulfuric acidcorrosion model for concrete was veried by experiments
2 Sulfuric Acid Corrosion Model for Concrete
Ca(OH)2 (calcium hydroxide) in concrete dissolves in waterto form the saturated Ca(OH)2 solution which produces Ca2+(calcium ion) and OHminus by ionization Because of the exis-tence of concentration gradient Ca2+ and OHminus diuse intothe soaking solution through the corrosion layer from theinner concrete However H+ (hydrogen ion) and SO4
2minus
diuse into the inner concrete through the corrosion layerfrom the soaking solution under the action of concentrationgradient thereby forming the reaction boundary layer Onthe outer boundary of the reaction boundary layer the OHminusconcentration is zero and the H+ concentration is theconcentration of the soaking solution H+ however on theinner boundary of the noncorrosion surface the H+ con-centration is zero and the OHminus concentration is the con-centration found in the saturated Ca(OH)2 solution esulfuric acid corrosion for concrete occurs in the reactionboundary layer as shown in Figure 1
In the process of sulfuric acid corrosion for concreteOHminus diuses from interior to exterior of concrete under theaction of concentration gradient and reacts with H+ in thesoaking solution to form the reaction boundary layer Onlywhen the OHminus of the concrete surface has been consumed byH+ in the soaking solution the excess of H+ continue tospread to the inner concrete in the concentration gradienteect and further react with OHminus inner concrete ereforethe whole process of sulfuric acid corrosion relies on thedissolution of Ca(OH)2 out of concrete and consumption byH+ in the soaking solution
Sulfuric acid corrosion for concrete belongs to strongacid corrosion Sulfuric acid reacts with Ca(OH)2 in con-crete and the dissolution of generated soluble calcium saltscauses the reaction process to continue and the alkalinity ofconcrete to decrease Reactions occurring in the reactionboundary layer formed by the sulfuric acid corrosion forconcrete can be represented as
According to (1) the mole ratio of OHminus and H+ is 1 1 inthe reaction process so the apparent diusion coecientfor concrete is considered to be a constant Assuming thatthe concentration change of OHminus in the reaction boundary
layer is consistent with the diusion process of homoge-neous reaction then the whole diusion process can beexpressed as
zCOHminus(x t)zt
DOHminus middotz2COHminus(x t)
zx2
minus k middot COHminus(x t) middot CH+(x t)
(2)
where x is the distance of a point within the reactionboundary layer from the inner boundary (m) and t is thesoaking time (s) k is the reaction rate constant for OHminus andH+ (Lmiddotmolminus1middotsminus1) Meanwhile COHminus(x t) and CH+(x t) arethe concentrations of OHminus and H+ at location x and time t(molmiddotLminus1) respectively DOHminus is the apparent diusion co-ecient for OHminus for concrete (m2middotsminus1)
Equation (3) gives the boundary conditions of (2) asCOHminus(0 t) COHminus COHminus(δ t) 0
CH+(δ t) CH+ CH+(0 t) 0(3)
where COHminus is the concentration of OHminus in the saturated Ca(OH)2 solution (molmiddotLminus1) CH+ is the concentration of H+ inthe soaking solution (molmiddotLminus1) and δ is the thickness of thereaction boundary layer (m)
Assuming that concentration distributions in the re-action boundary layer for OHminus and H+ are satised thefollowing functions are derived as
(4)where φ(θ) and ψ(θ) are the shape functions of concen-tration distributions in the reaction boundary layer for OHminusand H+ respectively δ(t) is the thickness function of thereaction boundary layer
Equations (3) and (4) show that φ(θ) and ψ(θ) mustsatisfy the following conditions as
φ(0) 1 φ(1) 0 φprime(1) 0
ψ(0) 0 ψ(1) 1 ψprime(0) 0(5)
When combined with (2) and (4) the result can beshown as
Inner boundary
Concrete
OHndash
Reactionboundary layer
Outer boundary
H+
Figure 1 Reaction boundary layer of sulfuric acid corrosion onconcrete
2 Advances in Materials Science and Engineering
δminus1(t) middot 11139461
0minusθ middot φprime(θ) middot dθ middot
dδ(t)
dt DOHminus middot δminus2(t) middot 1113946
1
0φPrime(θ) middot dθ minus k middot CH+ middot 1113946
1
0φ(θ) middot ψ(θ) middot dθ (6)
which allows solving (6) as
δ2(t) N middot DOHminus middot k middot P middot CH+( 1113857minus1
where S is the area of soaking surface (m2) and vH+ (t) is theacid consumption rate of concrete that is H+ consumptionper unit time (molmiddotsminus1)
Substituting (7) into (8) gives
vH+ (t) A middot [1minus exp(minusB middot t)]minus12
A S middot COHminus middot k middot N middot P middot DOHminus middot CH+( 111385712
B 2k middot P middot CH+ middot Mminus1
(9)
Equation (9) shows that the acid consumption rate ofconcrete is relatively high in the initial reaction stage decreasesrapidly with the increase of reaction time and will eventuallybecome a constant A Hence the whole process consists oftwo stages that is decline and stability)en the experimentalstudy and theoretical analysis for concrete subjected to sulfuricacid corrosion can be carried as shown in Section 3
3 Materials and Methods
31 Experimental Design and Specimen Preparation )euniform test design method [25 26] is a test design methodthat only considers the ldquouniform dispersionrdquo of the test pointin the test range It is designed by the well-designed tables theuniform design table )e uniform design table is usuallyrepresented by Un (qs) where U means uniform design nmeans n tests q indicates that every factor has q levels and sindicates that the table has s columns for example U8 (85)which means that 8 tests are required each factor has 8 levelsthe table has 5 columns and a maximum of 5 factors )ebiggest characteristic of uniform test design is that the numberof tests required is usually equal to the level number of factorsWhen the test factors have the same level number the uniformtest design needs less tests than the orthogonal test design
Considering the effects of the two factors of water-cementratio and soaking solutionrsquos pH value on the sulfuric acidcorrosion mechanism for concrete both factors have eightlevels (Table 1) Because this test is a problem of two factors andeight levels enabling better test results with fewer test numberssulfuric acid corrosion tests for concrete were designedaccording to the uniform test design method as shown inTable 2 Twenty-four concrete specimens were cast )e sizeswere all 100mmtimes 100mmtimes 100mm and each kind of water-cement ratio consisted of three specimens )e continuousgraded gravel of 5ndash16mmwas used as the coarse aggregate)econcrete mix proportions are in Table 3 Concrete specimenswere taken out from the standard curing room after 28 days
32 Sulfuric Acid Corrosion Tests for Concrete Five surfacesof concrete specimens were sealed with paraffin leaving onlyone surface as the exposed surface Eight plastic boxes wereused as the soaking pool and three concrete specimens wereplaced into each soaking pool In addition the exposedsurface of each concrete specimen was completely perpen-dicular to the bottom of the soaking pool )ese specimensremained in their boxes and soaking for 150 days at roomtemperature as shown in Figure 2
)e soaking solutions of sulfuric acid were prepared withdifferent initial pH values by mixing the distilled water andconcentrated sulfuric acid and the volume of soaking so-lution of each group was always 10 L )e change of soakingsolutionrsquos pH was measured by a portable pH meter in timeand then the soaking solution was titrated with sulfuric acidin time by a rubber head dropper and a cylinder so as toensure the soaking solutionrsquos pH value was basically con-stant At the same time the liquid phase was stirred to ensurea uniform concentration of sulfuric acid throughout thevolume of the liquid phase
In the early stage of experiment the soaking solution wastitrated with sulfuric acid when the measured pH value wasup to the titration pH value however in the final stage ofexperiment even if the measured pH value was not up to thetitration pH value the soaking solution was still titrated withsulfuric acid to the initial pH value Table 4 shows the ti-tration pH value and titration sulfuric acid concentrationDuring the titration process each titration time wasrecorded along with the amount of titration sulfuric acidand the average acid consumption rate was obtained bydividing the amount of titration sulfuric acid at each intervalbased on the consecutive titration time periods
4 Results and Discussion
41 Apparent Characteristics of Concrete Subjected to SulfuricAcid Corrosion After 150 days the concrete specimenssubjected to sulfuric acid corrosion were taken out withdifferent water-cement ratios in the soaking solutions ofdifferent pH values Figure 3 shows the apparent changes in
Advances in Materials Science and Engineering 3
the characteristics of concrete specimensWith the decrease ofpH value the color of each exposed surface of concretespecimen in turn was gray yellow and white)e gray surfaceindicated that the corrosion degree of the concrete specimensuffered sulfuric acid was light and the color of the exposedsurface was basically the same as the noncorrosion surface)e yellow surface revealed that the sulfuric acid corrosiondegree was serious and the surface of the concrete specimenhad a loose yellow sand layer )e white surface shows thata large amount of CaSO4 (calcium sulfate) was deposited onthe concrete specimen surface In the initial stage of thesulfuric acid corrosion of concrete the reaction rate was veryfast and a large amount of CaSO4 was produced At the sametime CaSO4 blocked the surface pores of concrete specimenwhich caused the corrosion reaction rate to gradually slowdown so the corrosion degree gradually decreased
)e sizes of concrete specimens were measured beforeand after sulfuric acid corrosion using a vernier caliper
)ese concrete specimen measurements of the averagecorrosion layer thicknessesrsquo exposure to sulfuric acid after150 days are shown in Figure 4 When the soaking solutionrsquospH value was 250 the corrosion layer thickness was thelargest and the sulfuric acid corrosion degree was the mostserious When the soaking solutionrsquos pH value was between250 and 400 with the decrease of pH value the corrosionlayer thickness increased and the sulfuric acid corrosiondegree became more and more serious )is may be becausein the process of sulfuric acid corrosion for concrete theformation rate of CaSO4 was not much different from thedissolution rate so the corrosion reaction continued intothe concrete interior However the corrosion layer thicknessdecreased with the decrease of pH value when the soakingsolutionrsquos pH value was between 200 and 250 leading toa progressively smaller sulfuric acid corrosion degree )ismay be because the formation rate of CaSO4 in the earlycorrosion reaction was far greater than its dissolution rate
since the nondissolved CaSO4 gradually deposited onconcrete specimen surface which blocked the surface poresand slowed down the corrosion reaction signicantly
42 Sulfuric Acid Corrosion Law for Concrete According tothe sulfuric acid corrosion tests for concrete the acidconsumption rate over time was measured as shown inFigure 5 e acid consumption rate of concrete in the earlystage was relatively high but it decreased rapidly andgradually stabilized with the corrosion reaction e wholeprocess consisted of two stages the descending and stableperiods e cuto point was approximately 800 hours Inaddition the lower the soaking solutionrsquos pH value was thehigher the initial acid consumption rate of concrete leadingto a greater sulfuric acid corrosion rate for concrete
5 Verification of the Sulfuric Acid CorrosionModel and Determination of an ApparentDiffusion Coefficient for OH2 for Concrete
51 Verication of the Sulfuric Acid Corrosion Model forConcrete To clearly show the variation law of the acidconsumption rate of concrete over time the measured data
within 800 hours were tted according to (9) e ttingparameters are seen in Table 5 and the tting results areshown in Figure 6 Except for the last three groups of
experimental data (9) gave all test specimens a higher fittingdegree )e theoretical model can reflect the change lawaffecting the acid consumption rate over time therebyverifying the accuracy of the theoretical model When thesoaking time was relatively long (200 hours) the measuredvalues of the acid consumption rate were slightly lower thanfitted values and this trend was more obvious with thedecrease of pH value in the soaking solution )is phe-nomenon is related to the flocculent CaSO4 on the concretesurface which is also called the boundary layer
As the solubility of CaSO4 decreases with the decrease ofsoaking solution pH value the boundary layer thicknessincreases with the decrease of pH value )e presence of theboundary layer results in a decrease in the reaction ratewhich slows down the formation rate of CaSO4 At the sametime CaSO4 is constantly dissolving out of the concrete toreduce the CaSO4 concentration in the reaction boundarylayer resulting in the dissolution of the boundary layerwhich increases the reaction rate )e deceleration or ac-celeration of the reaction rate caused by the formation ordissolution of the boundary layer will eventually reacha dynamic equilibrium
52 Determination of an Apparent Diffusion Coefficient forOHminus for Concrete Under a sulfuric acid corrosion envi-ronment the dissolution of Ca(OH)2 in concrete results inthe change of concrete pore structures which further resultsin the change of concretersquos apparent diffusion coefficientHowever the apparent diffusion coefficient for concrete isdifficult to measure directly and then the formula for cal-culating the apparent diffusion coefficient for OHminus forconcrete can be obtained by (9) as
DOHminus 2A2
B middot S2 middot C 2OHminusM middot N
(10)
Choosing a shape function which can satisfy (5) yields
φ(θ) (1minus θ)2
ψ(θ) θ2(11)
Substituting (11) in (7) gives
M 13
N 2
(12)
Substituting (12) in (10) yields
DOHminus 3A2
B middot S2 middot C 2OHminus
(13)
)e total area S of the exposed surfaces of each group ofconcrete specimens was 003m2 and the concentration of OHminusin the saturated Ca(OH)2 solution at 20degC was 0045molmiddotLminus1then the apparent diffusion coefficients for OHminus for concretewere obtained by using Table 5 and (13) as shown in Figure 7When the soaking solutionrsquos pH value was more than 250 theapparent diffusion coefficients for OHminus for concrete increased
slowly with the decrease of pH value and then increased rapidlywith the further decrease of pH value
53 Effects of Water-Cement Ratio Soaking Solutionrsquos pHValue and Cement Proportion on the Apparent DiffusionCoefficient for OHminus for Concrete Because the relationshipwas not directly determined between the apparent diffusioncoefficient for OHminus for concrete and water-cement ratio thesoaking solutionrsquos pH value and cement proportion of C(C+FA+CA) required an analysis by ACE (alternating con-ditional expectation) regression [27] of nonparametric re-gression where x1 x2 x3 and y are water-cement ratiosoaking solutionrsquos pH value cement proportion andln(DOHminus times 1013) respectively Searching for the trans-formation relations of φ1(x1) φ2(x2) φ3(x3) and θ(y)
which can satisfy the following mapping relation betweeninput parameters of x1 x2 x3 and function of y gave
)e nonparametric regression analysis was performedusing ACE )e fitting correlation coefficient was 09923and the fitting effect was very good Table 6 gives the valuesof each parameter before and after ACE regression and (16)gives the mapping relations of x1simφ1(x1) x2simφ2(x2)x3simφ3(x3) and ysimθ(y) obtained using ACE Figure 8 givesthe relationship between the experimental and regressionvalues for y which is in good agreement with each other andhas a positive proportion relationship It can be seen fromthis that ACE has a very good practical value
φ1 x1( 1113857 34610x1 minus 18173
φ2 x2( 1113857 minus15847x2 + 46946
φ3 x3( 1113857 123549x3 minus 23583
θ(y) 03545yminus 08446
(16)
Combined with (14) to (16) as
y 976x1 minus 447x2 + 3485x3 + 385 (17)
Namely
DOHminus 10minus13 times exp1113888976w
cminus 447 pH
+ 3485C
C + FA + CA+ 3851113889 (18)
Equation (18) showed that when the pH value decreasedwater-cement ratio and cement proportion increased thusthe corrosion degree of concrete subjected to sulfuric acidincreased in severity
6 Conclusions
With the decrease of soaking solutionrsquos pH value the colorof the exposed concrete specimen surface changed from gray
to yellow and then to white e corrosion layer thickness ofthe concrete specimen did not increase continuously withthe decrease of pH value When the soaking solutionrsquos pHvalue was 250 the corrosion layer thickness reached the
maximum value which means the sulfuric acid corrosiondegree of concrete was the most serious
A sulfuric acid corrosion model for concrete wasestablished based on the reaction boundary layer theoryand was solved by applying the separation of variablesen a theoretical formula for the acid consumption rateof concrete was obtained e sulfuric acid corrosionprocess of concrete can be divided into two stages namelythe rapid corrosion stage and the stable corrosion stageBecause of the eect of the boundary layer the measuredacid consumption rate of concrete was slightly lower thanthe theoretical value when the soaking time was relativelylong rough the sulfuric acid corrosion tests for concretethe accuracy of the sulfuric acid corrosion model forconcrete was veried is model can be used to predict thesulfuric acid corrosion mechanism for concrete in practicalengineering and to provide the foundation for steel cor-rosion prediction
e sulfuric acid corrosion tests for concrete wereplanned using uniform design e apparent diusion co-ecient for OHminus for concrete was chosen as the evaluationindex for the sulfuric acid corrosion degree of concrete andthen the calculation formula was obtained through non-parametric regression e results showed that the apparentdiusion coecient for OHminus for concrete increased whenthe pH value decreased and the water-cement ratio and
1 2 3 4 5 6 7 8Test group
033 058 092 414 12115587
36827
103783
0
300
600
900
1200
DO
Hndash
(10ndash1
3 m2 middotsndash1
)
Figure 7 Apparent diusion coecient for OHminus for concrete
Table 6 Values of each parameter before and after ACE regression
Figure 8 Comparison of the experimental and regression valuesfor y
Advances in Materials Science and Engineering 9
cement proportion increased )e uniform design andnonparametric regression had a high efficiency in the ex-perimental research and matched each other well which wasof great significance to this scientific research
Data Availability
)e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
)e authors declare that they have no conflicts of interest
Acknowledgments
)is research was financially funded by the China Post-doctoral Science Foundation (2017M622789) and the Na-tional Natural Science Foundation of China (51078175)
References
[1] K He H Yang Z B Lu F F Jia E P Wang and Q X DongldquoEffect of matrix modification on durability of cementitiouscomposites in an acid rain environmentrdquo Journal of WuhanUniversity of TechnologyndashMaterials Science Edition vol 29no 3 pp 498ndash503 2014
[2] M P Lavigne A Bertron C Botanch et al ldquoInnovativeapproach to simulating the biodeterioration of industrialcementitious products in sewer environment Part II vali-dation on CAC and BFSC liningsrdquo Cement and ConcreteResearch vol 79 pp 409ndash418 2016
[3] B Huber H Hilbig M M Mago J E Drewes and E MullerldquoComparative analysis of biogenic and chemical sulfuric acidattack on hardened cement paste using laser ablation-ICP-MSrdquo Cement and Concrete Research vol 87 pp 14ndash21 2016
[4] N De Belie J Monteny A Beeldens E Vincke D VanGemert and W Verstraete ldquoExperimental research andprediction of the effect of chemical and biogenic sulfuric acidon different types of commercially produced concrete sewerpipesrdquo Cement and Concrete Research vol 34 no 12pp 2223ndash2236 2004
[5] P K Mehta ldquoDurability of concretemdashfifty years of progressrdquoin Proceeding of the 2nd International Conference on ConcreteDurability ACI SP126ndash01 pp 1ndash32 Sapporo Japan 1991
[6] Y Yang T Ji X J Lin C Y Chen and Z X Yang ldquoBiogenicsulfuric acid corrosion resistance of new artificial reef concreterdquoConstruction and Building Materials vol 158 pp 33ndash41 2018
[7] L Gu P Visintin and T Bennett ldquoEvaluation of accelerateddegradation test methods for cementitious composites subjectto sulfuric acid attack application to conventional and alkali-activated concretesrdquo Cement and Concrete Compositesvol 87 pp 187ndash204 2018
[8] X Li Y X Lin K Lin and T Ji ldquoStudy on the degradationmechanism of sulphoaluminate cement sea sand concreteeroded by biological sulfuric acidrdquo Construction and BuildingMaterials vol 157 pp 331ndash336 2017
[9] E Hewayde M Nehdi E Allouche and G Nakhla ldquoEffect ofmixture design parameters and wetting-drying cycles on re-sistance of concrete to sulfuric acid attackrdquo Journal of Materialsin Civil Engineering vol 19 no 2 pp 155ndash163 2007
[10] Y F Fan Z Q Hu H Y Luan D W Wang and A Chen ldquoAstudy of deterioration of reinforced concrete beams under various
forms of simulated acid rain attack in the laboratoryrdquo StructuralEngineering and Mechanics vol 52 no 1 pp 35ndash49 2014
[11] A Grandclerc P Dangla and M Gueguen-MinerbeldquoModelling of the sulfuric acid attack on different types ofcementitious materialsrdquo Cement and Concrete Researchvol 105 pp 126ndash133 2018
[12] J Hill E A Byars J H Sharp C J Lynsdale J C Cripps andQ Zhou ldquoAn experimental study of combined acid andsulfate attack of concreterdquo Cement and Concrete Compositesvol 25 no 8 pp 997ndash1003 2003
[13] Z T Chang X J Song R Munn and M Marosszeky ldquoUsinglimestone aggregates and different cements for enhancingresistance of concrete to sulphuric acid attackrdquo Cement andConcrete Research vol 35 no 8 pp 1486ndash1494 2006
[14] H GMinW P Zhang andX L Gu ldquoEffects of load damage onmoisture transport and relative humidity response in concreterdquoConstruction and Building Materials vol 169 pp 59ndash68 2018
[15] H G Min W P Zhang X L Gu and R Cerny ldquoCoupledheat and moisture transport in damaged concrete under anatmospheric environmentrdquo Construction and Building Ma-terials vol 143 pp 607ndash620 2017
[16] W P Zhang H G Min and X L Gu ldquoTemperature responseand moisture transport in damaged concrete under an at-mospheric environmentrdquo Construction and Building Mate-rials vol 123 pp 290ndash299 2016
[17] W P Zhang H G Min X L Gu Y Xi and Y S XingldquoMesoscale model for thermal conductivity of concreterdquoConstruction and Building Materials vol 98 pp 8ndash16 2015
[18] S Mirvalad and M Nokken ldquoStudying thaumasite sulfateattack using compressive strength and ultrasonic pulse ve-locityrdquo Materials and Structures vol 49 no 10 pp 4131ndash4146 2016
[19] M O Yusuf ldquoPerformance of slag blended alkaline activatedpalm oil fuel ash mortar in sulfate environmentsrdquo Con-struction and Building Materials vol 98 pp 417ndash424 2015
[20] S D Xie L Qi and D Zhou ldquoInvestigation of the effects ofacid rain on the deterioration of cement concrete usingaccelerated tests established in laboratoryrdquo Atmospheric En-vironment vol 38 no 27 pp 4457ndash4466 2004
[21] M Bohm J Devinny F Jahani and G Rosen ldquoOn a moving-boundary systemmodeling corrosion in sewer pipesrdquo AppliedMathematics and Computation vol 92 no 2-3 pp 247ndash2691998
[22] M Bohm J Devinny F Jahani F B Mansfeld I G Rosenand C Wang ldquoA moving boundary diffusion model for thecorrosion of concrete wastewater systems simulation andexperimental validationrdquo in Proceedings of the AmericanControl Conference pp 1739ndash1743 San Diego CA USA1999
[23] F Jahani J Devinny F Mansfeld and I G Rosen ldquoIn-vestigations of sulfuric acid corrosion of concrete I modelingand chemical observationsrdquo Journal of Environmental Engi-neering vol 127 no 7 pp 572ndash579 2001
[24] Z G Song X S Zhang and H G Min ldquoConcentrationboundary layer model of mortar corrosion by sulfuric acidrdquoJournal of Wuhan University of TechnologyndashMaterials ScienceEdition vol 26 no 3 pp 527ndash532 2011
[25] K T FangUniformDesign and UniformDesign Table SciencePress Beijing China 1994 in Chinese
[26] K T Fang and C X Ma Orthogonal and Uniform Design ofExperiments Science Press Beijing China 2001 in Chinese
[27] A M Hasofer and J Qu ldquoResponse surface modelling ofmonte carlo fire datardquo Fire Safety Journal vol 37 no 8pp 772ndash784 2002
10 Advances in Materials Science and Engineering
CorrosionInternational Journal of
Hindawiwwwhindawicom Volume 2018
Advances in
Materials Science and EngineeringHindawiwwwhindawicom Volume 2018
exist erefore the prediction model for concrete corrosiondue to sulfuric acid needs to be further studied
Based on the theory of reaction boundary layer thispaper presents a sulfuric acid corrosion model for concretecombined with the authorsrsquo previous research results [24]us the apparent diusion coecient of OHminus (hydroxylion) for concrete was analyzed and the correspondingtheoretical formula was also put forward Long-term soakingtests for concrete subjected to sulfuric acid corrosion werecarried out for 150 days through applying uniform designand nonparametric regression is studyrsquos observations onthe eects of water-cement ratio and pH value on concretesulfuric acid corrosionmechanism led to an apparent diusioncoecient for OHminus for concrete At length the sulfuric acidcorrosion model for concrete was veried by experiments
2 Sulfuric Acid Corrosion Model for Concrete
Ca(OH)2 (calcium hydroxide) in concrete dissolves in waterto form the saturated Ca(OH)2 solution which produces Ca2+(calcium ion) and OHminus by ionization Because of the exis-tence of concentration gradient Ca2+ and OHminus diuse intothe soaking solution through the corrosion layer from theinner concrete However H+ (hydrogen ion) and SO4
2minus
diuse into the inner concrete through the corrosion layerfrom the soaking solution under the action of concentrationgradient thereby forming the reaction boundary layer Onthe outer boundary of the reaction boundary layer the OHminusconcentration is zero and the H+ concentration is theconcentration of the soaking solution H+ however on theinner boundary of the noncorrosion surface the H+ con-centration is zero and the OHminus concentration is the con-centration found in the saturated Ca(OH)2 solution esulfuric acid corrosion for concrete occurs in the reactionboundary layer as shown in Figure 1
In the process of sulfuric acid corrosion for concreteOHminus diuses from interior to exterior of concrete under theaction of concentration gradient and reacts with H+ in thesoaking solution to form the reaction boundary layer Onlywhen the OHminus of the concrete surface has been consumed byH+ in the soaking solution the excess of H+ continue tospread to the inner concrete in the concentration gradienteect and further react with OHminus inner concrete ereforethe whole process of sulfuric acid corrosion relies on thedissolution of Ca(OH)2 out of concrete and consumption byH+ in the soaking solution
Sulfuric acid corrosion for concrete belongs to strongacid corrosion Sulfuric acid reacts with Ca(OH)2 in con-crete and the dissolution of generated soluble calcium saltscauses the reaction process to continue and the alkalinity ofconcrete to decrease Reactions occurring in the reactionboundary layer formed by the sulfuric acid corrosion forconcrete can be represented as
According to (1) the mole ratio of OHminus and H+ is 1 1 inthe reaction process so the apparent diusion coecientfor concrete is considered to be a constant Assuming thatthe concentration change of OHminus in the reaction boundary
layer is consistent with the diusion process of homoge-neous reaction then the whole diusion process can beexpressed as
zCOHminus(x t)zt
DOHminus middotz2COHminus(x t)
zx2
minus k middot COHminus(x t) middot CH+(x t)
(2)
where x is the distance of a point within the reactionboundary layer from the inner boundary (m) and t is thesoaking time (s) k is the reaction rate constant for OHminus andH+ (Lmiddotmolminus1middotsminus1) Meanwhile COHminus(x t) and CH+(x t) arethe concentrations of OHminus and H+ at location x and time t(molmiddotLminus1) respectively DOHminus is the apparent diusion co-ecient for OHminus for concrete (m2middotsminus1)
Equation (3) gives the boundary conditions of (2) asCOHminus(0 t) COHminus COHminus(δ t) 0
CH+(δ t) CH+ CH+(0 t) 0(3)
where COHminus is the concentration of OHminus in the saturated Ca(OH)2 solution (molmiddotLminus1) CH+ is the concentration of H+ inthe soaking solution (molmiddotLminus1) and δ is the thickness of thereaction boundary layer (m)
Assuming that concentration distributions in the re-action boundary layer for OHminus and H+ are satised thefollowing functions are derived as
(4)where φ(θ) and ψ(θ) are the shape functions of concen-tration distributions in the reaction boundary layer for OHminusand H+ respectively δ(t) is the thickness function of thereaction boundary layer
Equations (3) and (4) show that φ(θ) and ψ(θ) mustsatisfy the following conditions as
φ(0) 1 φ(1) 0 φprime(1) 0
ψ(0) 0 ψ(1) 1 ψprime(0) 0(5)
When combined with (2) and (4) the result can beshown as
Inner boundary
Concrete
OHndash
Reactionboundary layer
Outer boundary
H+
Figure 1 Reaction boundary layer of sulfuric acid corrosion onconcrete
2 Advances in Materials Science and Engineering
δminus1(t) middot 11139461
0minusθ middot φprime(θ) middot dθ middot
dδ(t)
dt DOHminus middot δminus2(t) middot 1113946
1
0φPrime(θ) middot dθ minus k middot CH+ middot 1113946
1
0φ(θ) middot ψ(θ) middot dθ (6)
which allows solving (6) as
δ2(t) N middot DOHminus middot k middot P middot CH+( 1113857minus1
where S is the area of soaking surface (m2) and vH+ (t) is theacid consumption rate of concrete that is H+ consumptionper unit time (molmiddotsminus1)
Substituting (7) into (8) gives
vH+ (t) A middot [1minus exp(minusB middot t)]minus12
A S middot COHminus middot k middot N middot P middot DOHminus middot CH+( 111385712
B 2k middot P middot CH+ middot Mminus1
(9)
Equation (9) shows that the acid consumption rate ofconcrete is relatively high in the initial reaction stage decreasesrapidly with the increase of reaction time and will eventuallybecome a constant A Hence the whole process consists oftwo stages that is decline and stability)en the experimentalstudy and theoretical analysis for concrete subjected to sulfuricacid corrosion can be carried as shown in Section 3
3 Materials and Methods
31 Experimental Design and Specimen Preparation )euniform test design method [25 26] is a test design methodthat only considers the ldquouniform dispersionrdquo of the test pointin the test range It is designed by the well-designed tables theuniform design table )e uniform design table is usuallyrepresented by Un (qs) where U means uniform design nmeans n tests q indicates that every factor has q levels and sindicates that the table has s columns for example U8 (85)which means that 8 tests are required each factor has 8 levelsthe table has 5 columns and a maximum of 5 factors )ebiggest characteristic of uniform test design is that the numberof tests required is usually equal to the level number of factorsWhen the test factors have the same level number the uniformtest design needs less tests than the orthogonal test design
Considering the effects of the two factors of water-cementratio and soaking solutionrsquos pH value on the sulfuric acidcorrosion mechanism for concrete both factors have eightlevels (Table 1) Because this test is a problem of two factors andeight levels enabling better test results with fewer test numberssulfuric acid corrosion tests for concrete were designedaccording to the uniform test design method as shown inTable 2 Twenty-four concrete specimens were cast )e sizeswere all 100mmtimes 100mmtimes 100mm and each kind of water-cement ratio consisted of three specimens )e continuousgraded gravel of 5ndash16mmwas used as the coarse aggregate)econcrete mix proportions are in Table 3 Concrete specimenswere taken out from the standard curing room after 28 days
32 Sulfuric Acid Corrosion Tests for Concrete Five surfacesof concrete specimens were sealed with paraffin leaving onlyone surface as the exposed surface Eight plastic boxes wereused as the soaking pool and three concrete specimens wereplaced into each soaking pool In addition the exposedsurface of each concrete specimen was completely perpen-dicular to the bottom of the soaking pool )ese specimensremained in their boxes and soaking for 150 days at roomtemperature as shown in Figure 2
)e soaking solutions of sulfuric acid were prepared withdifferent initial pH values by mixing the distilled water andconcentrated sulfuric acid and the volume of soaking so-lution of each group was always 10 L )e change of soakingsolutionrsquos pH was measured by a portable pH meter in timeand then the soaking solution was titrated with sulfuric acidin time by a rubber head dropper and a cylinder so as toensure the soaking solutionrsquos pH value was basically con-stant At the same time the liquid phase was stirred to ensurea uniform concentration of sulfuric acid throughout thevolume of the liquid phase
In the early stage of experiment the soaking solution wastitrated with sulfuric acid when the measured pH value wasup to the titration pH value however in the final stage ofexperiment even if the measured pH value was not up to thetitration pH value the soaking solution was still titrated withsulfuric acid to the initial pH value Table 4 shows the ti-tration pH value and titration sulfuric acid concentrationDuring the titration process each titration time wasrecorded along with the amount of titration sulfuric acidand the average acid consumption rate was obtained bydividing the amount of titration sulfuric acid at each intervalbased on the consecutive titration time periods
4 Results and Discussion
41 Apparent Characteristics of Concrete Subjected to SulfuricAcid Corrosion After 150 days the concrete specimenssubjected to sulfuric acid corrosion were taken out withdifferent water-cement ratios in the soaking solutions ofdifferent pH values Figure 3 shows the apparent changes in
Advances in Materials Science and Engineering 3
the characteristics of concrete specimensWith the decrease ofpH value the color of each exposed surface of concretespecimen in turn was gray yellow and white)e gray surfaceindicated that the corrosion degree of the concrete specimensuffered sulfuric acid was light and the color of the exposedsurface was basically the same as the noncorrosion surface)e yellow surface revealed that the sulfuric acid corrosiondegree was serious and the surface of the concrete specimenhad a loose yellow sand layer )e white surface shows thata large amount of CaSO4 (calcium sulfate) was deposited onthe concrete specimen surface In the initial stage of thesulfuric acid corrosion of concrete the reaction rate was veryfast and a large amount of CaSO4 was produced At the sametime CaSO4 blocked the surface pores of concrete specimenwhich caused the corrosion reaction rate to gradually slowdown so the corrosion degree gradually decreased
)e sizes of concrete specimens were measured beforeand after sulfuric acid corrosion using a vernier caliper
)ese concrete specimen measurements of the averagecorrosion layer thicknessesrsquo exposure to sulfuric acid after150 days are shown in Figure 4 When the soaking solutionrsquospH value was 250 the corrosion layer thickness was thelargest and the sulfuric acid corrosion degree was the mostserious When the soaking solutionrsquos pH value was between250 and 400 with the decrease of pH value the corrosionlayer thickness increased and the sulfuric acid corrosiondegree became more and more serious )is may be becausein the process of sulfuric acid corrosion for concrete theformation rate of CaSO4 was not much different from thedissolution rate so the corrosion reaction continued intothe concrete interior However the corrosion layer thicknessdecreased with the decrease of pH value when the soakingsolutionrsquos pH value was between 200 and 250 leading toa progressively smaller sulfuric acid corrosion degree )ismay be because the formation rate of CaSO4 in the earlycorrosion reaction was far greater than its dissolution rate
since the nondissolved CaSO4 gradually deposited onconcrete specimen surface which blocked the surface poresand slowed down the corrosion reaction signicantly
42 Sulfuric Acid Corrosion Law for Concrete According tothe sulfuric acid corrosion tests for concrete the acidconsumption rate over time was measured as shown inFigure 5 e acid consumption rate of concrete in the earlystage was relatively high but it decreased rapidly andgradually stabilized with the corrosion reaction e wholeprocess consisted of two stages the descending and stableperiods e cuto point was approximately 800 hours Inaddition the lower the soaking solutionrsquos pH value was thehigher the initial acid consumption rate of concrete leadingto a greater sulfuric acid corrosion rate for concrete
5 Verification of the Sulfuric Acid CorrosionModel and Determination of an ApparentDiffusion Coefficient for OH2 for Concrete
51 Verication of the Sulfuric Acid Corrosion Model forConcrete To clearly show the variation law of the acidconsumption rate of concrete over time the measured data
within 800 hours were tted according to (9) e ttingparameters are seen in Table 5 and the tting results areshown in Figure 6 Except for the last three groups of
experimental data (9) gave all test specimens a higher fittingdegree )e theoretical model can reflect the change lawaffecting the acid consumption rate over time therebyverifying the accuracy of the theoretical model When thesoaking time was relatively long (200 hours) the measuredvalues of the acid consumption rate were slightly lower thanfitted values and this trend was more obvious with thedecrease of pH value in the soaking solution )is phe-nomenon is related to the flocculent CaSO4 on the concretesurface which is also called the boundary layer
As the solubility of CaSO4 decreases with the decrease ofsoaking solution pH value the boundary layer thicknessincreases with the decrease of pH value )e presence of theboundary layer results in a decrease in the reaction ratewhich slows down the formation rate of CaSO4 At the sametime CaSO4 is constantly dissolving out of the concrete toreduce the CaSO4 concentration in the reaction boundarylayer resulting in the dissolution of the boundary layerwhich increases the reaction rate )e deceleration or ac-celeration of the reaction rate caused by the formation ordissolution of the boundary layer will eventually reacha dynamic equilibrium
52 Determination of an Apparent Diffusion Coefficient forOHminus for Concrete Under a sulfuric acid corrosion envi-ronment the dissolution of Ca(OH)2 in concrete results inthe change of concrete pore structures which further resultsin the change of concretersquos apparent diffusion coefficientHowever the apparent diffusion coefficient for concrete isdifficult to measure directly and then the formula for cal-culating the apparent diffusion coefficient for OHminus forconcrete can be obtained by (9) as
DOHminus 2A2
B middot S2 middot C 2OHminusM middot N
(10)
Choosing a shape function which can satisfy (5) yields
φ(θ) (1minus θ)2
ψ(θ) θ2(11)
Substituting (11) in (7) gives
M 13
N 2
(12)
Substituting (12) in (10) yields
DOHminus 3A2
B middot S2 middot C 2OHminus
(13)
)e total area S of the exposed surfaces of each group ofconcrete specimens was 003m2 and the concentration of OHminusin the saturated Ca(OH)2 solution at 20degC was 0045molmiddotLminus1then the apparent diffusion coefficients for OHminus for concretewere obtained by using Table 5 and (13) as shown in Figure 7When the soaking solutionrsquos pH value was more than 250 theapparent diffusion coefficients for OHminus for concrete increased
slowly with the decrease of pH value and then increased rapidlywith the further decrease of pH value
53 Effects of Water-Cement Ratio Soaking Solutionrsquos pHValue and Cement Proportion on the Apparent DiffusionCoefficient for OHminus for Concrete Because the relationshipwas not directly determined between the apparent diffusioncoefficient for OHminus for concrete and water-cement ratio thesoaking solutionrsquos pH value and cement proportion of C(C+FA+CA) required an analysis by ACE (alternating con-ditional expectation) regression [27] of nonparametric re-gression where x1 x2 x3 and y are water-cement ratiosoaking solutionrsquos pH value cement proportion andln(DOHminus times 1013) respectively Searching for the trans-formation relations of φ1(x1) φ2(x2) φ3(x3) and θ(y)
which can satisfy the following mapping relation betweeninput parameters of x1 x2 x3 and function of y gave
)e nonparametric regression analysis was performedusing ACE )e fitting correlation coefficient was 09923and the fitting effect was very good Table 6 gives the valuesof each parameter before and after ACE regression and (16)gives the mapping relations of x1simφ1(x1) x2simφ2(x2)x3simφ3(x3) and ysimθ(y) obtained using ACE Figure 8 givesthe relationship between the experimental and regressionvalues for y which is in good agreement with each other andhas a positive proportion relationship It can be seen fromthis that ACE has a very good practical value
φ1 x1( 1113857 34610x1 minus 18173
φ2 x2( 1113857 minus15847x2 + 46946
φ3 x3( 1113857 123549x3 minus 23583
θ(y) 03545yminus 08446
(16)
Combined with (14) to (16) as
y 976x1 minus 447x2 + 3485x3 + 385 (17)
Namely
DOHminus 10minus13 times exp1113888976w
cminus 447 pH
+ 3485C
C + FA + CA+ 3851113889 (18)
Equation (18) showed that when the pH value decreasedwater-cement ratio and cement proportion increased thusthe corrosion degree of concrete subjected to sulfuric acidincreased in severity
6 Conclusions
With the decrease of soaking solutionrsquos pH value the colorof the exposed concrete specimen surface changed from gray
to yellow and then to white e corrosion layer thickness ofthe concrete specimen did not increase continuously withthe decrease of pH value When the soaking solutionrsquos pHvalue was 250 the corrosion layer thickness reached the
maximum value which means the sulfuric acid corrosiondegree of concrete was the most serious
A sulfuric acid corrosion model for concrete wasestablished based on the reaction boundary layer theoryand was solved by applying the separation of variablesen a theoretical formula for the acid consumption rateof concrete was obtained e sulfuric acid corrosionprocess of concrete can be divided into two stages namelythe rapid corrosion stage and the stable corrosion stageBecause of the eect of the boundary layer the measuredacid consumption rate of concrete was slightly lower thanthe theoretical value when the soaking time was relativelylong rough the sulfuric acid corrosion tests for concretethe accuracy of the sulfuric acid corrosion model forconcrete was veried is model can be used to predict thesulfuric acid corrosion mechanism for concrete in practicalengineering and to provide the foundation for steel cor-rosion prediction
e sulfuric acid corrosion tests for concrete wereplanned using uniform design e apparent diusion co-ecient for OHminus for concrete was chosen as the evaluationindex for the sulfuric acid corrosion degree of concrete andthen the calculation formula was obtained through non-parametric regression e results showed that the apparentdiusion coecient for OHminus for concrete increased whenthe pH value decreased and the water-cement ratio and
1 2 3 4 5 6 7 8Test group
033 058 092 414 12115587
36827
103783
0
300
600
900
1200
DO
Hndash
(10ndash1
3 m2 middotsndash1
)
Figure 7 Apparent diusion coecient for OHminus for concrete
Table 6 Values of each parameter before and after ACE regression
Figure 8 Comparison of the experimental and regression valuesfor y
Advances in Materials Science and Engineering 9
cement proportion increased )e uniform design andnonparametric regression had a high efficiency in the ex-perimental research and matched each other well which wasof great significance to this scientific research
Data Availability
)e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
)e authors declare that they have no conflicts of interest
Acknowledgments
)is research was financially funded by the China Post-doctoral Science Foundation (2017M622789) and the Na-tional Natural Science Foundation of China (51078175)
References
[1] K He H Yang Z B Lu F F Jia E P Wang and Q X DongldquoEffect of matrix modification on durability of cementitiouscomposites in an acid rain environmentrdquo Journal of WuhanUniversity of TechnologyndashMaterials Science Edition vol 29no 3 pp 498ndash503 2014
[2] M P Lavigne A Bertron C Botanch et al ldquoInnovativeapproach to simulating the biodeterioration of industrialcementitious products in sewer environment Part II vali-dation on CAC and BFSC liningsrdquo Cement and ConcreteResearch vol 79 pp 409ndash418 2016
[3] B Huber H Hilbig M M Mago J E Drewes and E MullerldquoComparative analysis of biogenic and chemical sulfuric acidattack on hardened cement paste using laser ablation-ICP-MSrdquo Cement and Concrete Research vol 87 pp 14ndash21 2016
[4] N De Belie J Monteny A Beeldens E Vincke D VanGemert and W Verstraete ldquoExperimental research andprediction of the effect of chemical and biogenic sulfuric acidon different types of commercially produced concrete sewerpipesrdquo Cement and Concrete Research vol 34 no 12pp 2223ndash2236 2004
[5] P K Mehta ldquoDurability of concretemdashfifty years of progressrdquoin Proceeding of the 2nd International Conference on ConcreteDurability ACI SP126ndash01 pp 1ndash32 Sapporo Japan 1991
[6] Y Yang T Ji X J Lin C Y Chen and Z X Yang ldquoBiogenicsulfuric acid corrosion resistance of new artificial reef concreterdquoConstruction and Building Materials vol 158 pp 33ndash41 2018
[7] L Gu P Visintin and T Bennett ldquoEvaluation of accelerateddegradation test methods for cementitious composites subjectto sulfuric acid attack application to conventional and alkali-activated concretesrdquo Cement and Concrete Compositesvol 87 pp 187ndash204 2018
[8] X Li Y X Lin K Lin and T Ji ldquoStudy on the degradationmechanism of sulphoaluminate cement sea sand concreteeroded by biological sulfuric acidrdquo Construction and BuildingMaterials vol 157 pp 331ndash336 2017
[9] E Hewayde M Nehdi E Allouche and G Nakhla ldquoEffect ofmixture design parameters and wetting-drying cycles on re-sistance of concrete to sulfuric acid attackrdquo Journal of Materialsin Civil Engineering vol 19 no 2 pp 155ndash163 2007
[10] Y F Fan Z Q Hu H Y Luan D W Wang and A Chen ldquoAstudy of deterioration of reinforced concrete beams under various
forms of simulated acid rain attack in the laboratoryrdquo StructuralEngineering and Mechanics vol 52 no 1 pp 35ndash49 2014
[11] A Grandclerc P Dangla and M Gueguen-MinerbeldquoModelling of the sulfuric acid attack on different types ofcementitious materialsrdquo Cement and Concrete Researchvol 105 pp 126ndash133 2018
[12] J Hill E A Byars J H Sharp C J Lynsdale J C Cripps andQ Zhou ldquoAn experimental study of combined acid andsulfate attack of concreterdquo Cement and Concrete Compositesvol 25 no 8 pp 997ndash1003 2003
[13] Z T Chang X J Song R Munn and M Marosszeky ldquoUsinglimestone aggregates and different cements for enhancingresistance of concrete to sulphuric acid attackrdquo Cement andConcrete Research vol 35 no 8 pp 1486ndash1494 2006
[14] H GMinW P Zhang andX L Gu ldquoEffects of load damage onmoisture transport and relative humidity response in concreterdquoConstruction and Building Materials vol 169 pp 59ndash68 2018
[15] H G Min W P Zhang X L Gu and R Cerny ldquoCoupledheat and moisture transport in damaged concrete under anatmospheric environmentrdquo Construction and Building Ma-terials vol 143 pp 607ndash620 2017
[16] W P Zhang H G Min and X L Gu ldquoTemperature responseand moisture transport in damaged concrete under an at-mospheric environmentrdquo Construction and Building Mate-rials vol 123 pp 290ndash299 2016
[17] W P Zhang H G Min X L Gu Y Xi and Y S XingldquoMesoscale model for thermal conductivity of concreterdquoConstruction and Building Materials vol 98 pp 8ndash16 2015
[18] S Mirvalad and M Nokken ldquoStudying thaumasite sulfateattack using compressive strength and ultrasonic pulse ve-locityrdquo Materials and Structures vol 49 no 10 pp 4131ndash4146 2016
[19] M O Yusuf ldquoPerformance of slag blended alkaline activatedpalm oil fuel ash mortar in sulfate environmentsrdquo Con-struction and Building Materials vol 98 pp 417ndash424 2015
[20] S D Xie L Qi and D Zhou ldquoInvestigation of the effects ofacid rain on the deterioration of cement concrete usingaccelerated tests established in laboratoryrdquo Atmospheric En-vironment vol 38 no 27 pp 4457ndash4466 2004
[21] M Bohm J Devinny F Jahani and G Rosen ldquoOn a moving-boundary systemmodeling corrosion in sewer pipesrdquo AppliedMathematics and Computation vol 92 no 2-3 pp 247ndash2691998
[22] M Bohm J Devinny F Jahani F B Mansfeld I G Rosenand C Wang ldquoA moving boundary diffusion model for thecorrosion of concrete wastewater systems simulation andexperimental validationrdquo in Proceedings of the AmericanControl Conference pp 1739ndash1743 San Diego CA USA1999
[23] F Jahani J Devinny F Mansfeld and I G Rosen ldquoIn-vestigations of sulfuric acid corrosion of concrete I modelingand chemical observationsrdquo Journal of Environmental Engi-neering vol 127 no 7 pp 572ndash579 2001
[24] Z G Song X S Zhang and H G Min ldquoConcentrationboundary layer model of mortar corrosion by sulfuric acidrdquoJournal of Wuhan University of TechnologyndashMaterials ScienceEdition vol 26 no 3 pp 527ndash532 2011
[25] K T FangUniformDesign and UniformDesign Table SciencePress Beijing China 1994 in Chinese
[26] K T Fang and C X Ma Orthogonal and Uniform Design ofExperiments Science Press Beijing China 2001 in Chinese
[27] A M Hasofer and J Qu ldquoResponse surface modelling ofmonte carlo fire datardquo Fire Safety Journal vol 37 no 8pp 772ndash784 2002
10 Advances in Materials Science and Engineering
CorrosionInternational Journal of
Hindawiwwwhindawicom Volume 2018
Advances in
Materials Science and EngineeringHindawiwwwhindawicom Volume 2018
where S is the area of soaking surface (m2) and vH+ (t) is theacid consumption rate of concrete that is H+ consumptionper unit time (molmiddotsminus1)
Substituting (7) into (8) gives
vH+ (t) A middot [1minus exp(minusB middot t)]minus12
A S middot COHminus middot k middot N middot P middot DOHminus middot CH+( 111385712
B 2k middot P middot CH+ middot Mminus1
(9)
Equation (9) shows that the acid consumption rate ofconcrete is relatively high in the initial reaction stage decreasesrapidly with the increase of reaction time and will eventuallybecome a constant A Hence the whole process consists oftwo stages that is decline and stability)en the experimentalstudy and theoretical analysis for concrete subjected to sulfuricacid corrosion can be carried as shown in Section 3
3 Materials and Methods
31 Experimental Design and Specimen Preparation )euniform test design method [25 26] is a test design methodthat only considers the ldquouniform dispersionrdquo of the test pointin the test range It is designed by the well-designed tables theuniform design table )e uniform design table is usuallyrepresented by Un (qs) where U means uniform design nmeans n tests q indicates that every factor has q levels and sindicates that the table has s columns for example U8 (85)which means that 8 tests are required each factor has 8 levelsthe table has 5 columns and a maximum of 5 factors )ebiggest characteristic of uniform test design is that the numberof tests required is usually equal to the level number of factorsWhen the test factors have the same level number the uniformtest design needs less tests than the orthogonal test design
Considering the effects of the two factors of water-cementratio and soaking solutionrsquos pH value on the sulfuric acidcorrosion mechanism for concrete both factors have eightlevels (Table 1) Because this test is a problem of two factors andeight levels enabling better test results with fewer test numberssulfuric acid corrosion tests for concrete were designedaccording to the uniform test design method as shown inTable 2 Twenty-four concrete specimens were cast )e sizeswere all 100mmtimes 100mmtimes 100mm and each kind of water-cement ratio consisted of three specimens )e continuousgraded gravel of 5ndash16mmwas used as the coarse aggregate)econcrete mix proportions are in Table 3 Concrete specimenswere taken out from the standard curing room after 28 days
32 Sulfuric Acid Corrosion Tests for Concrete Five surfacesof concrete specimens were sealed with paraffin leaving onlyone surface as the exposed surface Eight plastic boxes wereused as the soaking pool and three concrete specimens wereplaced into each soaking pool In addition the exposedsurface of each concrete specimen was completely perpen-dicular to the bottom of the soaking pool )ese specimensremained in their boxes and soaking for 150 days at roomtemperature as shown in Figure 2
)e soaking solutions of sulfuric acid were prepared withdifferent initial pH values by mixing the distilled water andconcentrated sulfuric acid and the volume of soaking so-lution of each group was always 10 L )e change of soakingsolutionrsquos pH was measured by a portable pH meter in timeand then the soaking solution was titrated with sulfuric acidin time by a rubber head dropper and a cylinder so as toensure the soaking solutionrsquos pH value was basically con-stant At the same time the liquid phase was stirred to ensurea uniform concentration of sulfuric acid throughout thevolume of the liquid phase
In the early stage of experiment the soaking solution wastitrated with sulfuric acid when the measured pH value wasup to the titration pH value however in the final stage ofexperiment even if the measured pH value was not up to thetitration pH value the soaking solution was still titrated withsulfuric acid to the initial pH value Table 4 shows the ti-tration pH value and titration sulfuric acid concentrationDuring the titration process each titration time wasrecorded along with the amount of titration sulfuric acidand the average acid consumption rate was obtained bydividing the amount of titration sulfuric acid at each intervalbased on the consecutive titration time periods
4 Results and Discussion
41 Apparent Characteristics of Concrete Subjected to SulfuricAcid Corrosion After 150 days the concrete specimenssubjected to sulfuric acid corrosion were taken out withdifferent water-cement ratios in the soaking solutions ofdifferent pH values Figure 3 shows the apparent changes in
Advances in Materials Science and Engineering 3
the characteristics of concrete specimensWith the decrease ofpH value the color of each exposed surface of concretespecimen in turn was gray yellow and white)e gray surfaceindicated that the corrosion degree of the concrete specimensuffered sulfuric acid was light and the color of the exposedsurface was basically the same as the noncorrosion surface)e yellow surface revealed that the sulfuric acid corrosiondegree was serious and the surface of the concrete specimenhad a loose yellow sand layer )e white surface shows thata large amount of CaSO4 (calcium sulfate) was deposited onthe concrete specimen surface In the initial stage of thesulfuric acid corrosion of concrete the reaction rate was veryfast and a large amount of CaSO4 was produced At the sametime CaSO4 blocked the surface pores of concrete specimenwhich caused the corrosion reaction rate to gradually slowdown so the corrosion degree gradually decreased
)e sizes of concrete specimens were measured beforeand after sulfuric acid corrosion using a vernier caliper
)ese concrete specimen measurements of the averagecorrosion layer thicknessesrsquo exposure to sulfuric acid after150 days are shown in Figure 4 When the soaking solutionrsquospH value was 250 the corrosion layer thickness was thelargest and the sulfuric acid corrosion degree was the mostserious When the soaking solutionrsquos pH value was between250 and 400 with the decrease of pH value the corrosionlayer thickness increased and the sulfuric acid corrosiondegree became more and more serious )is may be becausein the process of sulfuric acid corrosion for concrete theformation rate of CaSO4 was not much different from thedissolution rate so the corrosion reaction continued intothe concrete interior However the corrosion layer thicknessdecreased with the decrease of pH value when the soakingsolutionrsquos pH value was between 200 and 250 leading toa progressively smaller sulfuric acid corrosion degree )ismay be because the formation rate of CaSO4 in the earlycorrosion reaction was far greater than its dissolution rate
since the nondissolved CaSO4 gradually deposited onconcrete specimen surface which blocked the surface poresand slowed down the corrosion reaction signicantly
42 Sulfuric Acid Corrosion Law for Concrete According tothe sulfuric acid corrosion tests for concrete the acidconsumption rate over time was measured as shown inFigure 5 e acid consumption rate of concrete in the earlystage was relatively high but it decreased rapidly andgradually stabilized with the corrosion reaction e wholeprocess consisted of two stages the descending and stableperiods e cuto point was approximately 800 hours Inaddition the lower the soaking solutionrsquos pH value was thehigher the initial acid consumption rate of concrete leadingto a greater sulfuric acid corrosion rate for concrete
5 Verification of the Sulfuric Acid CorrosionModel and Determination of an ApparentDiffusion Coefficient for OH2 for Concrete
51 Verication of the Sulfuric Acid Corrosion Model forConcrete To clearly show the variation law of the acidconsumption rate of concrete over time the measured data
within 800 hours were tted according to (9) e ttingparameters are seen in Table 5 and the tting results areshown in Figure 6 Except for the last three groups of
experimental data (9) gave all test specimens a higher fittingdegree )e theoretical model can reflect the change lawaffecting the acid consumption rate over time therebyverifying the accuracy of the theoretical model When thesoaking time was relatively long (200 hours) the measuredvalues of the acid consumption rate were slightly lower thanfitted values and this trend was more obvious with thedecrease of pH value in the soaking solution )is phe-nomenon is related to the flocculent CaSO4 on the concretesurface which is also called the boundary layer
As the solubility of CaSO4 decreases with the decrease ofsoaking solution pH value the boundary layer thicknessincreases with the decrease of pH value )e presence of theboundary layer results in a decrease in the reaction ratewhich slows down the formation rate of CaSO4 At the sametime CaSO4 is constantly dissolving out of the concrete toreduce the CaSO4 concentration in the reaction boundarylayer resulting in the dissolution of the boundary layerwhich increases the reaction rate )e deceleration or ac-celeration of the reaction rate caused by the formation ordissolution of the boundary layer will eventually reacha dynamic equilibrium
52 Determination of an Apparent Diffusion Coefficient forOHminus for Concrete Under a sulfuric acid corrosion envi-ronment the dissolution of Ca(OH)2 in concrete results inthe change of concrete pore structures which further resultsin the change of concretersquos apparent diffusion coefficientHowever the apparent diffusion coefficient for concrete isdifficult to measure directly and then the formula for cal-culating the apparent diffusion coefficient for OHminus forconcrete can be obtained by (9) as
DOHminus 2A2
B middot S2 middot C 2OHminusM middot N
(10)
Choosing a shape function which can satisfy (5) yields
φ(θ) (1minus θ)2
ψ(θ) θ2(11)
Substituting (11) in (7) gives
M 13
N 2
(12)
Substituting (12) in (10) yields
DOHminus 3A2
B middot S2 middot C 2OHminus
(13)
)e total area S of the exposed surfaces of each group ofconcrete specimens was 003m2 and the concentration of OHminusin the saturated Ca(OH)2 solution at 20degC was 0045molmiddotLminus1then the apparent diffusion coefficients for OHminus for concretewere obtained by using Table 5 and (13) as shown in Figure 7When the soaking solutionrsquos pH value was more than 250 theapparent diffusion coefficients for OHminus for concrete increased
slowly with the decrease of pH value and then increased rapidlywith the further decrease of pH value
53 Effects of Water-Cement Ratio Soaking Solutionrsquos pHValue and Cement Proportion on the Apparent DiffusionCoefficient for OHminus for Concrete Because the relationshipwas not directly determined between the apparent diffusioncoefficient for OHminus for concrete and water-cement ratio thesoaking solutionrsquos pH value and cement proportion of C(C+FA+CA) required an analysis by ACE (alternating con-ditional expectation) regression [27] of nonparametric re-gression where x1 x2 x3 and y are water-cement ratiosoaking solutionrsquos pH value cement proportion andln(DOHminus times 1013) respectively Searching for the trans-formation relations of φ1(x1) φ2(x2) φ3(x3) and θ(y)
which can satisfy the following mapping relation betweeninput parameters of x1 x2 x3 and function of y gave
)e nonparametric regression analysis was performedusing ACE )e fitting correlation coefficient was 09923and the fitting effect was very good Table 6 gives the valuesof each parameter before and after ACE regression and (16)gives the mapping relations of x1simφ1(x1) x2simφ2(x2)x3simφ3(x3) and ysimθ(y) obtained using ACE Figure 8 givesthe relationship between the experimental and regressionvalues for y which is in good agreement with each other andhas a positive proportion relationship It can be seen fromthis that ACE has a very good practical value
φ1 x1( 1113857 34610x1 minus 18173
φ2 x2( 1113857 minus15847x2 + 46946
φ3 x3( 1113857 123549x3 minus 23583
θ(y) 03545yminus 08446
(16)
Combined with (14) to (16) as
y 976x1 minus 447x2 + 3485x3 + 385 (17)
Namely
DOHminus 10minus13 times exp1113888976w
cminus 447 pH
+ 3485C
C + FA + CA+ 3851113889 (18)
Equation (18) showed that when the pH value decreasedwater-cement ratio and cement proportion increased thusthe corrosion degree of concrete subjected to sulfuric acidincreased in severity
6 Conclusions
With the decrease of soaking solutionrsquos pH value the colorof the exposed concrete specimen surface changed from gray
to yellow and then to white e corrosion layer thickness ofthe concrete specimen did not increase continuously withthe decrease of pH value When the soaking solutionrsquos pHvalue was 250 the corrosion layer thickness reached the
maximum value which means the sulfuric acid corrosiondegree of concrete was the most serious
A sulfuric acid corrosion model for concrete wasestablished based on the reaction boundary layer theoryand was solved by applying the separation of variablesen a theoretical formula for the acid consumption rateof concrete was obtained e sulfuric acid corrosionprocess of concrete can be divided into two stages namelythe rapid corrosion stage and the stable corrosion stageBecause of the eect of the boundary layer the measuredacid consumption rate of concrete was slightly lower thanthe theoretical value when the soaking time was relativelylong rough the sulfuric acid corrosion tests for concretethe accuracy of the sulfuric acid corrosion model forconcrete was veried is model can be used to predict thesulfuric acid corrosion mechanism for concrete in practicalengineering and to provide the foundation for steel cor-rosion prediction
e sulfuric acid corrosion tests for concrete wereplanned using uniform design e apparent diusion co-ecient for OHminus for concrete was chosen as the evaluationindex for the sulfuric acid corrosion degree of concrete andthen the calculation formula was obtained through non-parametric regression e results showed that the apparentdiusion coecient for OHminus for concrete increased whenthe pH value decreased and the water-cement ratio and
1 2 3 4 5 6 7 8Test group
033 058 092 414 12115587
36827
103783
0
300
600
900
1200
DO
Hndash
(10ndash1
3 m2 middotsndash1
)
Figure 7 Apparent diusion coecient for OHminus for concrete
Table 6 Values of each parameter before and after ACE regression
Figure 8 Comparison of the experimental and regression valuesfor y
Advances in Materials Science and Engineering 9
cement proportion increased )e uniform design andnonparametric regression had a high efficiency in the ex-perimental research and matched each other well which wasof great significance to this scientific research
Data Availability
)e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
)e authors declare that they have no conflicts of interest
Acknowledgments
)is research was financially funded by the China Post-doctoral Science Foundation (2017M622789) and the Na-tional Natural Science Foundation of China (51078175)
References
[1] K He H Yang Z B Lu F F Jia E P Wang and Q X DongldquoEffect of matrix modification on durability of cementitiouscomposites in an acid rain environmentrdquo Journal of WuhanUniversity of TechnologyndashMaterials Science Edition vol 29no 3 pp 498ndash503 2014
[2] M P Lavigne A Bertron C Botanch et al ldquoInnovativeapproach to simulating the biodeterioration of industrialcementitious products in sewer environment Part II vali-dation on CAC and BFSC liningsrdquo Cement and ConcreteResearch vol 79 pp 409ndash418 2016
[3] B Huber H Hilbig M M Mago J E Drewes and E MullerldquoComparative analysis of biogenic and chemical sulfuric acidattack on hardened cement paste using laser ablation-ICP-MSrdquo Cement and Concrete Research vol 87 pp 14ndash21 2016
[4] N De Belie J Monteny A Beeldens E Vincke D VanGemert and W Verstraete ldquoExperimental research andprediction of the effect of chemical and biogenic sulfuric acidon different types of commercially produced concrete sewerpipesrdquo Cement and Concrete Research vol 34 no 12pp 2223ndash2236 2004
[5] P K Mehta ldquoDurability of concretemdashfifty years of progressrdquoin Proceeding of the 2nd International Conference on ConcreteDurability ACI SP126ndash01 pp 1ndash32 Sapporo Japan 1991
[6] Y Yang T Ji X J Lin C Y Chen and Z X Yang ldquoBiogenicsulfuric acid corrosion resistance of new artificial reef concreterdquoConstruction and Building Materials vol 158 pp 33ndash41 2018
[7] L Gu P Visintin and T Bennett ldquoEvaluation of accelerateddegradation test methods for cementitious composites subjectto sulfuric acid attack application to conventional and alkali-activated concretesrdquo Cement and Concrete Compositesvol 87 pp 187ndash204 2018
[8] X Li Y X Lin K Lin and T Ji ldquoStudy on the degradationmechanism of sulphoaluminate cement sea sand concreteeroded by biological sulfuric acidrdquo Construction and BuildingMaterials vol 157 pp 331ndash336 2017
[9] E Hewayde M Nehdi E Allouche and G Nakhla ldquoEffect ofmixture design parameters and wetting-drying cycles on re-sistance of concrete to sulfuric acid attackrdquo Journal of Materialsin Civil Engineering vol 19 no 2 pp 155ndash163 2007
[10] Y F Fan Z Q Hu H Y Luan D W Wang and A Chen ldquoAstudy of deterioration of reinforced concrete beams under various
forms of simulated acid rain attack in the laboratoryrdquo StructuralEngineering and Mechanics vol 52 no 1 pp 35ndash49 2014
[11] A Grandclerc P Dangla and M Gueguen-MinerbeldquoModelling of the sulfuric acid attack on different types ofcementitious materialsrdquo Cement and Concrete Researchvol 105 pp 126ndash133 2018
[12] J Hill E A Byars J H Sharp C J Lynsdale J C Cripps andQ Zhou ldquoAn experimental study of combined acid andsulfate attack of concreterdquo Cement and Concrete Compositesvol 25 no 8 pp 997ndash1003 2003
[13] Z T Chang X J Song R Munn and M Marosszeky ldquoUsinglimestone aggregates and different cements for enhancingresistance of concrete to sulphuric acid attackrdquo Cement andConcrete Research vol 35 no 8 pp 1486ndash1494 2006
[14] H GMinW P Zhang andX L Gu ldquoEffects of load damage onmoisture transport and relative humidity response in concreterdquoConstruction and Building Materials vol 169 pp 59ndash68 2018
[15] H G Min W P Zhang X L Gu and R Cerny ldquoCoupledheat and moisture transport in damaged concrete under anatmospheric environmentrdquo Construction and Building Ma-terials vol 143 pp 607ndash620 2017
[16] W P Zhang H G Min and X L Gu ldquoTemperature responseand moisture transport in damaged concrete under an at-mospheric environmentrdquo Construction and Building Mate-rials vol 123 pp 290ndash299 2016
[17] W P Zhang H G Min X L Gu Y Xi and Y S XingldquoMesoscale model for thermal conductivity of concreterdquoConstruction and Building Materials vol 98 pp 8ndash16 2015
[18] S Mirvalad and M Nokken ldquoStudying thaumasite sulfateattack using compressive strength and ultrasonic pulse ve-locityrdquo Materials and Structures vol 49 no 10 pp 4131ndash4146 2016
[19] M O Yusuf ldquoPerformance of slag blended alkaline activatedpalm oil fuel ash mortar in sulfate environmentsrdquo Con-struction and Building Materials vol 98 pp 417ndash424 2015
[20] S D Xie L Qi and D Zhou ldquoInvestigation of the effects ofacid rain on the deterioration of cement concrete usingaccelerated tests established in laboratoryrdquo Atmospheric En-vironment vol 38 no 27 pp 4457ndash4466 2004
[21] M Bohm J Devinny F Jahani and G Rosen ldquoOn a moving-boundary systemmodeling corrosion in sewer pipesrdquo AppliedMathematics and Computation vol 92 no 2-3 pp 247ndash2691998
[22] M Bohm J Devinny F Jahani F B Mansfeld I G Rosenand C Wang ldquoA moving boundary diffusion model for thecorrosion of concrete wastewater systems simulation andexperimental validationrdquo in Proceedings of the AmericanControl Conference pp 1739ndash1743 San Diego CA USA1999
[23] F Jahani J Devinny F Mansfeld and I G Rosen ldquoIn-vestigations of sulfuric acid corrosion of concrete I modelingand chemical observationsrdquo Journal of Environmental Engi-neering vol 127 no 7 pp 572ndash579 2001
[24] Z G Song X S Zhang and H G Min ldquoConcentrationboundary layer model of mortar corrosion by sulfuric acidrdquoJournal of Wuhan University of TechnologyndashMaterials ScienceEdition vol 26 no 3 pp 527ndash532 2011
[25] K T FangUniformDesign and UniformDesign Table SciencePress Beijing China 1994 in Chinese
[26] K T Fang and C X Ma Orthogonal and Uniform Design ofExperiments Science Press Beijing China 2001 in Chinese
[27] A M Hasofer and J Qu ldquoResponse surface modelling ofmonte carlo fire datardquo Fire Safety Journal vol 37 no 8pp 772ndash784 2002
10 Advances in Materials Science and Engineering
CorrosionInternational Journal of
Hindawiwwwhindawicom Volume 2018
Advances in
Materials Science and EngineeringHindawiwwwhindawicom Volume 2018
the characteristics of concrete specimensWith the decrease ofpH value the color of each exposed surface of concretespecimen in turn was gray yellow and white)e gray surfaceindicated that the corrosion degree of the concrete specimensuffered sulfuric acid was light and the color of the exposedsurface was basically the same as the noncorrosion surface)e yellow surface revealed that the sulfuric acid corrosiondegree was serious and the surface of the concrete specimenhad a loose yellow sand layer )e white surface shows thata large amount of CaSO4 (calcium sulfate) was deposited onthe concrete specimen surface In the initial stage of thesulfuric acid corrosion of concrete the reaction rate was veryfast and a large amount of CaSO4 was produced At the sametime CaSO4 blocked the surface pores of concrete specimenwhich caused the corrosion reaction rate to gradually slowdown so the corrosion degree gradually decreased
)e sizes of concrete specimens were measured beforeand after sulfuric acid corrosion using a vernier caliper
)ese concrete specimen measurements of the averagecorrosion layer thicknessesrsquo exposure to sulfuric acid after150 days are shown in Figure 4 When the soaking solutionrsquospH value was 250 the corrosion layer thickness was thelargest and the sulfuric acid corrosion degree was the mostserious When the soaking solutionrsquos pH value was between250 and 400 with the decrease of pH value the corrosionlayer thickness increased and the sulfuric acid corrosiondegree became more and more serious )is may be becausein the process of sulfuric acid corrosion for concrete theformation rate of CaSO4 was not much different from thedissolution rate so the corrosion reaction continued intothe concrete interior However the corrosion layer thicknessdecreased with the decrease of pH value when the soakingsolutionrsquos pH value was between 200 and 250 leading toa progressively smaller sulfuric acid corrosion degree )ismay be because the formation rate of CaSO4 in the earlycorrosion reaction was far greater than its dissolution rate
since the nondissolved CaSO4 gradually deposited onconcrete specimen surface which blocked the surface poresand slowed down the corrosion reaction signicantly
42 Sulfuric Acid Corrosion Law for Concrete According tothe sulfuric acid corrosion tests for concrete the acidconsumption rate over time was measured as shown inFigure 5 e acid consumption rate of concrete in the earlystage was relatively high but it decreased rapidly andgradually stabilized with the corrosion reaction e wholeprocess consisted of two stages the descending and stableperiods e cuto point was approximately 800 hours Inaddition the lower the soaking solutionrsquos pH value was thehigher the initial acid consumption rate of concrete leadingto a greater sulfuric acid corrosion rate for concrete
5 Verification of the Sulfuric Acid CorrosionModel and Determination of an ApparentDiffusion Coefficient for OH2 for Concrete
51 Verication of the Sulfuric Acid Corrosion Model forConcrete To clearly show the variation law of the acidconsumption rate of concrete over time the measured data
within 800 hours were tted according to (9) e ttingparameters are seen in Table 5 and the tting results areshown in Figure 6 Except for the last three groups of
experimental data (9) gave all test specimens a higher fittingdegree )e theoretical model can reflect the change lawaffecting the acid consumption rate over time therebyverifying the accuracy of the theoretical model When thesoaking time was relatively long (200 hours) the measuredvalues of the acid consumption rate were slightly lower thanfitted values and this trend was more obvious with thedecrease of pH value in the soaking solution )is phe-nomenon is related to the flocculent CaSO4 on the concretesurface which is also called the boundary layer
As the solubility of CaSO4 decreases with the decrease ofsoaking solution pH value the boundary layer thicknessincreases with the decrease of pH value )e presence of theboundary layer results in a decrease in the reaction ratewhich slows down the formation rate of CaSO4 At the sametime CaSO4 is constantly dissolving out of the concrete toreduce the CaSO4 concentration in the reaction boundarylayer resulting in the dissolution of the boundary layerwhich increases the reaction rate )e deceleration or ac-celeration of the reaction rate caused by the formation ordissolution of the boundary layer will eventually reacha dynamic equilibrium
52 Determination of an Apparent Diffusion Coefficient forOHminus for Concrete Under a sulfuric acid corrosion envi-ronment the dissolution of Ca(OH)2 in concrete results inthe change of concrete pore structures which further resultsin the change of concretersquos apparent diffusion coefficientHowever the apparent diffusion coefficient for concrete isdifficult to measure directly and then the formula for cal-culating the apparent diffusion coefficient for OHminus forconcrete can be obtained by (9) as
DOHminus 2A2
B middot S2 middot C 2OHminusM middot N
(10)
Choosing a shape function which can satisfy (5) yields
φ(θ) (1minus θ)2
ψ(θ) θ2(11)
Substituting (11) in (7) gives
M 13
N 2
(12)
Substituting (12) in (10) yields
DOHminus 3A2
B middot S2 middot C 2OHminus
(13)
)e total area S of the exposed surfaces of each group ofconcrete specimens was 003m2 and the concentration of OHminusin the saturated Ca(OH)2 solution at 20degC was 0045molmiddotLminus1then the apparent diffusion coefficients for OHminus for concretewere obtained by using Table 5 and (13) as shown in Figure 7When the soaking solutionrsquos pH value was more than 250 theapparent diffusion coefficients for OHminus for concrete increased
slowly with the decrease of pH value and then increased rapidlywith the further decrease of pH value
53 Effects of Water-Cement Ratio Soaking Solutionrsquos pHValue and Cement Proportion on the Apparent DiffusionCoefficient for OHminus for Concrete Because the relationshipwas not directly determined between the apparent diffusioncoefficient for OHminus for concrete and water-cement ratio thesoaking solutionrsquos pH value and cement proportion of C(C+FA+CA) required an analysis by ACE (alternating con-ditional expectation) regression [27] of nonparametric re-gression where x1 x2 x3 and y are water-cement ratiosoaking solutionrsquos pH value cement proportion andln(DOHminus times 1013) respectively Searching for the trans-formation relations of φ1(x1) φ2(x2) φ3(x3) and θ(y)
which can satisfy the following mapping relation betweeninput parameters of x1 x2 x3 and function of y gave
)e nonparametric regression analysis was performedusing ACE )e fitting correlation coefficient was 09923and the fitting effect was very good Table 6 gives the valuesof each parameter before and after ACE regression and (16)gives the mapping relations of x1simφ1(x1) x2simφ2(x2)x3simφ3(x3) and ysimθ(y) obtained using ACE Figure 8 givesthe relationship between the experimental and regressionvalues for y which is in good agreement with each other andhas a positive proportion relationship It can be seen fromthis that ACE has a very good practical value
φ1 x1( 1113857 34610x1 minus 18173
φ2 x2( 1113857 minus15847x2 + 46946
φ3 x3( 1113857 123549x3 minus 23583
θ(y) 03545yminus 08446
(16)
Combined with (14) to (16) as
y 976x1 minus 447x2 + 3485x3 + 385 (17)
Namely
DOHminus 10minus13 times exp1113888976w
cminus 447 pH
+ 3485C
C + FA + CA+ 3851113889 (18)
Equation (18) showed that when the pH value decreasedwater-cement ratio and cement proportion increased thusthe corrosion degree of concrete subjected to sulfuric acidincreased in severity
6 Conclusions
With the decrease of soaking solutionrsquos pH value the colorof the exposed concrete specimen surface changed from gray
to yellow and then to white e corrosion layer thickness ofthe concrete specimen did not increase continuously withthe decrease of pH value When the soaking solutionrsquos pHvalue was 250 the corrosion layer thickness reached the
maximum value which means the sulfuric acid corrosiondegree of concrete was the most serious
A sulfuric acid corrosion model for concrete wasestablished based on the reaction boundary layer theoryand was solved by applying the separation of variablesen a theoretical formula for the acid consumption rateof concrete was obtained e sulfuric acid corrosionprocess of concrete can be divided into two stages namelythe rapid corrosion stage and the stable corrosion stageBecause of the eect of the boundary layer the measuredacid consumption rate of concrete was slightly lower thanthe theoretical value when the soaking time was relativelylong rough the sulfuric acid corrosion tests for concretethe accuracy of the sulfuric acid corrosion model forconcrete was veried is model can be used to predict thesulfuric acid corrosion mechanism for concrete in practicalengineering and to provide the foundation for steel cor-rosion prediction
e sulfuric acid corrosion tests for concrete wereplanned using uniform design e apparent diusion co-ecient for OHminus for concrete was chosen as the evaluationindex for the sulfuric acid corrosion degree of concrete andthen the calculation formula was obtained through non-parametric regression e results showed that the apparentdiusion coecient for OHminus for concrete increased whenthe pH value decreased and the water-cement ratio and
1 2 3 4 5 6 7 8Test group
033 058 092 414 12115587
36827
103783
0
300
600
900
1200
DO
Hndash
(10ndash1
3 m2 middotsndash1
)
Figure 7 Apparent diusion coecient for OHminus for concrete
Table 6 Values of each parameter before and after ACE regression
Figure 8 Comparison of the experimental and regression valuesfor y
Advances in Materials Science and Engineering 9
cement proportion increased )e uniform design andnonparametric regression had a high efficiency in the ex-perimental research and matched each other well which wasof great significance to this scientific research
Data Availability
)e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
)e authors declare that they have no conflicts of interest
Acknowledgments
)is research was financially funded by the China Post-doctoral Science Foundation (2017M622789) and the Na-tional Natural Science Foundation of China (51078175)
References
[1] K He H Yang Z B Lu F F Jia E P Wang and Q X DongldquoEffect of matrix modification on durability of cementitiouscomposites in an acid rain environmentrdquo Journal of WuhanUniversity of TechnologyndashMaterials Science Edition vol 29no 3 pp 498ndash503 2014
[2] M P Lavigne A Bertron C Botanch et al ldquoInnovativeapproach to simulating the biodeterioration of industrialcementitious products in sewer environment Part II vali-dation on CAC and BFSC liningsrdquo Cement and ConcreteResearch vol 79 pp 409ndash418 2016
[3] B Huber H Hilbig M M Mago J E Drewes and E MullerldquoComparative analysis of biogenic and chemical sulfuric acidattack on hardened cement paste using laser ablation-ICP-MSrdquo Cement and Concrete Research vol 87 pp 14ndash21 2016
[4] N De Belie J Monteny A Beeldens E Vincke D VanGemert and W Verstraete ldquoExperimental research andprediction of the effect of chemical and biogenic sulfuric acidon different types of commercially produced concrete sewerpipesrdquo Cement and Concrete Research vol 34 no 12pp 2223ndash2236 2004
[5] P K Mehta ldquoDurability of concretemdashfifty years of progressrdquoin Proceeding of the 2nd International Conference on ConcreteDurability ACI SP126ndash01 pp 1ndash32 Sapporo Japan 1991
[6] Y Yang T Ji X J Lin C Y Chen and Z X Yang ldquoBiogenicsulfuric acid corrosion resistance of new artificial reef concreterdquoConstruction and Building Materials vol 158 pp 33ndash41 2018
[7] L Gu P Visintin and T Bennett ldquoEvaluation of accelerateddegradation test methods for cementitious composites subjectto sulfuric acid attack application to conventional and alkali-activated concretesrdquo Cement and Concrete Compositesvol 87 pp 187ndash204 2018
[8] X Li Y X Lin K Lin and T Ji ldquoStudy on the degradationmechanism of sulphoaluminate cement sea sand concreteeroded by biological sulfuric acidrdquo Construction and BuildingMaterials vol 157 pp 331ndash336 2017
[9] E Hewayde M Nehdi E Allouche and G Nakhla ldquoEffect ofmixture design parameters and wetting-drying cycles on re-sistance of concrete to sulfuric acid attackrdquo Journal of Materialsin Civil Engineering vol 19 no 2 pp 155ndash163 2007
[10] Y F Fan Z Q Hu H Y Luan D W Wang and A Chen ldquoAstudy of deterioration of reinforced concrete beams under various
forms of simulated acid rain attack in the laboratoryrdquo StructuralEngineering and Mechanics vol 52 no 1 pp 35ndash49 2014
[11] A Grandclerc P Dangla and M Gueguen-MinerbeldquoModelling of the sulfuric acid attack on different types ofcementitious materialsrdquo Cement and Concrete Researchvol 105 pp 126ndash133 2018
[12] J Hill E A Byars J H Sharp C J Lynsdale J C Cripps andQ Zhou ldquoAn experimental study of combined acid andsulfate attack of concreterdquo Cement and Concrete Compositesvol 25 no 8 pp 997ndash1003 2003
[13] Z T Chang X J Song R Munn and M Marosszeky ldquoUsinglimestone aggregates and different cements for enhancingresistance of concrete to sulphuric acid attackrdquo Cement andConcrete Research vol 35 no 8 pp 1486ndash1494 2006
[14] H GMinW P Zhang andX L Gu ldquoEffects of load damage onmoisture transport and relative humidity response in concreterdquoConstruction and Building Materials vol 169 pp 59ndash68 2018
[15] H G Min W P Zhang X L Gu and R Cerny ldquoCoupledheat and moisture transport in damaged concrete under anatmospheric environmentrdquo Construction and Building Ma-terials vol 143 pp 607ndash620 2017
[16] W P Zhang H G Min and X L Gu ldquoTemperature responseand moisture transport in damaged concrete under an at-mospheric environmentrdquo Construction and Building Mate-rials vol 123 pp 290ndash299 2016
[17] W P Zhang H G Min X L Gu Y Xi and Y S XingldquoMesoscale model for thermal conductivity of concreterdquoConstruction and Building Materials vol 98 pp 8ndash16 2015
[18] S Mirvalad and M Nokken ldquoStudying thaumasite sulfateattack using compressive strength and ultrasonic pulse ve-locityrdquo Materials and Structures vol 49 no 10 pp 4131ndash4146 2016
[19] M O Yusuf ldquoPerformance of slag blended alkaline activatedpalm oil fuel ash mortar in sulfate environmentsrdquo Con-struction and Building Materials vol 98 pp 417ndash424 2015
[20] S D Xie L Qi and D Zhou ldquoInvestigation of the effects ofacid rain on the deterioration of cement concrete usingaccelerated tests established in laboratoryrdquo Atmospheric En-vironment vol 38 no 27 pp 4457ndash4466 2004
[21] M Bohm J Devinny F Jahani and G Rosen ldquoOn a moving-boundary systemmodeling corrosion in sewer pipesrdquo AppliedMathematics and Computation vol 92 no 2-3 pp 247ndash2691998
[22] M Bohm J Devinny F Jahani F B Mansfeld I G Rosenand C Wang ldquoA moving boundary diffusion model for thecorrosion of concrete wastewater systems simulation andexperimental validationrdquo in Proceedings of the AmericanControl Conference pp 1739ndash1743 San Diego CA USA1999
[23] F Jahani J Devinny F Mansfeld and I G Rosen ldquoIn-vestigations of sulfuric acid corrosion of concrete I modelingand chemical observationsrdquo Journal of Environmental Engi-neering vol 127 no 7 pp 572ndash579 2001
[24] Z G Song X S Zhang and H G Min ldquoConcentrationboundary layer model of mortar corrosion by sulfuric acidrdquoJournal of Wuhan University of TechnologyndashMaterials ScienceEdition vol 26 no 3 pp 527ndash532 2011
[25] K T FangUniformDesign and UniformDesign Table SciencePress Beijing China 1994 in Chinese
[26] K T Fang and C X Ma Orthogonal and Uniform Design ofExperiments Science Press Beijing China 2001 in Chinese
[27] A M Hasofer and J Qu ldquoResponse surface modelling ofmonte carlo fire datardquo Fire Safety Journal vol 37 no 8pp 772ndash784 2002
10 Advances in Materials Science and Engineering
CorrosionInternational Journal of
Hindawiwwwhindawicom Volume 2018
Advances in
Materials Science and EngineeringHindawiwwwhindawicom Volume 2018
since the nondissolved CaSO4 gradually deposited onconcrete specimen surface which blocked the surface poresand slowed down the corrosion reaction signicantly
42 Sulfuric Acid Corrosion Law for Concrete According tothe sulfuric acid corrosion tests for concrete the acidconsumption rate over time was measured as shown inFigure 5 e acid consumption rate of concrete in the earlystage was relatively high but it decreased rapidly andgradually stabilized with the corrosion reaction e wholeprocess consisted of two stages the descending and stableperiods e cuto point was approximately 800 hours Inaddition the lower the soaking solutionrsquos pH value was thehigher the initial acid consumption rate of concrete leadingto a greater sulfuric acid corrosion rate for concrete
5 Verification of the Sulfuric Acid CorrosionModel and Determination of an ApparentDiffusion Coefficient for OH2 for Concrete
51 Verication of the Sulfuric Acid Corrosion Model forConcrete To clearly show the variation law of the acidconsumption rate of concrete over time the measured data
within 800 hours were tted according to (9) e ttingparameters are seen in Table 5 and the tting results areshown in Figure 6 Except for the last three groups of
experimental data (9) gave all test specimens a higher fittingdegree )e theoretical model can reflect the change lawaffecting the acid consumption rate over time therebyverifying the accuracy of the theoretical model When thesoaking time was relatively long (200 hours) the measuredvalues of the acid consumption rate were slightly lower thanfitted values and this trend was more obvious with thedecrease of pH value in the soaking solution )is phe-nomenon is related to the flocculent CaSO4 on the concretesurface which is also called the boundary layer
As the solubility of CaSO4 decreases with the decrease ofsoaking solution pH value the boundary layer thicknessincreases with the decrease of pH value )e presence of theboundary layer results in a decrease in the reaction ratewhich slows down the formation rate of CaSO4 At the sametime CaSO4 is constantly dissolving out of the concrete toreduce the CaSO4 concentration in the reaction boundarylayer resulting in the dissolution of the boundary layerwhich increases the reaction rate )e deceleration or ac-celeration of the reaction rate caused by the formation ordissolution of the boundary layer will eventually reacha dynamic equilibrium
52 Determination of an Apparent Diffusion Coefficient forOHminus for Concrete Under a sulfuric acid corrosion envi-ronment the dissolution of Ca(OH)2 in concrete results inthe change of concrete pore structures which further resultsin the change of concretersquos apparent diffusion coefficientHowever the apparent diffusion coefficient for concrete isdifficult to measure directly and then the formula for cal-culating the apparent diffusion coefficient for OHminus forconcrete can be obtained by (9) as
DOHminus 2A2
B middot S2 middot C 2OHminusM middot N
(10)
Choosing a shape function which can satisfy (5) yields
φ(θ) (1minus θ)2
ψ(θ) θ2(11)
Substituting (11) in (7) gives
M 13
N 2
(12)
Substituting (12) in (10) yields
DOHminus 3A2
B middot S2 middot C 2OHminus
(13)
)e total area S of the exposed surfaces of each group ofconcrete specimens was 003m2 and the concentration of OHminusin the saturated Ca(OH)2 solution at 20degC was 0045molmiddotLminus1then the apparent diffusion coefficients for OHminus for concretewere obtained by using Table 5 and (13) as shown in Figure 7When the soaking solutionrsquos pH value was more than 250 theapparent diffusion coefficients for OHminus for concrete increased
slowly with the decrease of pH value and then increased rapidlywith the further decrease of pH value
53 Effects of Water-Cement Ratio Soaking Solutionrsquos pHValue and Cement Proportion on the Apparent DiffusionCoefficient for OHminus for Concrete Because the relationshipwas not directly determined between the apparent diffusioncoefficient for OHminus for concrete and water-cement ratio thesoaking solutionrsquos pH value and cement proportion of C(C+FA+CA) required an analysis by ACE (alternating con-ditional expectation) regression [27] of nonparametric re-gression where x1 x2 x3 and y are water-cement ratiosoaking solutionrsquos pH value cement proportion andln(DOHminus times 1013) respectively Searching for the trans-formation relations of φ1(x1) φ2(x2) φ3(x3) and θ(y)
which can satisfy the following mapping relation betweeninput parameters of x1 x2 x3 and function of y gave
)e nonparametric regression analysis was performedusing ACE )e fitting correlation coefficient was 09923and the fitting effect was very good Table 6 gives the valuesof each parameter before and after ACE regression and (16)gives the mapping relations of x1simφ1(x1) x2simφ2(x2)x3simφ3(x3) and ysimθ(y) obtained using ACE Figure 8 givesthe relationship between the experimental and regressionvalues for y which is in good agreement with each other andhas a positive proportion relationship It can be seen fromthis that ACE has a very good practical value
φ1 x1( 1113857 34610x1 minus 18173
φ2 x2( 1113857 minus15847x2 + 46946
φ3 x3( 1113857 123549x3 minus 23583
θ(y) 03545yminus 08446
(16)
Combined with (14) to (16) as
y 976x1 minus 447x2 + 3485x3 + 385 (17)
Namely
DOHminus 10minus13 times exp1113888976w
cminus 447 pH
+ 3485C
C + FA + CA+ 3851113889 (18)
Equation (18) showed that when the pH value decreasedwater-cement ratio and cement proportion increased thusthe corrosion degree of concrete subjected to sulfuric acidincreased in severity
6 Conclusions
With the decrease of soaking solutionrsquos pH value the colorof the exposed concrete specimen surface changed from gray
to yellow and then to white e corrosion layer thickness ofthe concrete specimen did not increase continuously withthe decrease of pH value When the soaking solutionrsquos pHvalue was 250 the corrosion layer thickness reached the
maximum value which means the sulfuric acid corrosiondegree of concrete was the most serious
A sulfuric acid corrosion model for concrete wasestablished based on the reaction boundary layer theoryand was solved by applying the separation of variablesen a theoretical formula for the acid consumption rateof concrete was obtained e sulfuric acid corrosionprocess of concrete can be divided into two stages namelythe rapid corrosion stage and the stable corrosion stageBecause of the eect of the boundary layer the measuredacid consumption rate of concrete was slightly lower thanthe theoretical value when the soaking time was relativelylong rough the sulfuric acid corrosion tests for concretethe accuracy of the sulfuric acid corrosion model forconcrete was veried is model can be used to predict thesulfuric acid corrosion mechanism for concrete in practicalengineering and to provide the foundation for steel cor-rosion prediction
e sulfuric acid corrosion tests for concrete wereplanned using uniform design e apparent diusion co-ecient for OHminus for concrete was chosen as the evaluationindex for the sulfuric acid corrosion degree of concrete andthen the calculation formula was obtained through non-parametric regression e results showed that the apparentdiusion coecient for OHminus for concrete increased whenthe pH value decreased and the water-cement ratio and
1 2 3 4 5 6 7 8Test group
033 058 092 414 12115587
36827
103783
0
300
600
900
1200
DO
Hndash
(10ndash1
3 m2 middotsndash1
)
Figure 7 Apparent diusion coecient for OHminus for concrete
Table 6 Values of each parameter before and after ACE regression
Figure 8 Comparison of the experimental and regression valuesfor y
Advances in Materials Science and Engineering 9
cement proportion increased )e uniform design andnonparametric regression had a high efficiency in the ex-perimental research and matched each other well which wasof great significance to this scientific research
Data Availability
)e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
)e authors declare that they have no conflicts of interest
Acknowledgments
)is research was financially funded by the China Post-doctoral Science Foundation (2017M622789) and the Na-tional Natural Science Foundation of China (51078175)
References
[1] K He H Yang Z B Lu F F Jia E P Wang and Q X DongldquoEffect of matrix modification on durability of cementitiouscomposites in an acid rain environmentrdquo Journal of WuhanUniversity of TechnologyndashMaterials Science Edition vol 29no 3 pp 498ndash503 2014
[2] M P Lavigne A Bertron C Botanch et al ldquoInnovativeapproach to simulating the biodeterioration of industrialcementitious products in sewer environment Part II vali-dation on CAC and BFSC liningsrdquo Cement and ConcreteResearch vol 79 pp 409ndash418 2016
[3] B Huber H Hilbig M M Mago J E Drewes and E MullerldquoComparative analysis of biogenic and chemical sulfuric acidattack on hardened cement paste using laser ablation-ICP-MSrdquo Cement and Concrete Research vol 87 pp 14ndash21 2016
[4] N De Belie J Monteny A Beeldens E Vincke D VanGemert and W Verstraete ldquoExperimental research andprediction of the effect of chemical and biogenic sulfuric acidon different types of commercially produced concrete sewerpipesrdquo Cement and Concrete Research vol 34 no 12pp 2223ndash2236 2004
[5] P K Mehta ldquoDurability of concretemdashfifty years of progressrdquoin Proceeding of the 2nd International Conference on ConcreteDurability ACI SP126ndash01 pp 1ndash32 Sapporo Japan 1991
[6] Y Yang T Ji X J Lin C Y Chen and Z X Yang ldquoBiogenicsulfuric acid corrosion resistance of new artificial reef concreterdquoConstruction and Building Materials vol 158 pp 33ndash41 2018
[7] L Gu P Visintin and T Bennett ldquoEvaluation of accelerateddegradation test methods for cementitious composites subjectto sulfuric acid attack application to conventional and alkali-activated concretesrdquo Cement and Concrete Compositesvol 87 pp 187ndash204 2018
[8] X Li Y X Lin K Lin and T Ji ldquoStudy on the degradationmechanism of sulphoaluminate cement sea sand concreteeroded by biological sulfuric acidrdquo Construction and BuildingMaterials vol 157 pp 331ndash336 2017
[9] E Hewayde M Nehdi E Allouche and G Nakhla ldquoEffect ofmixture design parameters and wetting-drying cycles on re-sistance of concrete to sulfuric acid attackrdquo Journal of Materialsin Civil Engineering vol 19 no 2 pp 155ndash163 2007
[10] Y F Fan Z Q Hu H Y Luan D W Wang and A Chen ldquoAstudy of deterioration of reinforced concrete beams under various
forms of simulated acid rain attack in the laboratoryrdquo StructuralEngineering and Mechanics vol 52 no 1 pp 35ndash49 2014
[11] A Grandclerc P Dangla and M Gueguen-MinerbeldquoModelling of the sulfuric acid attack on different types ofcementitious materialsrdquo Cement and Concrete Researchvol 105 pp 126ndash133 2018
[12] J Hill E A Byars J H Sharp C J Lynsdale J C Cripps andQ Zhou ldquoAn experimental study of combined acid andsulfate attack of concreterdquo Cement and Concrete Compositesvol 25 no 8 pp 997ndash1003 2003
[13] Z T Chang X J Song R Munn and M Marosszeky ldquoUsinglimestone aggregates and different cements for enhancingresistance of concrete to sulphuric acid attackrdquo Cement andConcrete Research vol 35 no 8 pp 1486ndash1494 2006
[14] H GMinW P Zhang andX L Gu ldquoEffects of load damage onmoisture transport and relative humidity response in concreterdquoConstruction and Building Materials vol 169 pp 59ndash68 2018
[15] H G Min W P Zhang X L Gu and R Cerny ldquoCoupledheat and moisture transport in damaged concrete under anatmospheric environmentrdquo Construction and Building Ma-terials vol 143 pp 607ndash620 2017
[16] W P Zhang H G Min and X L Gu ldquoTemperature responseand moisture transport in damaged concrete under an at-mospheric environmentrdquo Construction and Building Mate-rials vol 123 pp 290ndash299 2016
[17] W P Zhang H G Min X L Gu Y Xi and Y S XingldquoMesoscale model for thermal conductivity of concreterdquoConstruction and Building Materials vol 98 pp 8ndash16 2015
[18] S Mirvalad and M Nokken ldquoStudying thaumasite sulfateattack using compressive strength and ultrasonic pulse ve-locityrdquo Materials and Structures vol 49 no 10 pp 4131ndash4146 2016
[19] M O Yusuf ldquoPerformance of slag blended alkaline activatedpalm oil fuel ash mortar in sulfate environmentsrdquo Con-struction and Building Materials vol 98 pp 417ndash424 2015
[20] S D Xie L Qi and D Zhou ldquoInvestigation of the effects ofacid rain on the deterioration of cement concrete usingaccelerated tests established in laboratoryrdquo Atmospheric En-vironment vol 38 no 27 pp 4457ndash4466 2004
[21] M Bohm J Devinny F Jahani and G Rosen ldquoOn a moving-boundary systemmodeling corrosion in sewer pipesrdquo AppliedMathematics and Computation vol 92 no 2-3 pp 247ndash2691998
[22] M Bohm J Devinny F Jahani F B Mansfeld I G Rosenand C Wang ldquoA moving boundary diffusion model for thecorrosion of concrete wastewater systems simulation andexperimental validationrdquo in Proceedings of the AmericanControl Conference pp 1739ndash1743 San Diego CA USA1999
[23] F Jahani J Devinny F Mansfeld and I G Rosen ldquoIn-vestigations of sulfuric acid corrosion of concrete I modelingand chemical observationsrdquo Journal of Environmental Engi-neering vol 127 no 7 pp 572ndash579 2001
[24] Z G Song X S Zhang and H G Min ldquoConcentrationboundary layer model of mortar corrosion by sulfuric acidrdquoJournal of Wuhan University of TechnologyndashMaterials ScienceEdition vol 26 no 3 pp 527ndash532 2011
[25] K T FangUniformDesign and UniformDesign Table SciencePress Beijing China 1994 in Chinese
[26] K T Fang and C X Ma Orthogonal and Uniform Design ofExperiments Science Press Beijing China 2001 in Chinese
[27] A M Hasofer and J Qu ldquoResponse surface modelling ofmonte carlo fire datardquo Fire Safety Journal vol 37 no 8pp 772ndash784 2002
10 Advances in Materials Science and Engineering
CorrosionInternational Journal of
Hindawiwwwhindawicom Volume 2018
Advances in
Materials Science and EngineeringHindawiwwwhindawicom Volume 2018
experimental data (9) gave all test specimens a higher fittingdegree )e theoretical model can reflect the change lawaffecting the acid consumption rate over time therebyverifying the accuracy of the theoretical model When thesoaking time was relatively long (200 hours) the measuredvalues of the acid consumption rate were slightly lower thanfitted values and this trend was more obvious with thedecrease of pH value in the soaking solution )is phe-nomenon is related to the flocculent CaSO4 on the concretesurface which is also called the boundary layer
As the solubility of CaSO4 decreases with the decrease ofsoaking solution pH value the boundary layer thicknessincreases with the decrease of pH value )e presence of theboundary layer results in a decrease in the reaction ratewhich slows down the formation rate of CaSO4 At the sametime CaSO4 is constantly dissolving out of the concrete toreduce the CaSO4 concentration in the reaction boundarylayer resulting in the dissolution of the boundary layerwhich increases the reaction rate )e deceleration or ac-celeration of the reaction rate caused by the formation ordissolution of the boundary layer will eventually reacha dynamic equilibrium
52 Determination of an Apparent Diffusion Coefficient forOHminus for Concrete Under a sulfuric acid corrosion envi-ronment the dissolution of Ca(OH)2 in concrete results inthe change of concrete pore structures which further resultsin the change of concretersquos apparent diffusion coefficientHowever the apparent diffusion coefficient for concrete isdifficult to measure directly and then the formula for cal-culating the apparent diffusion coefficient for OHminus forconcrete can be obtained by (9) as
DOHminus 2A2
B middot S2 middot C 2OHminusM middot N
(10)
Choosing a shape function which can satisfy (5) yields
φ(θ) (1minus θ)2
ψ(θ) θ2(11)
Substituting (11) in (7) gives
M 13
N 2
(12)
Substituting (12) in (10) yields
DOHminus 3A2
B middot S2 middot C 2OHminus
(13)
)e total area S of the exposed surfaces of each group ofconcrete specimens was 003m2 and the concentration of OHminusin the saturated Ca(OH)2 solution at 20degC was 0045molmiddotLminus1then the apparent diffusion coefficients for OHminus for concretewere obtained by using Table 5 and (13) as shown in Figure 7When the soaking solutionrsquos pH value was more than 250 theapparent diffusion coefficients for OHminus for concrete increased
slowly with the decrease of pH value and then increased rapidlywith the further decrease of pH value
53 Effects of Water-Cement Ratio Soaking Solutionrsquos pHValue and Cement Proportion on the Apparent DiffusionCoefficient for OHminus for Concrete Because the relationshipwas not directly determined between the apparent diffusioncoefficient for OHminus for concrete and water-cement ratio thesoaking solutionrsquos pH value and cement proportion of C(C+FA+CA) required an analysis by ACE (alternating con-ditional expectation) regression [27] of nonparametric re-gression where x1 x2 x3 and y are water-cement ratiosoaking solutionrsquos pH value cement proportion andln(DOHminus times 1013) respectively Searching for the trans-formation relations of φ1(x1) φ2(x2) φ3(x3) and θ(y)
which can satisfy the following mapping relation betweeninput parameters of x1 x2 x3 and function of y gave
)e nonparametric regression analysis was performedusing ACE )e fitting correlation coefficient was 09923and the fitting effect was very good Table 6 gives the valuesof each parameter before and after ACE regression and (16)gives the mapping relations of x1simφ1(x1) x2simφ2(x2)x3simφ3(x3) and ysimθ(y) obtained using ACE Figure 8 givesthe relationship between the experimental and regressionvalues for y which is in good agreement with each other andhas a positive proportion relationship It can be seen fromthis that ACE has a very good practical value
φ1 x1( 1113857 34610x1 minus 18173
φ2 x2( 1113857 minus15847x2 + 46946
φ3 x3( 1113857 123549x3 minus 23583
θ(y) 03545yminus 08446
(16)
Combined with (14) to (16) as
y 976x1 minus 447x2 + 3485x3 + 385 (17)
Namely
DOHminus 10minus13 times exp1113888976w
cminus 447 pH
+ 3485C
C + FA + CA+ 3851113889 (18)
Equation (18) showed that when the pH value decreasedwater-cement ratio and cement proportion increased thusthe corrosion degree of concrete subjected to sulfuric acidincreased in severity
6 Conclusions
With the decrease of soaking solutionrsquos pH value the colorof the exposed concrete specimen surface changed from gray
to yellow and then to white e corrosion layer thickness ofthe concrete specimen did not increase continuously withthe decrease of pH value When the soaking solutionrsquos pHvalue was 250 the corrosion layer thickness reached the
maximum value which means the sulfuric acid corrosiondegree of concrete was the most serious
A sulfuric acid corrosion model for concrete wasestablished based on the reaction boundary layer theoryand was solved by applying the separation of variablesen a theoretical formula for the acid consumption rateof concrete was obtained e sulfuric acid corrosionprocess of concrete can be divided into two stages namelythe rapid corrosion stage and the stable corrosion stageBecause of the eect of the boundary layer the measuredacid consumption rate of concrete was slightly lower thanthe theoretical value when the soaking time was relativelylong rough the sulfuric acid corrosion tests for concretethe accuracy of the sulfuric acid corrosion model forconcrete was veried is model can be used to predict thesulfuric acid corrosion mechanism for concrete in practicalengineering and to provide the foundation for steel cor-rosion prediction
e sulfuric acid corrosion tests for concrete wereplanned using uniform design e apparent diusion co-ecient for OHminus for concrete was chosen as the evaluationindex for the sulfuric acid corrosion degree of concrete andthen the calculation formula was obtained through non-parametric regression e results showed that the apparentdiusion coecient for OHminus for concrete increased whenthe pH value decreased and the water-cement ratio and
1 2 3 4 5 6 7 8Test group
033 058 092 414 12115587
36827
103783
0
300
600
900
1200
DO
Hndash
(10ndash1
3 m2 middotsndash1
)
Figure 7 Apparent diusion coecient for OHminus for concrete
Table 6 Values of each parameter before and after ACE regression
Figure 8 Comparison of the experimental and regression valuesfor y
Advances in Materials Science and Engineering 9
cement proportion increased )e uniform design andnonparametric regression had a high efficiency in the ex-perimental research and matched each other well which wasof great significance to this scientific research
Data Availability
)e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
)e authors declare that they have no conflicts of interest
Acknowledgments
)is research was financially funded by the China Post-doctoral Science Foundation (2017M622789) and the Na-tional Natural Science Foundation of China (51078175)
References
[1] K He H Yang Z B Lu F F Jia E P Wang and Q X DongldquoEffect of matrix modification on durability of cementitiouscomposites in an acid rain environmentrdquo Journal of WuhanUniversity of TechnologyndashMaterials Science Edition vol 29no 3 pp 498ndash503 2014
[2] M P Lavigne A Bertron C Botanch et al ldquoInnovativeapproach to simulating the biodeterioration of industrialcementitious products in sewer environment Part II vali-dation on CAC and BFSC liningsrdquo Cement and ConcreteResearch vol 79 pp 409ndash418 2016
[3] B Huber H Hilbig M M Mago J E Drewes and E MullerldquoComparative analysis of biogenic and chemical sulfuric acidattack on hardened cement paste using laser ablation-ICP-MSrdquo Cement and Concrete Research vol 87 pp 14ndash21 2016
[4] N De Belie J Monteny A Beeldens E Vincke D VanGemert and W Verstraete ldquoExperimental research andprediction of the effect of chemical and biogenic sulfuric acidon different types of commercially produced concrete sewerpipesrdquo Cement and Concrete Research vol 34 no 12pp 2223ndash2236 2004
[5] P K Mehta ldquoDurability of concretemdashfifty years of progressrdquoin Proceeding of the 2nd International Conference on ConcreteDurability ACI SP126ndash01 pp 1ndash32 Sapporo Japan 1991
[6] Y Yang T Ji X J Lin C Y Chen and Z X Yang ldquoBiogenicsulfuric acid corrosion resistance of new artificial reef concreterdquoConstruction and Building Materials vol 158 pp 33ndash41 2018
[7] L Gu P Visintin and T Bennett ldquoEvaluation of accelerateddegradation test methods for cementitious composites subjectto sulfuric acid attack application to conventional and alkali-activated concretesrdquo Cement and Concrete Compositesvol 87 pp 187ndash204 2018
[8] X Li Y X Lin K Lin and T Ji ldquoStudy on the degradationmechanism of sulphoaluminate cement sea sand concreteeroded by biological sulfuric acidrdquo Construction and BuildingMaterials vol 157 pp 331ndash336 2017
[9] E Hewayde M Nehdi E Allouche and G Nakhla ldquoEffect ofmixture design parameters and wetting-drying cycles on re-sistance of concrete to sulfuric acid attackrdquo Journal of Materialsin Civil Engineering vol 19 no 2 pp 155ndash163 2007
[10] Y F Fan Z Q Hu H Y Luan D W Wang and A Chen ldquoAstudy of deterioration of reinforced concrete beams under various
forms of simulated acid rain attack in the laboratoryrdquo StructuralEngineering and Mechanics vol 52 no 1 pp 35ndash49 2014
[11] A Grandclerc P Dangla and M Gueguen-MinerbeldquoModelling of the sulfuric acid attack on different types ofcementitious materialsrdquo Cement and Concrete Researchvol 105 pp 126ndash133 2018
[12] J Hill E A Byars J H Sharp C J Lynsdale J C Cripps andQ Zhou ldquoAn experimental study of combined acid andsulfate attack of concreterdquo Cement and Concrete Compositesvol 25 no 8 pp 997ndash1003 2003
[13] Z T Chang X J Song R Munn and M Marosszeky ldquoUsinglimestone aggregates and different cements for enhancingresistance of concrete to sulphuric acid attackrdquo Cement andConcrete Research vol 35 no 8 pp 1486ndash1494 2006
[14] H GMinW P Zhang andX L Gu ldquoEffects of load damage onmoisture transport and relative humidity response in concreterdquoConstruction and Building Materials vol 169 pp 59ndash68 2018
[15] H G Min W P Zhang X L Gu and R Cerny ldquoCoupledheat and moisture transport in damaged concrete under anatmospheric environmentrdquo Construction and Building Ma-terials vol 143 pp 607ndash620 2017
[16] W P Zhang H G Min and X L Gu ldquoTemperature responseand moisture transport in damaged concrete under an at-mospheric environmentrdquo Construction and Building Mate-rials vol 123 pp 290ndash299 2016
[17] W P Zhang H G Min X L Gu Y Xi and Y S XingldquoMesoscale model for thermal conductivity of concreterdquoConstruction and Building Materials vol 98 pp 8ndash16 2015
[18] S Mirvalad and M Nokken ldquoStudying thaumasite sulfateattack using compressive strength and ultrasonic pulse ve-locityrdquo Materials and Structures vol 49 no 10 pp 4131ndash4146 2016
[19] M O Yusuf ldquoPerformance of slag blended alkaline activatedpalm oil fuel ash mortar in sulfate environmentsrdquo Con-struction and Building Materials vol 98 pp 417ndash424 2015
[20] S D Xie L Qi and D Zhou ldquoInvestigation of the effects ofacid rain on the deterioration of cement concrete usingaccelerated tests established in laboratoryrdquo Atmospheric En-vironment vol 38 no 27 pp 4457ndash4466 2004
[21] M Bohm J Devinny F Jahani and G Rosen ldquoOn a moving-boundary systemmodeling corrosion in sewer pipesrdquo AppliedMathematics and Computation vol 92 no 2-3 pp 247ndash2691998
[22] M Bohm J Devinny F Jahani F B Mansfeld I G Rosenand C Wang ldquoA moving boundary diffusion model for thecorrosion of concrete wastewater systems simulation andexperimental validationrdquo in Proceedings of the AmericanControl Conference pp 1739ndash1743 San Diego CA USA1999
[23] F Jahani J Devinny F Mansfeld and I G Rosen ldquoIn-vestigations of sulfuric acid corrosion of concrete I modelingand chemical observationsrdquo Journal of Environmental Engi-neering vol 127 no 7 pp 572ndash579 2001
[24] Z G Song X S Zhang and H G Min ldquoConcentrationboundary layer model of mortar corrosion by sulfuric acidrdquoJournal of Wuhan University of TechnologyndashMaterials ScienceEdition vol 26 no 3 pp 527ndash532 2011
[25] K T FangUniformDesign and UniformDesign Table SciencePress Beijing China 1994 in Chinese
[26] K T Fang and C X Ma Orthogonal and Uniform Design ofExperiments Science Press Beijing China 2001 in Chinese
[27] A M Hasofer and J Qu ldquoResponse surface modelling ofmonte carlo fire datardquo Fire Safety Journal vol 37 no 8pp 772ndash784 2002
10 Advances in Materials Science and Engineering
CorrosionInternational Journal of
Hindawiwwwhindawicom Volume 2018
Advances in
Materials Science and EngineeringHindawiwwwhindawicom Volume 2018
experimental data (9) gave all test specimens a higher fittingdegree )e theoretical model can reflect the change lawaffecting the acid consumption rate over time therebyverifying the accuracy of the theoretical model When thesoaking time was relatively long (200 hours) the measuredvalues of the acid consumption rate were slightly lower thanfitted values and this trend was more obvious with thedecrease of pH value in the soaking solution )is phe-nomenon is related to the flocculent CaSO4 on the concretesurface which is also called the boundary layer
As the solubility of CaSO4 decreases with the decrease ofsoaking solution pH value the boundary layer thicknessincreases with the decrease of pH value )e presence of theboundary layer results in a decrease in the reaction ratewhich slows down the formation rate of CaSO4 At the sametime CaSO4 is constantly dissolving out of the concrete toreduce the CaSO4 concentration in the reaction boundarylayer resulting in the dissolution of the boundary layerwhich increases the reaction rate )e deceleration or ac-celeration of the reaction rate caused by the formation ordissolution of the boundary layer will eventually reacha dynamic equilibrium
52 Determination of an Apparent Diffusion Coefficient forOHminus for Concrete Under a sulfuric acid corrosion envi-ronment the dissolution of Ca(OH)2 in concrete results inthe change of concrete pore structures which further resultsin the change of concretersquos apparent diffusion coefficientHowever the apparent diffusion coefficient for concrete isdifficult to measure directly and then the formula for cal-culating the apparent diffusion coefficient for OHminus forconcrete can be obtained by (9) as
DOHminus 2A2
B middot S2 middot C 2OHminusM middot N
(10)
Choosing a shape function which can satisfy (5) yields
φ(θ) (1minus θ)2
ψ(θ) θ2(11)
Substituting (11) in (7) gives
M 13
N 2
(12)
Substituting (12) in (10) yields
DOHminus 3A2
B middot S2 middot C 2OHminus
(13)
)e total area S of the exposed surfaces of each group ofconcrete specimens was 003m2 and the concentration of OHminusin the saturated Ca(OH)2 solution at 20degC was 0045molmiddotLminus1then the apparent diffusion coefficients for OHminus for concretewere obtained by using Table 5 and (13) as shown in Figure 7When the soaking solutionrsquos pH value was more than 250 theapparent diffusion coefficients for OHminus for concrete increased
slowly with the decrease of pH value and then increased rapidlywith the further decrease of pH value
53 Effects of Water-Cement Ratio Soaking Solutionrsquos pHValue and Cement Proportion on the Apparent DiffusionCoefficient for OHminus for Concrete Because the relationshipwas not directly determined between the apparent diffusioncoefficient for OHminus for concrete and water-cement ratio thesoaking solutionrsquos pH value and cement proportion of C(C+FA+CA) required an analysis by ACE (alternating con-ditional expectation) regression [27] of nonparametric re-gression where x1 x2 x3 and y are water-cement ratiosoaking solutionrsquos pH value cement proportion andln(DOHminus times 1013) respectively Searching for the trans-formation relations of φ1(x1) φ2(x2) φ3(x3) and θ(y)
which can satisfy the following mapping relation betweeninput parameters of x1 x2 x3 and function of y gave
)e nonparametric regression analysis was performedusing ACE )e fitting correlation coefficient was 09923and the fitting effect was very good Table 6 gives the valuesof each parameter before and after ACE regression and (16)gives the mapping relations of x1simφ1(x1) x2simφ2(x2)x3simφ3(x3) and ysimθ(y) obtained using ACE Figure 8 givesthe relationship between the experimental and regressionvalues for y which is in good agreement with each other andhas a positive proportion relationship It can be seen fromthis that ACE has a very good practical value
φ1 x1( 1113857 34610x1 minus 18173
φ2 x2( 1113857 minus15847x2 + 46946
φ3 x3( 1113857 123549x3 minus 23583
θ(y) 03545yminus 08446
(16)
Combined with (14) to (16) as
y 976x1 minus 447x2 + 3485x3 + 385 (17)
Namely
DOHminus 10minus13 times exp1113888976w
cminus 447 pH
+ 3485C
C + FA + CA+ 3851113889 (18)
Equation (18) showed that when the pH value decreasedwater-cement ratio and cement proportion increased thusthe corrosion degree of concrete subjected to sulfuric acidincreased in severity
6 Conclusions
With the decrease of soaking solutionrsquos pH value the colorof the exposed concrete specimen surface changed from gray
to yellow and then to white e corrosion layer thickness ofthe concrete specimen did not increase continuously withthe decrease of pH value When the soaking solutionrsquos pHvalue was 250 the corrosion layer thickness reached the
maximum value which means the sulfuric acid corrosiondegree of concrete was the most serious
A sulfuric acid corrosion model for concrete wasestablished based on the reaction boundary layer theoryand was solved by applying the separation of variablesen a theoretical formula for the acid consumption rateof concrete was obtained e sulfuric acid corrosionprocess of concrete can be divided into two stages namelythe rapid corrosion stage and the stable corrosion stageBecause of the eect of the boundary layer the measuredacid consumption rate of concrete was slightly lower thanthe theoretical value when the soaking time was relativelylong rough the sulfuric acid corrosion tests for concretethe accuracy of the sulfuric acid corrosion model forconcrete was veried is model can be used to predict thesulfuric acid corrosion mechanism for concrete in practicalengineering and to provide the foundation for steel cor-rosion prediction
e sulfuric acid corrosion tests for concrete wereplanned using uniform design e apparent diusion co-ecient for OHminus for concrete was chosen as the evaluationindex for the sulfuric acid corrosion degree of concrete andthen the calculation formula was obtained through non-parametric regression e results showed that the apparentdiusion coecient for OHminus for concrete increased whenthe pH value decreased and the water-cement ratio and
1 2 3 4 5 6 7 8Test group
033 058 092 414 12115587
36827
103783
0
300
600
900
1200
DO
Hndash
(10ndash1
3 m2 middotsndash1
)
Figure 7 Apparent diusion coecient for OHminus for concrete
Table 6 Values of each parameter before and after ACE regression
Figure 8 Comparison of the experimental and regression valuesfor y
Advances in Materials Science and Engineering 9
cement proportion increased )e uniform design andnonparametric regression had a high efficiency in the ex-perimental research and matched each other well which wasof great significance to this scientific research
Data Availability
)e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
)e authors declare that they have no conflicts of interest
Acknowledgments
)is research was financially funded by the China Post-doctoral Science Foundation (2017M622789) and the Na-tional Natural Science Foundation of China (51078175)
References
[1] K He H Yang Z B Lu F F Jia E P Wang and Q X DongldquoEffect of matrix modification on durability of cementitiouscomposites in an acid rain environmentrdquo Journal of WuhanUniversity of TechnologyndashMaterials Science Edition vol 29no 3 pp 498ndash503 2014
[2] M P Lavigne A Bertron C Botanch et al ldquoInnovativeapproach to simulating the biodeterioration of industrialcementitious products in sewer environment Part II vali-dation on CAC and BFSC liningsrdquo Cement and ConcreteResearch vol 79 pp 409ndash418 2016
[3] B Huber H Hilbig M M Mago J E Drewes and E MullerldquoComparative analysis of biogenic and chemical sulfuric acidattack on hardened cement paste using laser ablation-ICP-MSrdquo Cement and Concrete Research vol 87 pp 14ndash21 2016
[4] N De Belie J Monteny A Beeldens E Vincke D VanGemert and W Verstraete ldquoExperimental research andprediction of the effect of chemical and biogenic sulfuric acidon different types of commercially produced concrete sewerpipesrdquo Cement and Concrete Research vol 34 no 12pp 2223ndash2236 2004
[5] P K Mehta ldquoDurability of concretemdashfifty years of progressrdquoin Proceeding of the 2nd International Conference on ConcreteDurability ACI SP126ndash01 pp 1ndash32 Sapporo Japan 1991
[6] Y Yang T Ji X J Lin C Y Chen and Z X Yang ldquoBiogenicsulfuric acid corrosion resistance of new artificial reef concreterdquoConstruction and Building Materials vol 158 pp 33ndash41 2018
[7] L Gu P Visintin and T Bennett ldquoEvaluation of accelerateddegradation test methods for cementitious composites subjectto sulfuric acid attack application to conventional and alkali-activated concretesrdquo Cement and Concrete Compositesvol 87 pp 187ndash204 2018
[8] X Li Y X Lin K Lin and T Ji ldquoStudy on the degradationmechanism of sulphoaluminate cement sea sand concreteeroded by biological sulfuric acidrdquo Construction and BuildingMaterials vol 157 pp 331ndash336 2017
[9] E Hewayde M Nehdi E Allouche and G Nakhla ldquoEffect ofmixture design parameters and wetting-drying cycles on re-sistance of concrete to sulfuric acid attackrdquo Journal of Materialsin Civil Engineering vol 19 no 2 pp 155ndash163 2007
[10] Y F Fan Z Q Hu H Y Luan D W Wang and A Chen ldquoAstudy of deterioration of reinforced concrete beams under various
forms of simulated acid rain attack in the laboratoryrdquo StructuralEngineering and Mechanics vol 52 no 1 pp 35ndash49 2014
[11] A Grandclerc P Dangla and M Gueguen-MinerbeldquoModelling of the sulfuric acid attack on different types ofcementitious materialsrdquo Cement and Concrete Researchvol 105 pp 126ndash133 2018
[12] J Hill E A Byars J H Sharp C J Lynsdale J C Cripps andQ Zhou ldquoAn experimental study of combined acid andsulfate attack of concreterdquo Cement and Concrete Compositesvol 25 no 8 pp 997ndash1003 2003
[13] Z T Chang X J Song R Munn and M Marosszeky ldquoUsinglimestone aggregates and different cements for enhancingresistance of concrete to sulphuric acid attackrdquo Cement andConcrete Research vol 35 no 8 pp 1486ndash1494 2006
[14] H GMinW P Zhang andX L Gu ldquoEffects of load damage onmoisture transport and relative humidity response in concreterdquoConstruction and Building Materials vol 169 pp 59ndash68 2018
[15] H G Min W P Zhang X L Gu and R Cerny ldquoCoupledheat and moisture transport in damaged concrete under anatmospheric environmentrdquo Construction and Building Ma-terials vol 143 pp 607ndash620 2017
[16] W P Zhang H G Min and X L Gu ldquoTemperature responseand moisture transport in damaged concrete under an at-mospheric environmentrdquo Construction and Building Mate-rials vol 123 pp 290ndash299 2016
[17] W P Zhang H G Min X L Gu Y Xi and Y S XingldquoMesoscale model for thermal conductivity of concreterdquoConstruction and Building Materials vol 98 pp 8ndash16 2015
[18] S Mirvalad and M Nokken ldquoStudying thaumasite sulfateattack using compressive strength and ultrasonic pulse ve-locityrdquo Materials and Structures vol 49 no 10 pp 4131ndash4146 2016
[19] M O Yusuf ldquoPerformance of slag blended alkaline activatedpalm oil fuel ash mortar in sulfate environmentsrdquo Con-struction and Building Materials vol 98 pp 417ndash424 2015
[20] S D Xie L Qi and D Zhou ldquoInvestigation of the effects ofacid rain on the deterioration of cement concrete usingaccelerated tests established in laboratoryrdquo Atmospheric En-vironment vol 38 no 27 pp 4457ndash4466 2004
[21] M Bohm J Devinny F Jahani and G Rosen ldquoOn a moving-boundary systemmodeling corrosion in sewer pipesrdquo AppliedMathematics and Computation vol 92 no 2-3 pp 247ndash2691998
[22] M Bohm J Devinny F Jahani F B Mansfeld I G Rosenand C Wang ldquoA moving boundary diffusion model for thecorrosion of concrete wastewater systems simulation andexperimental validationrdquo in Proceedings of the AmericanControl Conference pp 1739ndash1743 San Diego CA USA1999
[23] F Jahani J Devinny F Mansfeld and I G Rosen ldquoIn-vestigations of sulfuric acid corrosion of concrete I modelingand chemical observationsrdquo Journal of Environmental Engi-neering vol 127 no 7 pp 572ndash579 2001
[24] Z G Song X S Zhang and H G Min ldquoConcentrationboundary layer model of mortar corrosion by sulfuric acidrdquoJournal of Wuhan University of TechnologyndashMaterials ScienceEdition vol 26 no 3 pp 527ndash532 2011
[25] K T FangUniformDesign and UniformDesign Table SciencePress Beijing China 1994 in Chinese
[26] K T Fang and C X Ma Orthogonal and Uniform Design ofExperiments Science Press Beijing China 2001 in Chinese
[27] A M Hasofer and J Qu ldquoResponse surface modelling ofmonte carlo fire datardquo Fire Safety Journal vol 37 no 8pp 772ndash784 2002
10 Advances in Materials Science and Engineering
CorrosionInternational Journal of
Hindawiwwwhindawicom Volume 2018
Advances in
Materials Science and EngineeringHindawiwwwhindawicom Volume 2018
to yellow and then to white e corrosion layer thickness ofthe concrete specimen did not increase continuously withthe decrease of pH value When the soaking solutionrsquos pHvalue was 250 the corrosion layer thickness reached the
maximum value which means the sulfuric acid corrosiondegree of concrete was the most serious
A sulfuric acid corrosion model for concrete wasestablished based on the reaction boundary layer theoryand was solved by applying the separation of variablesen a theoretical formula for the acid consumption rateof concrete was obtained e sulfuric acid corrosionprocess of concrete can be divided into two stages namelythe rapid corrosion stage and the stable corrosion stageBecause of the eect of the boundary layer the measuredacid consumption rate of concrete was slightly lower thanthe theoretical value when the soaking time was relativelylong rough the sulfuric acid corrosion tests for concretethe accuracy of the sulfuric acid corrosion model forconcrete was veried is model can be used to predict thesulfuric acid corrosion mechanism for concrete in practicalengineering and to provide the foundation for steel cor-rosion prediction
e sulfuric acid corrosion tests for concrete wereplanned using uniform design e apparent diusion co-ecient for OHminus for concrete was chosen as the evaluationindex for the sulfuric acid corrosion degree of concrete andthen the calculation formula was obtained through non-parametric regression e results showed that the apparentdiusion coecient for OHminus for concrete increased whenthe pH value decreased and the water-cement ratio and
1 2 3 4 5 6 7 8Test group
033 058 092 414 12115587
36827
103783
0
300
600
900
1200
DO
Hndash
(10ndash1
3 m2 middotsndash1
)
Figure 7 Apparent diusion coecient for OHminus for concrete
Table 6 Values of each parameter before and after ACE regression
Figure 8 Comparison of the experimental and regression valuesfor y
Advances in Materials Science and Engineering 9
cement proportion increased )e uniform design andnonparametric regression had a high efficiency in the ex-perimental research and matched each other well which wasof great significance to this scientific research
Data Availability
)e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
)e authors declare that they have no conflicts of interest
Acknowledgments
)is research was financially funded by the China Post-doctoral Science Foundation (2017M622789) and the Na-tional Natural Science Foundation of China (51078175)
References
[1] K He H Yang Z B Lu F F Jia E P Wang and Q X DongldquoEffect of matrix modification on durability of cementitiouscomposites in an acid rain environmentrdquo Journal of WuhanUniversity of TechnologyndashMaterials Science Edition vol 29no 3 pp 498ndash503 2014
[2] M P Lavigne A Bertron C Botanch et al ldquoInnovativeapproach to simulating the biodeterioration of industrialcementitious products in sewer environment Part II vali-dation on CAC and BFSC liningsrdquo Cement and ConcreteResearch vol 79 pp 409ndash418 2016
[3] B Huber H Hilbig M M Mago J E Drewes and E MullerldquoComparative analysis of biogenic and chemical sulfuric acidattack on hardened cement paste using laser ablation-ICP-MSrdquo Cement and Concrete Research vol 87 pp 14ndash21 2016
[4] N De Belie J Monteny A Beeldens E Vincke D VanGemert and W Verstraete ldquoExperimental research andprediction of the effect of chemical and biogenic sulfuric acidon different types of commercially produced concrete sewerpipesrdquo Cement and Concrete Research vol 34 no 12pp 2223ndash2236 2004
[5] P K Mehta ldquoDurability of concretemdashfifty years of progressrdquoin Proceeding of the 2nd International Conference on ConcreteDurability ACI SP126ndash01 pp 1ndash32 Sapporo Japan 1991
[6] Y Yang T Ji X J Lin C Y Chen and Z X Yang ldquoBiogenicsulfuric acid corrosion resistance of new artificial reef concreterdquoConstruction and Building Materials vol 158 pp 33ndash41 2018
[7] L Gu P Visintin and T Bennett ldquoEvaluation of accelerateddegradation test methods for cementitious composites subjectto sulfuric acid attack application to conventional and alkali-activated concretesrdquo Cement and Concrete Compositesvol 87 pp 187ndash204 2018
[8] X Li Y X Lin K Lin and T Ji ldquoStudy on the degradationmechanism of sulphoaluminate cement sea sand concreteeroded by biological sulfuric acidrdquo Construction and BuildingMaterials vol 157 pp 331ndash336 2017
[9] E Hewayde M Nehdi E Allouche and G Nakhla ldquoEffect ofmixture design parameters and wetting-drying cycles on re-sistance of concrete to sulfuric acid attackrdquo Journal of Materialsin Civil Engineering vol 19 no 2 pp 155ndash163 2007
[10] Y F Fan Z Q Hu H Y Luan D W Wang and A Chen ldquoAstudy of deterioration of reinforced concrete beams under various
forms of simulated acid rain attack in the laboratoryrdquo StructuralEngineering and Mechanics vol 52 no 1 pp 35ndash49 2014
[11] A Grandclerc P Dangla and M Gueguen-MinerbeldquoModelling of the sulfuric acid attack on different types ofcementitious materialsrdquo Cement and Concrete Researchvol 105 pp 126ndash133 2018
[12] J Hill E A Byars J H Sharp C J Lynsdale J C Cripps andQ Zhou ldquoAn experimental study of combined acid andsulfate attack of concreterdquo Cement and Concrete Compositesvol 25 no 8 pp 997ndash1003 2003
[13] Z T Chang X J Song R Munn and M Marosszeky ldquoUsinglimestone aggregates and different cements for enhancingresistance of concrete to sulphuric acid attackrdquo Cement andConcrete Research vol 35 no 8 pp 1486ndash1494 2006
[14] H GMinW P Zhang andX L Gu ldquoEffects of load damage onmoisture transport and relative humidity response in concreterdquoConstruction and Building Materials vol 169 pp 59ndash68 2018
[15] H G Min W P Zhang X L Gu and R Cerny ldquoCoupledheat and moisture transport in damaged concrete under anatmospheric environmentrdquo Construction and Building Ma-terials vol 143 pp 607ndash620 2017
[16] W P Zhang H G Min and X L Gu ldquoTemperature responseand moisture transport in damaged concrete under an at-mospheric environmentrdquo Construction and Building Mate-rials vol 123 pp 290ndash299 2016
[17] W P Zhang H G Min X L Gu Y Xi and Y S XingldquoMesoscale model for thermal conductivity of concreterdquoConstruction and Building Materials vol 98 pp 8ndash16 2015
[18] S Mirvalad and M Nokken ldquoStudying thaumasite sulfateattack using compressive strength and ultrasonic pulse ve-locityrdquo Materials and Structures vol 49 no 10 pp 4131ndash4146 2016
[19] M O Yusuf ldquoPerformance of slag blended alkaline activatedpalm oil fuel ash mortar in sulfate environmentsrdquo Con-struction and Building Materials vol 98 pp 417ndash424 2015
[20] S D Xie L Qi and D Zhou ldquoInvestigation of the effects ofacid rain on the deterioration of cement concrete usingaccelerated tests established in laboratoryrdquo Atmospheric En-vironment vol 38 no 27 pp 4457ndash4466 2004
[21] M Bohm J Devinny F Jahani and G Rosen ldquoOn a moving-boundary systemmodeling corrosion in sewer pipesrdquo AppliedMathematics and Computation vol 92 no 2-3 pp 247ndash2691998
[22] M Bohm J Devinny F Jahani F B Mansfeld I G Rosenand C Wang ldquoA moving boundary diffusion model for thecorrosion of concrete wastewater systems simulation andexperimental validationrdquo in Proceedings of the AmericanControl Conference pp 1739ndash1743 San Diego CA USA1999
[23] F Jahani J Devinny F Mansfeld and I G Rosen ldquoIn-vestigations of sulfuric acid corrosion of concrete I modelingand chemical observationsrdquo Journal of Environmental Engi-neering vol 127 no 7 pp 572ndash579 2001
[24] Z G Song X S Zhang and H G Min ldquoConcentrationboundary layer model of mortar corrosion by sulfuric acidrdquoJournal of Wuhan University of TechnologyndashMaterials ScienceEdition vol 26 no 3 pp 527ndash532 2011
[25] K T FangUniformDesign and UniformDesign Table SciencePress Beijing China 1994 in Chinese
[26] K T Fang and C X Ma Orthogonal and Uniform Design ofExperiments Science Press Beijing China 2001 in Chinese
[27] A M Hasofer and J Qu ldquoResponse surface modelling ofmonte carlo fire datardquo Fire Safety Journal vol 37 no 8pp 772ndash784 2002
10 Advances in Materials Science and Engineering
CorrosionInternational Journal of
Hindawiwwwhindawicom Volume 2018
Advances in
Materials Science and EngineeringHindawiwwwhindawicom Volume 2018
to yellow and then to white e corrosion layer thickness ofthe concrete specimen did not increase continuously withthe decrease of pH value When the soaking solutionrsquos pHvalue was 250 the corrosion layer thickness reached the
maximum value which means the sulfuric acid corrosiondegree of concrete was the most serious
A sulfuric acid corrosion model for concrete wasestablished based on the reaction boundary layer theoryand was solved by applying the separation of variablesen a theoretical formula for the acid consumption rateof concrete was obtained e sulfuric acid corrosionprocess of concrete can be divided into two stages namelythe rapid corrosion stage and the stable corrosion stageBecause of the eect of the boundary layer the measuredacid consumption rate of concrete was slightly lower thanthe theoretical value when the soaking time was relativelylong rough the sulfuric acid corrosion tests for concretethe accuracy of the sulfuric acid corrosion model forconcrete was veried is model can be used to predict thesulfuric acid corrosion mechanism for concrete in practicalengineering and to provide the foundation for steel cor-rosion prediction
e sulfuric acid corrosion tests for concrete wereplanned using uniform design e apparent diusion co-ecient for OHminus for concrete was chosen as the evaluationindex for the sulfuric acid corrosion degree of concrete andthen the calculation formula was obtained through non-parametric regression e results showed that the apparentdiusion coecient for OHminus for concrete increased whenthe pH value decreased and the water-cement ratio and
1 2 3 4 5 6 7 8Test group
033 058 092 414 12115587
36827
103783
0
300
600
900
1200
DO
Hndash
(10ndash1
3 m2 middotsndash1
)
Figure 7 Apparent diusion coecient for OHminus for concrete
Table 6 Values of each parameter before and after ACE regression
Figure 8 Comparison of the experimental and regression valuesfor y
Advances in Materials Science and Engineering 9
cement proportion increased )e uniform design andnonparametric regression had a high efficiency in the ex-perimental research and matched each other well which wasof great significance to this scientific research
Data Availability
)e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
)e authors declare that they have no conflicts of interest
Acknowledgments
)is research was financially funded by the China Post-doctoral Science Foundation (2017M622789) and the Na-tional Natural Science Foundation of China (51078175)
References
[1] K He H Yang Z B Lu F F Jia E P Wang and Q X DongldquoEffect of matrix modification on durability of cementitiouscomposites in an acid rain environmentrdquo Journal of WuhanUniversity of TechnologyndashMaterials Science Edition vol 29no 3 pp 498ndash503 2014
[2] M P Lavigne A Bertron C Botanch et al ldquoInnovativeapproach to simulating the biodeterioration of industrialcementitious products in sewer environment Part II vali-dation on CAC and BFSC liningsrdquo Cement and ConcreteResearch vol 79 pp 409ndash418 2016
[3] B Huber H Hilbig M M Mago J E Drewes and E MullerldquoComparative analysis of biogenic and chemical sulfuric acidattack on hardened cement paste using laser ablation-ICP-MSrdquo Cement and Concrete Research vol 87 pp 14ndash21 2016
[4] N De Belie J Monteny A Beeldens E Vincke D VanGemert and W Verstraete ldquoExperimental research andprediction of the effect of chemical and biogenic sulfuric acidon different types of commercially produced concrete sewerpipesrdquo Cement and Concrete Research vol 34 no 12pp 2223ndash2236 2004
[5] P K Mehta ldquoDurability of concretemdashfifty years of progressrdquoin Proceeding of the 2nd International Conference on ConcreteDurability ACI SP126ndash01 pp 1ndash32 Sapporo Japan 1991
[6] Y Yang T Ji X J Lin C Y Chen and Z X Yang ldquoBiogenicsulfuric acid corrosion resistance of new artificial reef concreterdquoConstruction and Building Materials vol 158 pp 33ndash41 2018
[7] L Gu P Visintin and T Bennett ldquoEvaluation of accelerateddegradation test methods for cementitious composites subjectto sulfuric acid attack application to conventional and alkali-activated concretesrdquo Cement and Concrete Compositesvol 87 pp 187ndash204 2018
[8] X Li Y X Lin K Lin and T Ji ldquoStudy on the degradationmechanism of sulphoaluminate cement sea sand concreteeroded by biological sulfuric acidrdquo Construction and BuildingMaterials vol 157 pp 331ndash336 2017
[9] E Hewayde M Nehdi E Allouche and G Nakhla ldquoEffect ofmixture design parameters and wetting-drying cycles on re-sistance of concrete to sulfuric acid attackrdquo Journal of Materialsin Civil Engineering vol 19 no 2 pp 155ndash163 2007
[10] Y F Fan Z Q Hu H Y Luan D W Wang and A Chen ldquoAstudy of deterioration of reinforced concrete beams under various
forms of simulated acid rain attack in the laboratoryrdquo StructuralEngineering and Mechanics vol 52 no 1 pp 35ndash49 2014
[11] A Grandclerc P Dangla and M Gueguen-MinerbeldquoModelling of the sulfuric acid attack on different types ofcementitious materialsrdquo Cement and Concrete Researchvol 105 pp 126ndash133 2018
[12] J Hill E A Byars J H Sharp C J Lynsdale J C Cripps andQ Zhou ldquoAn experimental study of combined acid andsulfate attack of concreterdquo Cement and Concrete Compositesvol 25 no 8 pp 997ndash1003 2003
[13] Z T Chang X J Song R Munn and M Marosszeky ldquoUsinglimestone aggregates and different cements for enhancingresistance of concrete to sulphuric acid attackrdquo Cement andConcrete Research vol 35 no 8 pp 1486ndash1494 2006
[14] H GMinW P Zhang andX L Gu ldquoEffects of load damage onmoisture transport and relative humidity response in concreterdquoConstruction and Building Materials vol 169 pp 59ndash68 2018
[15] H G Min W P Zhang X L Gu and R Cerny ldquoCoupledheat and moisture transport in damaged concrete under anatmospheric environmentrdquo Construction and Building Ma-terials vol 143 pp 607ndash620 2017
[16] W P Zhang H G Min and X L Gu ldquoTemperature responseand moisture transport in damaged concrete under an at-mospheric environmentrdquo Construction and Building Mate-rials vol 123 pp 290ndash299 2016
[17] W P Zhang H G Min X L Gu Y Xi and Y S XingldquoMesoscale model for thermal conductivity of concreterdquoConstruction and Building Materials vol 98 pp 8ndash16 2015
[18] S Mirvalad and M Nokken ldquoStudying thaumasite sulfateattack using compressive strength and ultrasonic pulse ve-locityrdquo Materials and Structures vol 49 no 10 pp 4131ndash4146 2016
[19] M O Yusuf ldquoPerformance of slag blended alkaline activatedpalm oil fuel ash mortar in sulfate environmentsrdquo Con-struction and Building Materials vol 98 pp 417ndash424 2015
[20] S D Xie L Qi and D Zhou ldquoInvestigation of the effects ofacid rain on the deterioration of cement concrete usingaccelerated tests established in laboratoryrdquo Atmospheric En-vironment vol 38 no 27 pp 4457ndash4466 2004
[21] M Bohm J Devinny F Jahani and G Rosen ldquoOn a moving-boundary systemmodeling corrosion in sewer pipesrdquo AppliedMathematics and Computation vol 92 no 2-3 pp 247ndash2691998
[22] M Bohm J Devinny F Jahani F B Mansfeld I G Rosenand C Wang ldquoA moving boundary diffusion model for thecorrosion of concrete wastewater systems simulation andexperimental validationrdquo in Proceedings of the AmericanControl Conference pp 1739ndash1743 San Diego CA USA1999
[23] F Jahani J Devinny F Mansfeld and I G Rosen ldquoIn-vestigations of sulfuric acid corrosion of concrete I modelingand chemical observationsrdquo Journal of Environmental Engi-neering vol 127 no 7 pp 572ndash579 2001
[24] Z G Song X S Zhang and H G Min ldquoConcentrationboundary layer model of mortar corrosion by sulfuric acidrdquoJournal of Wuhan University of TechnologyndashMaterials ScienceEdition vol 26 no 3 pp 527ndash532 2011
[25] K T FangUniformDesign and UniformDesign Table SciencePress Beijing China 1994 in Chinese
[26] K T Fang and C X Ma Orthogonal and Uniform Design ofExperiments Science Press Beijing China 2001 in Chinese
[27] A M Hasofer and J Qu ldquoResponse surface modelling ofmonte carlo fire datardquo Fire Safety Journal vol 37 no 8pp 772ndash784 2002
10 Advances in Materials Science and Engineering
CorrosionInternational Journal of
Hindawiwwwhindawicom Volume 2018
Advances in
Materials Science and EngineeringHindawiwwwhindawicom Volume 2018
cement proportion increased )e uniform design andnonparametric regression had a high efficiency in the ex-perimental research and matched each other well which wasof great significance to this scientific research
Data Availability
)e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
)e authors declare that they have no conflicts of interest
Acknowledgments
)is research was financially funded by the China Post-doctoral Science Foundation (2017M622789) and the Na-tional Natural Science Foundation of China (51078175)
References
[1] K He H Yang Z B Lu F F Jia E P Wang and Q X DongldquoEffect of matrix modification on durability of cementitiouscomposites in an acid rain environmentrdquo Journal of WuhanUniversity of TechnologyndashMaterials Science Edition vol 29no 3 pp 498ndash503 2014
[2] M P Lavigne A Bertron C Botanch et al ldquoInnovativeapproach to simulating the biodeterioration of industrialcementitious products in sewer environment Part II vali-dation on CAC and BFSC liningsrdquo Cement and ConcreteResearch vol 79 pp 409ndash418 2016
[3] B Huber H Hilbig M M Mago J E Drewes and E MullerldquoComparative analysis of biogenic and chemical sulfuric acidattack on hardened cement paste using laser ablation-ICP-MSrdquo Cement and Concrete Research vol 87 pp 14ndash21 2016
[4] N De Belie J Monteny A Beeldens E Vincke D VanGemert and W Verstraete ldquoExperimental research andprediction of the effect of chemical and biogenic sulfuric acidon different types of commercially produced concrete sewerpipesrdquo Cement and Concrete Research vol 34 no 12pp 2223ndash2236 2004
[5] P K Mehta ldquoDurability of concretemdashfifty years of progressrdquoin Proceeding of the 2nd International Conference on ConcreteDurability ACI SP126ndash01 pp 1ndash32 Sapporo Japan 1991
[6] Y Yang T Ji X J Lin C Y Chen and Z X Yang ldquoBiogenicsulfuric acid corrosion resistance of new artificial reef concreterdquoConstruction and Building Materials vol 158 pp 33ndash41 2018
[7] L Gu P Visintin and T Bennett ldquoEvaluation of accelerateddegradation test methods for cementitious composites subjectto sulfuric acid attack application to conventional and alkali-activated concretesrdquo Cement and Concrete Compositesvol 87 pp 187ndash204 2018
[8] X Li Y X Lin K Lin and T Ji ldquoStudy on the degradationmechanism of sulphoaluminate cement sea sand concreteeroded by biological sulfuric acidrdquo Construction and BuildingMaterials vol 157 pp 331ndash336 2017
[9] E Hewayde M Nehdi E Allouche and G Nakhla ldquoEffect ofmixture design parameters and wetting-drying cycles on re-sistance of concrete to sulfuric acid attackrdquo Journal of Materialsin Civil Engineering vol 19 no 2 pp 155ndash163 2007
[10] Y F Fan Z Q Hu H Y Luan D W Wang and A Chen ldquoAstudy of deterioration of reinforced concrete beams under various
forms of simulated acid rain attack in the laboratoryrdquo StructuralEngineering and Mechanics vol 52 no 1 pp 35ndash49 2014
[11] A Grandclerc P Dangla and M Gueguen-MinerbeldquoModelling of the sulfuric acid attack on different types ofcementitious materialsrdquo Cement and Concrete Researchvol 105 pp 126ndash133 2018
[12] J Hill E A Byars J H Sharp C J Lynsdale J C Cripps andQ Zhou ldquoAn experimental study of combined acid andsulfate attack of concreterdquo Cement and Concrete Compositesvol 25 no 8 pp 997ndash1003 2003
[13] Z T Chang X J Song R Munn and M Marosszeky ldquoUsinglimestone aggregates and different cements for enhancingresistance of concrete to sulphuric acid attackrdquo Cement andConcrete Research vol 35 no 8 pp 1486ndash1494 2006
[14] H GMinW P Zhang andX L Gu ldquoEffects of load damage onmoisture transport and relative humidity response in concreterdquoConstruction and Building Materials vol 169 pp 59ndash68 2018
[15] H G Min W P Zhang X L Gu and R Cerny ldquoCoupledheat and moisture transport in damaged concrete under anatmospheric environmentrdquo Construction and Building Ma-terials vol 143 pp 607ndash620 2017
[16] W P Zhang H G Min and X L Gu ldquoTemperature responseand moisture transport in damaged concrete under an at-mospheric environmentrdquo Construction and Building Mate-rials vol 123 pp 290ndash299 2016
[17] W P Zhang H G Min X L Gu Y Xi and Y S XingldquoMesoscale model for thermal conductivity of concreterdquoConstruction and Building Materials vol 98 pp 8ndash16 2015
[18] S Mirvalad and M Nokken ldquoStudying thaumasite sulfateattack using compressive strength and ultrasonic pulse ve-locityrdquo Materials and Structures vol 49 no 10 pp 4131ndash4146 2016
[19] M O Yusuf ldquoPerformance of slag blended alkaline activatedpalm oil fuel ash mortar in sulfate environmentsrdquo Con-struction and Building Materials vol 98 pp 417ndash424 2015
[20] S D Xie L Qi and D Zhou ldquoInvestigation of the effects ofacid rain on the deterioration of cement concrete usingaccelerated tests established in laboratoryrdquo Atmospheric En-vironment vol 38 no 27 pp 4457ndash4466 2004
[21] M Bohm J Devinny F Jahani and G Rosen ldquoOn a moving-boundary systemmodeling corrosion in sewer pipesrdquo AppliedMathematics and Computation vol 92 no 2-3 pp 247ndash2691998
[22] M Bohm J Devinny F Jahani F B Mansfeld I G Rosenand C Wang ldquoA moving boundary diffusion model for thecorrosion of concrete wastewater systems simulation andexperimental validationrdquo in Proceedings of the AmericanControl Conference pp 1739ndash1743 San Diego CA USA1999
[23] F Jahani J Devinny F Mansfeld and I G Rosen ldquoIn-vestigations of sulfuric acid corrosion of concrete I modelingand chemical observationsrdquo Journal of Environmental Engi-neering vol 127 no 7 pp 572ndash579 2001
[24] Z G Song X S Zhang and H G Min ldquoConcentrationboundary layer model of mortar corrosion by sulfuric acidrdquoJournal of Wuhan University of TechnologyndashMaterials ScienceEdition vol 26 no 3 pp 527ndash532 2011
[25] K T FangUniformDesign and UniformDesign Table SciencePress Beijing China 1994 in Chinese
[26] K T Fang and C X Ma Orthogonal and Uniform Design ofExperiments Science Press Beijing China 2001 in Chinese
[27] A M Hasofer and J Qu ldquoResponse surface modelling ofmonte carlo fire datardquo Fire Safety Journal vol 37 no 8pp 772ndash784 2002
10 Advances in Materials Science and Engineering
CorrosionInternational Journal of
Hindawiwwwhindawicom Volume 2018
Advances in
Materials Science and EngineeringHindawiwwwhindawicom Volume 2018
![Sulfuric Acid is[1]](https://static.documents.pub/doc/80x56/552847e14a7959c93d8b4684/sulfuric-acid-is1.jpg)
