Degradation Modeling of Concrete Submitted to Biogenic Acid Attack

Cement and Concrete Research 70 (2015) 29–38

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Cement and Concrete Research

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Degradation modeling of concrete submitted to biogenic acid attack

Haifeng Yuan a,b,⁎, Patrick Dangla a, Patrice Chatellier c, Thierry Chaussadent c a Université Paris-Est, UMR Navier, UMR8205 CNRS/École des Ponts ParisTech 2 Allée Kepler, 77420 Champs-sur-Marne, France b Vanke Architecture Research Center, 8 Gongye East Road, 523808 Dongguan, China c Université Paris-Est, IFSTTAR, 14-20 Boulevard Newton, Cité Descartes, 77447 Marne la Valle Cedex 2, France article info abstract

Article history: Biodeterioration of concrete, which is very common in sewer system, results in significant structure degradation. Received 16 May 2014 The process can be described by the 3 following steps: Concrete surface neutralization providing appropriate Accepted 5 January 2015 environment for sulfur oxidizing bacteria (SOB) to grow, sulfuric acid (H2SO4) production by SOB on concrete Available online 21 January 2015 surface and chemical reaction between H2SO4 and cement hydration products. A reactive transport model is proposed to simulate the whole biodeterioration processes of concrete in contact with H S gas and SOB. This Keywords: 2 model aims at solving simultaneously transport and biochemistry/chemistry in biofilm and concrete by a global Sewer pipe Concrete (E) coupled approach. To simulate the neutralization process, the absorption of H2S gas, the dissolution of portlandite Organic acids (D) (CH), the decalcification of calcium silicate hydrates (C–S–H) and the precipitation of calcium sulfide (CaS) are Corrosion (C) considered. To obtain the amount of biogenic acid, the production rate of H2SO4 by SOB is calculated via a set

Modeling (E) of simpliﬁed models governed by pH. Coupling with the modeling of H2SO4 degradation process, the biodeterioration depth and the solid composition evolution could be predicted. A laboratory experiment reported in literature is simulated and the simulation results are compared with experimental results. © 2015 Elsevier Ltd. All rights reserved.

1. Introduction Step (2) Production of H2SO4 by SOB: Once the pH of concrete surface is reduced to 9, some strains of SOB start to grow and form Huge amount of concrete and cementitious materials is used in the biofilms on the concrete surface [4,5]. Although the wastewater systems. Some of the microorganisms in sewer pipes can bio-activity in biofilms is not fully understood, it is generally generate aggressive aqueous solutions which may damage cementi- believed that firstly H2Sinbiofilms is slowly oxidized to tious materials and reduce the material service time. It was estimated H2SO4 by neutrophilic sulfur-oxidizing microorganisms that the United States will need 390 billion dollars during the next (NSOM) [6].AfterpH has decreased to 4–5, acidophilic 20 years to repair the existing wastewater infrastructure [1].Thus, sulfur-oxidizing microorganisms (ASOM) produce large there is great interest in predicting the corrosion rate and the service amount of H2SO4, which makes the main contribution to the life of sewer pipes. biodeterioration of sewer pipe [7,8].H2SO4 solution and sulfate The most prominent biodegradation is biogenic sulfuric acid (BSA) is destructive to concrete. With sufficient sulfur source, the pH corrosion which can be found in sewer pipes containing H2S gas. The of concrete surface can be even reduced to 1 [5]. mechanism of such biodeterioration of concrete can be brieflydescribed Step (3) H2SO4 attack of concrete: Biogenic sulfuric acid penetrates into by the following three steps: concrete and reacts with CH and C–S–H. The ample supply of sulfate and the intrusion of the acid could result in the forma- Step (1) Neutralization of concrete surface: The pH of fresh concrete tion of ettringite (3CaO ⋅ Al O ⋅ 3CaSO ⋅ 32H O) which is (11–13) is too high for the sulfur-oxidizing bacteria (SOB) to 2 3 4 2 expansive [5,9]. However, some experimental observations survive. However, H S gases can be absorbed into concrete 2 [10,11] found that the boundary between corrosion products surface to react with portlandite (CH)1 and calcium silicate hy- and uncorroded concrete is quite clear and ettringite was not drate (C–S–H) which are the main Portland cement hydrates. present. According to the investigations conducted by Consequently, the pH of concrete surface can be reduced to Gabrisova et al. [12,13], ettringite starts to form at pH ranging less than 9 [2,3]. from 12.5 to 12. When pH decreases below 10.7, ettringite starts to decompose into gypsum. Since normally pHin ⁎ Corresponding author at: Université Paris-Est, UMR Navier, UMR8205 CNRS/École des biofilms is less than 3 [15], ettringite exists temporarily and Ponts ParisTech 2 Allée Kepler, 77420 Champs-sur-Marne, France. Tel.: + 86 18319040310. occasionally appears in the corrosion products during the E-mail address: [email protected] (H. Yuan). 1 biodeterioration of sewer pipes. Therefore, in this study only Cement chemistry notation is used throughout the paper: C ¼ CaO; S ¼ SiO2; H ¼ H2O; and S ¼ SO3. the precipitation of gypsum is considered during the sulfuric

acid attack process which takes place between the concrete The overall removal of hydrogen sulﬁde from a sewer atmosphere

surface and bioﬁlm–cement matrix interface. This step is depends on numerous conditions, such as H2S concentration levels, characterized by the production of a corroded layer consisting temperature, and relative humidity of the sewer atmosphere [3,25].

of gypsum (CaSO4 ⋅ 2H2O, noted as CSH2), silica gel (SiO2, Richard et al. [24] suggested that all released H2S from wastewater is noted as S) and moisture [14,16]. immediately absorbed by concrete surface, resulting in zero H2Sinthe gas phase. However, experimental results of Vollertsen et al. and Nielsen

et al. [25,26] revealed that transferring of H2S from the gas phase to the This step could decrease the performance of concrete since gypsum concrete surface is not an instantaneous process and absorption kinetics has barely no strength. should be taken into account. By experiments with pilot-scale sewer re-

For the chemical corrosion process, which directly results to the actors, Vollertsen et al. [25] found that the absorption rate FH2S could degradation of materials, our previous research [17] has proposed a be described as a power function in the gas phase H2S concentration reactive transport model to predict the behavior of Portland cement p . H2S concrete in contact with a given H2SO4 solution. However, in such a Furthermore, it is found that the corrosion is more severe at biogenic degradation process, the concentration of sulfuric acid is not downstream of some particular areas e.g. force main discharge points constant or given, but dominated by the biochemical reactions in the or drop structures, where release rates are higher than in other parts SOB community. Thus the biochemistry reactions taking place in the of the sewer [27]. Nielsen et al. [28] studied the influence of the fi bio lm system (step (1) and step (2)) should be simulated as well. air-flow in sewer on the absorption of H2S. Increased air-flow will Several models were reported to simulate the biochemical process, provide better mixing of the sewer atmosphere, as well as reduce the such as “Wastewater Aerobic/anaerobic Transformations in Sewer thickness of the diffusive boundary layer near surfaces. (WATS)” model [18] and sulfide oxidation model [19]. Nielsen et al. [28] presented an empirical relationship between the Yet, to our knowledge, no attempt has been made to model the neu- Reynolds (Re) number of the gas flow and the absorption rate. For the tralization of concrete surface and few models focus on the coupling of sake of simplicity, the effect of gas flow regime and temperature are ig- biochemical process and chemical corrosion process. With HYTEC, De nored in this paper. The nth order kinetics of H2S absorption of concrete Windtetal.[20] modeled a bioleaching test applied to ordinary Portland surface and biofilms is described as follows: cement pastes during 15 months. But the production rate of H2SO4 with different pH, diffusion of different species, equilibrium between F ¼ k pn ð1Þ the different solid phases, and the coupling between transport and H2S abs H2S reactions were not investigated specifically. where, p is the content of H S gas (ppm). k is the surface specific In this paper, a set of reactive transport modeling is expected to H2S 2 abs simulate the neutralization process of concrete surface and H2SO4 pro- H2S absorption rate constant, which is reported to vary between −8 −7 −2 −1 −n duction in SOB community. Thus, the reduction of pHofconcretesurface 6.25 × 10 and 3.12 × 10 mol S m s (ppm H2S) depend- and the pH evolution in SOB community can be predicted. Coupling ing on temperature [25]. The reaction order n is correlated with kabs, with the H2SO4 degradation modeling of concrete, the change of pHin with n approximately 0.5 for low kabs and 0.8 for high kabs. However, SOB community and the composition of pipe concrete are expected to the quantitative relationship among kabs, n and temperature is still be calculated during the biodeterioration process. Furthermore, unclear. According to the study of Joseph et al. [3], the rate of neutraliza- the degradation depth of concrete submitted to biogenic acid attack tion process significantly enhanced by the increase in temperature from will be predicted. Simulations results of a set of accelerated micro- 16 °C to 30 °C. Since temperature is constant and equal to 25 °C in this −7 −2 −1 −n biological tests conducted by De Muynck et al. [21] are presented and study, kabs is determined as 2 × 10 mol S m s (ppm H2S) compared with experimental results. and n = 0.75. Then the absorption rate of H2S versus content of H2Sin gas phase is plotted in Fig. 1. With a higher concentration, H2S gas will be absorbed into concrete surface faster. 2. Modeling of the neutralization process of concrete 2.2. Chemical reactions of aqueous H Sandconcrete The initial pH of ordinary Portland cement concrete is too high for 2 sulfur-oxidizing bacteria (SOB) to grow. Rigdon et al. [4,5] proposed Aqueous hydrogen sulfide dissociates in pore solution and releases that the microbial activity on the concrete surface is initiated at pH H+. As Portland cementitious materials, portlandite (CH) and calcium around 9. Thereafter, a succession of microbial communities, which silicate hydrates (C–S–H) are the solid phases able to react with H S, can utilize sulfide and/or its oxidized forms (such as element sulfur 2 calcium hydroxide can be dissolved and calcium sulfide (CaS) forms [3]) develops. The abiotic pH reduction of concrete surface results to an initial lag period before the start of active corrosion phase [22]. Therefore, the primary stage is the reduction of pH at the concrete surface, where pH decreases from about 12.5 to 9 by chemical acid reactions of CO2 and H2S with concrete. However, the experimental research conducted by Joseph et al. [3] suggested that H2S gas is the major factor for the surface pH reduction in sewers during early stages of exposure rather than carbonation. Thus this study concentrates on the effect of

H2S. Similar consideration was taken in the study of Lin [23].

2.1. Absorption of H2S

In sewer pipes, H2S can be absorbed from gas phase into pore solution of concrete and bioﬁlms from gas phase. Since only aqueous

H2S can react with concrete or be oxidized by SOB, the absorption of H2S governs the time of surface neutralization and the production of H2SO4. Therefore, the transferring of H2S from sewer gas to concrete surface or bioﬁlms is a crucial step. Fig. 1. H2S absorption rate at different H2S gas contents. H. Yuan et al. / Cement and Concrete Research 70 (2015) 29–38 31

when H2S is absorbed by concrete surface. These global reactions in the study of Shen et al. [32]. Generally speaking, the Ca/Si ratio of can be understood by combining three basic dissociation reactions C–S–H decreases from 1.7 for fresh hydrated Portland cement during (Eqs. (2)–(4)), which involve the minerals and the aqueous species in the neutralization process. By taking the Ca/Si ratio as a variable (x)in pore solution. the model, a constitutive-like equation is derived as a one to one Q CH Q CH þ − relationship between the Ca/Si ratio and : x ¼ χ . Thus, the CaðÞ OH ⇌ Ca2 þ 2OH ð2Þ KCH KCH 2 mass action law for C–S–H can be then generalized as follows: ⇌ 2þ þ − þ 0 þ ðÞ− ð Þ Z xCaO ySiO2 zH2O xCa 2xOH ySiO2 z x H2O 3 QCH Q K χðÞq ln SHt ¼ − CH dq ð8Þ 2þ 2− K 0 q CaS ⇌ Ca þ S ð4Þ SHt

where, t is the hydration level of the amorphous silica SH which can be Furthermore, CaS precipitation is not stable in acidic solution. When t fi – – obtained after a complete decalci cation of the C S H. KCH and KSH there is enough H2S, calcium hydrogen sulfide, which is soluble, would t (Q CH and Q ) are the equilibrium constants (ion activity product) of be produced as follows [29]: SHt portlandite and amorphous silica. This relationship was confirmed by þ ⇌ ðÞ: ð Þ CaS H2S Ca HS 2 5 comparing with experimental results in the study of Shen et al. [32].

fi Therefore the acidi cation of aqueous H2S will result in a series of 2.3. Effect of H2Sgaslevel homogeneous chemical reactions gathered in Table 1, where the equilibrium constants are given at 298 K. With the absorption of H2S in gas phase and the chemical reaction of The equilibrium conditions of these dissociation reactions depend H2S with concrete, the pH reduction of concrete surface can be calculat- on the concentration of H2S. The dissolution of CH and the decalcifica- ed. To verify the modeling of the neutralization process of concrete, we tion of C–S–H are very similar to those for H2SO4 attack, which were simulate a set of experiments conducted by Joseph et al. [3]. In the ex- detailed in our previous study of H2SO4 attack modeling [17]. For the periments, concrete coupons were exposed to different H2S gas levels equilibrium between CH and CaS, we have (4.5, 7.5, 15.8, 26.5, 48.9 ppm) in well-controlled laboratory chambers, where the temperature was kept at 25 °C. After a 1 year exposure, the Q Q ρ CaS ¼ CH H2S ð Þ pH on concrete surface was measured. The simulation and the experi- CH 6 KCaS KCH ρ H2S mental results are compared in Fig. 2 which indicate that our model where, K and Q are the equilibrium constant and ion activity product of − CH and CaS respectively. K =6.5×10−6 andK ¼ 7:9 10 7 ρCH (a) CH CaS H2S are the values of ρ defined by the coexistence of CH, CaS and aqueous H2S phase. It can be calculated by a given function of the solubility constants of other species as Eq. (7).

K2 K ρCH ¼ H2O CaS ð Þ H S 7 2 K K − K H2S HS CH

With the help of the constants mentioned above, it can be obtained − that ρCH ≈ 8:90 10 10 mol=L . Hence, CaS would not precipitate H2S when ρ b ρCH , while dissolution of CH takes place when ρ NρCH . H2S H2S H2S H2S In the model, the CH dissolution process follows a simple kinetic law which is assumed to be governed only by the difference of chemical potentials of H2S between the current state and the equilibrium state. The decalciﬁcation of C–S–H is described by a general characteriza- tion method based on thermodynamics rather than the (semi-)empirical models [30] or solid solution method [31]. The details can be found (b)

Table 1

Chemical reactions between aqueous H2S and concrete.

Aqueous reactions K

+ − −14 H2O ⇌ H +OH ¼ : KH2 O 1 0 10 − H2S ⇌ HS +H+ ¼ : −8 KH2 S 8 9 10 − 2− + − ⇌ − 13 HS S +H KHS ¼ 1:2 10 + 2+ − 1 CaOH ⇌ Ca +OH þ ¼ : KCaOH 1 66 10 − Ca2+ +S2 ⇌ CaS0 ¼ : 3 KCaS0 3 5 10 2+ − + 1 Ca +HS ⇌ CaHS þ ¼ : KCaHS 1 276 10 2+ 2− ⇌ 0 4 Ca +H2SiO4 CaH2SiO4 K 0 ¼ 3:89 10 CaH2 SiO4 2+ − ⇌ + 1 Ca +H3SiO4 CaH3SiO4 K þ ¼ 1:58 10 CaH3 SiO4 0 ⇌ 0 −3 SiO2 +2H2O H4SiO4 K 0 ¼ 1:94 10 SiO2 0 ⇌ − + −10 H4SiO4 H3SiO4 +H K 0 ¼ 1:55 10 H4 SiO4 − 2− + − H SiO ⇌ H SiO +H − 14 3 4 2 4 KH SiO ¼ 4:68 10 3 4 Fig. 2. (a) pH on concrete surface after exposure of 1 year in the experiments of [3];(b)the

The equilibrium constants are reported by [50–53]. lag time of surface neutralization process with different H2Slevel. 32 H. Yuan et al. / Cement and Concrete Research 70 (2015) 29–38 can predict the pH reduction of pipe surface during neutralization According to the experimental observations [10],theactivityofSOB process fairly well. increases until pH is reduced to a critical value. When pHislowerthan

It is well known that, high H2S gas level in sewer pipes results to a the critical value, H2SO4 production rate drops rapidly. In this paper, fast surface neutralization process. Since the SOB cannot grow on the production process of sulfuric acid in SOB media is divided into concrete surface until pH being reduced to 9, lower H2S level leads to two steps: longer lag time of biogenic H SO attack. For most of the in-situ condi- 2 4 • NSOB dominating step: When pH in SOB media is higher than the tions, corrosion materials are removed by flow of sewage periodically value of pH ,H SO is produced by NSOB, whose production rate and new surface where pH is too high for SOB growth is exposed NSOB 2 4 is quite low. cyclically. Thus, the lag time is crucial for biodeterioration of sewer • ASOB dominating step: When pHinSOBmediaislowerthanthevalue pipes. We conduct simulations of surface neutralization with different of pH ,H SO is produced by ASOB rather than NSOB which cannot H S gas level. We consider the lag time as the time of the decrease of NSOB 2 4 2 survive in acidic environment. The production rate of H SO keeps surface pH from 12.4 to 9. The lag time of biogenic H SO attack with 2 4 2 4 increasing until pHreachespH .WithpH below pH ,the different H S gas level is plotted in Fig. 2. NSOB NSOB 2 metabolic activity of ASOB is limited. Consequently, H SO production From Fig. 2, it is clear that more time is needed to reach the proper 2 4 rate is reduced from a peak value. environment for SOB with less H2S gas. For the condition of 10 ppm, biofilms could even not form if the period of flow is less than 80 days. When the H2S gas reaches more than 100 ppm, SOB could start to The curve of succession of SOB in different pHrangecanbefitted by a grow on the surface in few days. set lognormal functions (see Fig. 3). Thus such process can be expressed by functions of pHasfollows: 3. Modeling of the production of H2SO4 by SOB ðÞpH −pH 2 α − NSOB ASOB pH −pH : ¼ p0ffiffiffiffiffiffi 2σ NSOB ð Þ 2− NSOB RH SO −NSOB e 10 9 After being absorbed into concrete surface, S could be oxidized 2 4 σ 2π into element sulfur by a combination of biological and chemical ðÞ− 2 processes [33,25]. And the kinetic of hydrogen sulfide oxidation was α − pH pHASOB : ¼ p0ffiffiffiffiffiffi 2σ ð Þ ASOB RH SO −ASOB e 10 studied by several researchers [25,18]. However, Jensen et al. [18] 2 4 σ 2π found that biological hydrogen sulfide oxidation typically accounted for more than 95% of the total oxidation rate and that chemical oxida- where, α0 and σ are constants depending on SOB numbers and activity. In tion played a minor role. Thus the abiotic oxidation of hydrogen sulfide this paper, the value of α0 and σ are determined by fitting experimental is not taken into account in this study. measurements. When the environment of concrete surface is suitable for SOB To verify this relationship, we simulated the experiments conducted succession, biogenic sulfuric acid which attacks the concrete could be by De Muynck et al. [21]. In these experiments the pH evolution in pure produced from biofilms. According to literatures [34,22,35], the produc- SOB suspensions containing enough sulfur source was monitored tion rate of H2SO4 is controlled by the activity and the amount of SOB, for 10 days. To fit the experimental results we set pHNSOB =2.5 −7 which is determined by pH, sulfur source content, temperature and and pHASOB =1.5.WhenpH ≥ pHASOB, α0 =8×10 mol/L ⋅ s, σ = 3+ −7 the concentration of Al . For such a complex process, there is a lack 0.48; while α0 =4×10 mol/L ⋅ s, σ =0.24,whenpH ≤ pHASOB. of fundamental understanding of the quantitative relationship among The relationship between H2SO4 production rate and pH is plotted in all these factors. Fig. 4, which indicates that very few H2SO4 is produced until pH For the Portland cement based sewer pipes degraded heavily, the decreases to 4. With further decrease of pH, lots of H2SO4 is produced concentration of H2S in sewer could reach 400 ppm [5] and temperature by ASOB and the production rate rises sharply. Once pH has decreased is normally 25 °C to 30 °C [36]. Therefore we assume that sulfur source is below 1.5, the H2S production rate drops rapidly. not limiting for SOB, while no Al3+ exists and temperature is constant. The pH evolution obtained from both simulation and experiment is

Thus, in this simplified modeling the production of H2SO4 is only con- plotted in Fig. 4. In the experiment, as a result of the conversion of ele- trolled by pH which itself is determined by the amount of H2SO4.In mental sulfur to sulfuric acid by NSOB, pH decreases slightly during some experimental researches, the pH evolution in biofilms or SOB sus- early time. However, a sharp reduction of pH was observed after pension were measured [37,21]. Thus, it is possible to model the H2SO4 4 days of submersion due to the activity of ASOB. When pH is below production process by fitting the pH evolution. 1.5, the activity of ASOB is inhibited. Thus the production rate of

It is known that different types of SOB are active in different ranges H2SO4 starts to decrease from the peak value. However, the pHcon- of pH(seeFig. 3) and produce H2SO4 with different rates [22,38].Two tinues to decrease to about 1 after 10 days of testing. The comparison general categories of SOB can be differentiated based on their optimal between the modeling results and the experiment results is fairly good. pH for growth [38]: Neutrophilic Sulfur-Oxidizing Bacteria (NSOB), which develop at pH near neutral and are found at the beginning of 4. Modeling of the H2SO4 attack of concrete biodeterioration; Acidophilic Sulfur-Oxidizing Bacteria (ASOB), which prefer acidic media. Normally, the H2SO4 production rate of NSOB is Once H2SO4 is produced by bioﬁlms, cement-based materials are much slower than that of ASOB. directly in contact with H2SO4 which penetrates into the pores of concrete. As a strong acid, a series of homogeneous chemical reactions

between H2SO4 and concrete could result in the reduction of the concrete alkalinity and the dissolution of the calcium hydroxide. Gypsum accumulates on the concrete surface as a layer of white precipitate, while ettringite possibly forms in concrete core. In this paper the damage caused by ettringite is neglected. Thus the only corrosion product of biogenic sulfuric acid attack is gypsum which precipitates between the concrete surface and bioﬁlm–cement matrix interface. Since gypsum is expansive and insoluble, the volume of solid substances increases largely [39,14].

The modeling approach of the chemical reaction between H2SO4 and Fig. 3. Succession of SOB in different pHrange[54]. concrete and of the microstructure evolution of concrete was well H. Yuan et al. / Cement and Concrete Research 70 (2015) 29–38 33 (a) (a)

(b) (b)

Fig. 4. (a) H2SO4 production rate and pH; (b) the evolution of pHinpureSOBsuspension from 0 days to 10 days.

Fig. 5. Modeling of H2SO4 attack. (a) Solid concentration, Ca/Si ratio of C–S–H and porosity; (b) solid volume and inner pressure. demonstrated in our previous research [17]. By simulating a set of chemical H2SO4 attack experiments conducted by Kawai et al. [16],the modeling has been confirmed. dissolution/precipitation of solid phases, leads to the change of the According to the modeling, when ρ0 is high enough H2SO4 diffusion rate of aqueous species. ≥ −32 ( 3.9 × 10 mol/L), portlandite will start to dissolve. As the concen- To simulate the whole process of biodeterioration of sewer pipe, tration of H2SO4 is getting higher, decalcification process of calcium both of cementitious materials and SOB media where H2SO4 is produced silicate hydrate will take place. The porosity starts to increase due to should be considered in the modeling. The chemical and the bio- the dissolution of CH and C–S–H. Shortly, CSH2 starts to form in pores. chemical reactions are considered in cementitious material part and Since the molar volume of gypsum is larger than CH, the porosity biofilm part separately. Yet the various species not only diffuse in the decreases a little temporarily (see Fig. 5). After C–S–H and CH are dis- cementitious material and SOB media but also across the interface solved completely, CSH2 continues to form. As gypsum is compressible, between the two materials. the precipitation of gypsum exerts pressure in concrete (see Fig. 5), This work is implemented within the modeling platform, Bil,2 based which eventually results in the breaking of the concrete pore structure. on the finite volume methods. Compared to other reactive transport To account for this phenomenal the inner pressure drops to 0 once it codes [43,44], Bil can solve the couplings between the chemical reaches 3.5 MPa which is the strength of pores. The release of inner reactions and the transport equations in one step. pressure indicates the failure of pores. Meanwhile, the porosity and The coupling between the transport and the chemical/bio-chemical volume of gypsum gel increases again. reactions is treated with the help of a set of mass balance equations. The first subset of equations is the mass balance equations applied to each element A considered in the system (A = S, Ca, Si): 5. Reactive transport modeling ∂n A ¼ − div w ð11Þ The deterioration process is not only controlled by the production of ∂t A H2SO4 by SOB and its chemical reaction with cement hydrates but also by the transport of different species. Water saturation in pores of where nA represents the total molar content of element A per unit fl concrete is an important factor which could in uence the transport volume of porous medium (mol/L). There are two contributions to nA L S properties [40,41]. However, for sewer pipes degraded heavily, the bio- associated to the liquid and solid (or gel) phases: nA = ϕρA + nA,where L S deterioration chamber with high relative humidity (close to 98%) is ρA and nA are the concentration of element A in pore solution and solid commonly used to simulate the sewers' environment [3,42].Inthis paper, only diffusion of various species in saturated porous media is 2 Bil is developed by Patrick Dangla. The source code can be downloaded at http://perso. considered. Furthermore, the change of porosity, which is the result of lcpc.fr/dangla.patrick/bil/. 34 H. Yuan et al. / Cement and Concrete Research 70 (2015) 29–38 phase respectively (mol/L). The concentration of each element can be As a consequence, the charge is governed by a global balance equation found in Table 2, where nC − S − H represents the amount of element as follows: – – Si in all types of C S H gel with different Ca/Si ratio. Obviously, the X fl = 2 i ¼ z w ð17Þ total molar ow of A, wA mol m s , only pertains to the liquid i i i L phase and is decomposed in the same manner as ρA. – In the present study, we consider the electro-diffusion (Nernst where the summation stands for the ionic current and applies on the Plank equation) as the main transport mechanism as follows: set of electrolyte ions. Therefore an electric potential is generated in the medium providing electrostatic force on each ion so as to form an ¼ − ∇ρ þ ρ Fzi ∇ψ : ð Þ electroneutral pore solution. Therefore electroneutrality must hold in wi Di i i 12 RT the medium: X ρ ¼ : ð Þ Taking into account the evolution of porosity, the effective diffusion zi i 0 18 coefficient Di of each species i is calculated as follows [45]: i

¼ 0 : −4 9:95ϕ ð Þ Eqs. (11)–(18) are the set of the field equations governing the Di Di 2 9 10 e 13 coupling of transport and chemistry. where, D0 is the diffusion coefficient in pure water depending on the i 6. Simulation results and discussion radius of ion which is taken from the study of Lide et al. and Conway et al. [46,47]. ϕ is the porosity of concrete. Thus the diffusion coefficients In order to find the deterioration rate of concrete subjected to bio- would change during the porosity evolution, which could be calculated degradation, laboratory experiments have been done to simulate the by the model developed in our previous research [17]. corrosion process of concrete in different environments [1,21]. In this The porosity evolution is accounted by different methods for study, we simulated the experiment conducted by De Muynck et al. different conditions. During early time, gypsum precipitates in the [21]. In the experiment, CEM I cement concrete cylinders (W/C = pores, the change of porosity can be easily accounted for by a simple 0.37, H = 15 mm, D = 80 mm) were subjected to 8 cycles of accelerated balance of volume: test. Each cycle consisted in 4 steps: (1) incubation in H2Sgas (200 ppm) for 2 days; (2) submersion in 1.5 L of mixed cultures of ϕ ¼ ϕ 0− s − 0 ð Þ SOB obtained from a sewer pipe (medium composition: 10 g/L C V CSH2 nCSH2 nCSH2 14

ϕ0 s (a) where, C is the initial porosity of sample. V CSH2 is the molar volume of the solid phase of gypsum. After a complete ﬁlling of pores, the sample can be treated as cementitious pore structure with gypsum inclusion. In such condition, the porosity of the sample can be calculated as follows:

ϕ ¼ ϕ0 þ φ ϕ0 þ φ ð Þ C C CSH2 CSH2 15

φ φ where, C and CSH2 represent the porosity changes of cementitious materials and gypsum due to the pressure arising in samples. For the damaged materials, the microstructure can be considered as uncom- pressed gypsum gel with solid particles inclusion such as unreacted portlandite, C–S–H, quartz and other non-reactive phase. The porosity of the whole sample is:

ϕ ¼ ϕ 0ϕ 0 : ð16Þ C CSH2 (b) Besides mass balance of elements, each molecule, i,takesaﬁxed valence number, zi, hence carrying a constant charge. Since there is no source of charge, for each chemical reaction the charge keeps balanced.

Table 2 Concentration of each element.

L S Element Liquid phase ρA Solid phase nA

ρ þ ρ þ þ ρ SH2SO4 attack H SO HSO 2þ n 2 4 4 SO4 CSH2 þρ þ þ ρ 0 CaHSO4 CaSO4

H S attack ρ þ ρ − þ ρ 2− n 2 H2 S HS S CaS þρ þ þ ρ CaHS CaS0 Ca H2SO4 attack ρ 2þ þ ρ þ þ ρ þ nCH þ n Ca CaHSO4 CaOH CSH2 þρ þ ρ þ þ ρ þ 0 CaH SiO xnC−S−H CaSO4 CaH3 SiO4 2 4

ρ þ þ ρ þ þ ρ þ þ H2S attack Ca2 CaHS CaOH nCH nCaS þρ 0 þ ρ þ þ ρ þxn − − CaS CaH SiO CaH2 SiO4 C S H 3 4 Fig. 6. ThecalculatedabsorptionofH SandpH evolution proﬁles from 0 days to 2 days: ρ þ ρ − þ ρ 2 Si H2SO2/H2S attack 2− H SiO 0 nC − S − H H2 SiO4 3 4 H4 SiO4 þρ þ þ ρ þ ρ (a) Aqueous H2S concentration and pH evolution at surface; (b) pH evolution in concrete CaH SiO 0 CaH3 SiO4 2 4 SiO2 (H2S level = 200 ppm). H. Yuan et al. / Cement and Concrete Research 70 (2015) 29–38 35

elemental sulfur, 3 g/L KH2PO4, 0.1 g/L NH4Cl, 0.1 g/L MgClH2O) for 10 days; (3) submersion in distilled water for 2 days; and (4) drying at room temperature for 1 day. During the second step, the pH in the SOB suspensions was measured frequently. In the third steps, water was stirred. Thus the degradation products were removed by the third step. And the last step could eliminate SOB remaining on the concrete surface. At the end of each cycle, the change of thickness of the specimens was measured by an automated laser measurement system. Since the cycles are equal one to each other, we simulate the ﬁrst and second steps separately, while the removing of corrosion products and SOB are neglected. To simulate the test, concrete samples with the same size as that in experiments are considered. The size of representa- tive elementary volumes is 0.005 mm for concrete samples and 5 mm for SOB suspensions. Since the initial content of hydrates is absent from the experiment, we assumed that the concrete sample contain Fig. 8. The concentration of CaS and aqueous H2S at surface from 0 days to 2 days. initially 3.7 mol/L of portlandite and 3.5 mol/L of C–S–H as jennite based on the data from literature [48]. The initial porosity is 30%.

9.5 gradually. Due to the low ionization constant of H2S, the neutraliza- 6.1. Surface neutralization process tion rate of surface is low even if the H2S gas level is quite high at surface. After exposure of 2 days, the thickness of neutralized layer To simulate the ﬁst step, we consider the boundary conditions of reached to about 0.1 mm (see Fig. 6). constant H2S gas level (200 ppm), while no H2SO4 is present. For Since no H2SO4 is present during the neutralization process, CaS is numerical stability, the initial aqueous H2S concentration in concrete considered as the only corrosion product. The change in the volume of −9 sample is 1 × 10 mol/L, i.e., pH=12.4.H2S gas is absorbed into solid compounds after 1 days and 2 days of exposure are plotted in pore solution of concrete from the left surface, and the absorption rate Fig. 7. After 1 day, parts of CH and C–S–H are dissolved at the sample is governed by Eq. (1). The change of aqueous H2S concentration and surface, while CaS accumulates. The sample surface turns to a CaS-rich pH in the pore solution of surface part are plotted in Fig. 6. layer. Thus the solid volume of concrete sample is slightly larger than 3 As expected, H2Singasphaseisabsorbedintoporesolutionofcon- initial value, even if the molar volume of CaS (28 cm /mol [49]) is small- crete to neutralize the sample surface, where pH decreases from 12.4 to er than that of CH. After 2 days, CH at surface is completely dissolved (a) (a)

(b) (b)

Fig. 7. Solid volume and Ca/Si ratio of C–S–H of concrete after exposure in H2S (a) 1 day; Fig. 9. (a) The calculated pH evolution from 0 days to 10 days; (b) solid volume and Ca/Si (b) 2 days. ratio of C–S–H in initial concrete sample with neutralized surface. 36 H. Yuan et al. / Cement and Concrete Research 70 (2015) 29–38

while C–S–H is still partly decalciﬁed because of the lack of aqueous H2S. after 5 days. It causes the pH in concrete surface to decrease to 2 after More precipitation of CaS causes the further rising of solid volume of the 10 days of immersion. Such pH evolution can be explained as follows.

CaS-rich layer (see Fig. 7). However, the amount of aqueous H2Satsur- During the early time, the acid production is slower than the acid face is enough to dissolve the CaS precipitation. Thus, the volume of con- consumption. Due to the alkalinity of concrete, pH in SOB suspension crete surface starts to decrease after 1 days. Fig. 7 indicates that the close to concrete surface increases (see Fig. 10). After about 8 days, pH thickness of neutralized layer is approximately 0.1 mm after 2 days of starts to decrease because of the H2SO4 produced from bulk suspension exposure to H2S gas of 200 ppm. which refers to that part of suspension not influenced by concrete. The To illustrate the dissolution of CaS, the concentration of CaS and pH evolution in bulk SOB suspension is plotted in Fig. 10. Due to the aqueous H2S at concrete surface versus exposure time are plotted in low H2SO4 production rate of NSOB, pH in SOB suspension decreases Fig. 8. When aqueous H2S is absorbed into concrete, CaS starts to precip- very slightly during early time. Since lower pHcauseshigherin-situ itate until ρ increases to 7 × 10−4.9 mol/L. When aqueous H Sis H SO production rate, pH starts to decrease sharply after several H2S 2 2 4 more than that critical value, CaS starts to dissolve. days. When pH reaches 1.5, H2SO4 production starts to slow down. The change in pH of SOB suspension was measured during the experiments (see Fig. 10). The simulation results coincide with experimental 6.2. Biodeterioration process results. After immersion of 10 days, the calculated profiles of the volume of To simulate the second step of the experiment, we consider the con- solid phases are plotted in Fig. 11. Not only neutralized layer, but also crete sample with neutralized surface in contact with the SOB suspen- concrete core is degraded by biogenic H2SO4. Due to the diffusion of 2+ sion where H2SO4 is produced and penetrates into concrete. The Ca towards the gypsum precipitation front, lots of gypsum accumu- thickness and solid compositions of neutralized layer are determined lates at concrete surface. Thus a gypsum-rich layer can be found in by the simulation results of step 1. However, the simulation results in Fig. 11, and even though portlandite and C–S–H gel are dissolved, the Fig. 7 cannot be applied directly for the sake of numerical stability. volume of degraded zone is enlarged. Dsimulation indicates the degraded Thus, the pH value and solid concentration in neutralized layer are zone where materials are damaged by gypsum pressure. The dissolution simplified to vary linearly as indicated in Fig. 9. front where C–S–H starts to dissolve is indicated by the profile the Ca/Si During the biodeterioration process, the evolution of pHinbothcon- ratio of C–S–H gel which is followed by the dissolution front of CH. Be- crete and the SOB suspension part close to concrete surface are shown sides gypsum and amorphous silica, with Ca/Si ratio of 0, is observed in Fig. 9. During 5 days of immersion, pH in SOB suspension increases in the degraded zone as well. Fig. 11 shows a good agreement with from 7 to 9 rather than decrease. Therefore, pH in concrete surface al- most keeps at 10. However, pH in SOB suspension starts to decrease (a) (a)

(b) (b)

Fig. 11. (a) Solid volume and Ca/Si ratio of C–S–H after 10 days of immersion in SOB

Fig. 10. The pH evolution and production rate of H2SO4 from0to10days:(a)SOBclosedto suspension; (b) the predicted and measured corrosion depth (DSimulation represents the concrete surface; (b) bulk SOB suspension. degradation depth of the sample in simulation). H. Yuan et al. / Cement and Concrete Research 70 (2015) 29–38 37 experimental observations where gypsum layer, quartz were found in [3] A.P. Joseph, J. Keller, H. Bustamante, P.L. Bond, Surface neutralization and H2S oxidation at early stages of sewer corrosion: influence of temperature, relative humidity the corrosion products. and H2S concentration, Water Res. 46 (13) (2012) 4235–4245. In the experiments, rotation of the distilled water resulted in the [4] J.H. Rigdon, C.W. Beardsley, Corrosion of concrete by autotrophes, Corrosion 5 removal of corrosion products. Drying removes all the remaining SOB (1956) 60–62. [5] T. Mori, T. Nonaka, K. Tazaki, M. Koga, Y. Hikosaka, S. Noda, Interactions of nutrients, at the concrete surface. Thus we consider that all the cycles are identical. moisture and pH on microbial corrosion of concrete sewer pipes, Water Res. 26 (1) Consequently, the deterioration depth of all cycles is the same. The (1992) 29–37. predicted corrosion depth and that measured during experiment are [6] A. Bielefeldtand, M.G.D. Gutierrez-Padilla, S. Ovtchinnikov, J. Silverstein, M. compared in Fig. 11. The predicted corrosion rate is 0.22 mm/cycle, Hernandez, Bacterial kinetics of sulfur oxidizing bacteria and their biodeterioration rates of concrete sewer pipe samples, J. Environ. Eng. 136 (7) (2009) which coincide with experimental results. However, no corrosion 731–738. depth was measured after the first cycle of the experiment. The possible [7] C.D. Parker, The corrosion of concrete, Aust. J. Exp. Biol. Med. Sci. 23 (1) (1945) 81. fi reason is that during the curing time the samples were subjected to [8] C.D. Parker, Mechanics of corrosion of concrete sewers by hydrogen sul de, Sewage Ind. Waste. 23 (12) (1951) 1477–1485. carbonation, which could clog the pores of surface. Since the porosity [9] J.A. Redner, R.P. Hsi, E.J. Esfandi, Evaluating coatings for concrete in wastewater of the surface of sample was lower than inner, it took long time for facilities: update, J. Prot. Coat Linings 11 (12) (1994) 51–61. [10] S. Ehrich, L. Helard, R. Letourneux, J. Willocq, E. Bock, Biogenic and chemical sulfuric H2SO4 to penetrate into pores at the early time. Such explanation was fi acid corrosion of mortars, J. Mater. Civ. Eng. 11 (1999) 340. con rmed in our previous research [17]. [11] E. Vincke, J. Monteny, A. Beeldens, N. Belie, L. Taerwe, D. Van Gemert, W. Verstraete, Recent developments in research on biogenic sulfuric acid attack of concrete, Environmental Technologies to Treat Sulfur Pollution: Principles and Engineering. 7. Conclusions and prospects 2000. 515–541. [12] A. Gabrisova, J. Havlica, S. Sahu, Stability of calcium sulphoaluminate hydrates in water solutions with various pH values, Cem. Concr. Res. 21 (6) (1991) Subjected to biogenic acid attack, the durability of concrete may be 1023–1027. reduced heavily. In order to predict the biodeterioration process, a [13] A. Allahverdi, F.S. kvára, Acidic corrosion of hydrated cement based materials, – reactive transport model which couples the process of surface neutrali- Ceram. Silik. 44 (4) (2000) 152 160. [14] J. Davis, D. Nica, K. Shields, D. Roberts, Analysis of concrete from corroded sewer zation, the production of biogenic H2SO4 and the deterioration process pipe, Int. Biodeterior. Biodegrad. 42 (1) (1998) 75–84. of concrete was developed. [15] H. Satoh, M. Odagiri, T. Ito, S. Okabe, Microbial community structures and in situ sulfate-reducing and sulfur-oxidizing activities in biofilms developed on mortar In this model, the absorption of H2S of concrete surface, the produc- specimens in a corroded sewer system, Water Res. 43 (18) (2009) 4729–4739. tion of H2SO4 in SOB suspension where the activity of SOB is governed [16] K. Kawai, S. Yamaji, T. Shinmi, Concrete deterioration caused by sulfuric acid attack, by pH, the equilibrium of different solid phases and aqueous species in 10th DBMC International Conference on Durability of Building Materials and pore solution, the porosity evolution and diffusion evolution of each Component, 2005 (http://www.irbnet.de/daten/iconda/CIB_DC24731.pdf). [17] H. Yuan, P. Dangla, P. Chatellier, T. Chaussadent, Degradation modeling of concrete species are considered. submitted to sulfuric acid attack, Cem. Concr. Res. 53 (1) (2013) 267–277. The laboratory experiments of biodeterioration of cementitious [18] H. Jensen, A. Nielsen, T. Hvitved-Jacobsen, J. Vollertsen, Modeling of hydrogen materials conducted by De Muynck et al. [21] were simulated by this sulfide oxidation in concrete corrosion products from sewer pipes, Water Environ. Res. 81 (4) (2009) 365–373. model. The reduction of surface pH and the depth of neutralized layer [19] A. Nielsen, T. Hvitved-Jacobsen, J. Vollertsen, Kinetics and stoichiometry of sulfide during the neutralization step were determined. The evolution of oxidation by sewer biofilms, Water Res. 39 (17) (2005) 4119–4125. H2SO4 concentration in SOB suspension was calculated and it fitted [20] L. De Windt, P. Devillers, Modeling the degradation of Portland cement pastes by – the data measured during the experiments. With the source of biogenic biogenic organic acids, Cem. Concr. Res. 40 (8) (2010) 1165 1174. [21] W. De Muynck, N. De Belie, W. Verstraete, Effectiveness of admixtures, surface H2SO4, the evolution of solid compositions and porosity of materials treatments and antimicrobial compounds against biogenic sulfuric acid corrosion – were addressed. Therefore, the modeling of biogenic H2SO4 attack of concrete, Cem. Concr. Compos. 31 (3) (2009) 163 170. provides a prediction of the biodeterioration depth of materials. After [22] R.L. Islander, J.S. Devinny, F. Mansfeld, A. Postyn, H. Shih, Microbial ecology of crown corrosion in sewers, J. Environ. Eng. 117 (6) (1991) 751–770. immersion of 10 days, the deterioration depth is about 0.22 mm. The [23] E.S. Lin, A Modelling Study of H2S Absorption in Pure Water and in Rainwater, predicted biodeterioration depth during 8 cycles of submersion is NATIONAL University of Singapore, 2005. consistent with the experimental results. [24] D. Richard, Process Design Manual for Sulfide Control in Sanitary Sewerage Systems, U.S. E.P.A., 1974 However, the SOB activity in our modeling is still relatively crude. [25] J. Vollertsen, A.H. Nielsen, H.S. Jensen, T. Wium-Andersen, T. Hvitved-Jacobsen, Further research is needed to get the knowledge of the exact SOB Corrosion of concrete sewers—the kinetics of hydrogen sulfide oxidation, Sci. Total ecology in biofilm. The influence of environment factors and biological Environ. 394 (1) (2008) 162–170. [26] A.H. Nielsen, J. Vollertsen, H.S. Jensen, T. Wium-Andersen, T. Hvitved-Jacobsen, factors (e.g. temperature, H2S concentration, amount and type of SOB) Influence of pipe material and surfaces on sulfide related odor and corrosion in should be considered as well. For now, the surface neutralization sewers, Water Res. 42 (15) (2008) 4206–4214. process and biodeterioration process are simulated separately rather [27] J. Vollertsen, A.H. Nielsen, H.S. Jensen, E.A. Rudelle, T. Hvitved-Jacobsen, Modeling the corrosion of concrete sewers, 12th International Conference than continuously in our modeling. Thus, a model merging H2S attack on Urban Drainage, 2011. and bio-H2SO4 attack should be developed to simulate the in-situ [28] A.H. Nielsen, T. Hvitved-Jacobsen, J. Vollertsen, Effect of sewer headspace air-flow on biodeterioration process rather than laboratory experiment. Moreover, hydrogen sulfide removal by corroding concrete surfaces, Water Environ. Res. 84 – more accurate prediction of corrosion depth could be achieved with (3) (2012) 265 273. [29] A.F. Idriss, S.C. Negi, J.C. Jofriet, G.L. Hayward, Effect of hydrogen sulphide emissions the measured initial content of hydrates of concrete samples. on cement mortar specimens, Can. Biosyst. Eng. 43 (5) (2001) 23–28. [30] E. Reardon, An ion interaction model for the determination of chemical equilibria in cement/water systems, Cem. Concr. Res. 20 (2) (1990) 175–192. Acknowledgments [31] D. Kulik, M. Kersten, Aqueous solubility diagrams for cementitious waste stabiliza- tion systems: II, end-member stoichiometries of ideal calcium silicate hydrate solid solutions, J. Am. Ceram. Soc. 84 (12) (2001) 3017–3026. fi This study is funded by Sciencti c Strategy of IFSTTAR (No.ORSI RP- [32] J. Shen, P. Dangla, M. Thiery, Reactive transport modeling of CO2 through cementi- 2S10010) and Open Projects Foundation of Jiangsu Key Laboratory of tious materials under supercritical boundary conditions, Int. J. Greenhouse Gas Control 18 (2013) 75–87. Construction Materials (No. CM2014-04). [33] C. Parker, J. Prisk, The oxidation of inorganic compounds of sulfur by various sulfur bacteria, Soc. Gen. Microbiol. 8 (3) (1953) 344–364. [34] J. Harrison, P. Arthur, The acidophilic thiobacilli and other acidophilic bacteria that References share their habitat, J. Annu. Rev. Microbiol. 38 (1) (1984) 265–292. [35] J. Herisson, E.D. van Hullebusch, M. Moletta-Denat, P. Taquet, T. Chaussadent, [1] M. Gutiérrez-Padilla, A. Bielefeldt, S. Ovtchinnikov, M. Hernandez, J. Silverstein, Toward an accelerated biodeterioration test to understand the behavior of Portland Biogenic sulfuric acid attack on different types of commercially produced concrete and calcium aluminate cementitious materials in sewer networks, Int. Biodeterior. sewer pipes, Cem. Concr. Res. 40 (2) (2010) 293–301. Biodegrad. 84 (2012) 236–243. [2] N. Ismail, T. Nonaka, S. Noda, T. Mori, Effect of carbonation on microbial corrosion of [36] C. Yongsiri, J. Vollertsen, T. Hvitved-Jacobsen, Effect of temperature on air–water concrete, J. Civ. Eng. Manag. 20 (1993) 133–138. transfer of hydrogen sulfide, J. Environ. Eng. 130 (1) (2004) 104–109. 38 H. Yuan et al. / Cement and Concrete Research 70 (2015) 29–38

[37] E. Vincke, S. Verstichel, J. Monteny, W. Verstraete, A new test procedure for [46] D. Lide, CRC Handbook of Chemistry and Physics: A Ready-reference Book of biogenic sulfuric acid corrosion of concrete, Biodegradation 10 (6) (1999) Chemical and Physical Data, CRC Pr I Llc, 2004. 421–428. [47] B. Conway, B. Conway, Ionic Hydration in Chemistry and Biophysics, vol. [38] E. Hudon, S. Mirza, D. Frigon, Biodeterioration of concrete sewer pipes: state of the 741Elsevier, Amsterdam, 1981. art and research needs, J. Pipeline Syst. Eng. Pract. 2 (2) (2011) 42–52. [48] B. Huet, J. Prevost, G. Scherer, Quantitative reactive transport modeling of Portland

[39] S. Okabe, M. Odagiri, T. Ito, H. Satoh, Succession of sulfur-oxidizing bacteria in the cement in CO2-saturated water, Int. J. Greenhouse Gas Control 4 (3) (2010) microbial community on corroding concrete in sewer systems, Appl. Environ. 561–574. Microbiol. 73 (3) (2007) 971–980. [49] N. Wiberg, Holleman–Wiberg's Inorganic Chemistry, Academic Press, New York, [40] Y. Houst, F. Wittmann, H. Folker, Inﬂuence of porosity and water content on the 2001.

diffusivity of CO2 and O2 through hydrated cement paste, Cem. Concr. Res. 24 (6) [50] C. Tsonopoulos, D.M. Coulson, L.B. Inman, Ionization constants of water pollutants, (1994) 1165–1176. J. Chem. Eng. Data 21 (2) (1967) 190–193.

[41] D. Russell, P. Basheer, G. Rankin, A. Long, Effect of relative humidity and air perme- [51] Y. Su, K. Cheng, Y. Jean, Amplified potentiometric determination of pK00,pK0,pK1, ability on prediction of the rate of carbonation of concrete, P. I. Civil. Eng.—Struct. and pK2 of hydrogen sulfides with Ag2S ISE, Talanta 44 (10) (1997) 1757–1763. Buil., 146 (3), 2001, pp. 319–326. [52] S. Stronach, F. Glasser, Modelling the impact of abundant geochemical components + + [42] J. Monteny, E. Vincke, A. Beeldens, N. De Belie, L. Taerwe, D. Van Gemert, W. on phase stability and solubility of the CaO–SiO2–H2O system at 25 °C: Na ,K , 2− − 2 Verstraete, Chemical, microbiological, and in situ test methods for biogenic sulfuric SO4 ,Cl and CO3, Adv. Cem. Res. 9 (36) (1997) 167–181. acid corrosion of concrete, Cem. Concr. Res. 30 (4) (2000) 623–624. [53] J. Westall, J. Zachary, F. Morel, MINEQL: A computer program for the calculation of [43] C. Steefel, GIMRT, Version 1.2: Software for Modeling Multicomponent, Multidimen- chemical equilibrium composition of aqueous systems, Water Quality Laboratory, sional Reactive Transport, Users Guide: Livermore, California, Lawrence Livermore Ralph M. Parsons Laboratory for Water Resources and Environmental Engineering, National Laboratory Report UCRL-MA-143182, 2001. Department of Civil Engineering, Massachusetts Institute of Technology, 1976. [44] P. Lichtner, Flotran Users Manual, Rep. LA-UR-02 2349, 2001. [54] J. Herisson, Biodétérioration des matériaux cimentaires dans les ouvrages [45] C. Tognazzi, Couplage fissuration- dégradation chimique dans les matériaux d'assainissement: étude comparative du ciment d'aluminate de calcium et du cimentaires: caractérisation et modélisation, Ecole Nationale des Ponts et Chaussees, ciment Portland, Université Paris-Est, 2012. 1998.