Numerical Simulation of the Influence of Water Repellent Treatment on Carbonation of Concrete

Transcription

1 Hydrophobe IV 4 th International Conerence on Water Repellent Treatment o Building Materials Aediicatio Publishers, (2005) Numerical Simulation o the Inluence o Water Repellent Treatment on Carbonation o Concrete J. Heinrichs 1, St. Schmeiser 2 and A. Gerdes 1,2 1 Institute or Technical Chemistry, Water- and Geotechnology, Research Centre Karlsruhe, Germany 2 Faculty o Mechatronics and Science, University o Applied Sciences, Karlsruhe, Germany Abstract Chemical and physical processes, e.g. carbonation or penetration o chlorides cause numerous damages o reinorced concrete structures. The durability o these structures can be improved using surace protective systems, e.g. water repellent treatment. But the water repellent treatment alters the drying attitude o concrete. This in turn mainly inluences the process o carbonation. For an improved estimation o the corrosion risk or these structures a numerical model has been developed. The model describes the transport, storage and chemical reaction o the main inluence variables or carbonation o treated and untreated concrete. The knowledge o these processes is required or the assessment o new water repellent agents and gives inormation about the complex interrelationship respectively. For the numerical calculation the concrete is considered as a chemical solid-state reactor by using the inite-element-program FEMLAB. 27

2 J. Heinrichs, St. Schmeiser and A. Gerdes 1 Introduction Nowadays the durability o reinorced concrete becomes more and more important. The term durability comprises the maintenance o load capacity and the unctional eiciency o the construction over the whole service lie. Most o the damage mechanisms, e.g. sulphate attack or carbonation, are based on a reactive transport. This means that starting rom the material surace during the transport o concrete aggressive compounds through material components a chemical reaction takes place. The progress o this reactive transport depends on several actors, such as concetrating moisture distribution o the covercrete quality. Indeed this process needs then a lot o time. For example it can take decades until the carbonation reaches the reinorcement placed in a depth o 30 mm. But the application o preventive surace protection systems, e.g. water repellent treatment can change the rate o carbonation. Thereore, a modiication o the moisture distribution o the concrete is responsible which strongly aects the carbonation. The recent state o knowledge is ambiguous, hence the main ocus o this work is on the modelling o the carbonation o concrete treated with water repellent agents. On one hand side there are reerences that the rate o carbonation is reduced in treated concrete. On the other hand there are experimental investigations which reveal that treated concrete carbonates aster. Thereore this question must be clariied beore water repellent treatment can be applied in a common way. A requirement or the application o water repellent treatment in bigger scales is to clariy this question. In the introduced approach the porous cementious material is considered as a chemical solid-state reactor. For the simulation the especially or modelling o solid-state reactors designed program FEMLAB was chosen. 28

3 Numerical Simulation o the Inluence o Water Repellent Treatment on Carbonation o Concrete 2 Numerical investigation 2.1 Sotware The numerical modelling was perormed with the inite-element program FEMLAB (Version 3.0) distributed by Comsol. This program oers the opportunity to simulate complex physical and chemical processes which can be described by partial dierential equations. One main advantage o this program is the coupled analysis o dierent processes by using the option multiphysics. Here the user has access to an extensive model library with predeined applications which can be adjusted by the input o material parameters. The program also oers in an equation based modus the chance to deine partial dierential equations (PE-modus). The numerical simulations can be realised in 1, 2 or 3. Furthermore FEMLAB oers the solution o linear, non-linear, stationary, time-dependent and Eigenvalue problems. To simulate carbonation processes in concrete FEMLAB provides the "Chemical Engineering modul. In this modul mass balance like e.g. diusion, convection, or Navier-Stokes-equations can be solved. In this case only physical and chemical material parameters have to be deined, the corresponding equations are ormulated automatically by FEMLAB. 2.2 Modelling Preliminary remarks Validation o the model can not be shown yet, since by now corresponding experiments are still in the process. Instead well-known models rom literature were used to describe transport processes [4-10]. For the simulation ollowing assumptions are speciied: Two types o concrete specimens, untreated and treated with a water repellent agent, with a water-cement ratio o 0.5 and a cement content o 350 kg/m³ were investigated. In case o the treated concrete specimen the numerical model contains 2 layers. The assumed properties o these layers are listed in Table 1. In dierent parameter studies the penetration depth in treated concrete specimen is varying between 1 and 10 mm and specimen geometry is varying between 4 and 32 cm in length. All suraces o the specimens except the ront surace have been sealed. In this way unidirectional transport processes like moisture and CO 2 transport was enorced. Hence the model can be reduced to a one dimensional problem. 29

4 J. Heinrichs, St. Schmeiser and A. Gerdes In the beginning o the investigation concrete specimens are completely saturated by water (100% pore humidity corresponds to w s = 110 kg/m³). Constant environmental conditions are presumed, i.e. temperature is 20 C and relative humidity o the surrounding air is 75 %. CO 2 concentration c max is assumed to be 0.6 g/m³. This value represents the concentration in the atmosphere. All transport processes are described by Fick's 1. law, which is described in the ollowing chapter Model ormulation o carbonation Carbonation is based on a sequence o dierent reactions. Simpliied it can be expressed by the ollowing equation: H 2O Ca( OH ) + CO CaCO + H O (1) Carbonation takes place when CO 2 rom the surrounding air migrates through the pores into the concrete and reacts dissolved in the pore solution with the cement Ca(OH) 2 in the aqueous solutions. Thereby carbon dioxide is only transported via diusion through air illed pore volume o the concrete. iusion o carbon dioxide through aqueous solution can be excluded here. When the carbonation ront reaches the reinorcement, where in consequence o the declining ph-value in the carbonated part reinorcement corrosion can occur. Following conditions aect carbonation: - carbon dioxide concentration o the surrounding air, - concrete moisture, - chemical composition o the concrete, - concrete quality. Carbon dioxide transport can be described by Fick's 1. law o diusion, see below, equation (2). c δ + ( c) = R t (2) The driving orce or diusion is the gradient o carbon dioxide concentration c. Parameter denotes the diusion coeicient o CO 2 in concrete. The reaction o CO 2 is described by the reaction rate R. 30

5 Numerical Simulation o the Inluence o Water Repellent Treatment on Carbonation o Concrete (a) etermination o diusion coeicient The diusion coeicient o CO 2 can not be determined experimentally, because o the reaction o cement with CO 2 while carrying out the tests. Thereore the diusion coeicient is estimated by using the inert gas oxygen. iusion coeicient 0 o oxygen is assumed to be 3.8e-8 m²/s by Bunte [1]. That depends on temperature ϑ ( T, ), concrete moisture ϕ ( H, ), described by regression parameters a 1 a 4 (see Figure 1), and structural changes in the pore void due to carbonation ( KG, ), equations (4-6). The latter is expressed by the carbonation degree KG, equation (11), and depends on the material speciic parameter m B. iusion coeicient can be expressed by equation (3) [1, 8]: = 0 T, H, KG, (3) T, 273 = ϑ = a + 2 H, 1 α 4 1+ ( a3 a3 ϕ) a (4) (5) a 1 = a 2 = a 3 = a 3 = 5.75 KG, = exp[ mb KG] (6) (b) etermination o reaction rate R The consumption o CO 2 during the reaction with Ca(OH) 2, equation (1), is characterised by the input o the parameter R. This term is regarded as a sink term and describes the reaction rate v r o carbonation, which is inluenced by temperature T ( T,R ), concrete moisture ϕ ( H,R ), ormed by the parameters b 1 - b 4 (see Figure 1), the CO 2 concentration c ( K,R ), carbonation degree KG ( KG,R ) as well as by concrete speciic parameter, equation (8-11). Reaction rate R can be expressed by equation (7) [8, 10]: R vr = T, R H, R K, R KG, R = α (7) 31

6 J. Heinrichs, St. Schmeiser and A. Gerdes Saetta [10] derived the reaction rate k o the carbonation rom the Arrhenius approach or temperature dependent reactions. A is the requency actor, E 0 denotes the activation energy or reaction (both are empirical constants), R w is the gas constant o water vapour and α describes the inluence o an open system. E = = 0 T, R k A exp Rw T = b + 2 H, R 1 b4 1+ ( b3 b3 ϕ) b b 1 = b 2 = b 3 = 3.50 b 3 = 4.00 (8) (9) K, R = c c max KG mit KG KG, R = 1, = g g max (10) (11) The carbonation degree KG describes the progress o reaction between calcium hydroxide and carbon dioxide and is expressed by the amount o bound carbon dioxide g and the maximum bonding capacity g max towards CO 2. In Figure 1 the inluence o moisture on the diusion o carbon dioxide and the ollowing reaction with calcium hydroxide in concrete is shown. In both processes a strong moisture dependency is obvious. At a relative humidity higher than 90 %, the reaction rate is high, but no diusion o CO 2 takes place through the saturated pores. At a relative humidity below 50 % reaction almost stops, whereas here the carbon dioxide is able to migrate unhindered through the dry pore void o the concrete Model ormulation o moisture transport In porous materials moisture is only transported and stored in the pores. The size and shape o the pores is mainly dependent on the water-cement-ratio The transport o moisture in concrete is based on several transport mechanism each with dierent driving orces. O main importance is the liquid transport, consisting o capillary conduction and surace diusion, and the 32

7 Numerical Simulation o the Inluence o Water Repellent Treatment on Carbonation o Concrete Figure 1: Inluence o relative humidity on the reaction rate o carbonation (H,R) and CO 2 diusion coeicient (H,) respectively water vapour diusion. The reason or the liquid transport is a capillary pressure gradient. As the distribution o the capillary pressure in porous materials is unknown, Krischer [5] uses the liquid water content w as driving potential. The reason or water vapour transport is the water vapour partial pressure p. The balance equation o the moisture content can be expressed by an approach with the 1. diusion law by Fick, equation (12) [6-8]. w t + ( w w ) + t g + ( g p) = R (12) Regarding mono-layered structures, e.g. untreated concrete, the material moisture can be reduced to the liquid water content w, because the gaseous raction w g is very small compared to the total water quantity. In multi-layered structures with complex pore-systems, e.g. concrete with water repellent agents, the several layers have dierent adsorption-desorption isotherms and diusion coeicients, The morterial moisture or the two layers must also be taken into account. For the mathematical speciication the equation (12) must be transormed in a potential dimension. For that the relative humidity ϕ was selected, equation (13) [2]. 33

8 J. Heinrichs, St. Schmeiser and A. Gerdes ϕ δ + ( ϕ) = R t (13) The conversion in this potential dimension was made by the actor δ, equation (14). The irst term displays the time-dependent alteration o the liquid water and the second term the alteration o water vapour. The value in the brackets displays the volume o the gas-illed pore space. The connection between the content o liquid water w and relative humidity ϕ is perormed by the moisture storage unction, equation (15). δ = c H H w p w ϕ w s = + ψ ϕ RwT ρw ρw ϕ (14) w = ( ϕ) = w s ( k 1) ϕ k ϕ (15) The characterisation o the moisture storage unction or the untreated concrete is perormed by an approximation unction, derived rom the BET-theory by Künzel [7]. In this approach w s is the saturated water content o the concrete and k is an approximated parameter which can be calculated by the equilibrium water content at 80 % relative humidity. (a) etermination o moisture diusion coeicient For the untreated concrete the moisture diusion coeicient consists the coeicients o the gaseous water g and liquid water, equation (16) [8]. For the treated concrete only the moisture vapour diusion coeicient g is essential, see Table 1. = + g (16) The moisture vapour diusion coeicient g is shown in equation (17): g = g 0 p s (17) 34

9 Numerical Simulation o the Inluence o Water Repellent Treatment on Carbonation o Concrete It has to be mentioned that g is constant or the whole drying period which means it is independent rom the material moisture content. The determination o this coeicient is based on the ideal gas equation, water vapour diusion resistance index µ and the water vapour saturation pressure p s, which is temperature ϑ dependent, equations (18-20) [4]. p s aϑ = exp b + ϑ (18) a = b = C ürϑ 0 C g 0 = µ R = w T P0 T 2,3 10 P 273 (19) (20) The calculation o liquid transport coeicient is demonstrated in equation (21) [4]: = w w ϕ (21) Thereby w / ϕ is the derivation o the moisture storage unction. The liquid transport coeicient is mainly inluenced by the material moisture and the temperature ϑ. Kiessl [4] developed an exponential unction, which can be described by the moisture conducting parameter o the dry concrete,tr (or w = 0) and the water saturated concrete,s (or w = w s ), equation (22). w w, s ϑ =, tr exp ln ws, tr 40 (22) Because o the moisture balance that has to be equilibrated with the hygric environmental conditions, on the material surace exchange processes with the environment take place. This is also taken into account in the numerical 35

10 J. Heinrichs, St. Schmeiser and A. Gerdes model. The exchange o the moisture amount q H normal to the surace ollows as described in equation (23) [8]: q H = k c ( c ϕ ) b O (23) In this equation k c is the moisture transer parameter and c b is the relative humidity o the ambient air, being dependent on temperature and pressure. (b) etermination o parameter R The water produced due to the process o carbonation is an additional water source R within the concrete. Indeed this is not considered in the numerical model, this means R = 0 (Table 1). In a ully with water repellent treated layer no carbonation does appear and thereore R is also Model ormulation o water repellent treatment The water repellent agent penetrates by capillary transport into the concrete boundary layer. A hydrophobic silicon ilm is then ormed by a chemical reaction. In the hydrophobic zone moisture transport takes place only via diusion. It is urther assumed that in this area no carbonation takes place [3]. A list o the assumed parameters or the speciic transport processes, described by Fick's law, is given in Table 1. The list is subdivided regarding the water repellent treated part and the untreated part o the concrete. Since there is no reaction o the CO 2 in the treated section, R is equal zero. The CO 2 diusion coeicient depends on temperature ( T, ) and a actor which describes the alteration o the pore void due to water repellent treatment ( B, ). This actor attenuates the diusion coeicient value o the water vapour, g, as well. Since numerical modelling uses the relative air humidity as the driving potential, the parameter δ is introduced. The value ψ denotes the pore volume. On the basis o these parameters the numerical model or carbonation inside a water repellent treated concrete can be simulated. 3 Results and discussion 3.1 Preliminary remarks As already mentioned in chapter 2.2.2, essentially the progress o carbonation depends on the moisture distribution o concrete. For that reason at irst, the drying o concrete has to be simulated in some investigations at irst. In 36

11 Numerical Simulation o the Inluence o Water Repellent Treatment on Carbonation o Concrete Table 1: Compilation o assumed parameter R,, and δ or the two transport processes in each concrete layer, i.e. the water repellent treated part and the untreated part CO 2 - transport moisture transport treated R = 0 untreated R = α T, R H, R K, R KG, R = 0 T, B, = 0 T, H, KG, δ = 1 δ = 1 R = 0 R = 0 g B, = ( g + ) δ = KG, p = s H ψ RT δ = c H parameter studies the penetration depth o the treated layer and specimen length is varying, respectively. On the basis o these investigations the calculation o the carbonation progress has to be made. 3.2 Moisture transer Introduction By means o the diusion coeicients (liquid and water vapour) deined in equation (16), the moisture proile as unction o drying time can be calculated. Figure 2 and Figure 3 show the moisture distribution o an untreated concrete and a treated concrete with a 10 mm penetration depth (w/c = 0.5 and w s = 110 kg/m³) ater dierent drying times (1 month, 1 year and 10 years). As described in chapter the driving potential by the capillary transport and the water vapour diusion can be calculated by the relative humidity ϕ. The result is a moisture distribution beyond the specimens length in percent, Figure 2. An important act in this case is the existence o vapour water, only. In contrast to liquid water, the amount o water as water vapour is very low. That means the water content o the untreated and the treated concrete is uncomparable to each other in the irst 10 mm. Thereore the moisture has to be denoted in kg/m³, Figure 3. Water vapour transport proceeds only in the impregnation layer, which has an important inluence on drying o concrete. That s why Figure 2 and Figure 3 show a clear dierence between the untreated and the treated concrete. 37

12 J. Heinrichs, St. Schmeiser and A. Gerdes Figure 2: Moisture distribution o an untreated concrete specimen and a treated concrete specimen with 10 mm penetration depth ater dierent drying times, reerred to the relative humidity in %. Figure 3: Moisture distribution o an untreated concrete specimen and a treated concrete specimen with 10 mm penetration depth ater dierent drying times, reerred to the material moisture in kg/m³. 38

13 Numerical Simulation o the Inluence o Water Repellent Treatment on Carbonation o Concrete Figure 4: Moisture distribution o an 8 cm concrete specimen with dierent penetration depths o the water repellent layer ater one year (w/c = 0.5). While the treated concrete specimen is showing nearly 100 % o moisture content in a depth o 10 mm ater one month, the untreated specimen dried already out to a value o 92 %. That corresponds to a moisture content o approximately 67 kg/m³. Even ater one year there is a big dierence between the specimens. Ater 10 years both specimens reach the moisture balance o 75 % (w = 31 kg/m³). Furthermore, the treated concrete specimen is orming a horizontal plateau directed to the water repellent layer, which will be kept until the moisture balance is reached. The water content in the water repellent layer is nearly zero. The untreated concrete shows on the other hand a steady developed moisture proile. Because o the dierent moisture proiles it is presumed, that this act has a strong inluence to the carbonation, which is even inluenced by the moisture content ierent penetration depth o the water repellent layer The thickness o the water repellent layer can be controlled and depends on dierent products o water repellent treatment that is used. That s the reason why it is necessary to take a statement about the drying behaviour o treated concrete with dierent penetration depths. 39

14 J. Heinrichs, St. Schmeiser and A. Gerdes Figure 5: Moisture distribution o an untreated and a water repellent treated concrete specimen with a penetration depth o 10 mm with dierent specimen lengths ater one year (w/c = 0.5). The results are represented in Figure 4 ater a drying time o one year. Penetration depths o 1 mm (corresponding to an emulsion), 5 mm and 10 mm (or example with an Octyltriethoxysilan) were surveyed. The total length o the concrete specimens is 8 cm. Figure 4 shows that a reduction o the penetration depth o the impregnation eects a aster drying. Then the moisture proile is approaching to an untreated concrete. With a penetration depth o 1 mm the treated concrete specimen corresponds to the drying behaviour o an untreated concrete. Experiments o Gerdes [3] supporting this result ierent specimen length Another parameter, which could inluence the drying process is the specimen length. For this reason a moisture distribution proile or 4 cm, 8 cm and 16 cm concrete specimens (w/c 0.5) has been calulated or a duration o drying o one year. Now an untreated and a water repellent treated concrete with a penetration depth o 10 mm are surveyed. The results are compiled in Figure 5. Figure 5 shows, that the drying process depends strongly on the specimen length. With an increasing length o the concrete specimen increased the time which is needed to reach the balance in moisture content. The reason 40

15 Numerical Simulation o the Inluence o Water Repellent Treatment on Carbonation o Concrete Figure 6: Temporal distribution o the carbonation o an untreated and a water repellent treated concrete specimen with a penetration depth o 10 mm (8 cm concrete specimen, w/c = 0.5). is the higher volume o the water reservoir. This provides the capillary transport o water rom the interior o the specimen to the covercrete. Furthermore, the length o the specimen has a stronger inluence to the moisture content o a treated concrete specimen than o an untreated concrete specimen. In that way it can be expected that the progress o carbonation will be change signiicantly. 3.3 Carbonation Basis to the calculation o carbonation constitutes on one hand the approach o the diusion coeicient or carbon dioxide in concrete with equation (3) and on the other hand on the reaction rate, equation (7). Both parameters depend on the moisture distribution in concrete, Figure 1. So the drying has to be taken into account. On this condition a time-dependent carbonation proile can be calculated. Further actors inluence the carbonation. But these are not taken into account in the computer model, or example the liberated water o carbonation (hence simpliied stoichiometric calculation ollow: by 1 g CO 2 result to 0.41 g H 2 O), equation (1). This is an additional water source in the interior o concrete. Figure 6 shows the results o an untreated and treated concrete specimen with a penetration depth o 10 mm ater 1, 5 and 10 years drying. Carbona- 41

16 J. Heinrichs, St. Schmeiser and A. Gerdes Figure 7: Carbonation depths o dierent concrete specimens ater 10 years (untreated, 5 mm and 10 mm water repellent treated layer, specimen lengths o 4, 8, 16 and 32 cm) tion will be expressed with the carbonation degree KG. The specimen length is 8 cm and the w/c is 0.5. The carbon dioxide migrates through the impregnated layer easily without any chemical reaction. Hence the carbonation process starts behind the water repellent layer. This should lead to a higher carbonation depth compared to untreated concrete under the same conditions. Figure 7 shows the calculated carbonation depths or several concrete specimens, depending on dierent specimen lengths (specimen 1-3: 4 cm, specimen 4-6: 8 cm, specimen 7-9: 16 cm and specimen 10-12: 32 cm) and on dierent penetration depths o the water repellent layer. The carbonation depth is deined or a carbonation degree o 0.9. The unambiguous trend is obvious: the carbonation depth or the untreated concrete is sligthly reduces with an increasing specimen length. For the treated concrete the ollowing can be mentioned. The carbonation depth o these specimens is signiicantly higher compared to the untreated specimens. With increasing length o the treated specimen the carbonation depth decreases. This goes along with an reduction o the thickness o the carbonated layer. Furthermore, carbonation is signiicantly lower in a treated concrete. But then the carbonation ront is deeper as a result o th non-carbonable impregnated layer, Figure 6. 42

17 Numerical Simulation o the Inluence o Water Repellent Treatment on Carbonation o Concrete Out rom that in the ollwoing an example is given to show the inluence o water repellent treatments on the carbonation rate. For example, i the carbonation ront reaches the reinorcement, which is located in a depth o 30 mm, the corrosion risk increase. Assuming a length o 32 cm or the concrete member Starting rom this point o view or the concrete member with a length o 32 cm the carbonation ront will reach the reinorcement ater 145 years. In comparision to that or the treated concrete specimens the carbonation ront reach the reinorcement earlier (5 mm penetration depth approximately 125 years and 10 mm penetration depth approximately 100 years). The dimensions o the concrete specimens (9-11) corresponds more to a real building as the specimens 1-9 and thereore, they are more realisitc. Further decisive actors or the carbonation progress are the seasonal change o relative humidity and the temperature. Likewise rain and drying periods inluences the carbonation. I these actors are considered, eventually the carbonation would continue slowly as shown. So the calculation demonstrates only a labour test, i.e. with constant surrounding conditions (drying to 75 % relative humidity). Experiments should validate the existing numerical model. 4 Conclusions From the results the ollowing conclusions can be drawn: - The interaction o chemical and physical processes, i.e. drying and carbonation o untreated and treated concrete specimens, was realised in a numerical model to investigate the corrosion risk o reinorced concrete structures. FEMLAB is a suitable program or the simulation o reactive transports. The results o these investigations are important or the application in practice and or urther development o water repellent systems. - It is shown, that the drying behaviour o treated and untreated concrete specimens is quite dierent. This shows the results o a parameter study varying penetration depth and geometry o the specimens. Both parameters have a strong inluence on drying and out o it on the carbonation. This could be an explanation or the dierent results in literature about the carbonation o water repellent treated concrete. In these studies the geometry o the test specimens was not taken into consideration. For example, the carbonation process is delayed with an increasing specimen length because the drying rate is lowered and consequently liquid water in the pores hinders the carbon dioxide to migrate into the concrete. 43

18 J. Heinrichs, St. Schmeiser and A. Gerdes - For the realistic simulation o the carbonation process o treated concrete other actors such as the climatic conditions, liberating o water due to the carbonation process or the inluence o cracks must be taken into account. - The results o the simulation indicate that or concrete members with a thickness o 32 cm the carbonation ront do not reach the reinorcement during a typical servce lie o 100 years. 5 Reerences [1] Bunte,.: Zum Karbonatisierungsbedingten Verlust der auerhatigkeit von Außenbauteilen aus Stahlbeton. issertation, TU Braunschweig, [2] Bazant, Z.P.; Najjer, L.J.: rying o concrete as a nonlinear diusion problem. In Cement and Concrete Research 1, pp , [3] Gerdes, A.H.: Transport und chemische Reaktion siliciumorganischer Verbindungen in der Betonrandzone. Building Material Report No.15, Aediicato Verlag, [4] Kiessl, K.: Kapillarer und dampörmiger Feuchtetransport in mehrschichtigen Bauteilen rechnerische Erassung und bauphysikalische Anwendung. issertation, Essen, [5] Krischer, O.: ie wissenschatlichen Grundlagen der Trocknungstechnik. Springer-Verlag, Berlin u.a., [6] Krus, M.: Feuchtetransport- und Speicherkoeizienten poröser mineralischer Baustoe. Theoretische Grundlagen und neue Messtechniken. issertation, Universität Stuttgart, [7] Künzel, H.M.: Verahren zur ein- und zweidimensionalen Brechnung des gekoppelten Wärme- und Feuchtetransports in Bauteilen mit einachen Kennwerten. issertation, Universität Stuttgart, [8] Steens, A.: Modellierung von Karbonatisierung und Chloridbindung zur numerischen Analyse der Korrosionsgeährdung der Betonbewehrung. issertation, TU Braunschweig, Institut ür Statik, [9] Sadouki, H.; Wittmann, F.H.: Inluence o Water Repellent Treatment on rying o Concrete. Proceedings o Hydrophobe II. Aediicatio Publishers, Freiburg, pp , [10] Saetta, A.V.; Schreler, B.A.; Vitaliani, R.V.: 2 Model or Carbonation and Moisture / Heat Flow in porous Materials. In Cement and Concrete Research, Volume 25, No. 8, pp ,