THERMO-HYDRO-IONIC TRANSPORT THROUGH AN IMMERGED TUBE TUNNEL FOR A SERVICE LIFE OF 120 YEARS

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1 THERMO-HYDRO-IONIC TRANSPORT THROUGH AN IMMERGED TUBE TUNNEL FOR A SERVICE LIFE OF 120 YEARS Xiaoyun Pang (1), Kefei Li (1) and Patrick Dangla (2) (1) Civil Engineering Department, Tsinghua University, Beijing , P.R. China (2) UniversitéParis-EST, Laboratoire Navier CNRS, 77420, Champs-sur-Marne, France Abstract This paper investigates the multi-species transport of ions in the sea water through the concrete wall of an immerged sea tunnel. The immerged tube tunnel is a part of the sea link project of Hong Kong-Zhuhai-Macau having a service life of 120 years. The wall of the tube tunnel is subject to sea water on the external side and dry (marine) air on the internal (traffic) side. A thermo-hydro-ionic model is established for the ions transport through the tunnel wall considering the mass, heat and electrical charge conservations. With the environmental data and the physical properties from the structural concrete, the ions profiles are calculated using the THI model for a service life of 120 years. Simulation results at 120 years show that (1) the extents of internal drying and external wetting of tunnel wall are well overlapped; (2) the internal drying creates a concentration peak for ions on internal surface; (3) the external leaching drives OH - ions out and the leaching depth is 1.8cm; (4) the corrosion initiation range attains 65cm but the corrosion current is below depassivation threshold. 1. INTRODUCTION The Hong Kong-Zhuhai-Macau sea link project includes sea bridges of 28.8 km (three navigable spans), two artificial islands and an immerged tube tunnel of 5.6 km. One of the main technical requirements is to achieve the service life of 120 years for the concrete structures in an aggressive marine environment. The concrete immersed tube tunnel is made of four cast-in-place segments of 112.5m long and 27 prefabricated segments of 180m long, and these segments are connected by water-proof connections. Each prefabricated segment itself is composed of 8 sub-segments of 22.5m long and these sub-segments are made in the prefabrication factory near the HZM project site. The cross section of tube tunnel is composed of two traffic tubes and one auxiliary tunnel in the middle part of section. The thickness of tunnel wall is 1.50m. The segments are assembled by post-prestress forming a tunnel unit of 180m's long, floated to the project site and sunk on the sea bed, 40m below the sea level. The tunnel wall is exposed directly to sea water and the durability of tunnel wall is ensured by the structure concrete. This paper investigates the durability-related processes of ion species transport and provides quantitative basis for the durability design of tunnel wall for 120 years service life. 453

2 2. THERMO-HYDRO-IONIC TRANSPORT The transport processes are investigated on a representative elementary volume (REV) of material. The connected capillary porosity, ϕ, includes liquid-occupied porosity ϕ l and gasoccupied porosity ϕ g, and the liquid saturation degree s l is defined as s l =ϕ l /ϕ. The gas phase is composed of dry air and water vapour. The gas pressure P g is the addition of dry air pressure P a and vapor pressure P v. Both gas phases are considered as perfect gas, obeying P i M i = ρ i RT where M i is the molar mass of gas i (mol/kg) and ρ i the density of gas i (kg/m 3 ). In the following the subscripts sk, l, g refer to the solid skeleton, liquid phase and gas phases respectively. 2.1 Heat conservation The heat conservation states that the entropy change rate of REV is equal to the convection heat by fluid flow and the conduction heat by temperature gradient. The heat conservation can be written as, 1 (1) Stot wa Sa wvs v ww Sw T T with Stot sk 1 Ssk wslsw i 1 Si (2) ia,v where S tot, sk, w, a, v stand respectively for the entropy of REV, solid skeleton, pore water, dry air and water vapour (J/K). λ stands for the thermal conductivity of REV (W/m/K), which can be expressed as [1], 1 1 sk (3) sk 1 3 sll sgg sk where λ i (i= sk, g, l) stands for the conduction properties of different phases. The two terms at the right of Eq.(1) are respectively convection and conduction terms for heat transfer. The fluxes of pore water and gas phases write, kintkrl (4) ww w Pl M wjw l k k E E M M w P f s D P E int rg 0 a v v,a a,v a,v a,v g, l g g g a,v g RT where k int is the intrinsic permeability (m 2 ), k rg,rl stand for the relative permeability to gas/liquid(-), μ g,l are the viscosities of gas/liquid (kg/m/s), E a,v are the molar fraction of dry air/vapor in gas mixture (-), J w is diffusion flux of water in solution (mol/m 2 /s), and R the ideal gas constant (J/mol/K). 2.2 Ion transport Pore solution and sea water contain multiple ion species [2]. Seven ions species are considered in the modelling: Na +, H +, Ca 2+, OH - in pore solution, Mg 2+, Ca 2+, Na +, H +, OH -, SO 4 2-, Cl - in sea water. The transport of Ca 2+, Mg 2+ and OH - is associated with the dissolution of Mg(OH) 2 (MH), Ca(OH) 2 (CH) and C-S-H, and thus related to equilibriums between the (5) 454

3 hydrates and pore solution. Note N i the molar concentration (mol/m 3 ) of species i and w i its flux (mol/m 2 /s). The mass conservation of ion species writes, Ni (6) div wi 0 with Ni cisl ni t The term n i stands for molar amount of ion i adsorbed by solid phases or contained in solvable solid phases. In this modelling, the ion adsorption is considered for Cl - ions and the solvable solid phases include MH, CH and C-S-H. The chloride adsorption is mainly dependent the aqueous chloride concentration c Cl and the C-S-H content, while the solvable phase contents, n MH,CH,CSH, are related to the concentration of aqueous ions through the dissolution equilibriums, i.e., n Cl n Cl c Cl, ncsh, nmh,ch,csh nmh,ch,csh ci (7) The detailed dissolution equilibriums can be found in [3]. The ion flux w i includes convection by pore solution flow and diffusion flux J i by concentration gradient, k int k rl (8) wi ci Pl Ji l with e zicif Ji Di ci ci lni RT Here the diffusion flux J i considers the concentration gradient ci, ion activity ln i and local electrical potential. The term F is Faraday constant (C/mol), z i is the valence of ion i, i is the chemical activity of species i. Due to the presence of multi-species ions in solution, the conservation of electrical charge should also be observed through Poisson s equation, 2 F (10) cz i i 0 i where ε refers to the dielectric constant of the medium (F/m). Introducing the electrical neutrality condition into Poisson s equation gives the conservation law for electrical charge in terms of electrical current j (A/m 2 ), F c z 0 : div j 0 with j F J z i i (11) i i i i (9) 2.3 Fluid transport The fluid phases include dry air (gas), vapour (gas) and pore solution (liquid). The mass conservation of dry air writes, ma (12) div( wa ) 0 t Note that the transport of pore solution can include the dissolution of solid phases in skeleton as well as the adsorption of ions from aqueous environment (solution) into solid surface. Thus, the mass conservation of total mass of REV,, is written here as, m tot 455

4 m and k k div w w w 0 with wl l P tot int rl a v l l t l tot i=a,v,l CH,CSH,MH 0 i s i i m m m n In the above equation m 0 s stands for insolvable solid mass. For porous materials, the capillary pressure Pc Pg Pl is related to the pore saturation s l through the characteristic curve [4], b b (15) P ( s ) a s 1 c l l 1 1/ where a (Pa) and b are parameters of characteristic curves. 2.4 Model summary The expressions from Eq.(1) to Eq.(14) give the complete equations for the THI model. This THI model has 15 basic variables, including the temperature T, concentration of ions c i (Mg 2+, Ca 2+, Na +, H +, OH -, SO 4 2-, Cl - ), pore saturation s l, pore liquid pressure P l, gas pressure P g electrical potential, and the solid solvable phases n CH,CSH,MH. The THI model is solved through finite volume method, and its numerical implementation for one dimension application is realized in an open code Bil-2.0 [5]. 3. CONCRETE TUNNEL WALL 3.1 Material and properties The concrete material used for the prefabrication of tunnel tube segment is presented in Table 1 for the main proportioning parameter and the transport properties. Table 1: Proportioning and properties for tunnel concrete Proportioning/Properties Value w/b ratio (-) 0.35 Compressive strength at 28d (MPa) 56.4 Porosity (-) 0.11 Dry density (kg/m 3 ) 2279 Chloride diffusivity at 90d (10-12 m 2 /s) 3.0 Intrinsic permeability (10-22 m 2 ) 7.2 Resistivity at 90d (m) 345 Among the parameters, the chloride diffusivity and electrical resistivity are measured on the laboratory specimens at age of 90d, and the intrinsic permeability is deduced from the chloride diffusivity through Katz-Thompson equation k int =d 2 c /(C*F KT )[6], with d c as the characteristic pore diameters of concretes, C=226, and F KT the ratio between the chloride diffusivity of concrete and the chloride diffusivity D 0 Cl in water. Accordingly the intrinsic permeability is evaluated through this relation with D 0 Cl = m 2 /s and d c =9.0nm (13) (14) 456

5 following a microstructure characterization of cement-based materials with mineral admixture [7]. 3.2 Thermo-hydro-ionic simulations To study the transport processes of tunnel wall exposed in sea water, different working cases are considered: two cases of sea pressure (LP,NP) and two cases of temperature (LT, NT). The case LP (low pressure) neglects the sea water pressure; the case NP (normal pressure) considers the sea water pressure of 40m depth on the external surface of tunnel wall. The case LT (low temperature) imposes a thermal gradient of 15 o C on wall external surface, representing the possible cooling effect of sea water on external surface of tunnel wall; the case NT (normal temperature) adopts the same temperature for internal and external sides of tunnel wall. Table 2: Boundary and initial conditions for THI simulations Variable Internal boundary Initial condition External boundary (Traffic air) (Concrete) (Sea water) T (K) /NT, /LT s l (-) P l (MPa) /LP, 0.506/NP c Cl, SO4 (mmol/l) - 0,0 400, 15 C H,OH (mmol/l) , , 10-4 c Na,Mg,Ca (mmol/l) - 70, 0, , 1.24, 27.6 c CH,CSH,MH (mmol/l) ,700,0 0,0,0 (V) The initial pore saturation is assumed as 0.8 for tunnel wall concrete. The internal side of tunnel is imposed by a drying humidity of 70% and the corresponding pore saturation is estimated as 0.75 through the moisture isotherm of the concrete. The liquid pressure P l is evaluated from Eq.(15) by using the pore saturation s l and setting the P g =P atm =0.101 MPa. Table 2 provides the boundary and initial conditions for the THI simulations, and the parameters used in simulations are summarized as follows: the chloride sorptivity is retained as m 3 /kg; the values for heat capacity C sk,w,v,a are respectively 1300 J/kg/K, 4180 J/kg/K, 1800 J/kg/K and 1000 J/kg/K; the values for thermal conductivity sk,w,g are respectively 1.12 W/m/K, 0.60 W/m/K and 0.26 W/m/K; the parameters a, b for moisture characteristic curve in Eq.(15) are respectively 53.3 MPa and THERMO-HYDRO-IONIC TRANSPORT 4.1 Moisture profile The moisture transport results are given in Figure 1, showing the evolution of profiles under NTLP case, and profiles for different cases (LT/NT, LP/NP) at t=120 years. From the profile evolution it can be seen that the drying extent from internal side and wetting extent 457

6 from external side are well overlapped. For different working cases, notable difference exists between LT and NT cases and the s l profiles are more advanced into internal wall side for NT case, meaning the external cooling reduces the moisture transport rate. However, the influence of hydraulic pressure of 40m sea water is negligible between LP and NP cases. This is due to the fact that the hydraulic pressure of 40m sea water, 0.506MPa, is nearly two magnitudes lower than the pore capillary pressure, e.g. p c =40.4MPa as s l =0.8. Thus the hydraulic pressure of sea water can be neglected for transport processes. Figure 1: Evolution of s l under NTLP case (left) and moisture profiles at t=120 years (right) Figure 2: Cl - profiles (left) and OH - profiles (right) at t=120 years 4.2 Concentration profile The concentration profiles of Cl - and OH - ions are presented in Figure 2. The Cl - ions transport into the concrete wall from sea water by ion diffusion and sea water infiltration. The thermal effect (LT/NT) shows more influence on Cl - profiles than pressure effect (LP/NP). The chloride penetration depths attain 1.0m. A peak of c Cl near external side is observed for all cases, related to the dissolution of the C-S-H hydrates, the main absorbent for Cl - ions. On the external side the OH - ions transport to sea water by diffusion, thus c OH decreases towards the external surface. This diffusion perturbs the dissolution equilibriums between the solvable solid phases and the aqueous ions. On the internal side, c OH increases sharply near the internal surface due to the surface evaporation. By this mechanism, the concentration of ions builds up on the surface. Among all working cases NTNP is found to be the most unfavourable case. 458

7 4.3 Leaching The leaching process can well be captured by the Ca 2+ profiles in Figure 3. Leaching occurs on the external side of tunnel wall exposed directly to sea water. Due to the OH - outflow c Ca reaches to a high level and the concentration peak is due to the local dissolution of CH and C-S-H near the external surface. Between this peak and the external surface CH is totally dissolved and can no longer buffer Ca 2+ ions into pore solution. The peak marks the leaching fronts for concretes where CH phase is totally dissolved. The leaching depth, under NTNP case, is 1.8cm at t=120 years. Although this leaching depth is quite small compared to the wall thickness the influential depth of OH - transport reaches more than 1.0m. Figure 3: Ca 2+ profiles (left) and corrosion initation range (right) at t=120 years 4.4 Corrosion analysis The corrosion of reinforcement steel bars in tunnel wall includes two distinct stages: corrosion initiation and corrosion propagation. The corrosion initiation is influenced mainly by ph value, oxygen and chloride concentrations in pore solution [8]. The usual indicator for corrosion initiation is the Cl-OH concentration ratio, estimated as 1.0 from the salinity (32.9 g/kg) and annual average temperature [9]. Using the obtained c Cl and c OH profiles from THI simulation for NTNP case, the initiation range is illustrated in Figure 3 and the initiation range reaches 0.65m for t=120 years. Using a model from [10] the corrosion current is evaluated on the basis of the environmental data of project. The model takes into account both resistivity controlled mechanism of corrosion (low and medium pore saturation levels) and oxygen controlled cathode mechanism (high saturation level). The electrical resistivity and properties in Table 1 are used to calculate the corrosion current. The obtained results show, due to the very high pore saturation within the corrosion initiation range, the corrosion current is always lower than 0.1 μa/cm 2, a nominal threshold value proposed by [11]. In other words, steel with corrosion current lower than this value can be regarded as still passivated. 5. CONCLUDING REMARKS This paper presents a complete thermo-hydro-ionic modelling of ion transport in concrete porous materials. For the immersed tube tunnel wall exposed directly to sea water, seven ions are considered as the transport species. The established model is 459

8 solved through finite volume method and capable to solve one dimension multi-species and multi-fields transport processes for the tunnel wall. For the immersed tube tunnel in HZM project, the impact of thermal gradient on transport processes is more important than the 40m sea water pressure. The drying creates a peak of OH - concentration on internal surface of tunnel wall while the leaching depth is 1.8cm. The corrosion initiation range is found to be 65cm and the corrosion current is estimated as inferior to 0.1μA/cm 2. The THI simulations predict very low durability risk for the tunnel wall in HZM projects through the leaching depth and corrosion current. Additional protection measures are still recommended since the construction errors, concrete inhomogeneity and possible concrete cracking are not considered in the simulations. ACKNOWLEDGEMENTS This research is support by China Science and Technology Support Planning, Grant No. 2011BAG07B04. REFERENCES [1] Fabbri, A., Coussy, O., Fen-Chong, T. and Monteriro, P.J.M., 'Are dicing salts necessary to promote scaling in concrete? ', J. Eng. Mech.-ASCE 134(2008) [2] Li, Y.H. and Gregory, S., 'Diffusion of ions in sea water and in deep-sea sediments', Geochim. Cosmochim. Ac. 38(1974) [3] Shen, J.Y., 'Reactive Transport Modeling of CO 2 through Cementitious Materials under CO 2 Geological Storage Conditions', PhD Thesis (UniversitéParis-Est, France, 2013). [4] Van Genuchenten, M.T., 'A closed-form equation for predicting the hydraulic conductivity of unsaturated soil', Soil Sci. Soc. Am. J. 44(1980) [5] Dangla, P., Bil: A modelling platform based on finite volume/element methods, lcpc.fr/dangla.patrick/bil, [6] Katz, A.J. and Thompson, A. H., 'Quantitative prediction of permeability in porous rock', Phys. Rev. B 34(1986), [7] Li, K.F., Zeng, Q., Luo, M.Y. and Pang, X.Y., 'Effective of self-desiccation on pore structure of paste and mortar incorporating 70% GGBS', Constr. Build. Mater. 51(2014), [8] Hausmann, D.A., 'Steel corrosion in concrete - How does it occur?', Materials Protection 6(1967) [9] Shi, X.M., Nguyen, T.A., Kumar, P. and Liu, Y.J., 'A phenomenological model for the chloride threshold of pitting corrosion of steel in simulated concrete pore solutions', Anti-Corros. Method M. 58(2011) [10] Ghods, P., Isgor O.B. and Pour-Ghaz, M., 'Experimental verification and application of a practical corrosion model for uniformly depassivated steel in concrete', Mater. Struct. 41(2008), [11] DuraCrete, 'Probabilistic performance based durability design of concrete structures: Modelling of degradation', Contract BRPR-CT , Project BE , Document BE /R4-5 (The Netherlands, 1998). 460

Simulation of the concrete chloride NT build-492 migration test

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