A Simple Approach to Modeling Chloride Diffusion into Cracked Reinforced Concrete Structures

Transcription

1 Journal of Civil Engineering Research 215, 5(5): DOI: /j.jce A Simple Approach to Modeling Chloride Diffusion into Cracked Reinforced Conete Structures Thuy Ninh Nguyen, Hoang Quoc Vu * Building Materials Lab., Faculty of Civil Engineering, Ho Chi Minh City University of Technology, Viet Nam Abstract Up to now, several models of chloride ingress into conete and acked conete have been proposed to simulate the chloride penetration. In the present paper, besides ack widths, ack depths were recognized as a key parameter affecting the chloride penetration depth. A short term test of chloride diffusion was used to evaluate the influence of ack depths on the chloride penetration depth. By subjecting reinforced conete beams to bending moments, acked conete was generated and investigated as natural acks. In the field, reinforced conete structures are under the influence of combined factors such as acking, loads and marine environment, so in this paper a numerical model was developed and proposed to predict the chloride profile at the ack location of acked conete members. In experiments, OPC, Fly ash and Silica-fume conete were used to verify the proposed model. The comparison between predicted and experimental results showed the fitting well. Keywords Crack, Reinforced conete, Chloride diffusion, Crack depth 1. Introduction Nowadays, the durability as well as chloride indicted corrosion of reinforced conete structures in marine environment is very important and becomes serious problems in construction technology. Generally, the chloride could attack the pore structure [1, 2], and was recognized as a main factor leading to corrosion of the reinforcing steel in marine environment [3]. The appearance of acks due to service load causes the ineasing rate of chloride ingress into reinforced conete structures. Up to now, many researchers have tried to take into account the influence of ack widths on the chloride ingress into conete structures [4-6]. Besides ack widths, ack lengths are also a key parameter; especially, under loading, the ack depth will rise during all the stages in the life of a conete structure where it strongly affects the chloride penetration depth. However, the studies on the effects of ack lengths on the chloride penetration are not clear and complete. The chloride penetration in conete, furthermore, is also under the impact of various loads. [7]. Mien et al investigated to simulate the chloride penetration in plain conete with invisible acks under the combined action of cyclic loading and tidal environment [8, 9]. Because of embedding reinforcing steel in real conete structure, visible acks often appear and stabilize or rate * Corresponding author: vqhoang@hcmut.edu.vn (Hoang Quoc Vu) Published online at Copyright 215 Scientific & Academic Publishing. All Rights Reserved under varying loads. In addition, in the field there are various factors affecting conete structures such as natural acks due to loading and marine environment. Moreover, when the ack occurs in the conete cover, the rate of chloride ion is accelerated to diffuse into the conete structure. The chloride profile from the ack tip to inside the conete varies with the ack depth and becomes the main cause of corrosion of reinforcing steel. Therefore, this study is carried out to investigate the impacts of real ack characteristics, such as ack widths and ack depths, on the chloride penetration in acked reinforced conete structures. The migration chloride coefficient [1] will be determined based on the combination of ASTM C122 and Nordtest NT build 492. A numerical model is proposed to predict the chloride penetration into the acks of reinforced conete structures; especially the chloride profile from the ack tip to inside the conete should be predicted exactly. 2. Development of Model Generally, it is concluded that the chloride diffusion into the whole ack of conete must be recognized as two-dimensional diffusion because the diffusion of chloride is not only from the exposed surface to inside the conete but also through the ack plane exposed to salt solution. However, from the ack tip to inside the unacked conete zone, the two-dimensional chloride diffusion should be back the one-dimensional chloride diffusion because the whole ack is closed. With a simple proposed approach for predicting the chloride profile only at the ack location of acked

2 98 Thuy Ninh Nguyen et al.: A Simple Approach to Modeling Chloride Diffusion into Cracked Reinforced Conete Structures conete, the 1D chloride diffusion model based on Fisk s 2 nd Law equation (1) will be proposed Ct C = Da t x 2 t 2 For the plain conete, under coupling cyclic load, the apparent diffusion coefficient of conete is modified by Mien et al [9] as follows: c, ref (1) D = D. f ( T ). f ( t). f ( h). f ( SR) / φ (2) a Where: f4(sr) is a function of the dependence of D c on the load levels (SR) and φ is the chloride binding capacity of a cement, which depends on the content component of C 3 A in cement. The equation (2) is applied to model the chloride penetration in plain conete under the combination of cyclic load in case invisible acks appear. However, in the real structure with the embedded steel reinforcement in conete, the visible ack will occur on the reinforced conete structure under various loads. Until now, many researchers have concluded that the ack width plays a role in ineasing the chloride penetration into acked conete. However, in the real reinforced conete structure under flexural load, the acks occur on the surface of tension zone and extend from the tension surface to the neutral axis due to the ineasing magnitude of loading or number of load cycles. In this research, the ack depth is also considered to have an important role in ineasing the depth of chloride penetration, and it is defined as the straight distance from the ack mouth to the ack width that is 3 µm. In some previous studies, they have concluded if the ack width is less a threshold value it seldom affects the chloride diffusion. These proposed threshold values are approximately 5 µm [11], 53 µm [12] or 3 µm [13, 14]. Consequently, to evaluate the chloride ingress into visible acks of conete structures, the chloride diffusion coefficient (D a ) should be modified and developed to become the chloride diffusion coefficient at ack (D ) as follows: D = D = fw (, LD, ) (3) a un Where: D a, D is a function considering the dependence of D un on the ack width (W) and the ack depth (L). Conclusively, the illustration of updated chloride diffusion coefficient of the plain and reinforced conete with the load can be presented as follows, Figure 1. The concept of model development is based on the assumption that chloride will ingress into conete by penetrating through the whole acks, then diffusing into the unacked conete zones at the ack tip, Figure 2. Firstly, the chloride will diffuse through the acks and is governed by the chloride diffusion coefficient at ack (D ), (Figure 2a). Then, the chloride ions continually diffuse into the unacked conete zones at the tip of acks and are governed by the chloride diffusion coefficient at unacked conete zones (D un-eff ), (Figure 2b). This chloride diffusion coefficient (D un-eff ) is affected and governed by the ack depth. P P P P Steel Bar D a=d c D a=d c*f 4(SR) D =f(w,l,d un) Figure 1. The illustration of modified chloride diffusion coefficient Cracked Beam Average chloride diffusion coefficient (Dav) Cracked Conete Chloride diffusion coefficient through ack (D) Un-acked Conete Chloride diffusion coefficient effected by ack length (Dun-eff) W1 L W2 = 3 µm = W1 L W2 = 3 µm + W2 = 3 µm (a) (b) Figure 2. The concept for chloride diffusion coefficient at ack conete

3 Journal of Civil Engineering Research 215, 5(5): Under the above assumption, the chloride diffusion in acked conete is calculated using the equation of Fisk s 2 nd Law in which the proposed average coefficient (D av ) is used: C 2 2 t t t = D C C a = D 2 av 2 t x x D av D + Dun eff = (4) 2 Where: D is calculated based on the ack width (W) following the equation by Djerbi [13] below: D m s = x w x D m s x ( / ) (2 1 ) 4 1, when 3µ m w 8µ m 2 1 ( / ) 14 1, when w > 8µ m However, in their research [13], the ack wall is separated and parallel, but in the real structure and this research, the ack width is reduced with the ack depth. So, the ack width is approximately calculated by the average of ack mouth (W 1 ) and ack width of 3 µm (W 2 ). w1+ w2 w1+ 3 w = = (6) 2 2 Where: W 1 is ack mount (µm). W 2 = 3 (µm). Under the effect of ack depth, the chloride diffusion coefficient of unacked conete zone, which is from the ack tip to inside the unacked conete zone, will become a function of ack depth, equation (7), and be found out by the experiment program. D = f( LD, ) (7) un eff Where: L (mm) is the ack depth from the tension surface to where the ack width would equal 3 µm (W 2 ); D unc r is the chloride diffusion coefficient of unacked conete. 3. Experiment Program Xun SPECIMEN Figure 3. The concept of the penetration depth at ack location of reinforced conete The signification of the experiment procedure is to evaluate the influence of chloride diffusion coefficient of unacked zone at ack tip (D un-eff ) on the ack depth (L). This correlation is investigated based on the comparison between the chloride concentration depth at unacked conete and acked conete (Figure 3). This experiment L un X (5) will be based on the short-term diffusion test (STDT) which is modified by combining ASTM C122 and Nordtest NT build 492 (Figure 4). 3% NaCl solution in aylic reservoir Chloride penetration Brass mesh electrode at each specimen Applied potential and current readings - +.3N NaOH solution in aylic reservoir 1 mm cubic conete with epoxy-coated exposed surface Figure 4. Set up of short-term diffusion test combined by ASTM C122 and Nordtest NT build 492 The concept of this experiment is illustrated on Figure 3, in which x un is the chloride penetration depth of unacked conete; L is the ack depth and x is the chloride penetration depth at ack tip. Based on Nordtest NT build 492, the chloride diffusion coefficient is calculateded as follows: And: Where: D un D Rt xun α xun =. (8) zfe t Rt x α x =. (9) zfe t RT 2c α erf = L 1 d 2. 1 U 2 E = zfe c ; z: absolute value of ion valence, for chloride, z = 1; F: Faraday constant, F = J/(V.mol); U: absolute value of the applied voltage, V; R: gas constant, R = J/(K.mol); T: average value of the initial and final temperatures in the anolyte solution, K; L: thickness of the specimen, m; t: test duration, seconds; erf 1: inverse of error function; cd: chloride concentration at which the color changes, cd.7 N for OPC conete; c: chloride.

4 1 Thuy Ninh Nguyen et al.: A Simple Approach to Modeling Chloride Diffusion into Cracked Reinforced Conete Structures concentration in the catholyte solution, c 2 N. Under the same condition of environment and the conete properties, the ratio of x and x un would be assumed as the linear relation to the ack depth (L). The penetration depth of ack tip conete (x ) is expressed by a function of the ack depth (L) and the chloride penetration depth at unacked conete (x un ). Moreover, if the ack depth equals zero (no ack) as the boundary condition, the x will equal x un. Consequently, the penetration depth of ack tip conete (x ) is computed by the following equation: Similarly, we have: x = al. + x (1) un D al D. un eff = 1 + un (11) Where: a, a 1 - are the experiment coefficient; L is the ack depth from the exposed surface to the ack tip. Conclusively, with the equation (11), the chloride diffusion coefficient at ack (D ) would be predicted by the chloride diffusion coefficient of unacked conete (D un ) and ack depth (L). In this study, three types of water to cement ratio (W/C) of conete properties investigated are.4,.5, and.6. The conete proportions used to study are presented in Table 1. The sand and coarse aggregate were washed and dried before casted to clear their initial chloride content. Beam series W/C Table 1. Mix proportion per one cubic meter of conete Cement (OPC) (kg) Water (kg) After casted with size of 1x1x5, these beam specimens were cured in the mould for one day. After released from the mould, they were continually cured in the tap water for 27 days. Then, single acks on the beam were generated by the bending test with three-point load; the ack depth was varied by changing the magnitude of applied loads. The cubic specimens containing the acks were sawn from the acked beams. Before the chloride diffusion test was used, the ack depth and ack width of cubic specimens were measured by rule and digital mioscope. Due to the complicated tortuosity of the ack plane, it is very difficult to determine where the ack tip is by eye. Therefore, in this study, the respective ack depth instead of ack depth would be proposed to survey and it was measured from the tension surface to where the ack width would equal 3 µm. The chloride ion migration into these acked cubic specimens was tested by STDT which was modified half-cell from cylinder specimens to cubic specimens. The applied voltage for testing was 6 V and the duration of testing was 1 hours. After tested by STDT, the acked cubic specimens were split along the ack plane into two parts. The silver nitrate.1 M was then sprayed on the split surface of the conete. After 15 minutes, the chloride penetration depth was measured as visible white precipitation of silver chloride appeared at ack tip (x ). The procedure of the STDT test is illustrated in Figure 5. Sand (kg) Coarse Agg. (kg) av. Comp. Str. (MPa) av. Slump (cm) , , , Figure 5. The schematically experimental procedure

5 Journal of Civil Engineering Research 215, 5(5): The Correlation between Crack Depth and Crack Width From the experiment results illustrated in Figure 6, it is not difficult to recognize the trends of influence of respective ack depth on the residual ack with the varying W/C ratios are similar. In fact almost all the materials of the beams are similar except for the W/C ratio which causes the differences in compressive strength. However, its influence on the opening ack width is not significant; the steel bars used in the experiment are smooth reinforcing steel, so their stiffness is more important. Another reason is that the ack widths and depths were investigated under linear elastic condition and measured as the applied load retired. It seems that when the ack width ineases to a itical value, it will be constant. That is when the value of ack width reaches the yield strength of the reinforced conete beam Influence of Crack Depth on the Chloride Penetration Depth Cracks affect strongly the chloride concentration depth. Generally, the chloride ions penetrate through the acked path into conete causing the depth of chloride concentration to inease, Figure 7. The experiment results showed the effects of respective ack depth on the chloride penetration depth as in Figure 8. In Figure 8, the chloride penetration depth ineased linear with the respective ack depth and the magnitude of that studied is from zero to 6 mm. The results also showed that the depth of chloride penetration when W/C was.6 was higher than when W/C was.5 and.4 at the same depth of ack. It is explained by the influence of the conete density on the chloride penetration depth. Normally, the density of conete with W/C of.6 is less than the conete with W/C of.5 and.4. From this figure, it is easy to regconize that the rates of ineasing the chloride penetration depth are similar when the W/C varies from.4 to.6. From these results, the coefficient of a of equation (1) was found to equal.53, as follows: aa = =.53 3 So, the equation (1) which desibes the influence of ack depth on the chloride penetration depth at ack location is as follows: x =.53* L+ x (12) un 7 6 y = x x R² =.915 y = -2358x x R² =.927 Respective ack depdth (mm) W/C=.4 W/C=.5 1 y = -218.x x R² = Residual Crack Width (mm) W/C=.6 Multinomial (W/C=.4) 多项式 Multinomial (W/C=.4) (W/C=.5) 多项式 Multinomial (W/C=.5) (W/C=.5) 多项式 (W/C=.6) Figure 6. The correlation between respective ack depth and residual ack width (a) (b) Figure 7. The difference between chloride concentration depth at unacked (a) and acked conete (b), (W/C =.5)

6 12 Thuy Ninh Nguyen et al.: A Simple Approach to Modeling Chloride Diffusion into Cracked Reinforced Conete Structures 8. Chloride penetration depth (mm) y =.514x R² =.735 y =.557x R² =.832 W/C=.4 W/C=.5 W/C=.6 y =.51x R² =.849 线性 Linear (W/C=.4) 线性 Linear (W/C=.5) 线性 Linear (W/C=.6) (W/C=.5) Respective Crack Figure 8. The chloride penetration depth at ack conete versus the respective ack depth 8 Chloride diffusion coefficient (x1-12 m/s2) y =.561x R² =.735 y =.63x R² =.832 y =.569x R² =.852 W/C=.4 W/C=.5 W/C=.6 线性 Linear (W/C=.4) (W/C=.4) Linear (W/C=.5) 线性 (W/C=.5) Linear (W/C=.5) 线性 (W/C=.6) Respective Crack Figure 9. The influence of ack depth on the chloride diffusion coefficient by STDT 3.3. The Influence of Crack Depth on the Chloride Diffusion Coefficient at Cracked Conete Figure 9 shows the results of the influence of ack depth on the chloride diffusion coefficient by the STDT. Similar to the results of chloride penetration depth, the chloride diffusion coefficient at acked conete ineases when the ack depth ineases. Furthermore, the rates of ineasing chloride diffusion coefficient following the ineasing ack depth are similar when the ratios of water to cement vary. It can be concluded that the rate of ineasing the penetration depth and diffusion coefficient of chloride, when the ack depth varies, is independent of the proportion of conete (W/C) as concluded by Djerbi [13]. From the experiment results, the coefficient a1 of the equation (11) is calculated as follows: a1 = =.58 3 So, the equation (11) desibing the influence of ack depth (L) on the ratio of chloride diffusion coefficient between acked and unacked conete would be presented as below: 12 Dun eff.58 L*1 Dun = + (13) Where: L is respective ack depth (mm).

7 Journal of Civil Engineering Research 215, 5(5): Verification Program The two back to back of acked conete beams were immerged into salt solution of 1% NaCl under static load during several periods. After immersion in salt solution, the chloride profiles were collected at acked and unacked location of those beams (Figure 1). Three types of conete including OPC conete, FA conete, SF conete, were used in the experiment. The 1D chloride diffusion model used the surface chloride concentration at the location of ack and the average chloride diffusion coefficient (D av ) to estimate the chloride content at the ack location. The results of 1D chloride diffusion model fitted very well with the experimental results. The experiments also showed that the chloride profiles at acked locations were higher than at unacked locations SF (1%) Conete; W/B =.6; 2 months Prediction at ack Experiment at ack Fick Law Fitting curve Figure 12. Comparison between predicted and experimental results (Silicafume Conete, 2-month immersion) FA (2%) Conete; W/B =.6; 2 months Collecting the conete powder at unacked location Collecting the conete powder at acked location Figure 1. Immersion of acked beam into salt solution and location for collecting the conete powder Fick law fitting curve OPC; W/C=.4; 2 months Fick Law fitting curve Figure 11. Comparison between predicted and experimental results (OPC, 2-month immersion) By applying the Fisk s 2nd Law (equation 1) and the updated chloride diffusion coefficient at acked conete, (equation 4), the chloride profile is calculated. Then, the comparisons between the predicted and experimental results are plotted in Figure 11 to Figure 2. Figure 13. Comparison between predicted and experimental results (Fly Ash Conete, 2-month immersion) OPC; W/C =.5; 4 months Fick Law fitting curve Figure 14. Comparison between predicted and experimental results (OPC, 4-month immersion)

8 14 Thuy Ninh Nguyen et al.: A Simple Approach to Modeling Chloride Diffusion into Cracked Reinforced Conete Structures SF (1%) Conete; W/B =.6; 4 months FA (2%) Conete; W/B =.6; 8 months Fick Law Fitting Curve Fick Law Fittting curve Figure 15. Comparison between predicted and experimental results (Silicafume Conete, 4-month immersion) Figure 18. Comparison between predicted and experimental results (Fly Ash Conete, 8-month immersion) FA (2%) Conete; W/B =.6; 4 months Fick Law Fitting Curve SF (1%) Conete, W/B = Fick Law Fitting curve Figure 16. Comparison between predicted and experimental results (Fly Ash Conete, 4 -month immersion) Figure 19. Comparison between predicted and experimental results (Silicafume Conete, 12-month immersion) SF (1%) Conete; W/B =.6; 8 months Fick Law Fitting curve FA (2%) Conete, W/B =.6; 12 months Fick Law Fitting curve Figure 17. Comparison between predicted and experimental results (Silicafume Conete, 8-month immersion) Figure 2. Comparison between predicted and experimental results (Fly Ash Conete, 12-month immersion)

9 Journal of Civil Engineering Research 215, 5(5): Conclusions The characteristics of acks, such as ack widths and ack lengths (L), were investigated to find out their influences on the chloride penetration into the acked conete structure. The results of this research showed that ack lengths had strong influences on the rate of chloride penetration into acked reinforced conete structures. The depth of chloride concentration ineased with the ack depth and their trends were independent of the proportion of conete. The research also indicated that the service load had a significant role in ineasing the chloride penetration through the varying ack depths. The proposed model provided the simple approach to evaluating the chloride profile of conete at acks. This updated model will become an important solution to evaluate the remained service life of conete structures when the acks appear. The research also found out the influence of the capillary suction mechanism on the chloride penetration into acked conete during the early period of immersion. ACKNOWLEGMENTS This research is funded by Vietnam National University HoChiMinh City (VNU-HCM) under grant number C /HĐ-KHCN and has been carried out at Building Materials Laboratory, HoChiMinh City University of Technology, Viet Nam. REFERENCES [1] Sugiyama, T., W. Ritthichauy, and Y. Tsuji, Experimental investigation and numerical modeling of chloride penetration and calcium dissolution in saturated conete. Cement and Conete Research, (1): p [2] Sugiyama, T., T.W. Bremner, and Y. Tsuji, Determination of chloride diffusion coefficient and gas permeability of conete and their relationship. Cement and Conete Research, (5): p [3] Bermudez, M.A. and P. Alaejos, Models for Chloride Diffusion Coefficients of Conetes in Tidal Zone. Materials Journal, (1): p [4] Wang, K., et al., Permeability Study of Crack Conete. Cement and Conete Research, (3): p. 12. [5] Aldea, C.-M., S.P. Shah, and A. Karr, Effect of Cracking on Water and Chloride Permeability of Conete. Journal of Materials in Civil Engineering, (3): p. 6. [6] Marsavina, L., et al., Experimental and numerical determination of the chloride penetration in acked conete. Construction and Building Materials : p. 1. [7] Lim, C.C., N. Gowripalan, and V. Sirivivatnanon, Mioacking and chloride permeability of conete under uniaxial compression. Cement & Conete Composites, 2. 22: p. 7. [8] Mien, T.V., B. Stitmannaithum, and T. Nawa, Chloride penetration into conete using various cement types under flexural cyclical load and tidal evironment. The IES Journal Part A: Civil & Structural Engineering, 29. 2(3): p. 13. [9] Mien, T.V., B. Stitmannaithum, and T. Nawa, Simulation of chloride penetration into conete structures subjected to both cyclic flexural loads and tidal effects. Computers and Conete, 29. 6: p. 15. [1] Sugiyama, T., Y. Tsuji, and T.W. Bremner, Relationship between coulomb and migration coefficient of chloride ions for conete in a steady-state chloride migration test. Magazine of Conete Research, (1): p [11] Takewaka, K., T. Yamaguchi, and S. Maeda, Simulation Model for Deterioration of Conete Structures due to Chloride Attack. Journal of Advanced Conete Technology, 23. 1: p. 8. [12] Ismail, M., et al., Effect of ack opening on the local diffusion of chloride in inert materials. Cement and Conete Research p. 5. [13] Djerbi, A., et al., Influence of traversing ack on chloride diffusion into conete. Cement and Conete Research, : p. 7. [14] Ismail, M., et al., Effect of ack opening on the local diffusion of chloride in acked mortar samples. Cement and Conete Research, (8-9): p