Service Life Prediction of Reinforced Concrete in a Sea-Crossing Railway Bridge in Jiaozhou Bay: a Case Study

applied sciences

Article Service Life Prediction of Reinforced Concrete in a Sea-Crossing Railway Bridge in Jiaozhou Bay: A Case Study

Zhe Li 1,2 , Zuquan Jin 1,2,*, Tiejun Zhao 1,2, Penggang Wang 1,2, Lixiao Zhao 1,2, Chuansheng Xiong 1,2 and Yue Kang 1,2

1 School of Civil Engineering, Qingdao University of Technology, Qingdao 266033, China 2 Cooperative Innovation Center of Engineering Construction and Safety in Shandong Blue Economic Zone, Qingdao 266033, China * Correspondence: [email protected]

Received: 24 July 2019; Accepted: 22 August 2019; Published: 1 September 2019

Abstract: Reinforced bar corrosion induced by chloride ingression is one of the most significant threats to the durability of concrete structures in marine environments. The concrete cover thickness, compressive strength, chloride diffusion coefficient, and surface defects of reinforced concrete in the Jiaozhou Bay sea-crossing railway bridge were measured. The temperature and relative humidity in the concrete and the loading applied onto the reinforced concrete were monitored. Based on the DuraCrete model, a revised model for the service life prediction of concrete structures was established, considering the effects of temperature and loading on the chloride diffusion coefficient. Further, the reliability indexes of the reinforced concrete box girder, pier, and platform, located in the marine and land sections, in relation to service lives lasting various numbers of years, were calculated. The measured and calculated results show that the mean cover thicknesses of concrete piers in the marine and land sections are 52 mm and 36 mm, respectively, and the corresponding standard deviations are 5.21 mm and 3.18 mm, respectively. The mean compressive strengths of concrete in the marine and land sections are 56 MPa and 46 MPa, respectively. The corresponding standard deviations are 2.45 MPa and 2.67 MPa, respectively. The reliability indexes of the reinforced concrete box girder and platform in the marine section, under the condition of a service life of 100 years, are 1.81 and 1.76, respectively. When the corrosion-resistant reinforced bar was used in the pier structure in the marine section, its reliability index increased to 2.01. Furthermore, the reliability index of the reinforced concrete damaged by salt fog in the land section was 1.71.

Keywords: reinforced concrete; sea-crossing railway bridge; service life prediction; reliability index

1. Introduction With the development of modern society and technology, more and more huge reinforced concrete (RC) structures have been built in China [1–3], such as Hong Kong-Zhuhai-Macau (HZM) bridge (49.968 km long, in service), Hangzhou Bay bridge (36 km long, in service) and Jiaozhou Bay bridge (36.48 km long, in service). As reinforced concrete sea-crossing bridges service in marine environments, chloride ions penetrate the concrete cover and result in the corrosion of the reinforced bars, thereby causing serious damage to the bridge structures [4–8]. Many problems caused by the corrosion of reinforced bars have been reported all over the world. Further, corrosion-associated maintenance and repair of reinforced concrete (RC) structures have cost multiple billions of USD per annum [9]. In some developed countries, nearly 3.5% of their gross national product (GNP) has been applied in the repair cost [10]. In order to reduce the repair cost, the durability design of RC structures,

Appl. Sci. 2019, 9, 3570; doi:10.3390/app9173570 www.mdpi.com/journal/applsci Appl. Sci. 2019, 9, 3570 2 of 18 in particular, those exposed to marine environments, has been recognized as an effective means to ensure the service life of concrete structures, which has been a focus of researchers and engineers all over the world [11–13]. Service life prediction modeling has become one of the current major issues in the design of concrete structures. Using the third-moment method, Zhang [14] developed a time-dependent probability assessment for chloride-induced corrosion of RC structures. In order to provide corrective parameters for service life prediction, Li [15] investigated the time-dependent chloride penetration into concrete in marine environments. Considering the effect of the materials’ heterogeneity when exposed to a marine tidal zone, Wang [16] developed a service life prediction model. Attari and Mcnally [17] explored a probabilistic assessment of the influence of the age factor on the service life prediction using concrete with limestone cement/ground granulated blast slag (GGBS) binders. Yu [18,19] developed a service life prediction model considering freeze–thaw fatigue, taking into account fly ash and slag. Hackl and Kohler [20] developed a reliability assessment which uses the coupled effect of corrosion initiation and progression to represent the deterioration of reinforced concrete structures. Considering the action of loading, chloride ions’ transport path, and the binding capacity of concrete, a series of service life prediction models were developed by Sun [21]. Based on the experimental and theoretical studies on chloride transportation into concrete in marine environments, a service life prediction model was developed in DuraCrete, Life 365, and Chinese code for the durability design of concrete structures. However, Hostis [22] highlighted that most of the experimental studies on the corrosion of reinforced concrete structures are tested in the laboratory by means of accelerated measurement. Hence, the experimental data may not be representative compared to the “in situ” behavior. Samson [23] also emphasized that it is undesirable to predict the long-term service life of structures on the basis of laboratory sample measurements, which is a limitation to reliable predictions. Further, the measurement results obtained by Jin [24,25] showed that there were fluctuations in the durability parameters of lining concrete, such as concrete cover, concrete strength, and chloride diffusion coefficient, in the Jiaozhou Bay subsea tunnel, and the service life was also predicted. However, there is still limited research on the service life prediction of real marine projects, such as sea-crossing bridges, offshore platforms, and subsea tunnels. The Jiaozhou Bay sea-crossing railway bridge is about 16.337 km long, and 2.006 km is in the marine area. It is the control bridge for the Qingdao–Lianyungang city railway network. At Qingdao, where the bridge is located, the relative humidity is 62–86%, which is the most suitable humidity range for carbonation. The chloride content in the seawater is about 16,000 mg/L, and the annual average sea fog days is about 58 days. Hence, the penetration of chloride ions into concrete is seriously threatening the durability of the bridge. In order to improve the concrete durability of the Jiaozhou Bay sea-crossing railway bridge, high-performance concrete and corrosion-resistant reinforced bars have been used in the pier structures, which are in the marine tidal and splash zones. The values of the key durability coefficients, such as the chloride diffusion coefficient of concrete, concrete cover thickness, and curing age of reinforced concrete, have been assigned based on the Chinese durability design code. However, the difference in the quality control of the concrete structure on site causes the durability index of the reinforced concrete to fluctuate. Therefore, the actual service life of the reinforced concrete may not meet the designed service life of the Jiaozhou Bay sea-crossing railway bridge. The objectives of this study are to determine the actual durability coefficient of the concrete in the Jiaozhou Bay sea-crossing railway bridge, and to monitor the environmental temperature, relative humidity, and the loading applied onto the reinforced concrete. Based on the measured durability parameters of concrete, the actual service life of the reinforced concrete in the Jiaozhou Bay sea-crossing railway bridge, in different structures, is predicted according to the revised DuraCrete model.

2. Materials and Mix Proportion of Concrete A Chinese standard 52.5 R(II) Portland cement was supplied by Shanshui cement corporation in China. Class F ﬂy ash was used as a mineral admixture. River sand with a ﬁneness modulus of 2.5 and Appl. Sci. 2019, 9, x FOR PEER REVIEW 3 of 18

Bay sea-crossing railway bridge, in different structures, is predicted according to the revised DuraCrete model.

2.Appl. Materials Sci. 2019, 9and, 3570 Mix Proportion of Concrete 3 of 18 A Chinese standard 52.5 R(II) Portland cement was supplied by Shanshui cement corporation in China. Class F fly ash was used as a mineral admixture. River sand with a fineness modulus of coarse aggregates of crushed stone with sizes of 5–10 mm, 10–20 mm, and 20–31.5 mm from Daxin 2.5 and coarse aggregates of crushed stone with sizes of 5–10 mm, 10–20 mm, and 20–31.5 mm from Corporation were used. A new type of corrosion-resistant reinforced bar, Cr10Mo1 alloy, was used in Daxin Corporation were used. A new type of corrosion-resistant reinforced bar, Cr10Mo1 alloy, was the cross-sea section of the concrete bridge, as shown in Figure1. The new type of reinforced bar is used in the cross-sea section of the concrete bridge, as shown in Figure 1. The new type of alloyed with about wt.10% Cr and wt.1% Mo, consisting of granular bainite with ferrite between the reinforced bar is alloyed with about wt.10% Cr and wt.1% Mo, consisting of granular bainite with grains, and was developed by Southeast University [26]. Laboratory tests showed that the Cr10Mo1 ferrite between the grains, and was developed by Southeast University [26]. Laboratory tests reinforced bar has a critical chloride threshold level ﬁve times higher than that of carbon steel [27]. showed that the Cr10Mo1 reinforced bar has a critical chloride threshold level five times higher This is the ﬁrst time that this new type of alloy has been used in a huge construction project in China, than that of carbon steel [27]. This is the first time that this new type of alloy has been used in a and the price is about 8000 RMB per ton (equal to 1140 USD per ton, approximately). The chemical huge construction project in China, and the price is about 8000 RMB per ton (equal to 1140 USD per compositions of the CR (corrosion-resistant reinforced bar) and LC (low-carbon steel) are shown in ton, approximately). The chemical compositions of the CR (corrosion-resistant reinforced bar) and Table1. LC (low-carbon steel) are shown in Table 1. Table 1. Chemical compositions of corrosion-resistant (CR) and low-carbon (LC) steel. Table 1. Chemical compositions of corrosion-resistant (CR) and low-carbon (LC) steel. Chemical Composition (wt. %) Type Chemical Composition (wt. %) Type Fe C Si Mn P S V Cr Mo Fe C Si Mn P S V Cr Mo CR CRBal. Bal.0.01 0.010.49 0.491.49 1.49 0. 0.0101 0.010.01 0.060.06 10.3610.36 1.16 1.16 LC LC Bal. Bal.0.22 0.220.53 0.531.44 1.44 0.02 0.02 0.020.02 0.040.04 // / /

According to the service environment, two types of high-performance concrete were used in the pier structures of the Jiaozhou Bay sea-crossingsea-crossing railway bridge. One One type is C40 concrete with water/cementwater/cement ratioratio (w(w/b)/b) = =0.33 0.33 and and was was used used in in the th lande land section. section. The The other other type type is C50 is concreteC50 concrete with withw/b = w/b0.3 and= 0.3 was and used was in used the marine in the section.marine Thesectio mixturen. The proportionsmixture proportions for the two for types the of two concrete types areof concreteshown in are Table shown2. After in curing Table the2. concretesAfter curing in a the standard concretes room in for a 28 standard days, the room compressive for 28 strengthsdays, the compressiveof the two types strengths of concrete of the were two 47.5types MPa of concre and 58.2te were MPa, 47.5 respectively. MPa and 58.2 MPa, respectively.

Table 2. Mix proportions of concrete used in the land and marine sections (kg(kg/m/m33).

Air Air AggregateAggregate (mm) (mm) SuperSuper ComponentComponent CementCement FlyFly Ash Ash SandSand WaterWater EntrainingEntraining 5–10 10–20 20–31.5 PlastizerPlastizer 5–10 10–20 20–31.5 AgentAgent LandLand section section 315 315 135 135 207 207 414 414 414414 721 721 149149 4 4 2.7 2.7 Marine section 336 144 208 416 416 709 144 5.28 2.88 Marine section 336 144 208 416 416 709 144 5.28 2.88

FigureFigure 1. 1. ReinforcedReinforced concrete concrete pier pier of of th thee Jiaozhou Jiaozhou Bay Bay sea-crossing sea-crossing railway railway bridge bridge (marine (marine section). section). 3. Durability Coeﬃcients of Constructed Reinforced Concrete 3. Durability Coefficients of Constructed Reinforced Concrete 3.1. Concrete Cover Thickness and Compressive Strength The service life of reinforced concrete was determined by concrete cover thickness and its properties, and the margins for the cover thicknesses suggested by DuraCrete were 20 mm, 14 mm, and 8 mm, which represent high, normal, and low repair cost, respectively. The concrete compressive Appl. Sci. 2019, 9, x FOR PEER REVIEW 4 of 18

3.1. Concrete Cover Thickness and Compressive Strength The service life of reinforced concrete was determined by concrete cover thickness and its Appl. Sci. 2019, 9, 3570 4 of 18 properties, and the margins for the cover thicknesses suggested by DuraCrete were 20 mm, 14 mm, and 8 mm, which represent high, normal, and low repair cost, respectively. The concrete strengthcompressive was measured strength bywas a rebound measured apparatus by a (manufacturedrebound apparatus by Runjie (manufactured Corporation), by and Runjie also theCorporation), cover thickness and ofalso the the pier cover structures thickness was of tested the pier by a structures cover thickness was tested meter by (manufactured a cover thickness by

Meiyumeter Corporation), (manufactured as by shown Meiyu in FigureCorporation),2. The actual as shown concrete in Figure cover 2. of The the actual reinforced concrete concrete cover piers of the in Jiaozhou Bay(a) sea-crossing railway bridge is1.0 shown in Figure3. The measured concrete cover reinforced25 concrete piers in Jiaozhou Bay sea-crossing(b) railway bridge is shown in Figure 3. The 0.9 thicknessmeasured of theconcrete piers incover the marinethickness and of land the sectionspiers0.8 in followedthe marine a normal and land distribution. sections followed The mean a covernormal 20 thicknessesdistribution. of theThe concrete mean cover piers thicknesses in theμ=52mm marine of andthe0.7 landconcrete sections piers were in the 52 marine mm and and 36 mm,land respectively.sections were δ=5.21mm 0.6 15

The52 correspondingmm and 36 mm, standard respectively. deviations The werecorresponding 5.21 0.5 mm andstandard 3.18 mm,deviations respectively. were 5.21 The mm maximum and 3.18 0.4 dimm,ﬀerence respectively.10 between the The measured maximum and difference designed between cover thicknesses the measured of the andy=0.041x-1.623 concrete designed piers cover was thicknesses less than Probability

Frenquency 0.3 15of mm. the Therefore,concrete piers to ensure was thatless thethan concrete 15 mm. is madeTheref moreore, durable,to ensure it isthat veryR2 =0.963the important concrete tois controlmade more the 5 0.2 coverdurable, thickness it is very in situ. important to control the cover0.1 thickness in situ. 0 0.0 35 40 45 50 55 60 65 35 40 45 50 55 60 65 Cover thickness (mm) Cover thickness (mm)

0.5

δ=3.18mm 15 0.4 y=0.073x-2.042

Probability 2 Frequency 0.3 10 R =0.933 0.2 5 0.1 0.0 0 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 26 28 30 32 34 36 38 40 42 44 Cover thickness (mm) Cover thickness (mm) FigureFigure 2. Rebound2. Rebound strength strength and coverand cover thickness thickness tests at piers.tests at (a )piers. Rebound (a) strength;Rebound ( bstrength;) Cover thickness. (b) Cover thickness.

(a) 1.0 25 (b) 0.9 0.8 20 μ=52mm 0.7 δ=5.21mm 0.6 15

0.5 0.4 10 y=0.041x-1.623 Probability

Frenquency 0.3 R2=0.963 5 0.2 0.1 0 0.0 35 40 45 50 55 60 65 35 40 45 50 55 60 65 Cover thickness (mm) Cover thickness (mm)

0.5

δ=3.18mm 15 0.4 y=0.073x-2.042

Probability 2 Frequency 0.3 10 R =0.933 0.2 5 0.1 0.0 0 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 26 28 30 32 34 36 38 40 42 44 Cover thickness (mm) Cover thickness (mm) Figure 3. Concrete cover thickness of piers in the marine section and the land section. (a) Frequency (marine section); (b) Probability (marine section); (c) Frequency (land section); (d) Probability (land section).

Figure 3. Concrete cover thickness of piers in the marine section and the land section. (a) Frequency Figure(marine 3. Concrete section); cover (bthickness) Probability of piers (marine in the section);marine section (c) Frequency and the land (land section. section); (a) Frequency (d) Probability (marine(land section); section). (b) Probability (marine section); (c) Frequency (land section); (d) Probability (land section). After curing in situ, the compressive strength and rebound strength of the casting concrete specimens (100 mm 100 mm 100 mm) used in the marine and land sections were measured by a × × compression-testing machine and rebound hammer, respectively. As shown in Figure4, the linear relationships between the compressive strength and the average rebound strength of the concrete

Appl. Sci. 2019, 9, x; doi: FOR PEER REVIEW www.mdpi.com/journal/applsci Appl. Sci. 2019, 9, 3570 5 of 18

Appl. Sci. 2019, 9, x FOR PEER REVIEW 2 of 6 specimens were obtained. In order to evaluate the actual compression strength of the large volume of 3 pier concrete59.0 (exceeding 300 m ), the rebound47.5 strengths of the pier concrete in the marine and land (a) 58.5 (b) sections were measured by a rebound hammer,47.0 and then the compressive strengths were calculated 58.0 using the regressed linear relationships (Figure46.54) based on the measured rebound strengths, which 57.5 are shown57.0 in Figure5. The compressive strengths46.0 of the concrete in the marine and land sections

also follow56.5 a normal distribution. Further, the mean45.5 compressive strengths of concrete in the marine 56.0 y=1.31x-19.52 and land sections are 56 MPaR and2=0.995 46 MPa, respectively.45.0 The correspondingy=1.08x-5.04 standard deviations are 55.5 R2=0.995 2.45 MPa55.0 and 2.67 MPa, respectively. The designed44.5 compressive strengths of the concrete in the marine and land54.5 sections are 50 MPa and 40 MPa, respectively.44.0 Hence, the actual mean compressive strength Average Average rebound strength (MPa) 56.5 57.0 57.5 58.0 58.5 59.0 59.5 60.0 Average rebound strength (MPa) 45.5 46.0 46.5 47.0 47.5 48.0 48.5 of the concreteCompressive is higher than strength the designed(MPa) strength. However,Compressive the strength minimum (MPa) measured compressive strength is less than the designed strength, by about 7.2%.

Appl. Sci. 2019Figure, 9, x FOR 4. Linear PEER relationshipsREVIEW between compressive strength and average rebound strength for concrete3 of 6 Figurein 4. theLinear marine relationships and land sections.between (compressivea) Marine section; strength (b) and Land average section. rebound strength for concrete in the marine and land sections. (a) Marine section; (b) Land section.

(a) 1.0 25 (b) 0.9 0.8 20 μ=56MPa 0.7 σ=2.45MPa 0.6 15

0.5 y=0.075x-3.667 0.4 R2=0.936 10 Probability

Frequency 0.3 0.2 5 0.1 0.0 0 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 48 50 52 54 56 58 60 62 64 Compressive strength (MPa) Compressive strength (MPa)

1.0 35 (c) (d) 0.9 30 0.8 0.7 25 μ=46MPa 0.6 σ=2.67 20 0.5

15 0.4 y=0.07x-2.17 Frequency Probability 0.3 R2=0.901 10 0.2 5 0.1 0.0 0 3738394041424344454647484950515253545556 36 38 40 42 44 46 48 50 52 54 56 Compressive strength (MPa) Compressive strength (MPa)

Figure 5. Compressive strength of piers in the marine section and the land section (a) Frequency (marine section); (b) Cover thickness probability (marine section); (c) Frequency (land section); (d) Cover Figurethickness 5. Compressive probability strength (land section).of piers in the marine section and the land section (a) Frequency (marine section); (b) Cover thickness probability (marine section); (c) Frequency (land section); (d) Cover thickness probability (land section).

Appl. Sci. 2019, 9, 3570 6 of 18

3.2. Concrete Surface Defects Concrete surface defects, such as air bubbles and exposed aggregates, shorten the chloride ions’ migration depth. A digital camera was used to capture the surface morphology of the concrete pier in the marine section. The images show that there are a number of tiny holes and bubbles caused by inadequate vibration of concrete on the surface. Using Image Pro Plus software, the color uniformity, bubble number, and area on the surface of the reinforced concrete were calculated, as shown in Figure6. Figure6b shows that the standard deviation of the gray level of the eastern concrete pier surface is 22.05 pixels. This is an indication that the concrete surface is relative shiny. Further, the relationship between the bubble area and the number of bubbles can be expressed by a power function. Bubbles with small areas (i.e., 4–9 mm2) represent the largest percentage of the total bubble number. On the other hand, bubbles with large areas (i.e., 49–174 mm2) represent the largest percentage of the total bubble area. This is because the large-area bubbles can easily break up into many small-area bubbles duringAppl. Sci. construction, 2019, 9, x FOR PEER and REVIEW the small-area bubbles cannot be easily removed. 5 of 6

Figure 6. Concrete surface defects. (a) Concrete surface; (b) Gray level processing; (c) Bubble area calculation;Figure 6. Concrete (d) Relationship surface defects. between (a) Concrete bubble surface; area and (b) bubble Gray level number; processing; (e) Percentage (c) Bubble area of bubbles area occupied;calculation; (f) Percentage(d) Relationship of bubble between number bubble occupied.area and bubble number; (e) Percentage of bubbles area occupied; (f) Percentage

3.3. Chloride30 Diffusion Coefficient The rapid25 chloride migration (RCM) test was conducted to determine the apparent chloride diffusion coe20 fficient of the concrete according to Chinese design code for marine concrete (GB/T

5 Atmespheric Average temperatureAverage (℃) 0 Concrete 123456789101112 Month Appl. Sci. 2019, 9, 3570 7 of 18

50476-2008) [28]. For the concrete used in the marine and land sections, after curing in situ for 28 days, the mean chloride diffusion coefficients were 2.32 10 12 m2/s and 4.38 10 12 m2/s, respectively. × − × − Zhao [29] reported that the relationship between the chloride diffusion coefficient and the compressive strength can be expressed by the exponential function. Figure5 shows that the compressive strengths of concrete follow a normal distribution. Therefore, the mean chloride diffusion coefficients of concrete in the marine section and the land section are 2.32 10 12 m2/s and 4.38 10 12 m2/s, and their × − × − corresponding standard deviations are 0.10 m2/s and 0.23 m2/s, respectively. For the reinforced concrete structure subjected to loading, the loading affects the chloride ions’ penetration, and sulfate and frost damage to the concrete. Based on the assumption of uniaxial compression load, the influence of load level (the ratio of uniaxial load to the prismatic compressive strength of the concrete specimen) on the chloride ion diffusion coefficient can be ignored due to the excellent compressive strength of high-performance concrete when the stress level does not exceed 0.3 [30]. However, if the stress level is higher than 0.3, the diffusion coefficient of chloride ions will be increased because of the formation of micro-cracks inside the concrete. Hence, if the sustained loading effect is not taken into account in the assessment of the durability of the structure, this will give an inaccurate prediction of the service life of the structure [31]. In order to evaluate the stress applied on the concrete, six reinforced stress gauges were installed inside the concrete. Figure7 shows the arrangement of the reinforced stress gauges. Due to the self-calibration process, the strain of the reinforced concrete can be calculated using the following equation:

σ = K[ε ε KT(T T )] (1) 0 − i − − 0

where σ is the strain of the reinforced concrete, K is the coefficient of the monitoring sensor, ε0 is the initial strain, εi is the final strain, KT is the temperature coefficient, T is the final temperature, and T0 is the initial temperature.

Figure 7. Schematic diagram of the arrangement of reinforced stress gauges in concrete piers. Figure 7. Schematic diagram of the arrangement of reinforced stress gauges in concrete piers. Figure8 shows that the stress applied onto the vertical bar decreases with time, and the stress 60 applied onto the horizontal bar increases with time. Wan [32] developed a relationship between the axial load and the chloride50 ion diffusion coefficient of concrete, as shown in Table3. Considering the effect of the loading and because of the measured stress applied Sensor1 onto the reinforced concrete, 40 Sensor2 the enlargement coefficient ks of 1.02 was selected. Sensor3 30 Sensor4 Sensor5 20 Sensor6 Stress (MPa) Stress

0 16.08.2017 10.10.2017 26.11.2017

Figure 8. Variation of stress applied on reinforced bars with time.

Figure 11. Events during a service life.

Appl. Sci. 2019, 9, x; doi: FOR PEER REVIEW www.mdpi.com/journal/applsci Appl. Sci. 2019, 9, x FOR PEER REVIEW 7 of 18 diffusion coefficients of concrete in the marine section and the land section are 2.32×10−12 m2/s and 4.38×10 − 12 m2/s, and their corresponding standard deviations are 0.10 m2/s and 0.23 m2/s, respectively. For the reinforced concrete structure subjected to loading, the loading affects the chloride ions’ penetration, and sulfate and frost damage to the concrete. Based on the assumption of uniaxial compression load, the influence of load level (the ratio of uniaxial load to the prismatic compressive strength of the concrete specimen) on the chloride ion diffusion coefficient can be ignored due to the excellent compressive strength of high-performance concrete when the stress level does not exceed 0.3 [30]. However, if the stress level is higher than 0.3, the diffusion coefficient of chloride ions will be increased because of the formation of micro-cracks inside the concrete. Hence, if the sustained loading effect is not taken into account in the assessment of the durability of the structure, this will give an inaccurate prediction of the service life of the structure [31]. In order to evaluate the stress applied on the concrete, six reinforced stress gauges were installed inside the concrete. Figure 7 shows the arrangement of the reinforced stress gauges. Due to the self-calibration process, the strain of the reinforced concrete can be calculated using the following equation:

휎 = 퐾[휀0 − 휀푖 − 퐾푇(푇 − 푇0)] (1) where 휎 is the strain of the reinforced concrete, K is the coefficient of the monitoring sensor,

휀0 is the initial strain, 휀푖 is the final strain, 퐾푇 is the temperature coefficient, T is the final temperature, and 푇0 is the initial temperature.

Appl. Sci. 2019, 9, 3570 8 of 18

Figure 7. Schematic diagram of the arrangement of reinforced stress gauges in concrete piers. 60

50 Sensor1 40 Sensor2 Sensor3 30 Sensor4 Sensor5 20 Sensor6

Stress (MPa)

0 16.08.2017 10.10.2017 26.11.2017 Figure 8. Variation of stress applied on reinforced bars with time. Figure 8. Variation of stress applied on reinforced bars with time.

TableTable 3. 3.RelationshipRelationship between between axial axial load load and and the the enlargement enlargement coefficient coeﬃcient ks kofs of퐷푅퐶푀DRCM. .

LoadingLoading EnlargementEnlargement LoadingLoading EnlargementEnlargement Coefficient Appl. Sci. 2019, 9, x FOR PEER REVIEW 8 of 18 Level LevelCoefficientCoefficient ks of k푫s 푹푪푴of D RCM LevelLevel Coekffis ofcient 푫푹푪푴ks of DRCM Figure 8 shows0 that0 the stress 1applied 1 onto the vertical bar0 decreases 0 with time,1 1and the stress Concrete 0.2 0.20.90 0.90ConcreteConcrete 0.2 0.20.98 0.98 appliedConcrete onto the horizontal bar increases with time. Wan [32] developed a relationship between the 0.3 0.95without 0.3 0.99 axialwithwith flyload fly and ash the0.3 chloride ion diffusion0.95 coefficientwithout of concrete, 0.3 as shown in Table0.99 3. Considering ash 0.5 1.02fly ashfly ash 0.5 1.04 the effect of the0.5 loading and because1.02 of the measured stress applied0.5 onto the reinforced1.04 concrete, 0.8 0.81.08 1.080.8 0.81.17 1.17 the enlargement coefficient ks of 1.02 was selected. 3.4. Temperature and Relative Humidity Evolution in Concrete 3.4. Temperature and Relative Humidity Evolution in Concrete The temperature and relative humidity (RH) in concrete affects the chloride ions’ transportation, The temperature and relative humidity (RH) in concrete affects the chloride ions’ and large changes in temperature and RH can even cause the concrete to crack. High temperature will transportation, and large changes in temperature and RH can even cause the concrete to crack. increase the migration capacity of chloride ions in concrete, considering the time-varying performance High temperature will increase the migration capacity of chloride ions in concrete, considering the of temperature response, and thus the transport of chloride ions in concrete will be affected by time-varying performance of temperature response, and thus the transport of chloride ions in temperature. Moreover, the internal temperature of concrete is greatly influenced by the service concrete will be affected by temperature. Moreover, the internal temperature of concrete is greatly environment [33]. Temperature and humidity sensors were pre-embedded inside the concrete at a influenced by the service environment [33]. Temperature and humidity sensors were pre-embedded depth of 25 mm from the concrete surface, and a wireless transportation apparatus was used to collect inside the concrete at a depth of 25 mm from the concrete surface, and a wireless transportation the monitoring data automatically, as shown in Figure9. apparatus was used to collect the monitoring data automatically, as shown in Figure 9.

FigureFigure 9.9. SensorSensor andand apparatus.apparatus. ( a) Temperature andand humidityhumidity sensor;sensor; ((bb)) WirelessWireless transportationtransportation apparatusapparatus (with(with solarsolar panel).panel).

BecauseBecause thethe relative relative humidity humidity in thein marinethe marine section section is often is higheroften thanhigher 80%, than the 80%, relative the humidity relative inhumidity concrete in in tidalconcrete zones in is alwaystidal zones 100%. is Figure always 10 shows100%. theFigure variation 10 shows of the temperaturethe variation inside of thethe concretetemperature as compared inside the to concrete the atmospheric as compared temperature. to the atmospheric It can be seen temperature. that the temperature It can be seen inside that thethe concretetemperature is significantly inside the aconcreteffectedby is thesignificantly atmospheric affected temperature, by the atmospheric especially near temperature, the concrete especially surface. Thenear principlethe concrete of continuoussurface. The temperature principle of variationcontinuous meets temperature the regularity variation of meets the Fourier the regularity transform of formula;the Fourier hence, transform the formula formula; of the hence, temperature the formula response of the inside temperature the concrete response was fitted inside as Equationthe concrete (2) andwas Equationfitted as Equation (3). After 2 appropriately and Equation fitting, 3. After Equation appropriately (2) can befitting, rewritten Equation as Equation 2 can be (4). rewritten as Equation 4.

5 Atmespheric Average temperatureAverage (℃) 0 Concrete 123456789101112 Month Figure 10. Comparison between atmospheric temperature and concrete temperature.

2𝑛𝜋 2𝑛𝜋 𝑇(𝑡) =𝑇 𝐴 𝑐𝑜𝑠 (𝑡−𝑡 )𝐵 𝑠𝑖𝑛 (𝑡−𝑡 ) (2) 𝑃 𝑃 Appl. Sci. 2019, 9, x FOR PEER REVIEW 6 of 6 Appl. Sci. 2019, 9, 3570 9 of 18

Figure 10. Comparison between atmospheric temperature and concrete temperature.

Figure 10. ComparisonX∞ between2n atmosphericπ temperature2 nandπ concrete temperature. T(t) = Ta + An cos (t t ) + Bn sin (t t ) (2) P − 0 P − 0 n=1

 2 R P h 2nπ i  An = Ta(t) cos (t t0) dt  P 0 h P − i (3)  2 R P 2nπ  Bn = Ta(t) sin (t t0) dt P 0 P − π π T = 16.64 + 14.38 cos (t 7) + 2.48 cos (t 9.15) (4) Figure 7. Schematic diagram of the arrangement6 − of reinforced 3stress− gauges in concrete piers.

where Ta is the annual average temperature,◦C; An and Bn are amplitude coeﬃcients, respectively; t is 60 time in months; t0 is the month that has the maximum average temperature; and P is 12 [34]. 50 4. Revised Service Life Prediction Model Suggested by DuraCrete Sensor1 40 Sensor2 The performance evolution of a concrete structure with respect Sensor3 to reinforced corrosion and related events, from reinforced depassivation30 to construction collapse, Sensor4 is shown in Figure 11. During the ﬁrst period, chloride ions penetrate into the concrete and induce Sensor5 the depassivation of the reinforced 20 Sensor6

bar. This period is named (MPa) Stress the design service life of concrete in marine environments. Since there are ﬂuctuations in the durability10 parameters of concrete, a reliability design is introduced into the durability design, and the design idea is shown in Figure 12. The probability of failure within the 0 period [0, T] can be expressed by16.08.2017 Equation (5),10.10.2017 and the limit26.11.2017 state function can be written as Equation (6). The service life prediction model of concrete in chloride environments, as suggested by DuraCrete, is shown as EquationFigure (7). 8. Variation of stress applied on reinforced bars with time.

FigureFigure 11. 11. EventsEvents during during a service a service life. life.

Appl. Sci. 2019, 9, x; doi: FOR PEER REVIEW www.mdpi.com/journal/applsci Appl. Sci. 2019, 9, x FOR PEER REVIEW 9 of 18

2 2𝑛𝜋 ⎧𝐴 = 𝑇(𝑡) 𝑐𝑜𝑠 (𝑡−𝑡 ) 𝑑𝑡 ⎪ 𝑃 𝑃 (3) ⎨ 2 2𝑛𝜋 ⎪𝐵 = 𝑇(𝑡) 𝑠𝑖𝑛 (𝑡−𝑡) 𝑑𝑡 ⎩ 𝑃 𝑃 𝜋 𝜋 𝑇 = 16.64 14.38 𝑐𝑜𝑠 (𝑡−7) 2.48𝑐𝑜𝑠 (𝑡 − 9.15) (4) 6 3

where 𝑇 is the annual average temperature,°C; 𝐴 and 𝐵 are amplitude coefficients, respectively; 𝑡is time in months; 𝑡 is the month that has the maximum average temperature; and P is 12 [34].

4. Revised Service Life Prediction Model Suggested by DuraCrete The performance evolution of a concrete structure with respect to reinforced corrosion and related events, from reinforced depassivation to construction collapse, is shown in Figure 11. During the first period, chloride ions penetrate into the concrete and induce the depassivation of the reinforced bar. This period is named the design service life of concrete in marine environments. Since there are fluctuations in the durability parameters of concrete, a reliability design is introduced into the durability design, and the design idea is shown in Figure 12. The probability of failure within the period [0, T] can be expressed by Equation 5, and the limit state function can be written as Equation 6. The service life prediction model of concrete in chloride environments, as suggested by DuraCrete, is shown as Equation.7.

Appl. Sci. 2019, 9, 3570 10 of 18 Figure 11. Events during a service life.

FigureFigure 12. Probability 12. Probability of failu of failurere and and target target service service life. life. P f (T) = 1 P g(x, t) > 0, t[0, T] (5) 𝑃(𝑇) =1−𝑃−𝑔(𝑥,) 𝑡 0,𝑡𝜖0,𝑇 (5) g(x, t) = R(t) S(t) (6) 𝑔(𝑥,) 𝑡 =𝑅(𝑡) −𝑆−(𝑡) (6)       Ccr w   x ∆x  AC γC 1 er f  −  = 0 (7) s,cl s,cl   q n  γCcr − · b ·  −  t0 cl   2 γR k k D t cl · e,cl· c,cl RCM,0 t · where R(t) and S(t) are the time-variant resistance and the load variable, respectively; Ccr is the

eigenvalue of the critical chloride ion concentration; γCcr is the fractional coeﬃcient of the critical

chloride ion concentration; ACs,cl is the regression coeﬃcient of the chloride ion concentration at the concrete surface and the water/cement ratio relationship in concrete; w/b is the water/cement ratio;

γCs,cl is the fractional coeﬃcient of the chloride concentration at the concrete surface; X is the cover

thickness (mm); ∆x is the construction deviation of the cover thickness (mm); γRcl is the fractional coefficient of chloride ion diffusion; ke,cl is the environment influencing the coefficient of chloride ion diffusion; kc,cl is the curing coefficient of chloride ion diffusion; DRCM,0 is the coefficient of chloride ion diffusion; t0 is the testing time during the diffusion test; ncl is the degradation coefficient of chloride R x 2 diffusion; t is the design life span of the structure. Further, the error formula is erf(x) = 2 e y dy. √π 0 − As mentioned above, both the load level and temperature affect the chloride diffusion coefficient of concrete. The loading factor ‘ks’ and temperature factor ‘kt’ were introduced into the model, and they are shown, respectively, in Equations (8) and (9). It is worth noting that the revised DuraCrete model (Equation (8)) was improved from Equation (7), whose chloride diffusion coefficient DRCM,0 was multiplied by the loading factor ‘ks’ and temperature factor ‘kt’ in order to enlarge the chloride diffusion coefficient considering the effect of the two parameters. Reference [35] highlighted the temperature factor, which needs to be further considered, and in Equation (9), T is the monthly average temperature monitored by embedded relative temperature and humidity sensors. According to Equation (9), it was concluded that different monthly values contribute to various mean values of temperature factor ‘kt’. As shown in Figure 10, the minimum value of average monthly temperature was 2 ◦C (275 K) and the maximum was 28 ◦C (301 K), respectively. Correspondingly, the minimum and maximum values of ‘kt’ were 0.41 and 1.31, respectively. Even if the maximum ‘kt’ value were to be used, resulting in the minimum value of the remaining service life, it would still satisfy the designed service life of 100 years.       Ccr w   x ∆x  AC γC 1 er f  −  = 0 (8) s,cl s,cl   q n  γCcr − · b ·  −  t0 cl   2 γR k k ks kt D t cl · e,cl· c,cl· · · RCM,0 t ·

where ks is the loading factor, kt is the temperature factor, q is the constant of the average " !# T 1 1 kt = exp q (9) T0 T0 − T Appl. Sci. 2019, 9, 3570 11 of 18

activation energy (q = 3739 K for PFA and q = 2776 K for OPC [35]), and T0 = 293 K (20 ◦C). Using Equation (10), the surface chloride ion concentration of the concrete can be calculated.

The characteristic values of the regression parameter ACs,cl and critical chloride concentration CCR for diﬀerent types of concrete in diﬀerent corrosion zones are shown in Tables4 and5, respectively.

w C = A γ (10) s,cl Cs,cl · b · Cs,cl

Table 4. Characteristic values of the regression parameter ACs,cl (%, relative to binder).

OPC PFA GGBS SF Atmospheric 2.57 4.42 3.05 3.23 Tidal and Splash 7.76 7.45 6.77 7.96 Submerged 10.3 10.8 5.06 12.5

Table 5. Characteristic values of the critical chloride concentration Ccr (%, relative to binder).

Water/cement w/b = 0.4 w/b = 0.5 ratio (w/b) = 0.3 Submerged 2.3 2.1 1.6 Splash and Tidal 0.9 0.8 0.5

The chloride ion diffusion coefficient of concrete decreases with exposure time, and is inversely proportional to corrosion time [36–39]. Further, the age factors of different types of concrete in different corrosion zones are shown in Table6. It is worth mentioning that the chloride ion di ffusion coefficient DRCM,0 decreases with time, and actually stabilizes gradually as time increases, to a certain degree. In this model, DRCM,0 is modified through the change in the age factor ncl, and DRCM,0 is obtained through a short-time RCM test. Hence, the age factor ncl corresponds to the instantaneous chloride diffusion coefficient in this paper.

Table 6. Age factor of the chloride diﬀusion coeﬃcient ncl.

OPC PFA GGBS SF Atmospheric 0.65 0.66 0.85 0.79 Tidal and Splash Zones 0.37 0.93 0.60 0.39 Submerged 0.30 0.69 0.71 0.62

Additionally, chloride ions’ penetration into concrete is affected by the environment and the curing age [40]. The chloride diffusion coefficient can be expressed by Equations (11) and (12), and the characteristic values of the environment factor and the curing factor are shown in Tables7 and8. Further, the partial factors relevant for structures in a marine environment are shown in Table9.

Table 7. Characteristic values of the environment factor ke,cl.

OPC GGBS Atmospheric 0.68 1.98 Splash Zone 0.27 0.78 Tidal Zone 0.92 2.70 Submerged 1.32 3.88 Appl. Sci. 2019, 9, 3570 12 of 18

Table 8. Characteristic values of the curing factor kc,cl.

Curing Time 1 d 3 d 7 d 28 d

kc,cl 2.08 1.50 1 0.79

Table 9. Partial factors for structures in a marine environment.

Cost of Mitigation of Risk High Normal Low Relative to the Cost of Repair ∆x (mm) 20 14 8

γCcr 1.20 1.06 1.03

γCs,cl 1.70 1.40 1.20

γRcl 3.25 2.35 1.50 Appl. Sci. 2019, 9, x FOR PEER REVIEW 12 of 18 n t0 cl Dt = γR k k ks kt D t (11) in order to provide further evidence forcl · ethe,cl· cdurability,cl· · · RCM performance,0 t · assessment (Figure 13). The acceptance criterion was defined in2 terms of the reliability index,2 𝛽, as follows:13 DRCM,0 mm /year = DRCM,28days m /s 3.1536 10 (12) × × 𝛽=−∅ 𝑃 (13) According to Equation (8), the chloride diffusion coefficient DRCM and the cover thickness x are wherethe most 𝑃 significant is the probability factors that of a fftheect theconsidered servicelife even oft a concreteoccurring structure. within the Inorder considered to investigate reference the periodtarget reliability (service life).β, Monte-Carlo (MC) simulations were carried out using the software Matlab in order to provideAccording further to evidencethe Chinese for theunified durability standard performance for reliability assessment design (Figureof building 13). Thestructures acceptance (GB 50068-2017),criterion was the defined calculation in terms formula of the reliability of the index,reliabilityβ, as index follows: 𝛽 is shown as Equation 13. The reliability index 𝛽 is relevant to the failure probability 𝑃, and the relationship between the two 1 β =𝛽 ∅− P f (13) factors is shown in Table 10. In this paper, −= 1.645 (5% failure probability) was regarded as a target reliability because the construction is not allowed to be repaired during the designed service wherelife. BasedP f is on the the probability results of ofthe the re consideredliability analyses event occurringcarried out within by the the partial considered factor method, reference the period risk (serviceacceptance life). criterion was defined. According to the Chinese unified standard for reliability design of building structures (GB

50068-2017),Table the calculation 10. Relationship formula between of the the reliability failure probability index β is 𝑃 shown and the as reliability Equation index (13). The𝛽. reliability index β is relevant to the failure probability P f , and the relationship between the two factors is shown in Table 10. In this paper,Failureβ = 1.645 Probability (5% failure 𝑷𝒇 probability) wasReliability regarded Index as a target𝜷 reliability because the construction is not allowed to be5% repaired during the designed service1.645 life. Based on the results of the reliability analyses carried out10% by the partial factor method, the1.282 risk acceptance criterion was deﬁned.

Figure 13. ProgrammingProgramming language of Monte-Carlo simulation.

5. Service Life Predictions

5.1. Reinforced Concrete in the Marine Section Chloride penetration into concrete is much more severe than carbonation-induced corrosion of reinforced bars in concrete structures in marine environments. Therefore, only chloride-induced corrosion of reinforced bars was considered, and the revised DuraCrete model (Equation 8) was used to predict the service life of a concrete structure. Since it is difficult to measure the concrete cover thicknesses of the box girder and platform, the designed cover thicknesses and the corresponding standard deviations with assumptions were used in the service life prediction calculations. On the other hand, the measured concrete cover thickness of the pier concrete was used in the service life prediction calculations. Figure 14 shows a photograph of the Jiaozhou Bay sea-crossing railway bridge in its completed state. Appl. Sci. 2019, 9, 3570 13 of 18

Table 10. Relationship between the failure probability P f and the reliability index β.

Failure Probability Pf Reliability Index β 5% 1.645 10% 1.282

5. Service Life Predictions

5.1. Reinforced Concrete in the Marine Section Chloride penetration into concrete is much more severe than carbonation-induced corrosion of reinforced bars in concrete structures in marine environments. Therefore, only chloride-induced corrosion of reinforced bars was considered, and the revised DuraCrete model (Equation (8)) was used to predict the service life of a concrete structure. Since it is diﬃcult to measure the concrete cover thicknesses of the box girder and platform, the designed cover thicknesses and the corresponding standard deviations with assumptions were used in the service life prediction calculations. On the other hand, the measured concrete cover thickness of the pier concrete was used in the service life prediction calculations. Figure 14 shows a photograph of the Jiaozhou Bay sea-crossing railway bridge inAppl. its Sci. completed 2019, 9, x FOR state. PEER REVIEW 13 of 18

Figure 14. JiaozhouJiaozhou Bay sea-crossing railway bridge (completed).

5.1.1. Box GirderTable Concrete 11. Parameters used in the revised DuraCrete model in the marine section.

The box girder𝛾 concrete𝐶 located𝐴 in the𝛾 atmospheric X zones∆𝑥 and𝛾 carbon 𝑘 reinforced 𝑘 bars were𝑛 used𝑤𝑏⁄ in Parameters , , , , this structure. The(-) characteristic(%) value(%) of the(-) critical(mm) chloride (mm) concentration (-) (-) Ccr is(-) 0.9% relative(-) to(-) the binder.Box girder The characteristic1.2 0.9 value of the4.42 regression1.7 parameter50 A8 Cs,cl is3.25 4.42%, 0.68 and that 0.79 of the age 0.66 factor 0.3ncl is 0.66Pie becauser w.t.1.2 30%0.9/4.5 fly ash replacement 7.46 1.7 of cement 52 was 5.21 used 3.25 in the0.27 concrete. 0.79 The characteristic 0.93 0.3 valuePlatform of the concrete1.03 cover2.3 x is 5010.8 mm (designed1.2 value),60 and8 the margin1.5 1.32 for the concrete0.79 0.69 cover ∆ 0.3x is 8 mm. The main durability parameters used in the service life prediction model are shown in Table 11. After5.1.1. curingBox Girder for 28 Concrete days, the measured apparent chloride diffusion coefficient of the box girder concrete is 2.32 10 12 m2/s. The reliability indexes of the box girder concrete for different service lives were The× box− girder concrete located in the atmospheric zones and carbon reinforced bars were calculated and are shown in Figure 15, and then t = 223.9 years and reliability index β = 1.81 were used in this structure. The characteristic value of the critical chloride concentration 𝐶 is 0.9% calculated for when the box girder concrete service life is 100 years. relative to the binder. The characteristic value of the regression parameter 𝐴, is 4.42%, and that of the age factor n is 0.66 because w.t. 30% fly ash replacement of cement was used in the Table 11. Parameters used in the revised DuraCrete model in the marine section. concrete. The characteristic value of the concrete cover x is 50 mm (designed value), and the margin X ∆x for Parametersthe concreteγ cover(-) C ∆𝑥(%) is A8 mm.(%) γThe (-)main durability γparameters(-) k (-) usedk (-)in then (-)servicew/b (-)life Ccr cr Cs,cl Cs,cl (mm) (mm) Rcl e,cl c,cl cl prediction model are shown in Table 11. After curing for 28 days, the measured apparent chloride Box girder 1.2 0.9 4.42 1.7 50 8 3.25 0.68 0.79 0.66 0.3 −12 2 diffusionPier coefficient1.2 of 0.9the/4.5 box girder7.46 concrete 1.7 is 52 2.32×10 5.21 m 3.25/s. The 0.27reliability 0.79 indexes 0.93 of the 0.3 box girderPlatform concrete for1.03 different 2.3 service 10.8 lives 1.2were ca 60lculated 8 and are 1.5 shown 1.32 in Figure 0.79 15, 0.69 and then 0.3 t = 223.9 years and reliability index β = 1.81 were calculated for when the box girder concrete service life is 100 years.

Figure 15. Reliability index calculated by the Monte-Carlo simulation for the box girder concrete.

5.1.2. Pier Concrete Corrosion-resistant reinforced bars were used to improve the durability of the reinforced concrete. The characteristic value of the concrete cover x is 52 mm, and the margin for the concrete cover ∆𝑥 is 5.21 mm. After curing for 28 days, the measured apparent chloride diffusion coefficient of the pier concrete was 2.32×10−12m2/s. The main durability parameters used in the service life prediction model are shown in Table 11. The reliability indexes of the pier concrete with carbon Appl. Sci. 2019, 9, x FOR PEER REVIEW 13 of 18

Figure 14. Jiaozhou Bay sea-crossing railway bridge (completed).

Table 11. Parameters used in the revised DuraCrete model in the marine section.

𝛾 𝐶 𝐴 𝛾 X ∆𝑥 𝛾 𝑘 𝑘 𝑛 𝑤𝑏⁄ Parameters , , , , (-) (%) (%) (-) (mm) (mm) (-) (-) (-) (-) (-) Box girder 1.2 0.9 4.42 1.7 50 8 3.25 0.68 0.79 0.66 0.3 Pier 1.2 0.9/4.5 7.46 1.7 52 5.21 3.25 0.27 0.79 0.93 0.3 Platform 1.03 2.3 10.8 1.2 60 8 1.5 1.32 0.79 0.69 0.3

5.1.1. Box Girder Concrete The box girder concrete located in the atmospheric zones and carbon reinforced bars were used in this structure. The characteristic value of the critical chloride concentration 𝐶 is 0.9% relative to the binder. The characteristic value of the regression parameter 𝐴, is 4.42%, and that of the age factor n is 0.66 because w.t. 30% fly ash replacement of cement was used in the concrete. The characteristic value of the concrete cover x is 50 mm (designed value), and the margin for the concrete cover ∆𝑥 is 8 mm. The main durability parameters used in the service life prediction model are shown in Table 11. After curing for 28 days, the measured apparent chloride diffusion coefficient of the box girder concrete is 2.32×10−12 m2/s. The reliability indexes of the box girder concrete for different service lives were calculated and are shown in Figure 15, and then t = Appl.223.9 Sci. years2019, and9, 3570 reliability index β = 1.81 were calculated for when the box girder concrete service14 of 18 life is 100 years.

Figure 15. Reliability index calculated by the Monte-Carlo simulation for the box girder concrete.concrete.

5.1.2. Pier Concrete Corrosion-resistant reinforcedreinforced bars bars were were used used to improve to improve the durability the durability of thereinforced of the reinforced concrete. Theconcrete. characteristic The characteristic value of the value concrete of the cover concretex is 52cover mm, x andis 52 the mm, margin and the for themargin concrete for the cover concrete∆x is 5.21 mm.∆𝑥 After curing for 28 days, the measured apparent chloride diﬀusion coeﬃcient of the pier Appl.cover Sci. 2019 is, 95.21, x FOR mm. PEER After REVIEW curing for 28 days, the measured apparent chloride diffusion coefficient14 of 18 concrete was 2.32 10 12m2/s. The main durability parameters used in the service life prediction model of the pier concrete× −was 2.32×10−12m2/s. The main durability parameters used in the service life are shown in Table 11. The reliability indexes of the pier concrete with carbon reinforced bars and with reinforcedprediction modelbars and are with shown corrosion-resistant in Table 11. The reinreliabforcedility indexesbars were of thecalculated pier concrete and are with shown carbon in corrosion-resistantFigure 16. reinforced bars were calculated and are shown in Figure 16.

Figure 16. Reliability index calculated by the Monte-Carlo simulation for the pier concrete.

Table 1111 shows shows that that the the critical critical chloride chloride concentration concentration for thefor carbonthe carbon reinforced reinforced bars in bars the splashin the zonesplash is 0.9%.zone Onis 0.9%. the other On hand,the other as the corrosion-resistanthand, as the corrosion-resistant reinforced bars arereinforced more corrosion-resistant, bars are more thecorrosion-resistant, critical chloride the concentration critical chloride for the concentrat corrosion-resistantion for the reinforcedcorrosion-resistant bars in thereinforced splash zonebars in is 4.5%the splash [41–43 zone]. For is the 4.5% pier [41–43]. concrete For with the carbon pier conc reinforcedrete with bars, carbon the reliability reinforced index bars, of thethe reinforcedreliability concreteindex of the after reinforced 100 years concrete of service after is 100 only years 0.03. of Onservice the otheris only hand, 0.03. On for the other pier concretehand, for with the corrosion-resistantpier concrete with corrosion-resistant reinforced bars, the reinforced reliability ba indexrs, the of reliability the reinforced index concrete of the reinforced after 100 concrete years of serviceafter 100 is years nearly of 2.0. service The is higher nearly reliability 2.0. The higher index canreliability be attributed index can to thebe attributed higher critical to the chloride higher concentrationcritical chloride in concentration the corrosion-resistant in the corrosion-resistant reinforced bars as reinforced compared bars to that as incompared the carbon to that reinforced in the bars.carbon Further, reinforced the service bars. Further, life of the the pier service with corrosion-resistant life of the pier with reinforced corrosion-resistant bars in the marine reinforced section bars is 263.2in the years,marine and section its reliability is 263.2 years, index isand 2.01 its when reliability serving index for is 100 2.01 years. when serving for 100 years.

5.1.3. Platform Concrete For thethe platformplatform concreteconcrete located located in in the the submerged submerged zone, zone, the the designed designed characteristic characteristic value value of the of concretethe concrete cover coverx is 60 x mm, is 60 and mm, the marginand the for margin the concrete for the cover concrete∆x is 8 cover mm. Since∆𝑥 is it is8 dimm.ﬃcult Since to repair it is the platform concrete, the partial factor for the critical chloride concentration γCcr is 1.03. The main difficult to repair the platform concrete, the partial factor for the critical chloride concentration 𝛾 durabilityis 1.03. The parameters main durability used inparameters the service used life predictionin the service model life prediction are shown model in Table are 11 shown. The reliability in Table indexes11. The ofreliability the platform indexes concrete of the for platform diﬀerent concrete service yearsfor different were calculated service andyears are were shown calculated in Figure and 17. Theare shown service in life Figure is 113.6 17. years The andservice the life reliability is 113.6 index years is and 1.76 the for reliability the platform index concrete is 1.76 with for 100the serviceplatform years. concrete with 100 service years.

Figure 17. Reliability index calculated by the Monte-Carlo simulation for the platform concrete.

Figure 16. Reliability index calculated by the Monte-Carlo simulation for the pier concrete.

Table 11 shows that the critical chloride concentration for the carbon reinforced bars in the splash zone is 0.9%. On the other hand, as the corrosion-resistant reinforced bars are more corrosion-resistant, the critical chloride concentration for the corrosion-resistant reinforced bars in the splash zone is 4.5% [41–43]. For the pier concrete with carbon reinforced bars, the reliability index of the reinforced concrete after 100 years of service is only 0.03. On the other hand, for the pier concrete with corrosion-resistant reinforced bars, the reliability index of the reinforced concrete after 100 years of service is nearly 2.0. The higher reliability index can be attributed to the higher critical chloride concentration in the corrosion-resistant reinforced bars as compared to that in the carbon reinforced bars. Further, the service life of the pier with corrosion-resistant reinforced bars in the marine section is 263.2 years, and its reliability index is 2.01 when serving for 100 years.

5.1.3. Platform Concrete For the platform concrete located in the submerged zone, the designed characteristic value of the concrete cover x is 60 mm, and the margin for the concrete cover ∆𝑥 is 8 mm. Since it is difficult to repair the platform concrete, the partial factor for the critical chloride concentration 𝛾 is 1.03. The main durability parameters used in the service life prediction model are shown in Table 11. The reliability indexes of the platform concrete for different service years were calculated and Appl.are shown Sci. 2019 ,in9, 3570Figure 17. The service life is 113.6 years and the reliability index is 1.76 for15 ofthe 18 platform concrete with 100 service years.

Figure 17. ReliabilityReliability index calculated by the Monte-Carlo simulation for the platform concrete.

5.2. Reinforced Concrete in the Land Section The reinforced concrete in the Jiaozhou Bay sea-crossing railway bridge in the land section was mainly damaged by salt fog, and concrete with a compressive strength grade of C40 and a cover thickness of 35 mm was used. The The service service environment environment of the reinforced concrete in the land section can be divided into atmospheric zones, zones, and and the the mainly mainly durability durability parameters parameters are are listed listed in in Table Table 12.12. Appl. Sci. 2019, 9, x FOR PEER REVIEW 15 of 18 The apparent chloride diﬀusion coeﬃcient was 4.38 10 12 m2/s, and the concrete cover thickness was The apparent chloride diffusion coefficient was 4.38×10× − −12 m2/s, and the concrete cover thickness 36 mm with a margin of 3.18 mm. The reliability index of the reinforced concrete located in the land was 36 mm with a margin of 3.18 mm. The reliability index of the reinforced concrete located in the section, in service for 100 years, is 1.71, while the predicted service life is 173.8 years, which meets the land section, in service for 100 years, is 1.71, while the predicted service life is 173.8 years, which designed service life requirement (Figure 18). meets the designed service life requirement (Figure 18).

Table 12. Parameters used in the revised DuraCrete model in the land section. Table 12. Parameters used in the revised DuraCrete model in the land section. X ∆x Parameters γC (-)𝛾 C cr (%)𝐶 ACs,cl (%)𝐴 γ Cs,cl (-)𝛾 X ∆𝑥γ Rcl (-)𝛾 ke,cl𝑘(-) kc,𝑘cl (-) n𝑛cl(-) 𝑤𝑏w/⁄b (-) Parameters cr , ,(mm) (mm) , , (-) (%) (%) (-) (mm) (mm) (-) (-) (-) (-) (-) Land 1.2 2.24 7.46 1.7 36 3.18 3.25 0.92 0.79 0.93 0.33 LandSection Section 1.2 2.24 7.46 1.7 36 3.18 3.25 0.92 0.79 0.93 0.33

Figure 18. Reliability index calculated by the Monte-Carlo simulation (land section).

6. Conclusions This paper discusses the influenceinfluence of covercover thickness,thickness, compressive strength, chloride didiffusionffusion coecoefficient,fficient, and surface defects, as well as thethe micro-environmentmicro-environment of concrete on the service life of the Jiaozhou Bay sea-crossing railwayrailway bridge.bridge. The te temperaturemperature and relative humidity in the concrete and the loading applied applied onto onto the the reinforced reinforced concrete concrete were were measured. measured. For For the the reinforced reinforced concrete concrete in inthe the service service environment environment of ofthe the bridge, bridge, the the service service life life prediction prediction model model was was revised revised according toto suggestions by DuraCrete.DuraCrete. The mainmain durability parameters were determined based on DuraCreteDuraCrete guidelines and the measured results. Further, using the revised model, the reliability indexes of the service life of concrete with carbon reinforced bars and with corrosion-resistant reinforced bars were calculated. Based on the measured da datata and the analyses, as described in this paper, the conclusions are as follows: 1. According to the in situ measurements, the actual mean compressive strength of the concrete is higher than the designed value, while the maximum difference between the measured and designed cover thicknesses of the concrete piers is less than 15 mm. Due to the non-uniform vibration during concreting, there are defects on the concrete surface. Further, the temperature at the concrete surface varies with the atmospheric temperature. The applied load testing shows that the concrete structure suffers the effect of loading, which results in a larger chloride diffusion coefficient. 2. According to the suggestions by DuraCrete, the model was revised by adding two parameters, i.e., the loading factor ‘ks’ and the temperature factor ‘kt’. The added parameters affect the service life prediction; moreover, the revised prediction model was used in the service life predictions. 3. The partial factor method and Monte-Carlo simulations were used to predict the service life and the reliability index. The results show that by comparing the concrete in the marine and land sections, the predicted remaining service life of the Jiaozhou Bay sea-crossing railway bridge can meet the designed 100 years, based on the revised DuraCrete model. Additionally, the reliability index calculations based on the Monte-Carlo simulations show that the results of the partial factor method are relatively reliable.

Author Contributions: Conceptualization, Z.Q. Jin and T.J. Zhao; Formal analysis, Z. Li.; Investigation, Z. Li.; Methodology, Z.Q. Jin and T.J. Zhao; Resources, Z.Q. Jin and T.J. Zhao; Software, P.G. Wang; Supervision, Z.Q. Jin and T.J. Zhao; Writing-original draft, Z. Li; Appl. Sci. 2019, 9, 3570 16 of 18

1. According to the in situ measurements, the actual mean compressive strength of the concrete is higher than the designed value, while the maximum difference between the measured and designed cover thicknesses of the concrete piers is less than 15 mm. Due to the non-uniform vibration during concreting, there are defects on the concrete surface. Further, the temperature at the concrete surface varies with the atmospheric temperature. The applied load testing shows that the concrete structure suffers the effect of loading, which results in a larger chloride diffusion coefficient. 2. According to the suggestions by DuraCrete, the model was revised by adding two parameters, i.e., the loading factor ‘ks’ and the temperature factor ‘kt’. The added parameters affect the service life prediction; moreover, the revised prediction model was used in the service life predictions. 3. The partial factor method and Monte-Carlo simulations were used to predict the service life and the reliability index. The results show that by comparing the concrete in the marine and land sections, the predicted remaining service life of the Jiaozhou Bay sea-crossing railway bridge can meet the designed 100 years, based on the revised DuraCrete model. Additionally, the reliability index calculations based on the Monte-Carlo simulations show that the results of the partial factor method are relatively reliable.

Author Contributions: Conceptualization, Z.J. and T.Z.; Formal analysis, Z.L.; Investigation, Z.L.; Methodology, Z.J. and T.Z.; Resources, Z.J. and T.Z.; Software, P.W.; Supervision, Z.J. and T.Z.; Writing-original draft, Z.L.; Writing-review and editing, Z.L., C.X., Y.K. and L.Z.; For other cases, all authors have contributed equally. Funding: National Key R&D Program of China Grant No. 2017YFB0310000, Key Research and Development Program of Shandong Province No. 2019GGX102053, National Natural Science Foundation of China (NSF) Grant No. 51678318, 51709253, 51420105015 and 51608286, Chinese National 973 projects Grant No. 2015CB655100, 111 Project and Chinese Scholarship Council (CSC). Conﬂicts of Interest: The authors declare no conﬂict of interest.

References

1. Mou, B.; Li, X.; Qiao, Q.Y.; He, B.J.; Wu, M.L. Seismic behavior of frame corner joints under bidirectional cyclic loading test. Eng. Struct. 2019, 196, 109316. [CrossRef] 2. Mou, B.; Bai, Y.T. Experimental investigation on shear behavior of H-shaped beam-to-CFST column connections with irregular panel zone. Eng. Struct. 2018, 168, 487–504. [CrossRef] 3. Qiao, Q.Y.; Zhang, W.W.; Mou, B.; Cao, W.L. Seismic behavior of exposed concrete filled steel tube column bases with embedded reinforcing bars: Experimental investigation. Thin Walled Struct. 2019, 136, 367–381. [CrossRef] 4. Rostam, S.; Faber, M. Probabilistic Performance Based Durability Design of Concrete Structures. In Nordic Concrete Research; Norsk Betongforening: Espoo, Finland, 1996. 5. Chang, H.L. Chloride binding capacity of pastes influenced by carbonation under three conditions. Cem. Concr. Compos. 2017, 84, 1–9. [CrossRef] 6. Chang, H.L.; Mu, S.; Feng, P. Influence of carbonation on “maximum phenomenon” under cyclic wetting and drying condition. Cem. Concr. Res. 2018, 103, 95–109. [CrossRef] 7. Li, N.; Farzadnia, N.; Shi, C. Microstructural changes in alkali-activated slag mortars induced by accelerated carbonation. Cem. Concr. Res. 2017, 100, 214–226. [CrossRef] 8. Yu, Y.; Zhu, H. Influence of Rubber Size on Properties of Crumb Rubber Mortars. Materials 2016, 9, 527. [CrossRef][PubMed] 9. Chang, H.; Mu, S.; Xie, D.; Wang, P. Influence of pore structure and moisture distribution on chloride “maximum phenomenon” in surface layer of specimens exposed to cyclic drying-wetting condition. Constr. Build. Mater. 2017, 131, 16–30. [CrossRef] 10. Li, Z.; Jin, Z.; Zhao, T.; Wang, P.; Li, Z.; Xiong, C.; Zhang, K. Use of a novel electro-magnetic apparatus to monitor corrosion of reinforced bar in concrete. Sens. Actuators A Phys. 2019, 286, 14–27. [CrossRef] 11. Xiong, C.; Li, W.; Jin, Z.; Gao, X.; Wang, W.; Tian, H.; Han, P.; Song, L.; Jiang, L. Preparation of phytic acid conversion coating and corrosion protection performances for steel in chlorinated simulated concrete pore solution. Corros. Sci. 2018, 139, 275–288. [CrossRef] Appl. Sci. 2019, 9, 3570 17 of 18

12. Xiong, C.; Jiang, L.; Xu, Y.; Chu, H.; Jin, M.; Zhang, Y. Deterioration of pastes exposed to leaching, external sulfate attack and the dual actions. Constr. Build. Mater. 2016, 116, 52–62. [CrossRef] 13. Zhu, W.J.; Francois, R.; Zhang, C.P.; Zhang, D.L. Propagation of corrosion-induced cracks of the RC beam exposed to marine environment under sustained load for a period of 26 years. Cem. Concr. Res. 2018, 103, 66–76. [CrossRef] 14. Zhang, X.; Wang, J.; Zhao, Y.; Tang, L.; Xing, F. Time-dependent probability assessment for chloride induced corrosion of RC structures using the third-moment method. Constr. Build. Mater. 2015, 76, 232–244. [CrossRef] 15. Wu, L.; Li, W.; Yu, X. Time-dependent chloride penetration in concrete in marine environments. Constr. Build. Mater. 2017, 152, 406–413. [CrossRef] 16. Wang, Y.; Wu, L.; Wang, Y.; Li, Q.; Xiao, Z. Prediction model of long-term chloride diffusion into plain concrete considering the effect of the heterogeneity of materials exposed to marine tidal zone. Constr. Build. Mater. 2018, 159, 297–315. [CrossRef] 17. Attari, A.; McNally, C.; Richardson, M.G. A probabilistic assessment of the influence of age factor on the service life of concretes with limestone cement/GGBS binders. Constr. Build. Mater. 2016, 111, 488–494. [CrossRef] 18. Yu, H.F.; Ma, H.X.; Yan, K. An equation for determining freeze-thaw fatigue damage in concrete and a model for predicting the service life. Constr. Build. Mater. 2017, 137, 104–116. [CrossRef] 19. Yu, H.; Da, B.; Ma, H.; Zhu, H.; Yu, Q.; Ye, H.; Jing, X. Durability of concrete structures in tropical atoll environment. Ocean Eng. 2017, 135, 1–10. [CrossRef] 20. Hackl, J.; Kohler, J. Reliability assessment of deteriorating reinforced concrete structures by representing the coupled effect of corrosion initiation and progression by Bayesian networks. Struct. Saf. 2016, 62, 12–23. [CrossRef] 21. Yu, H.F.; Sun, W.; Yan, L.H.; Ma, H.Y. Study on prediction of concrete service life I-theoretical model. J. Chin. Ceram. Soc. 2002, 30, 686–690. (In Chinese) 22. Poupard, O.; L’Hostis, V.; Catinaud, S.; Petre-Lazar, I. Corrosion damage diagnosis of a reinforced concrete beam after 40 years natural exposure in marine environment. Cem. Concr. Res. 2006, 36, 504–520. [CrossRef] 23. Marchand, J.; Samson, E. Predicting the service-life of concrete structures—Limitations of simplified models. Cem. Concr. Compos. 2009, 31, 515–521. [CrossRef] 24. Jin, Z.Q.; Zhao, T.J.; Hou, B.R.; Li, Q.Y. Service life prediction of lining concrete for Jiaozhou Bay Subsea Tunnel. J. Civ. Archit. Environ. Eng. 2009, 31, 86–91. (In Chinese) 25. Jin, Z.Q.; Sun, W.; Hou, B.R.; Zhang, P. Key parameters of constructed lining concrete in Jiaozhou Bay Subsea Tunnel. J. Cent. South Univ. Sci. Technol. 2011, 42, 810–816. (In Chinese) 26. Ai, Z.Y.; Jiang, J.Y.; Sun, W.; Song, D.; Ma, H.; Zhang, J.C.; Wang, D.Q. Passive behavior of alloy corrosion-resistant steel Cr10Mo1 in simulating concrete pore solutions with different pH. Appl. Surf. Sci. 2016, 389, 1126–1136. [CrossRef] 27. Ai, Z.Y.; Sun, W.; Jiang, J.Y.; Song, D.; Ma, H.; Zhang, J.C.; Wang, D.Q. Corrosion-resistant steel Cr10Mo1 in simulating concrete pore solutions: Combination effects of pH and chloride. Materials 2016, 9, 749. [CrossRef] 28. Tang, L.P. Engineering expression of the ClinConc model for prediction of free and total chloride ingress in submerged marine concrete. Cem. Concr. Res. 2008, 38, 1092–1097. 29. Zhao, T.J.; Jin, Z.Q.; Wang, M.P.; Zhao, J.Z. Environmental condition and durability of lining concrete in Jiaozhou Bay Subsea Tunnel. Chin. J. Rock Mech. Eng. 2007, 26, 3823–3829. (In Chinese) 30. Jin, Z.; Zhao, X.; Zhao, T.; Yang, L. Interaction between compressive load and corrosive-ion attack on reinforced concrete with accelerated potentiostatic corrosion. Constr. Build. Mater. 2016, 113, 805–814. [CrossRef] 31. Xu, J.; Li, F.; Zhao, J.; Huang, L. Model of time-dependent and stress-dependent chloride penetration of concrete under sustained axial pressure in the marine environment. Constr. Build. Mater. 2018, 170, 207–216. [CrossRef] 32. Wan, X.M.; Su, Q.; Zhao, T.J.; Ren, X.B. Micro-cracking and chloride penetration of concrete under uniaxial compression. J. Civ. Archit. Environ. Eng. 2013, 35, 104–110. (In Chinese) 33. Zhao, R.; Jin, Z.Q.; Cao, J.R.; Du, F.Y.; Kang, Y. Numerical simulation of chloride ions transportation considering temperature and humidity in marine environment. Ocean Eng. 2018, 36, 99–106. (In Chinese) [CrossRef] Appl. Sci. 2019, 9, 3570 18 of 18

34. Zhao, L.X.; Wang, P.G.; Zhao, T.J.; Wang, L.Q.; Tian, Y.P.; Wang, Y. Research on temperature action spectrum and temperature response of concrete under natural environment in Qingdao. Bull. Chin. Ceram. Soc. 2018, 37, 2770–2774. (In Chinese) 35. Amey, S.L.; Johnson, D.A.; Miltenberger, M.A. Predicting the service life of concrete marine structures: An environmental methodology. ACI Struct. J. 1998, 95, 205–214. 36. Bao, J.W.; Wang, L.C. Combined effect of water and sustained compressive loading on chloride penetration into concrete. Constr. Build. Mater. 2017, 156, 708–718. [CrossRef] 37. Wang, L.; Bao, J.; Ueda, T. Prediction of mass transport in cracked-unsaturated concrete by mesoscale lattice model. Ocean Eng. 2016, 127, 144–157. [CrossRef] 38. Bao, J.W.; Wang, L.C. Effect of short-term sustained uniaxial loadings on water absorption of concrete. J. Mater. Civ. Eng. 2017, 29, 04016234. [CrossRef] 39. Petcherdchoo, A. Time dependent models of apparent diffusion coefficient and surface chloride for chloride transport in fly ash concrete. Constr. Build. Mater. 2013, 38, 497–507. [CrossRef] 40. Yu, Z.; Ye, G. New perspective of service life prediction of fly ash concrete. Constr. Build. Mater. 2013, 48, 764–771. [CrossRef] 41. Li, K.F.; Li, Q.W.; Zhou, X.G.; Fan, Z.H. Durability design of the Hong Kong-Zhuhai-Macao Sea-Link Project: Principle and procedure. J. Bridge Eng. 2015, 20, 341–352. [CrossRef] 42. Li, Q.W.; Li, K.F.; Zhou, X.G.; Zhang, Q.M.; Fan, Z.H. Model-based durability design of concrete structures in Hong Kong-Zhuhai-Macao Sea-Link Project. Struct. Saf. 2015, 53, 1–12. [CrossRef] 43. Ai, Z.Y.; Sun, W.; Jiang, J.Y.; Ma, H.; Zhang, J.C.; Song, D. Passive behavior of new alloy corrosion resistant

steel Cr10Mo1 in chloride-containing environment. Mater. Rev. 2016, 30, 92–118. (In Chinese)

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