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Life cycle embodied energy analysis of RC structures considering chloride-induced corrosion in seismic regions
Structures 25 (2020) 839–848
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Life cycle embodied energy analysis of RC structures considering chlorideinduced corrosion in seismic regions
T
⁎
Runqing Yua, Li Chenb, , Diandian Zhanga, Zhenhui Wanga a b
PLA Air Force Second Service Group of Engineering and Technology, Guangzhou 510403, China Engineering Research Center of Safety and Protection of Explosion & Impact of Ministry of Education, Southeast University, Nanjing 211189, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Life cycle analysis Embodied energy RC structures Chloride-induced corrosion Seismic fragility
Reinforced concrete (RC) structures consume large amounts of energy supply and cause continuing pollution. During the life cycle of RC structures, operating and embodied energy are significant contributors to the whole energy demand. The embodied energy is smaller than the operating energy but its proportion in the total lifecycle energy is increasing. Present study presented a life cycle embodied energy assessment (LCEEA) framework for a typical RC structures in seismic regions. First, numerical model to calculate the seismic response of corroded RC structures was established and verified. It shows that the numerical model together with zero-length section element and the suitable material model could predict the seismic responses of RC columns well. Then, seismic fragility was calculated using probabilistic seismic demand model. The embodied energy consumed in repair were calculated in detail for different damage levels. Finally, the life cycle embodied energy was obtained. Influences of chloride-induced corrosion on the life-cycle embodied energy (LCEE) were analyzed. The proposed assessment frame and calculated results show that the chloride-induced corrosion increase the life cycle embodied energy obviously, especially for the strong earthquake. Furthermore, increase in the embodied energy due to the corrosion was larger if the facilities were considered.
1. Introduction World widely, RC structures consume large amounts of energy and causing pollution. Reducing the energy consumed by RC structures is very meaningful in environmental protection, but firstly the energy should be well calculated. The consumed energy mainly includes operating and embodied energy, of which operating energy accounts for 80–90% and embodied energy accounts for 10–20% [1]. Because operating energy is larger than embodied energy, previous studies and practices mainly forced on the reduction of operating energy. For example, Kim et al. [2] employed liquid desiccant in cooling system. Through energy simulation and analysis, they found that 51% operating energy was saved compared with the conventional variable air volume system. Embaye et al. [3] simulated the panel radiators and rooms with pulsed flow and constant conditions. Results shows that the using flow pulsation for radiator increase the heat output by 25%, which saved the operating energy. Reducing of operating energy leads to the increasing proportion of embodied energy in turn. Calculation of embodied energy becomes even more necessary. The embodied energy includes two parts: the initial embodied energy consumed in the initial construction and installations, the
⁎
recurring embodied energy consumed in the maintenance and repair [1]. The initial embodied energy was calculated directly according to the initial design and usually reduced by optimizing the initial design [4]. The recurring embodied energy is consumed in the whole life cycle, which indicates the life cycle assessment (LCA) of embodied energy is necessary [5]. The LCA tools have been successfully applied in the environmental design and provided many useful suggestion on reducing the environmental impacts [6] and costs [7]. Similarly, LCA of embodied energy is meaningful. Life cycle embodied energy assessment (LCEEA) is relatively difficult to be calculated because the recurring embodied energy consuming by repair strategies were affected by the natural hazards. Although the calculation of recurring embodied energy is a little complicated, some useful researches have been conducted. Padgett and Tapia [8] firstly explored the role that the natural hazard plays in affecting long-term sustainability in detail. Their study shows the aging and deterioration have a big influence on the life cycle embodied energy. However, their research object was bridge infrastructure, which was quite different from RC buildings. Gencturk et al. [9] developed a life-cycle environmental impact assessment framework for RC buildings. The seismic hazard was considered but the deterioration was ignored.
Corresponding author. E-mail address: [email protected] (L. Chen).
https://doi.org/10.1016/j.istruc.2020.03.049 Received 8 July 2019; Received in revised form 24 March 2020; Accepted 24 March 2020 2352-0124/ © 2020 Published by Elsevier Ltd on behalf of Institution of Structural Engineers.
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Fig. 1. Flowchart of the proposed LCEEA framework.
This study presented a framework to calculate the life-cycle embodied energy of corroded RC structures. First, the calculated framework was presented in detail. Then, a typical corroded RC structures was used to describe the calculated framework step by step. The influences of deterioration on the life-cycle embodied energy were discussed at last.
Fig. 2. Illustration of calculation of.ERIM .
DS; pi (IM ) is the probability density of IM in the ith year; pi (∙ ∙) is the conditional probability. If four damage states are defined, as shown in Fig. 2, then the first part of Eq. (5), ∫ ERDS dDS , could be estimated by
2. Life cycle embodied energy assessment framework
∫ ERDS dDS ≈
RC structures inevitably suffer deterioration in their life cycle. The deterioration could be caused by many factors, such as chloride ion, carbonation, freeze–thaw action, stray current. Among those factors, the chloride ion induced corrosion plays a major role, especially in the offshore area [10]. Therefore, present study only considered the chloride ion induced corrosion. The proposed life cycle embodied energy assessment (LCEEA) framework is shown in Fig. 1. The embodied energy mainly consists of the initial embodied energy and the recurring embodied energy [1], given by Eq. (1).
EE = EI + ER
∑ mi Mi + Ec
[P (θmax ≥ θmax 2) − P (θmax (θmax ≥ θmax 3)
(1)
(2)
3. Numerical modeling of corroded RC structures The chloride ion induced corrosion affects the mechanics behavior of RC structures by reducing the cross section of steel, the material strength and the bond-slip strength between reinforcement and concrete. Mechanics behavior of corroded RC structures could be well simulated using Opensees software. The cross section of steel is simulated by reducing the cross section area. The material strength of steel and concrete are simulated using the corroded material model. The bondslip strength between reinforcement and concrete is simulated using the zero-length section elements together with Bond_SP01 model proposed by Zhao and Sritharan [13].
N
∑i =1 ERi
(3)
where N is the service life of buildings; ERi is the average annual recurring embodied energy. ERi is influenced by the seismic fragility and the repair strategies, calculated by
ERi =
∫ ERDS dDS∙ ∫ pi (DS EDP ) ∙pi (EDP IM ) dim
(5)
where θmax is the maximum drift angle of story; P (∙) is the probability of exceedance. In the life cycle of common RC buildings, the embodied energy contained in facilities was quite large, about 12.5 percent of the initial embodied energy of building [11]. However, facilities were replaced regularly under normal circumstances. The life span of facilities was about five to seven years [12]. This means that the embodied energy contained in facilities per year is approximately 2.5 percent of the initial embodied energy, which is quite small compared with the embodied energy consumed in repair. Therefore, embodied energy contained in facility was ignored in this condition. However, for some special buildings which contain large facilities, the embodied energy should not be ignored.
where mi is the quantity of materials; Mi is the energy content of material per unit quantity; Ec is the energy consumed in construction of structures. The recurring embodied energy is influenced by the maintenance strategies, the seismic fragility and the repair strategies. The maintenance practices are not always applied, especially for small buildings. Therefore, the maintenance practices are not considered in present study. The recurring embodied energy consumed by the repair and rebuild practices after earthquake is calculated by Eqs. (3) and (4).
ER =
ER2 + ER3 2 ER3 + ER 4 ≥ θmax 3)] + P 2
[P (θmax ≥ θmax1) − P (θmax ≥ θmax 2)] +
where EE is the embodied energy; EI is the initial embodied energy; ER is the recurring embodied energy. The initial embodied energy is dependent on the initial design, therefore it is time-independent. EI is calculated by Eq. (2) according to Ramesh et al. [1].
EI =
ER1 ER1 + ER2 [1 − P (θmax ≥ θmax1)] + 2 2
(4)
3.1. Reduction of reinforcement cross section
where DS is the damage states, e.g. maximum drift angle in present study; IM is the ground motion intensity measure, e.g. peak ground acceleration in present study; ERDS is the ER corresponds to different
The loss rate of reinforcement cross section is equal to the loss rate of mass if uniform corrosion was considered. Therefore, 840
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reinforcement enhanced strain; εsyc is the corroded reinforcement yield strain; ηs,cr is critical point of ηs (t ) . When ηs (t ) > ηs,cr , the enhanced strain will be coincide to the yield strain. Present study took ηs (t ) = 20%.
f ytc =
1 − 1.049ηs (t ) f y0 1 − ηs (t )
(11)
futc and εsuc are the ultimate strength and the ultimate strain respectively, calculated by Eqs.(12) and (13). fuc =
1 − 1.119ηs (t ) fu0 1 − ηs (t )
(12)
εsuc = e−2.501ηs (t ) εsu0
where εsu0 is the uncorroded reinforcement ultimate strain; fu0 is the uncorroded reinforcement ultimate strength.
Fig. 3. Tensile strength of corroded and uncorroded reinforcement.
3.3. Reduction of concrete compressive strength
2
d − x corr ⎞ ηs (t ) = 1 − ⎛ 0 d0 ⎠ ⎝ ⎜
x corr =
∫0
t
⎟
(6)
λ (t ) dt
According to Coronelli and Gambarova [16], the time-varying compressive strength of corroded cover concrete is taken as
(7)
fccc =
where ηs (t ) is the loss rate of reinforcement cross section; d 0 is the original diameter; λ (t ) is the annual corrosion rate, calculated by Eq. (8) [14].
λ (t ) = 0.0115(0.3683ln(t ) + 1.1305)(mm a)
(8)
(9)
where εshc is enhanced strain, calculated by Eq. (10).
(
)
⎧ fytc + εsh0 − fy0 ⎛1 − ηs (t ) ⎞ (η (t ) ≤ η ) s s,cr ⎪ Es0 Es 0 ηs,cr ⎝ ⎠ = f ytc ⎨ εsyc = E (ηs (t ) > ηs,cr ) ⎪ s0 ⎩
(14)
ε1 = 2πnbars (vrs − 1) x cp b0
(15)
d0 [1 − 2
1 − ηs (t ) ]
(16)
where fcc0 is the compressive strength of uncorroded concrete; εcc0 is the strain at fcc0 ; nbars is the number of reinforcements in the compressive zone; vrs is a coefficient and vrs = 2 ; d 0 is the diameter of reinforcements; b0 is the width of cross section. The compressive strength of corroded core concrete and corroded cover strength are shown in Fig. 4. For cover concrete, the main reason of strength decrease is the corrosion of concrete. For core concrete, the core concrete strength decreased because of the weakening of hoop effect [17]. The hoop effects were calculated according to Mander et al. [18]
The tensile strength of corroded reinforcement are shown in Fig. 3. Tensile strength is calculated by Eq.(9) according to Zhang et al. [15].
Es0 εsc (εsc ≤ f yc Es0) ⎧ ⎪ f ytc (f ytc Es0 < εsc ≤ εshc ) fs = ⎨ εsc − εshc f (f − f ytc )(εsc > εshc ) + ⎪ ytc εsuc − εshc utc ⎩
fcc 0 1 + 0.1ε1 εcc 0
x cp =
3.2. Reduction of reinforcement strength
εshc
(13)
3.4. Bond stress-slip relationship The bond stress-slip relationship for plain reinforcing bars proposed by CEB [19] was adopted, shown by Eq. (17).
(10)
where f y0 is the uncorroded reinforcement yield strength; f ytc is the corroded reinforcement yield strength, calculated by Eq. (11); Es0 is the uncorroded reinforcement elastic modulus; εsh0 is the uncorroded
τ (s s1 )α s ≤ s1 τ=⎧ u ⎨ ⎩ τu s ≤ s1
(a)
(17)
(b)
Fig. 4. Compressive strength of (a) Corroded core concrete and (b) Corroded cover strength. 841
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Fig. 5. (a) Test specimen and (b) Regions to measure the amounts of corrosion (c) Simulated model.
where s is slip; τ is bond stress. According to the study of Melo et al. [20], s1 and α were taken as 0.1 mm and 0.5, respectively. For corroded hot rolled bars, τu was taken as 0.3 fccc .
Table 2 Uncorroded material properties.
Reinforcement Stirrup Concrete
3.5. Simulated model and verification Tests conducted by Yang et al. [21] are used to validate the numerical model. Details for specimen are shown in Fig. 5 (a). In order to measure the amounts of corrosion, the test specimens are divided into four regions. Rebar and stirrups of each regions were taken out of the tested specimens and measure the practical average mass amounts of corrosion. The four regions are shown in Fig. 5(b). The mass amounts of corrosion are listed in Table 1. Material properties are listed in Table 2. RC columns are simulated using Opensees software. The integral model are shown in Fig. 5(c). The concrete and steel are simulated using the model listed in Section 3.1 ~ 3.5. Hysteretic material model and Concrete 1 were adopted to model the steel and concrete respectively. Force-Based Beam-Column Element were used to simulate RC columns. The zero-length section elements together with Bond_SP01 model were incorporated in the structural model to simulate the slip between concrete and steel bars [13]. Simulated results are listed in Fig. 6. The simulated results agree well with the test data for both specimens A and B, which shows that the numerical model could predict the response of RC column well. The maximum horizontal load of specimen B is smaller than that of specimen A. This is because the specimen B suffer more serious corrosion than specimen A.
Yield strength
Ultimate tensile/compressive strength
372 MPa 607.4 MPa
573 MPa 727.5 MPa 46.4 MPa
structures, a typical RC structure suffers from corrosion was studied. Overall dimensions of RC frame are shown in Fig. 7. The cross section of beam and column are shown in Fig. 8. The used materials are C40 for concrete, HRB335 for longitudinal bars and HPB235 for stirrups. Detail descriptions of the RC structure are shown in Table 3.
4.1. Method to calculate seismic fragility Present study used the probabilistic seismic demand model (PSDM) to calculate the seismic fragility. The PSDM could be conducted using stripe-method or cloud-method [22]. The strip-method, which was termed as incremental dynamic analysis (IDA), was more accurate on the calculation of fragility curves [23]. Therefore, present study chose the strip-method to obtain the relations between IM and EDP. The calculation process is described in Fig. 9. According to Liu and Hwang [24], the engineering demand parameter (EDP) could be calculated by
EDP = α (IM ) β
(18)
where α and β are coefficients to be determined. Therefore, the failure probability is given by
4. Time-dependent seismic fragility of corroded RC structure In order to calculate the life cycle embodied energy of corroded RC
] ⎤ ⎡ ln [EDP C ⎡ ln [α (PGA) β θ ]̂ ⎤ Pf = Φ ⎢ ⎥ = Φ⎢ ⎥ 2 2 βc + βd ⎥ βc2 + βd2 ⎢ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦
Table 1 Amounts of corrosion. Rebar
Stirrup
Region
1
2
3
4
1
2
3
Specimen A Specimen B
0.9% 3.3%
13.25% 16.8%
3.74% 4.5%
2.9% 2.6%
1.9% 7.7%
7.74% 9.0%
1.9% 3.2%
(19)
where Pf is the cumulative failure probability; θ ̂ is the mean value of damage quantification; βc and βd are the dispersion of engineering capacity and engineering response, respectively. βc is determined from data of the ground motion and βd is determined from the data of IDA curves.
4
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Fig. 6. Comparison of test data and simulated results (a) Specimen A (b) Specimen B.
Fig. 7. Overall dimensions of RC frame (a) Plane (b) 1–1 profile.
4.2. Statistical variations of parameters For corroded RC structures, uncertainties existed in material characteristics, structural dimensions, corrosion initiation time and ground motion records. Uncertainties in material characteristics and structural dimensions have little effect on the seismic damage of RC structures [25]. Therefore, only uncertainties in corrosion initiation time and ground motion records were considered in present study. Uncertainties in ground motion records referred to the varieties of ground motion records that may occur in a certain region. A set of 20 records are selected from Next Generation Attenuation -West2 database
Fig. 8. Cross section of beam and column.
Table 3 Detail descriptions of RC frame. Floor No.
Reinforcement of beams 300 mm × 500 mm Top side
1 2 3 4 5
2Φ20 2Φ20 2Φ16 2Φ20 2Φ18
+ + + + +
4Φ20 4Φ20 4Φ20 2Φ22 2Φ20
Reinforcement of columns 450 mm × 450 mm
Bottom side
Stirrup
Stirrup
Outside column
Inner column
4Φ18 4Φ18 4Φ18 4Φ18 4Φ18
Φ8@200
Φ8@150
12Φ16
12Φ16
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Fig. 11. Distribution of ground motion intensity.
erf (θ) =
2 π
∫0
θ
2
e−t dt
(21)
The corrosion initial time is uncertain because parameters in Eqs. (20) and (21) are uncertain. In present study, the variables distribution characteristics are listed in Table 4. Those distribution characteristics are recommended by Ghosh and Padgett [27] and Yu et al. [28] in their studies. The corrosion initiation time is simulated for 1000 times using Monte Carlo method. Calculated results are shown in Fig. 12. The goodness of fit is 0.9795. This means that the initiation time is fitted well using Power law distribution. The mean initiation time is 3.52 year.
Fig. 9. Calculation of fragility curves.
4.3. Damage level state and the consumed embodied energy Present study use θmax to define the damage states, shown in Table 5. The damage quantification and the damage description are determined according to FEMA 356 [29], GB50011-2010 [30] and the building grading standards of earthquake damage [31]. The secondary structural members are not considered in present study, but the damage descriptions are still presented in the table as references for determining the percentage of member damage. Embodied energy coefficients are listed in Table 6. The embodied energy contained in unit materials and the embodied energy consumed by large equipment are adopted from Padgett and Tapia [8]. The embodied energy consumed by human is adopted from Jiao et al. [32]. When earthquake occurred, the reliability of RC structures would suddenly decrease. Then, some repair measures were needed in order to recovery the building function. The embodied energy consumed in repair after earthquake was determined by the post-earthquake structural states. The damage states and corresponding repair activities of RC columns are listed in Table 7. The heavy damage is considered as the concrete crush and steel yielding in the zones of plastic hinges. The moderate damage is considered as the crush of cover and core concrete. The superficial damage is considered as the occurrence of cracks which does not affect the functions of RC members. The damage states and repair activities of RC beams are listed in
Fig. 10. Selected ground motion records.
[26], as shown in Fig. 10. The magnitude and distance of those records are shown in Fig. 11. Those records covers a range of distance-to-ruptured area between 10 km and 100 km and the magnitudes is set to 5.5–8.0. The corrosion initiation time is important to calculate the decrease of material strength and area of cross section. According to Ghosh and Padgett [27], the corrosion initiation time is taken as −2
Tcorr =
C 2 ⎡ −1 ⎛ C0 − Ccr ⎞ ⎤ erf 4Dc ⎢ ⎝ C0 ⎠ ⎥ ⎦ ⎣ ⎜
Table 4 Variables distribution characteristics.
⎟
(20)
where C is the concrete cover thickness (cm); Dc is the chloride diffusion coefficient (cm2/year); Tcorr is the corrosion initiation time; C0 is equilibrium chloride concentration at the concrete surface; Ccr is critical chloride concentration; erf is Gaussian error function, represented as 844
Variables
Mean
Cov.
Distribution
C0 (%) Dc (cm2/year) Ccr (%) C (cm)
0.10 1.29 0.040 2
0.100 0.100 0.100 0.200
Lognormal Lognormal Lognormal Normal
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Table 6 Consumed embodied Energy. Material
Embodied energy
Epoxy Concrete Grout Steel Concrete pump Hydraulic jacking system Dump truck Human
1404 MJ/m3 2762 MJ/m3 3496 MJ/m3 245757 MJ/m3 2770 MJ/day 1704 MJ/day 17559 MJ/day 320.1 MJ/Person-day
damage quantifications. Those figures were used to calculate the probabilities of different damage levels. For example, the probabilities of different damage levels under PGA = 0.5g are obtained using Fig. 16(a) ~ 16(c), shown in Fig. 17. It obviously shows that hazardous failure (D4) becomes dominant with the increase of year. Fig. 12. Calculation of corrosion initiation time.
5. Exceedance probability of life cycle embodied energy Table 8. The superficial damage is considered as the crush of cover concrete. The moderate damage is considered as the crush of cover concrete and core concrete. The heavy damage is considered as the concrete crush and steel yielding. Damage of RC beams was considered more severe than that of columns because strong columns and weak beams were required according to the principles of earthquake resistant design GB50011-2010 [30]. Using the Tables 5–8, the consumed embodied energy under different damage states are calculated, shown in Fig. 13. The consumed energy under state D1 is little because most of structural members have no damage under D1 state. A large difference of consumed energy exists between D1 and D2. This is because the repair strategy of D2 is conservative. Under state D2, many structural members have surface cracks. The crack will be dangerous if it is deep enough. However, it is hard to estimate the depth of crack. Therefore, the common acceptable repair method in engineering practice is epoxy injection to all open cracks. This will increase the consumed energy of state D2 significantly. The different between D2 and D3 is also very large. This is because structures suffer more serious damage under state D3, which need more embodied energy to repair.
The exceedance probability is more convenient to assess the consumed energy. In order to calculate the exceedance probability, seismic hazard should be presented. Seismic hazard analysis is to predict the probability of different seismic intensities occurring in a certain area. The distribution of PGA is extreme-II distribution according to Cornell [33], described as
FPGA (PGA) = 1 − P (IM ) = e−(u
(23)
where k is a coefficient reflecting the seismic hazard in different regions, u is the mode of PGA. The occurrence in 50 years was assumed as δ , then
k lgu = k lgPGA0 + lg(−ln(1 − δ ))
(24)
where PGA0 is the design value of PGA. Therefore,
P50 (IM ) = 1 − e ln(1 − δ )(PGA0
pga)k
(25)
where P (PGA ≥ pga) is the probability of exceedance (POE) of IM in 50 years. Combining the seismic fragility curves and the seismic hazard analyses, exceedance probability life cycle embodied energy was calculated. As shown in Fig. 18, the value of embodied energy increases if corrosion is considered. For example, the value of embodied energy increases by about 8% (from 7.26 to 7.67) when considering corrosion for an exceedance probability of 0.41. This is because corroded RC structures are more vulnerable to damage. However, the increase is slight, this is because the consumed embodied energy of different state is not very large. If there are facilities contained many embodied energy in the building, the increase will be more significant. For example, we assume facilities contains embodied energy ES = 3 × 1012J . Under damage state D1, D2, D3 and D4, we assumed the corresponding embodied energy consumed in the repair of facilities are 0.05ES , 0.5ES , 0.75ES and ES . The assumed value is meaningful because we assume the facilities are a little damaged under D1 but totally damaged under D4. Then, the
4.4. Seismic fragility and discussion Using the simulation model, incremental dynamic analyses (IDA) were conducted. For the erosional structure in a certain year, twenty simulations were performed. Each simulation has a random corrosion initial time. Fig. 14 shows the IDA curves for the structure in the 5th year. The relations between θmax and peak ground acceleration (PGA) were obtained by curve fitting, shown as Eq. (22). Then, fragility curves were obtained using Eqs. (19) and (22). As shown in Fig. 15, the uncertainty of corrosion initial time (CIT) has a slight influence on the fragility curves. (22)
lnθmax = 0.76001 + 0.81036lnPGA
PGA)k
Fig. 16(a) ~ 16(c) show the seismic fragility curves for different Table 5 Definition of damage states. Damage state
Superficial damage(D1) Moderate damage(D2) Heavy damage(D3) Hazardous failure(D4)
Damage quantification θmax
≤ 1 100 1 50 ∼ 1 100 1 25 ∼ 1 50 >1 25
Damage description Primary member
Secondary member
90% 75% 75% 75%
75% no damage, 25% superficial damage 75% moderate damage, 25% heavy damage 75% heavy damage, 25% moderate damage 100% heavy damage
no damage, 10% superficial damage superficial damage, 25% moderate damage moderate damage, 25% heavy damage heavy damage, 25% moderate damage
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Table 7 Repair activities for RC columns. Damage level
Action
Superficial damage Moderate damage Heavy damage
Epoxy injection to open cracks Removal and replacement of damaged cover and core concrete Concrete removal and placement Replacement of longitudinal rebar Replacement of transverse rebar
Unit
Large equipment used
2
m m3
Concrete pump; Hydraulic jacking system; Dump trucks.
m3 ton
Repair time (man-hour/unit) 0.6 4.3 4.3 13.9 21.3
Table 8 Repair activities for RC beams. Damage level
Action
Superficial damage Moderate damage Heavy damage
Removal and replacement of damaged cover concrete Removal and replacement of damaged cover and core concrete Concrete removal and placement Replacement of longitudinal rebar Replacement of transverse rebar
Unit
Large equipment used
3
m m3 m3 ton
Concrete pump; Hydraulic jacking system; Dump trucks.
Repair time (man-hour/unit) 0.6 4.3 4.3 11.9 20.0
Fig. 15. Fragility curves of RC frame (5 years).
Fig. 13. Embodied energy consumed in repair actions.
simulated models were built to study the response of corroded RC structures. Special attentions were paid to the repair actions after earthquake. Influences of corrosion and facilities on the embodied energy were discussed at last. Numerical models to simulate the corroded RC structures were proposed. The numerical model considers the reduction of steel cross section, the reduction of material strength and the slip between concrete and steel. Simulated results were verified by comparing with the experimental data. It shows that the proposed numerical model simulates the seismic response of RC structures well. For a typical RC structure, the fragility curves were obtained using probabilistic seismic demand model. Calculated results showes that the failure probability obviously decreases with the increases of years. The influence of corrosion initial time (CIT) on the fragility curves were analyzed. Results shows that uncertainty of CIT of reinforcement has a slight influence on the fragility curves. This indicates that the uncertainty of CIT could be ignored for the rapid fragility estimation in the engineering. The embodied energy consumed in repair increases dramatically as the seismic damage worsens. For the RC structure studied in present study, values of embodied energy increases from 3 GJ to 2526 GJ as the damage state worsens from D1 to D4. Therefore, the embodied energy consumed in repair should be calculated in life cycle embodied energy assessment, especially for severe damage. Value of embodied energy increases by about 8% if corrosion is considered. If the embodied energy of facilities is calculated, the
Fig. 14. IDA curves of RC frame (5 years).
exceedance probability of embodied energy are shown in Fig. 18 (dotted lines). The value of embodied energy increases by about 12% (from 8.25 to 9.23) when considering corrosion. 6. Conclusions Present study presents a framework to calculate the life cycle embodied energy considering corrosion and seismic hazards. Detailed 846
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Fig. 16. Fragility curves for different damage quantifications (a) θmax = 1 100 (b) θmax = 1 50 (c)θmax = 1 25.
Fig. 18. Exceedance probability curves for embodied energy.
increase value becomes 12%. This means that it is better to consider the influence of corrosion during the life cycle sustainability assessment. Fig. 17. Probability of different damage levels (PGA = 0.5g ).
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to 847
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influence the work reported in this paper.
structures. J Struct Eng 2004;130(10):1570–7. [15] Zhang W, Shang D, Gu X. Stress-strain relationship of corroded steel bars. J Tongji Univ 2006;34(5):586–92. [16] Coronelli D, Gambarova P. Structural assessment of corroded reinforced concrete beams: modeling guidelines. J Struct Eng 2004;130(8):1214–24. [17] Deng P, Zhang C, Pei S, Jin Z. Modeling the impact of corrosion on seismic performance of multi-span simply-supported bridges. Constr Build Mater 2018;185:193–205. [18] Mander JAB, Priestley MJN. Theoretical stress-strain model for confined concrete. J Struct Eng 1988;114(8):1804–26. [19] CEB-217. Bulletin d’Information N. 217 — selected justification notes. Comité EuroInternational du Béton. 1993. [20] Melo J, Fernandes C, Varum H, Rodrigues H, Costa A, Rêde A. Numerical modelling of the cyclic behavior of RC elements built with plain reinforcing bars. Eng Struct 2011;33(2):273–86. [21] Yang SY, Song XB, Jia HX, Chen X, Liu XL. Experimental research on hysteretic behaviors of corroded reinforced concrete columns with different maximum amounts of corrosion of rebar. Constr Build Mater 2016;121:319–27. [22] Yu XH, Lu DG, Wang GY. Discussions on probabilistic seismic demand models. Eng Mech 2013;30(8):172–9. [23] Zhang J, Huo YL. Evaluating effectiveness and optimum design of isolation devices for highway bridges using the fragility function method. Eng Struct 2009;31(8):1648–60. [24] Liu J, Hwang H. Seismic fragility analysis of reinforced concrete bridges. China Civil Eng J 2004;6(37):47–51. [25] Lee T, Mosalam KM. Seismic demand sensitivity of reinforced concrete shear-wall building using FOSM method. Earthq Eng Struct D 2010;34(14):1719–36. [26] PEER (Pacific Earthquake Engineering Research Center). PEER Ground Motion Database; 2013. http://ngawest2.berkeley.edu/ [accessed 15 June 2019]. [27] Ghosh J, Padgett JE. Aging considerations in the development of time-dependent seismic fragility curves. J Struct Eng 2010;136(12):1497–511. [28] Yu RQ, Chen L, Fang Q, Yan HC. An improved nonlinear analytical approach to generate fragility curves of reinforced concrete columns subjected to blast loads. Adv Struct Eng 2017;21(3):396–414. [29] FEMA 356. Prestandard and commentary for the seismic rehabilitation of buildings. Report No. 356, Federal Emergency Management Agency, Washington DC. 2000. [30] GB50011-2010. Natioanl standard of the people republic of China. Code for seismic design of building. China Architecture and Building Press; 2010. [31] Ministry of housing and urban-rural development of the People’s Republic of China (MOHURD). The building grading standards of earthquake damage, Beijing. 1990. [32] Jiao Y, Lloyd CR, Wakes SJ. The relationship between total embodied energy and cost of commercial buildings. Energ Build 2012;52:20–7. [33] Cornell CA. Engineering seismic risk analysis. B Seismol Soc Am 1968;58(11 Suppl 1):S183–8.
Acknowledgement The authors acknowledge the financial support from National Natural Science Foundation of China (Grant No. 51978166). References [1] Ramesh T, Prakash R, Shukla KK. Life cycle energy analysis of buildings: An overview. Energ Build 2010;42(10):1592–600. [2] Kim MH, Park JY, Sung MK, Choi AS, Jeong JW. Annual operating energy savings of liquid desiccant and evaporative-cooling-assisted 100% outdoor air system. Energ Build 2014;76(11):538–50. [3] Embaye M, Al-Dadah RK, Mahmoud S. Numerical evaluation of indoor thermal comfort and energy saving by operating the heating panel radiator at different flow strategies. Energ Build 2016;121:298–308. [4] Yu RQ, Zhang DD, Yan HC. Embodied energy and cost optimization of RC beam under blast load. Math Probl Eng 2017;2017:1–8. [5] Fraile-Garcia E, Ferreiro-Cabello J, Martinez-Camara E, Jimenez-Macias E. Repercussion the use phase in the life cycle assessment of structures in residential buildings using one-way slabs. J Clean Prod 2017;143:191–9. [6] Ferreiro-Cabello J, Fraile-Garcia E, Martinez-Camara E, Perez-de-la-Parte M. Sensitivity analysis of Life Cycle Assessment to select reinforced concrete structures with one-way slabs. Eng Struct 2017;132(FEB.1):586–96. [7] Ferreiro-Cabello J, Fraile-Garcia E, Martinez DPAE, Martinez DPAFJ. Minimizing greenhouse gas emissions and costs for structures with flat slabs. J Clean Prod 2016;137(nov.20):922–30. [8] Padgett JE, Tapia C. Sustainability of natural hazard risk mitigation: life cycle analysis of environmental indicators for bridge infrastructure. J Infrastruct Syst 2013;19(4):395–408. [9] Gencturk B, Hossain K, Lahourpour S. Life cycle sustainability assessment of RC buildings in seismic regions. Eng Struct 2016;110:347–62. [10] Shi JJ, Sun W. Recent research on steel corrosion in concrete. J Chin Ceram Soc 2010;38(9):1753–64. [11] Treloar GJ. The environmental impact of construction–a case study. Sydney: Australia and New Zealand Architectural Science Association; 1996. [12] Treloar GJ, McCoubrie A, Love PED, lyer-Raniga U. Embodied energy analysis of fixtures, fittings and furniture in office buildings. Facilities 1999;17(11):403–10. [13] Zhao J, Sritharan S. Modeling of strain penetration effects in fiber-based analysis of reinforced concrete structures. ACI Struct J 2007;104(2):133. [14] Li CQ. Reliability based service life prediction of corrosion affected concrete
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Structures journal homepage: www.elsevier.com/locate/structures
Life cycle embodied energy analysis of RC structures considering chlorideinduced corrosion in seismic regions
T
⁎
Runqing Yua, Li Chenb, , Diandian Zhanga, Zhenhui Wanga a b
PLA Air Force Second Service Group of Engineering and Technology, Guangzhou 510403, China Engineering Research Center of Safety and Protection of Explosion & Impact of Ministry of Education, Southeast University, Nanjing 211189, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Life cycle analysis Embodied energy RC structures Chloride-induced corrosion Seismic fragility
Reinforced concrete (RC) structures consume large amounts of energy supply and cause continuing pollution. During the life cycle of RC structures, operating and embodied energy are significant contributors to the whole energy demand. The embodied energy is smaller than the operating energy but its proportion in the total lifecycle energy is increasing. Present study presented a life cycle embodied energy assessment (LCEEA) framework for a typical RC structures in seismic regions. First, numerical model to calculate the seismic response of corroded RC structures was established and verified. It shows that the numerical model together with zero-length section element and the suitable material model could predict the seismic responses of RC columns well. Then, seismic fragility was calculated using probabilistic seismic demand model. The embodied energy consumed in repair were calculated in detail for different damage levels. Finally, the life cycle embodied energy was obtained. Influences of chloride-induced corrosion on the life-cycle embodied energy (LCEE) were analyzed. The proposed assessment frame and calculated results show that the chloride-induced corrosion increase the life cycle embodied energy obviously, especially for the strong earthquake. Furthermore, increase in the embodied energy due to the corrosion was larger if the facilities were considered.
1. Introduction World widely, RC structures consume large amounts of energy and causing pollution. Reducing the energy consumed by RC structures is very meaningful in environmental protection, but firstly the energy should be well calculated. The consumed energy mainly includes operating and embodied energy, of which operating energy accounts for 80–90% and embodied energy accounts for 10–20% [1]. Because operating energy is larger than embodied energy, previous studies and practices mainly forced on the reduction of operating energy. For example, Kim et al. [2] employed liquid desiccant in cooling system. Through energy simulation and analysis, they found that 51% operating energy was saved compared with the conventional variable air volume system. Embaye et al. [3] simulated the panel radiators and rooms with pulsed flow and constant conditions. Results shows that the using flow pulsation for radiator increase the heat output by 25%, which saved the operating energy. Reducing of operating energy leads to the increasing proportion of embodied energy in turn. Calculation of embodied energy becomes even more necessary. The embodied energy includes two parts: the initial embodied energy consumed in the initial construction and installations, the
⁎
recurring embodied energy consumed in the maintenance and repair [1]. The initial embodied energy was calculated directly according to the initial design and usually reduced by optimizing the initial design [4]. The recurring embodied energy is consumed in the whole life cycle, which indicates the life cycle assessment (LCA) of embodied energy is necessary [5]. The LCA tools have been successfully applied in the environmental design and provided many useful suggestion on reducing the environmental impacts [6] and costs [7]. Similarly, LCA of embodied energy is meaningful. Life cycle embodied energy assessment (LCEEA) is relatively difficult to be calculated because the recurring embodied energy consuming by repair strategies were affected by the natural hazards. Although the calculation of recurring embodied energy is a little complicated, some useful researches have been conducted. Padgett and Tapia [8] firstly explored the role that the natural hazard plays in affecting long-term sustainability in detail. Their study shows the aging and deterioration have a big influence on the life cycle embodied energy. However, their research object was bridge infrastructure, which was quite different from RC buildings. Gencturk et al. [9] developed a life-cycle environmental impact assessment framework for RC buildings. The seismic hazard was considered but the deterioration was ignored.
Corresponding author. E-mail address: [email protected] (L. Chen).
https://doi.org/10.1016/j.istruc.2020.03.049 Received 8 July 2019; Received in revised form 24 March 2020; Accepted 24 March 2020 2352-0124/ © 2020 Published by Elsevier Ltd on behalf of Institution of Structural Engineers.
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Fig. 1. Flowchart of the proposed LCEEA framework.
This study presented a framework to calculate the life-cycle embodied energy of corroded RC structures. First, the calculated framework was presented in detail. Then, a typical corroded RC structures was used to describe the calculated framework step by step. The influences of deterioration on the life-cycle embodied energy were discussed at last.
Fig. 2. Illustration of calculation of.ERIM .
DS; pi (IM ) is the probability density of IM in the ith year; pi (∙ ∙) is the conditional probability. If four damage states are defined, as shown in Fig. 2, then the first part of Eq. (5), ∫ ERDS dDS , could be estimated by
2. Life cycle embodied energy assessment framework
∫ ERDS dDS ≈
RC structures inevitably suffer deterioration in their life cycle. The deterioration could be caused by many factors, such as chloride ion, carbonation, freeze–thaw action, stray current. Among those factors, the chloride ion induced corrosion plays a major role, especially in the offshore area [10]. Therefore, present study only considered the chloride ion induced corrosion. The proposed life cycle embodied energy assessment (LCEEA) framework is shown in Fig. 1. The embodied energy mainly consists of the initial embodied energy and the recurring embodied energy [1], given by Eq. (1).
EE = EI + ER
∑ mi Mi + Ec
[P (θmax ≥ θmax 2) − P (θmax (θmax ≥ θmax 3)
(1)
(2)
3. Numerical modeling of corroded RC structures The chloride ion induced corrosion affects the mechanics behavior of RC structures by reducing the cross section of steel, the material strength and the bond-slip strength between reinforcement and concrete. Mechanics behavior of corroded RC structures could be well simulated using Opensees software. The cross section of steel is simulated by reducing the cross section area. The material strength of steel and concrete are simulated using the corroded material model. The bondslip strength between reinforcement and concrete is simulated using the zero-length section elements together with Bond_SP01 model proposed by Zhao and Sritharan [13].
N
∑i =1 ERi
(3)
where N is the service life of buildings; ERi is the average annual recurring embodied energy. ERi is influenced by the seismic fragility and the repair strategies, calculated by
ERi =
∫ ERDS dDS∙ ∫ pi (DS EDP ) ∙pi (EDP IM ) dim
(5)
where θmax is the maximum drift angle of story; P (∙) is the probability of exceedance. In the life cycle of common RC buildings, the embodied energy contained in facilities was quite large, about 12.5 percent of the initial embodied energy of building [11]. However, facilities were replaced regularly under normal circumstances. The life span of facilities was about five to seven years [12]. This means that the embodied energy contained in facilities per year is approximately 2.5 percent of the initial embodied energy, which is quite small compared with the embodied energy consumed in repair. Therefore, embodied energy contained in facility was ignored in this condition. However, for some special buildings which contain large facilities, the embodied energy should not be ignored.
where mi is the quantity of materials; Mi is the energy content of material per unit quantity; Ec is the energy consumed in construction of structures. The recurring embodied energy is influenced by the maintenance strategies, the seismic fragility and the repair strategies. The maintenance practices are not always applied, especially for small buildings. Therefore, the maintenance practices are not considered in present study. The recurring embodied energy consumed by the repair and rebuild practices after earthquake is calculated by Eqs. (3) and (4).
ER =
ER2 + ER3 2 ER3 + ER 4 ≥ θmax 3)] + P 2
[P (θmax ≥ θmax1) − P (θmax ≥ θmax 2)] +
where EE is the embodied energy; EI is the initial embodied energy; ER is the recurring embodied energy. The initial embodied energy is dependent on the initial design, therefore it is time-independent. EI is calculated by Eq. (2) according to Ramesh et al. [1].
EI =
ER1 ER1 + ER2 [1 − P (θmax ≥ θmax1)] + 2 2
(4)
3.1. Reduction of reinforcement cross section
where DS is the damage states, e.g. maximum drift angle in present study; IM is the ground motion intensity measure, e.g. peak ground acceleration in present study; ERDS is the ER corresponds to different
The loss rate of reinforcement cross section is equal to the loss rate of mass if uniform corrosion was considered. Therefore, 840
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reinforcement enhanced strain; εsyc is the corroded reinforcement yield strain; ηs,cr is critical point of ηs (t ) . When ηs (t ) > ηs,cr , the enhanced strain will be coincide to the yield strain. Present study took ηs (t ) = 20%.
f ytc =
1 − 1.049ηs (t ) f y0 1 − ηs (t )
(11)
futc and εsuc are the ultimate strength and the ultimate strain respectively, calculated by Eqs.(12) and (13). fuc =
1 − 1.119ηs (t ) fu0 1 − ηs (t )
(12)
εsuc = e−2.501ηs (t ) εsu0
where εsu0 is the uncorroded reinforcement ultimate strain; fu0 is the uncorroded reinforcement ultimate strength.
Fig. 3. Tensile strength of corroded and uncorroded reinforcement.
3.3. Reduction of concrete compressive strength
2
d − x corr ⎞ ηs (t ) = 1 − ⎛ 0 d0 ⎠ ⎝ ⎜
x corr =
∫0
t
⎟
(6)
λ (t ) dt
According to Coronelli and Gambarova [16], the time-varying compressive strength of corroded cover concrete is taken as
(7)
fccc =
where ηs (t ) is the loss rate of reinforcement cross section; d 0 is the original diameter; λ (t ) is the annual corrosion rate, calculated by Eq. (8) [14].
λ (t ) = 0.0115(0.3683ln(t ) + 1.1305)(mm a)
(8)
(9)
where εshc is enhanced strain, calculated by Eq. (10).
(
)
⎧ fytc + εsh0 − fy0 ⎛1 − ηs (t ) ⎞ (η (t ) ≤ η ) s s,cr ⎪ Es0 Es 0 ηs,cr ⎝ ⎠ = f ytc ⎨ εsyc = E (ηs (t ) > ηs,cr ) ⎪ s0 ⎩
(14)
ε1 = 2πnbars (vrs − 1) x cp b0
(15)
d0 [1 − 2
1 − ηs (t ) ]
(16)
where fcc0 is the compressive strength of uncorroded concrete; εcc0 is the strain at fcc0 ; nbars is the number of reinforcements in the compressive zone; vrs is a coefficient and vrs = 2 ; d 0 is the diameter of reinforcements; b0 is the width of cross section. The compressive strength of corroded core concrete and corroded cover strength are shown in Fig. 4. For cover concrete, the main reason of strength decrease is the corrosion of concrete. For core concrete, the core concrete strength decreased because of the weakening of hoop effect [17]. The hoop effects were calculated according to Mander et al. [18]
The tensile strength of corroded reinforcement are shown in Fig. 3. Tensile strength is calculated by Eq.(9) according to Zhang et al. [15].
Es0 εsc (εsc ≤ f yc Es0) ⎧ ⎪ f ytc (f ytc Es0 < εsc ≤ εshc ) fs = ⎨ εsc − εshc f (f − f ytc )(εsc > εshc ) + ⎪ ytc εsuc − εshc utc ⎩
fcc 0 1 + 0.1ε1 εcc 0
x cp =
3.2. Reduction of reinforcement strength
εshc
(13)
3.4. Bond stress-slip relationship The bond stress-slip relationship for plain reinforcing bars proposed by CEB [19] was adopted, shown by Eq. (17).
(10)
where f y0 is the uncorroded reinforcement yield strength; f ytc is the corroded reinforcement yield strength, calculated by Eq. (11); Es0 is the uncorroded reinforcement elastic modulus; εsh0 is the uncorroded
τ (s s1 )α s ≤ s1 τ=⎧ u ⎨ ⎩ τu s ≤ s1
(a)
(17)
(b)
Fig. 4. Compressive strength of (a) Corroded core concrete and (b) Corroded cover strength. 841
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Fig. 5. (a) Test specimen and (b) Regions to measure the amounts of corrosion (c) Simulated model.
where s is slip; τ is bond stress. According to the study of Melo et al. [20], s1 and α were taken as 0.1 mm and 0.5, respectively. For corroded hot rolled bars, τu was taken as 0.3 fccc .
Table 2 Uncorroded material properties.
Reinforcement Stirrup Concrete
3.5. Simulated model and verification Tests conducted by Yang et al. [21] are used to validate the numerical model. Details for specimen are shown in Fig. 5 (a). In order to measure the amounts of corrosion, the test specimens are divided into four regions. Rebar and stirrups of each regions were taken out of the tested specimens and measure the practical average mass amounts of corrosion. The four regions are shown in Fig. 5(b). The mass amounts of corrosion are listed in Table 1. Material properties are listed in Table 2. RC columns are simulated using Opensees software. The integral model are shown in Fig. 5(c). The concrete and steel are simulated using the model listed in Section 3.1 ~ 3.5. Hysteretic material model and Concrete 1 were adopted to model the steel and concrete respectively. Force-Based Beam-Column Element were used to simulate RC columns. The zero-length section elements together with Bond_SP01 model were incorporated in the structural model to simulate the slip between concrete and steel bars [13]. Simulated results are listed in Fig. 6. The simulated results agree well with the test data for both specimens A and B, which shows that the numerical model could predict the response of RC column well. The maximum horizontal load of specimen B is smaller than that of specimen A. This is because the specimen B suffer more serious corrosion than specimen A.
Yield strength
Ultimate tensile/compressive strength
372 MPa 607.4 MPa
573 MPa 727.5 MPa 46.4 MPa
structures, a typical RC structure suffers from corrosion was studied. Overall dimensions of RC frame are shown in Fig. 7. The cross section of beam and column are shown in Fig. 8. The used materials are C40 for concrete, HRB335 for longitudinal bars and HPB235 for stirrups. Detail descriptions of the RC structure are shown in Table 3.
4.1. Method to calculate seismic fragility Present study used the probabilistic seismic demand model (PSDM) to calculate the seismic fragility. The PSDM could be conducted using stripe-method or cloud-method [22]. The strip-method, which was termed as incremental dynamic analysis (IDA), was more accurate on the calculation of fragility curves [23]. Therefore, present study chose the strip-method to obtain the relations between IM and EDP. The calculation process is described in Fig. 9. According to Liu and Hwang [24], the engineering demand parameter (EDP) could be calculated by
EDP = α (IM ) β
(18)
where α and β are coefficients to be determined. Therefore, the failure probability is given by
4. Time-dependent seismic fragility of corroded RC structure In order to calculate the life cycle embodied energy of corroded RC
] ⎤ ⎡ ln [EDP C ⎡ ln [α (PGA) β θ ]̂ ⎤ Pf = Φ ⎢ ⎥ = Φ⎢ ⎥ 2 2 βc + βd ⎥ βc2 + βd2 ⎢ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦
Table 1 Amounts of corrosion. Rebar
Stirrup
Region
1
2
3
4
1
2
3
Specimen A Specimen B
0.9% 3.3%
13.25% 16.8%
3.74% 4.5%
2.9% 2.6%
1.9% 7.7%
7.74% 9.0%
1.9% 3.2%
(19)
where Pf is the cumulative failure probability; θ ̂ is the mean value of damage quantification; βc and βd are the dispersion of engineering capacity and engineering response, respectively. βc is determined from data of the ground motion and βd is determined from the data of IDA curves.
4
842
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Fig. 6. Comparison of test data and simulated results (a) Specimen A (b) Specimen B.
Fig. 7. Overall dimensions of RC frame (a) Plane (b) 1–1 profile.
4.2. Statistical variations of parameters For corroded RC structures, uncertainties existed in material characteristics, structural dimensions, corrosion initiation time and ground motion records. Uncertainties in material characteristics and structural dimensions have little effect on the seismic damage of RC structures [25]. Therefore, only uncertainties in corrosion initiation time and ground motion records were considered in present study. Uncertainties in ground motion records referred to the varieties of ground motion records that may occur in a certain region. A set of 20 records are selected from Next Generation Attenuation -West2 database
Fig. 8. Cross section of beam and column.
Table 3 Detail descriptions of RC frame. Floor No.
Reinforcement of beams 300 mm × 500 mm Top side
1 2 3 4 5
2Φ20 2Φ20 2Φ16 2Φ20 2Φ18
+ + + + +
4Φ20 4Φ20 4Φ20 2Φ22 2Φ20
Reinforcement of columns 450 mm × 450 mm
Bottom side
Stirrup
Stirrup
Outside column
Inner column
4Φ18 4Φ18 4Φ18 4Φ18 4Φ18
Φ8@200
Φ8@150
12Φ16
12Φ16
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Fig. 11. Distribution of ground motion intensity.
erf (θ) =
2 π
∫0
θ
2
e−t dt
(21)
The corrosion initial time is uncertain because parameters in Eqs. (20) and (21) are uncertain. In present study, the variables distribution characteristics are listed in Table 4. Those distribution characteristics are recommended by Ghosh and Padgett [27] and Yu et al. [28] in their studies. The corrosion initiation time is simulated for 1000 times using Monte Carlo method. Calculated results are shown in Fig. 12. The goodness of fit is 0.9795. This means that the initiation time is fitted well using Power law distribution. The mean initiation time is 3.52 year.
Fig. 9. Calculation of fragility curves.
4.3. Damage level state and the consumed embodied energy Present study use θmax to define the damage states, shown in Table 5. The damage quantification and the damage description are determined according to FEMA 356 [29], GB50011-2010 [30] and the building grading standards of earthquake damage [31]. The secondary structural members are not considered in present study, but the damage descriptions are still presented in the table as references for determining the percentage of member damage. Embodied energy coefficients are listed in Table 6. The embodied energy contained in unit materials and the embodied energy consumed by large equipment are adopted from Padgett and Tapia [8]. The embodied energy consumed by human is adopted from Jiao et al. [32]. When earthquake occurred, the reliability of RC structures would suddenly decrease. Then, some repair measures were needed in order to recovery the building function. The embodied energy consumed in repair after earthquake was determined by the post-earthquake structural states. The damage states and corresponding repair activities of RC columns are listed in Table 7. The heavy damage is considered as the concrete crush and steel yielding in the zones of plastic hinges. The moderate damage is considered as the crush of cover and core concrete. The superficial damage is considered as the occurrence of cracks which does not affect the functions of RC members. The damage states and repair activities of RC beams are listed in
Fig. 10. Selected ground motion records.
[26], as shown in Fig. 10. The magnitude and distance of those records are shown in Fig. 11. Those records covers a range of distance-to-ruptured area between 10 km and 100 km and the magnitudes is set to 5.5–8.0. The corrosion initiation time is important to calculate the decrease of material strength and area of cross section. According to Ghosh and Padgett [27], the corrosion initiation time is taken as −2
Tcorr =
C 2 ⎡ −1 ⎛ C0 − Ccr ⎞ ⎤ erf 4Dc ⎢ ⎝ C0 ⎠ ⎥ ⎦ ⎣ ⎜
Table 4 Variables distribution characteristics.
⎟
(20)
where C is the concrete cover thickness (cm); Dc is the chloride diffusion coefficient (cm2/year); Tcorr is the corrosion initiation time; C0 is equilibrium chloride concentration at the concrete surface; Ccr is critical chloride concentration; erf is Gaussian error function, represented as 844
Variables
Mean
Cov.
Distribution
C0 (%) Dc (cm2/year) Ccr (%) C (cm)
0.10 1.29 0.040 2
0.100 0.100 0.100 0.200
Lognormal Lognormal Lognormal Normal
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Table 6 Consumed embodied Energy. Material
Embodied energy
Epoxy Concrete Grout Steel Concrete pump Hydraulic jacking system Dump truck Human
1404 MJ/m3 2762 MJ/m3 3496 MJ/m3 245757 MJ/m3 2770 MJ/day 1704 MJ/day 17559 MJ/day 320.1 MJ/Person-day
damage quantifications. Those figures were used to calculate the probabilities of different damage levels. For example, the probabilities of different damage levels under PGA = 0.5g are obtained using Fig. 16(a) ~ 16(c), shown in Fig. 17. It obviously shows that hazardous failure (D4) becomes dominant with the increase of year. Fig. 12. Calculation of corrosion initiation time.
5. Exceedance probability of life cycle embodied energy Table 8. The superficial damage is considered as the crush of cover concrete. The moderate damage is considered as the crush of cover concrete and core concrete. The heavy damage is considered as the concrete crush and steel yielding. Damage of RC beams was considered more severe than that of columns because strong columns and weak beams were required according to the principles of earthquake resistant design GB50011-2010 [30]. Using the Tables 5–8, the consumed embodied energy under different damage states are calculated, shown in Fig. 13. The consumed energy under state D1 is little because most of structural members have no damage under D1 state. A large difference of consumed energy exists between D1 and D2. This is because the repair strategy of D2 is conservative. Under state D2, many structural members have surface cracks. The crack will be dangerous if it is deep enough. However, it is hard to estimate the depth of crack. Therefore, the common acceptable repair method in engineering practice is epoxy injection to all open cracks. This will increase the consumed energy of state D2 significantly. The different between D2 and D3 is also very large. This is because structures suffer more serious damage under state D3, which need more embodied energy to repair.
The exceedance probability is more convenient to assess the consumed energy. In order to calculate the exceedance probability, seismic hazard should be presented. Seismic hazard analysis is to predict the probability of different seismic intensities occurring in a certain area. The distribution of PGA is extreme-II distribution according to Cornell [33], described as
FPGA (PGA) = 1 − P (IM ) = e−(u
(23)
where k is a coefficient reflecting the seismic hazard in different regions, u is the mode of PGA. The occurrence in 50 years was assumed as δ , then
k lgu = k lgPGA0 + lg(−ln(1 − δ ))
(24)
where PGA0 is the design value of PGA. Therefore,
P50 (IM ) = 1 − e ln(1 − δ )(PGA0
pga)k
(25)
where P (PGA ≥ pga) is the probability of exceedance (POE) of IM in 50 years. Combining the seismic fragility curves and the seismic hazard analyses, exceedance probability life cycle embodied energy was calculated. As shown in Fig. 18, the value of embodied energy increases if corrosion is considered. For example, the value of embodied energy increases by about 8% (from 7.26 to 7.67) when considering corrosion for an exceedance probability of 0.41. This is because corroded RC structures are more vulnerable to damage. However, the increase is slight, this is because the consumed embodied energy of different state is not very large. If there are facilities contained many embodied energy in the building, the increase will be more significant. For example, we assume facilities contains embodied energy ES = 3 × 1012J . Under damage state D1, D2, D3 and D4, we assumed the corresponding embodied energy consumed in the repair of facilities are 0.05ES , 0.5ES , 0.75ES and ES . The assumed value is meaningful because we assume the facilities are a little damaged under D1 but totally damaged under D4. Then, the
4.4. Seismic fragility and discussion Using the simulation model, incremental dynamic analyses (IDA) were conducted. For the erosional structure in a certain year, twenty simulations were performed. Each simulation has a random corrosion initial time. Fig. 14 shows the IDA curves for the structure in the 5th year. The relations between θmax and peak ground acceleration (PGA) were obtained by curve fitting, shown as Eq. (22). Then, fragility curves were obtained using Eqs. (19) and (22). As shown in Fig. 15, the uncertainty of corrosion initial time (CIT) has a slight influence on the fragility curves. (22)
lnθmax = 0.76001 + 0.81036lnPGA
PGA)k
Fig. 16(a) ~ 16(c) show the seismic fragility curves for different Table 5 Definition of damage states. Damage state
Superficial damage(D1) Moderate damage(D2) Heavy damage(D3) Hazardous failure(D4)
Damage quantification θmax
≤ 1 100 1 50 ∼ 1 100 1 25 ∼ 1 50 >1 25
Damage description Primary member
Secondary member
90% 75% 75% 75%
75% no damage, 25% superficial damage 75% moderate damage, 25% heavy damage 75% heavy damage, 25% moderate damage 100% heavy damage
no damage, 10% superficial damage superficial damage, 25% moderate damage moderate damage, 25% heavy damage heavy damage, 25% moderate damage
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Table 7 Repair activities for RC columns. Damage level
Action
Superficial damage Moderate damage Heavy damage
Epoxy injection to open cracks Removal and replacement of damaged cover and core concrete Concrete removal and placement Replacement of longitudinal rebar Replacement of transverse rebar
Unit
Large equipment used
2
m m3
Concrete pump; Hydraulic jacking system; Dump trucks.
m3 ton
Repair time (man-hour/unit) 0.6 4.3 4.3 13.9 21.3
Table 8 Repair activities for RC beams. Damage level
Action
Superficial damage Moderate damage Heavy damage
Removal and replacement of damaged cover concrete Removal and replacement of damaged cover and core concrete Concrete removal and placement Replacement of longitudinal rebar Replacement of transverse rebar
Unit
Large equipment used
3
m m3 m3 ton
Concrete pump; Hydraulic jacking system; Dump trucks.
Repair time (man-hour/unit) 0.6 4.3 4.3 11.9 20.0
Fig. 15. Fragility curves of RC frame (5 years).
Fig. 13. Embodied energy consumed in repair actions.
simulated models were built to study the response of corroded RC structures. Special attentions were paid to the repair actions after earthquake. Influences of corrosion and facilities on the embodied energy were discussed at last. Numerical models to simulate the corroded RC structures were proposed. The numerical model considers the reduction of steel cross section, the reduction of material strength and the slip between concrete and steel. Simulated results were verified by comparing with the experimental data. It shows that the proposed numerical model simulates the seismic response of RC structures well. For a typical RC structure, the fragility curves were obtained using probabilistic seismic demand model. Calculated results showes that the failure probability obviously decreases with the increases of years. The influence of corrosion initial time (CIT) on the fragility curves were analyzed. Results shows that uncertainty of CIT of reinforcement has a slight influence on the fragility curves. This indicates that the uncertainty of CIT could be ignored for the rapid fragility estimation in the engineering. The embodied energy consumed in repair increases dramatically as the seismic damage worsens. For the RC structure studied in present study, values of embodied energy increases from 3 GJ to 2526 GJ as the damage state worsens from D1 to D4. Therefore, the embodied energy consumed in repair should be calculated in life cycle embodied energy assessment, especially for severe damage. Value of embodied energy increases by about 8% if corrosion is considered. If the embodied energy of facilities is calculated, the
Fig. 14. IDA curves of RC frame (5 years).
exceedance probability of embodied energy are shown in Fig. 18 (dotted lines). The value of embodied energy increases by about 12% (from 8.25 to 9.23) when considering corrosion. 6. Conclusions Present study presents a framework to calculate the life cycle embodied energy considering corrosion and seismic hazards. Detailed 846
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Fig. 16. Fragility curves for different damage quantifications (a) θmax = 1 100 (b) θmax = 1 50 (c)θmax = 1 25.
Fig. 18. Exceedance probability curves for embodied energy.
increase value becomes 12%. This means that it is better to consider the influence of corrosion during the life cycle sustainability assessment. Fig. 17. Probability of different damage levels (PGA = 0.5g ).
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to 847
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influence the work reported in this paper.
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