Time-dependent seismic performance assessment of a single-degree-of-freedom frame subject to corrosion

Engineering Failure Analysis 19 (2012) 109–122

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Time-dependent seismic performance assessment of a single-degree-of-freedom frame subject to corrosion Hakan Yalciner ⇑, Serhan Sensoy, Ozgur Eren Department of Civil Engineering, Eastern Mediterranean University, Famagusta T.R., North Cyprus via Mersin 10, Turkey

a r t i c l e

i n f o

Article history: Received 3 January 2011 Accepted 28 September 2011 Available online 5 October 2011 Keywords: Corrosion Deterioration Seismic analyses Building failures

a b s t r a c t Corrosion of reinforcement bars in concrete is directly responsible for serious damage to concrete structures, which may result in premature failure of the structures as a function of time. Therefore, it is necessary to evaluate its damage on the structural performance level. Many models have been developed to predict the corrosion rate of steel in concrete and its effects on structures. It is also possible to evaluate and identify the seismic performance level of reinforced concrete (RC) structures. This study contributes to an understanding of the relationship between these two topics as a function of time to predict the performance level of corroded RC buildings. Three combined parameters (loss of the cross sectional area of reinforcement bars, reduction of the concrete strength, and additional displacement due to slip) as a consequence of corrosion effects were calculated as a function of the corrosion rate for five different time periods (i.e., non-corroded (t: 0), 25, 50, 75, and 100 years). Obtained results were used to perform nonlinear time-history analyses for 20 ground motion records. The results showed that the effect of the corrosion of steel on the seismic performance level is highly significant, and it should be considered carefully in performance analysis. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction A structure that is originally designed to meet code specifications may not have the same margin of safety once the structure has undergone significant corrosion [1]. Corrosion of the reinforcement bars of RC structures may cause serious problems within the economical life of the structure under the action of earthquake excitation or even service loads. Therefore, for both economical and safety issues, time-dependent corrosion models are needed to prevent serious damage to RC structures. For this purpose, in recent years, many studies have been performed to predict the service life of RC structures subject to corrosion. One of the well known studies was done by Bazˇant [2], and then Tuutti [3], Morinaga [4], Andrade et al. [5], Liu and Weyers [6], Pantazopoulou and Papoulia [7], and Li [8] followed this trend. These studies established the foundation of further models that can be linked to the assessment of the performance level of corroded RC structures as a function of time. In the literature, it is possible to find studies that state that ‘‘corrosion affects the structural performance’’ (e.g., [3,9–14]), but none of these studies include an analytically drawn framework for identifying the performance level of RC structures subject to corrosion, especially as a function of time, to define the reduction in the performance level (i.e., immediate occupancy (IO), life safety (LS) and collapse prevention (CP)) by using incremental dynamic analyses (IDA). Moreover, the corrosion models developed to predict corrosion rate (e.g., [4,15,16]), crack width (e.g., [5,7,17,18]), and bond– slip relationship (e.g., [19–22]) are generally studied separately from each other by many authors. These models, which were

⇑ Corresponding author. Tel.: +90 392630 1497; fax: +90 392630 2869. E-mail addresses: [email protected] (H. Yalciner), [email protected] (S. Sensoy), [email protected] (O. Eren). 1350-6307/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfailanal.2011.09.010

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separately studied and developed, can be used in structural analyses with modifications to achieve more accurate results for corroded RC structures. It is believed that performance assessment and effects of corrosion must be integrated with each other, especially as a function of time. In this study, in contrast to previous studies, three combined effects of corrosion (the loss of the cross sectional area of the reinforcement bars, the reduction of the concrete compressive strength and the bond–slip relationship) were used in nonlinear analyses to predict the time-dependent performance level of corroded single-degree-of-freedom (SDOF) systems as a function of the corrosion rate. 2. Structural deterioration due to corrosion Once corrosion occurs (break down of the passive film) in structural members, the performance level of structures decreases with time due to different effects. These effects could be a reduction in the cross sectional area of the reinforcement bars, internal cracks in structural members, reduction in the concrete strength, additional lateral displacement due to slipping and cracking of the concrete cover due to the expansion of corrosion products. Reinforcements subjected to corrosion attack suffer a loss of strength and loss of ductility; thus, the original strength of the reinforcement cannot be used for predicting the strength of deteriorated steel reinforcement [23]. The storage energy capacity of a section decreases by losing the ductility of reinforcement bars with reduced energy dissipation through inelastic behaviour. Corrosion also causes a buckling problem for structures, where a reinforcement bar might buckle before reaching its yield capacity and thus the load-carrying capacity of the damaged structure is reduced. As a consequence of volumetric expansion, the concrete strength decreases as a function of crack width, where the loss of ductility of the columns is inevitable under seismic loading. An experimental study was done by Coronelli and Gambarova [24] to investigate the ultimate bond strength and the reduced concrete strength of corroded reinforcement bars with different depths of corrosion attacks. In that study, the reduction of concrete strength varied from 38% to 45% due to corrosion. Fig. 1a and b shows two examples of corroded RC structures exposed to salt attack with varying distances from the seaside (150 and 50 m) in Cyprus. As shown in Fig. 1, a serious strength degradation occurred due to the volume expansion of corrosion rust. The degradation causes a reduction in the overall stiffness and ductility of the structural system and thus may increase the natural periods of the system. In addition to the loss of concrete cover, an RC member can be damaged due to the loss of bonding between steel and concrete. At the macro level, the dimensional loss of lugs of ribbed bars due to corrosion

Fig. 1. Strength degradation due to corrosion: (a) An old constructed RC building in Palm beach, 1983, (b) Apostolo andreas monastery in Karpaz, 1985.

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directly affects the adhesion between the reinforcement and concrete. The degradation of bond–slip relationships causes increases in the global drift ratio of RC structures. A study done by Sezen and Moehle [25] to predict the anchorage slip of reinforcement bars indicated that slip deformations, even for non-corroded reinforcement bars, contribute 25–40% of the total lateral displacement. Therefore, in this study, slip deformation as a consequence of corrosion was also considered to be a matter of serious academic interest to predict the time-dependent performance level of RC buildings. 3. Nonlinear material modelling In this study, the moment–curvature relationships of the RC SDOF model considered were used to predict inelastic behaviour of the model. Moment–curvature relationships predict the behaviour of the sections, and here they predicted the behaviour of a section at any load as a function of the corrosion rate. The actual material behaviour is nonlinear; thus, moment–curvature relationships help to determine the load–deformation behaviour of concrete sections accurately by using nonlinear material stress–strain relationships. Many studies have been done to model the stress–strain relationships of confined and unconfined concrete (e.g., Hognestad [26], Kent and Park [27], Mander et al. [28], Saatcioglu and Razvi [29]). In this study, the analysis of confined corroded column of the SDOF model was performed by using two different models developed by Kent and Park [27], and Saatcioglu and Razvi [29]. Then for each case (non-corroded, 25,50,75 and 100 years), those that gave higher demands (lower elastic and inelastic stiffness and lower yield strength) were selected to be used in IDA of 20 different earthquake ground motion records. In addition to concrete, the stress–strain relationship of steel must also be modelled. Different models have been developed to define the stress–strain relationship of steel. For instance, for hot rolled steel, Kent and Park [30] and Thompson and Park [31] proposed different models. For cold work steel, Kato [32], Petersson and Popov [33] and Stanton and McNiven [34] investigated other models. In this study, Mander’s [35] model was used to model the stress–strain relationship of steel, which can be used either for both hot rolled steel and cold work steel. The steel and concrete classes selected were S420 (420 MPa) and C20 (20 MPa), respectively. The elastic modulus of concrete pffiffiffiffi (Ec ¼ 3250 fc0 þ 14000 MPa) was calculated according to TS 500 [36]. The mechanical properties of steel in the analyses were selected according to TS 500 [36], where the minimum rupture strength (fsu) was equal to 500 MPa, the yield strain (ey) was equal to 0.0021, the strain hardening (esh) was equal to 0.008, the minimum rupture extension (esu) was equal to 0.12% and the elastic modulus of steel (Es) was taken as 200,000 MPa. 4. Time-dependent corrosion model 4.1. Modifications to the model of Vecchio and Collins [38] In this study, a modification to the corrosion model is suggested to predict the reduced concrete strength as a function of the corrosion rate. Once the corrosion rate is either known or predicted, the reduction in the concrete strength can be calculated. Any available empirical models (e.g., [4,37]) to predict the corrosion rate (icorr) can be used with the new methodology proposed in this study. A model developed by Vecchio and Collins [38] was used to predict the reduced concrete strength based on the total crack width. According to Vecchio and Collins [38], the reduced concrete strength can be calculated by the following equation:

fc ¼

fc0 1 þ K e1 =eco

ð1Þ

where fc is the reduced concrete strength, fc0 is the concrete compressive strength, K is the coefficient related to the bar roughness and diameter (for medium-diameter ribbed bars, a value of K = 0.1 was proposed by Cape [39]), eco is the strain at the peak compressive stress and e1 is the average tensile strain in the cracked concrete at right angles to the direction of the applied compression. In Eq. (1), e1 can be calculated by the following equation:

e1 ¼

bf  b0 b0

ð2Þ

where bf is the width increased by corrosion cracking, b0 is the section width in the virgin state, and the approximation of the increased width can be calculated by the following equation:

bf  b0 ¼ nbars wcr

ð3Þ

where nbars is the number of bars in the top layer (compressed bars), and wcr is the total crack width for a given corrosion level. The study done by Coronelli and Gambarova [24] used the crack width model of Molina et al. [40] in the model developed by Vecchio and Collins [38] to calculate the reduced concrete strength. Molina et al. [40] assumed the volumetric expansion of the oxides with respect to the virgin material, which was equal to two. Therefore, the diameter of each bar was assumed to increase at twice the depth of the corrosion attack. The volumetric expansion due to the corrosion depends on the thickness of the corrosion product as a function of the corrosion rate. Moreover, the types of corrosion rust products, such as ferrous and ferric hydroxide (Fe(OH)2 and Fe(OH)3), are effective parameters to calculate the rate of volumetric expansion. Thus, the volumetric expansion varies as a function of the corrosion rate and the type of corrosion products

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for different time periods. Therefore, the model suggested by Coronelli and Gambarova [24] cannot be used for time-dependent analyses due to the assumption of volumetric expansion by Molina et al. [40]. In this study, the model proposed by Li et al. [41] was used in order to predict the crack width as a function of the corrosion rate. The model developed by Li et al. [41] can calculate volumetric expansion as a function of the corrosion rate by taking into account the exact rebar spacing and corrosion products to predict an accurate time to cracking and crack width as a function of the corrosion rate. In the model developed by Li et al. [41], the corrosion induced concrete crack width is expressed by the following equation:

wcr ¼ 2pb½c5 b

pffiffi ð a1Þ

þ c6 b

pffiffi ð a1Þ



ft 4pds ðtÞ 2pbft pffiffi pffiffi  ¼ a a Eef Eef ð1  mc Þ=ða=bÞ þ ð1 þ mc Þðb=aÞ

ð4Þ

where ds(t) is the thickness of the corrosion product form, ft is the tensile strength of concrete, Eef is the effective elastic modulus of concrete, mc is the Poisson’s ratio of concrete, a is the tangential stiffness reduction factor (see the detailed algorithm for computing tangential stiffness reduction factor by Li et al. [41]), a is the inner radii of the thick-wall cylinder (a = (db + 2d0)/2), db is the diameter of the reinforcement bars, d0 is the thickness of the annular layer of concrete pores, b is the outer radii of the thick-wall cylinder (b = S/2), S is the rebar spacing, and c5 and c6 are boundary conditions as proposed by Li et al.[41]. The crack width model proposed by Li et al. [41] used the model developed by Liu and Weyers [6] to calculate thickness of the corrosion product form, as given in the following equation:

ds ðtÞ ¼

  W rust ðtÞ 1 arust  pðdb þ 2d0 Þ qrust qst

ð5Þ

where Wrust(t) is the mass of rust per unit length of rebar, arust is the coefficient related to the type of rust, qrust is the density of rust, and qst is the density of steel. To calculate the mass of rust per unit length of rebar, Eq. (6) was proposed by Liu and Weyers [6]:

W rust ðtÞ ¼ ½2

Z

t

0:105ð1=arust Þpdb icorr ðtÞdt1=2

ð6Þ

0

As shown in Eq. (4), the concrete crack width model is a function of thickness of the corrosion product form, and the thickness of the corrosion product form is a function of the mass of rust per unit length of rebar while considering the type of corrosion products. Once the corrosion rate is determined as a function of time, the mass of rust per unit length of rebar (see Eq. (6)) can be calculated as a function of the corrosion rate. The predicted time-dependent mass of rust per unit length of rebar can predict the thickness of the corrosion product form as a function of the corrosion rate and type (see Eq. (5)). The calculation of the time-dependent mass of rust per unit length of rebar gives the time-dependent reduced concrete strength by substituting Eq. (4) into Eq. (3). For this study, the width increase due to corrosion cracking to calculate time-dependent reduced concrete strength is expressed by the following equation:

bf  b0 ¼ nbars

4pds ðtÞ 2pbft pffiffi pffiffi  Eef ð1  mc Þ=ða=bÞ a þ ð1 þ mc Þðb=aÞ a

! ð7Þ

4.2. Bond–slip relationship This study goes one step further by considering the bond–slip relationships of the SDOF system as a consequence of the corrosion effects. The reduction of the steel bar diameter and the loss of bonding between the steel and concrete have a relevant influence on the performance level of RC structures. This study adopted the bond–slip model used by Sezen and Setzler [42] to predict the additional lateral displacement due to slip as a consequence of the corrosion effects. The model of Sezen and Setzler [42] was compared with five other analytical models proposed by other researchers (e.g., [43–47]) and experimental results (e.g., [47,48]). In short, Sezen and Setzler [42] assumed a value of the elastic uniform bond stress (ub) for elastic steel stresses and an inelastic uniform bond stress (u0b ) for stresses greater than the yield stress [42]. The model developed by Sezen and Setzler [42] was proposed to calculate slip rotation (hs) by using the following equations:

hs ¼

es fs db for 8ub ðd  cÞ

hs ¼

db ðey fy þ 2ðes þ ey Þðfs  fy ÞÞ for 8ub ðd  cÞ

es 6 ey

ð8Þ

es > ey

ð9Þ

where es is the strain in the reinforcement bar, fs is the stress in the reinforcement bar, fy is the yield stress in the reinforcement bar, d is the section depth, and c is the neutral axis depth. As shown in Eqs. (8) and (9), the slip rotation is dependent on the material properties. Because the behaviour of the reinforcement bars (i.e., the strain and stress in the reinforcement bars) and section capacity change as a function of time due to corrosion effects, the additional displacement due to slip can also be calculated as a function of corrosion rate for different time periods. For this study, to predict the slip rotation as a

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consequence of the corrosion effects, the bond stress proposed in by Stanish et al. [49] was used to calculate the bond stress as a function of the corrosion level and the concrete compressive strength instead of assuming a uniform bond stress as Sezen and Setzler did [42]. By using time-dependent moment–curvature relationships as a consequence of corrosion effects, the additional lateral displacement due to slip can be calculated by multiplying the slip rotation along the height (L) of the column by the following equation:

Ds ¼ h s  L

ð10Þ

If the distribution of curvatures along the height of the column for a given lateral load and corresponding linear moment diagram are known, the first top displacement (D1) of the structure can be obtained by integrating area under the curvature diagram to find the rotation and computing the moment of the area. By summing up the additional displacement due to slip (Ds) and the first obtained top displacement (D1) under lateral loading, the time-dependent total lateral top displacement (Dt) of the structure can be obtained. Therefore, in this study, the time-dependent total lateral top displacement of the corroded RC structures is expressed by the following equation:

Dt ¼ D1 þ Ds

ð11Þ

5. Time-dependent nonlinear analyses of the SDOF system A SDOF system was analysed as a function of the corrosion rate for different time periods. To analyse the frame, it was assumed that the frame of the structure assessed was located very close to the seaside, the soil group was classified as soft clay (group D), the building importance factor (I) was taken as 1, the effective ground acceleration coefficient (A0) was taken to be 0.3 g, and the calculated spectral acceleration (Sa) was equal to 0.75 g according to the Turkish earthquake code [50]. The member names and sectional dimensions (units of cm) of the frame are shown in Fig. 2. To predict the loss in the cross sectional area of the reinforcement bars and the reduction in the concrete strength as a function of time, the values of the basic variables are given in Table 1.

B1

P

19

13

44 8

44

300

50

13

18 2.5

8/10

19 C1

25

C2 400

Fig. 2. Dimensions of the RC frame.

Table 1 Values of basic variables. Symbol

Value

Source:

icorr

0.35 lA/cm2 0.2 2.1 MPa 3600 kg/m3 7850 kg/m3 0.57 12.5 lm 2.35 8518 MPa

Present study [36] [36] [41] [41] [41] [41] [51] [51]

mc ft

qrust qst arust d0

ucr Eef

Note: ucr is the creep coefficient of concrete.

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220

Non-corroded (T: 0), Kent and Park [27]

200

T: 25 years, Kent and Park [27]

Momnent (kN-m)

180

T: 50 years, Kent and Park [27]

160 T: 75 years, Kent and Park [27]

140 120

T: 100 years, Kent and Park [27]

100

Non-corroded (T: 0), Saatcioglu and Razvi [29]

80

T: 25 years, Saatcioglu and Razvi [29]

60

T: 50 years, Saatcioglu and Razvi [29]

40 T: 75 years, Saatcioglu and Razvi [29]

20

T: 100 years,Saatcioglu and Razvi [29]

0 0

0.05

0.1

0.15

0.2

0.25

Curvature (rad/m) Fig. 3. Time-dependent moment–curvature relationships.

Once the corrosion rate is known as a function of time, the reduced concrete strength of each time period can be predicted as a function of the corrosion rate by using Eq. (7). The calculated reduction in the concrete strength in the time periods of 25 years, 50 years, 75 years and 100 years are 15%, 23%, 28%, and 32%, respectively. For each time period, the time-dependent moment–curvature relationships of a rectangular confined column section (C1) were calculated according to the models developed by Kent and Park [27] and Saatcioglu and Razvi [29]. To model these two stress–strain relationships of confined concrete, a new software program SEMAp [52] was used. SEMAp [52] can model the stress–strain relationships of steel and concrete according to user input. To perform time-dependent moment–curvature relationships, a constant 15-ton axial load was assumed for each time period. Fig. 3 shows the predicted pairs of moment–curvature relationships by considering the loss in cross sectional area of the reinforcement bars and the reduced concrete strength as a function of the corrosion rate. As shown in Fig. 3, there are very small differences between the models developed by Kent and Park [27] and Saatcioglu and Razvi [29]. The model developed by Saatcioglu and Razvi [29] indicates more optimistic results for further structural analyses. Therefore, the results of the model developed by Kent and Park [27] were used for the time-dependent moment–curvature relationships. It should be noted that even the Saatcioglu and Razvi [29] model could have been used for further analyses. The reduction of the performance level of the frame due to corrosion would be inevitable in IDA when compared with the non-corroded (t: 0) frame. In Fig. 3, the time-dependent moment–curvature relationships of the RC section (C1) assessed indicate three segments: the elastic region prior to cracking, the post-cracking branch between the cracking and yield points and the post-yield segment beyond yielding. In Fig. 3, the area under the curvature represents the energy stored or dissipated by the assessed cor-

3500

(b)

3500

3000

3000

2500

2500

Axial load (kN)

Axial load (kN)

(a)

2000 1500 1000

2000 1500 1000

0.5Ac. f'c

0.5Ac. f'c 500

500

0

0 0

50

100

150

200

250

300

Moment (kN-m) Non-corroded (T: 0) T: 25 years T: 50 years

0

50

100

150

200

250

300

Moment (kN-m) T: 75 years T: 100 years

Non-corroded (T: 0) T: 25 years T: 50 years

T: 75 years T: 100 years

Fig. 4. Time dependent M–N diagrams of the C1 column: (a) Kent and Park [27], (b) Saatcioglu and Razvi [29].

H. Yalciner et al. / Engineering Failure Analysis 19 (2012) 109–122

115

300

Load (kN)

250 200 150 100 50 0 0

5

10

15

20

25

30

Displacement (mm) Non-corroded (T: 0)

T: 75 years

T: 25 years

T: 100 years

T: 50 years

Fig. 5. Time-dependent load–displacement relationships.

Maximum moment (kN-m)

roded RC column. As shown in Fig. 3, due to time-dependent corrosion effects, the section capacity and energy dissipation are reduced with time, while the rotation is increased for lower moment values, which causes greater lateral displacement of the frame. In addition, stiffness degradation occurs due to the premature yielding of the reinforcement bars. For instance, the premature yielding moment of the C1 column for time periods of 25, 50, 75 and 100 years are 10%, 19%, 26%, and 35%, respectively. With increasing time and corrosion effects, the reduction in the load carrying capacity of an RC column subjected axial loading can be determined from the moment–load (M–N) interaction diagrams. The results of the time-dependent M–N interaction diagrams of all cases of the column assessed are plotted and shown in Fig. 4a and b. Time-dependent interaction diagrams were used to predict moment capacity of a corroded RC section. In Fig. 4, the line of 0.5Acfc0 represents the maximum allowable load that can be carried by a section according to Turkish earthquake code 2007 [50], where Ac is the cross sectional area of a section. On this line, the moment capacity of the corroded RC section decreases as a function of time due to corrosion. The moment capacity of the C1 column of the non-corroded frame based on model developed by Kent and Park [27] is 277 kN-m on this line, but this capacity decreases to 244 kN-m, 220 kN-m, 200 kN-m, and 184 kN-m after 25, 50, 75 and 100 years, respectively. These results also support the above finding on the time-dependent moment–curvature relationships of the corroded column, where serious strength degradation occurs due to corrosion. The predicted time-dependent moment–curvature relationships were used to predict the lateral displacement (D1) of the frame. To simplify the frame analyses, a rigid beam (B1) was assumed, which gives the column curve a double curvature, and the point of inflection is in the middle. For each time period of the frame analyses, lateral loads were applied incrementally to the frame until the column assessed reached its ultimate moment capacity. Fig. 5 shows the predicted timedependent load–top displacement relationships by computing the moment of the area relative to the cantilever column. As shown in Fig. 5, there is an obvious deterioration in the section capacity due to corrosion, resulting in a decrease of the ductility, initial and post yielding stiffness of the frame. Due to the time-dependent effects of corrosion, the reductions in the initial stiffness of the frame for corresponding time periods of 25, 50, 75 and 100 years are 9%, 14%, 26%, and 28%, 220 200 180 160 140 120 100 80 60 40 20 0 0

0.01

0.02

0.03

0.04

0.05

0.06

Strain ( s) Non-corroded (T: 0)

T: 75 years

T: 25 years

T: 100 years

T: 50 years

Fig. 6. Time-dependent moment–strain relationships.

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Lateral load (kN)

300 250 200 150 100 50 0 0

10

20

30

40

50

60

Slip displacement (mm) Non-corroded (T: 0) T: 25 years T: 50 years

T: 75 years T: 100 years

Fig. 7. Time-dependent load–slip displacement.

respectively. In Fig. 5, the time-dependent load–displacement relationships were obtained by considering the two effects of corrosion (time dependent loss of steel area and reduced concrete strength), where the slip effect was not considered, to see the effect of the bond–slip relationship on the structural behaviour. Therefore, the model developed by Sezen and Setzler [42] was used to define this effect on the time-dependent structural behaviour. For each case (non-corroded, 25 years, 50 years, 75 years and 100 years), the time-dependent moment–curvature relationships were used to calculate timedependent effective depth of the neutral axis and the strain and stress in the reinforcement bar. The time-dependent relationships between the calculated maximum moment (Mmax) of the column base and the corresponding strain (es) in the tensile longitudinal bars are shown in Fig. 6. As expected, with increasing time, the same strain deformation occurs with lower moment values. If the force and corresponding time-dependent stress–strain relationships of the reinforcement bar embedded in concrete are known, the time-dependent slip rotation can be calculated by using Eqs. (8) and (9). At this point, there is one difficulty in predicting the slip on the yield plateau region. This problem has also been reported in the literature by some authors (e.g., [42,46]). When the tension steel yields in concrete, the depth of the neutral axis comes close to the compression side of the section. In Eq. (9), in the yield plateau region, (d-c) increases, and the resulting slip rotation decreases. Thus, no additional slip occurs from the yield strain to the start of strain hardening of the reinforcement bars. To avoid this problem, Sezen and Setzler [42] recommended using a modest strain hardening in the yield plateau region. This recommendation was adopted in this study, and a slope of 2% of the elastic modulus of steel was used. The predicted timedependent displacement due to slip as a consequence of the corrosion effects are shown in Fig. 7. According to the slip results of the non-corroded column, there is a good agreement between the displacement obtained due to slip and the experimental study done by Sezen and Moehle [25]. As mentioned earlier, the experimental study done by Sezen and Moehle [25] indicated that slip deformations contributed 25% to 40% of the total lateral displacement. For the non-corroded column, the calculated additional displacement due to slip was 45%. However, the experimental study done by Sezen and Moehle [25] was not time-dependent. Therefore, it is inevitable to have more lateral displacement with increasing time when taking into account the corrosion effects. The displacement due to slip showed different behaviour in the elastic, yield and strain hardening regions due to the applied load and measured strain relations. The results of the slip displacement in the three regions on the reinforcement bar as a function of time are summarised in Table 2. As shown in Table 2, for each plateau of the reinforcement bars, the corrosion caused an increase in the slip displacement at a lower lateral force. For instance, in the elastic region, the calculated slip displacement of the non-corroded column is equal to 4 mm when the lateral force is 220 kN, whilst the same displacement occurs when lateral force is 190 kN 25 years after construction. The results showed that the increase in the lateral displacement is more significant for 50, 75 and

Table 2 Results of the slip displacement in the three regions on the reinforcement bar. Frame

Before crushing of concrete

es < ey Non-corroded (t: 0) t: 25 years t: 50 years t: 75 years t: 100 years

After crushing of concrete

ey < es < esh

es > esh

es > esh

Pmax (kN)

Ds (mm)

Pmax (kN)

Ds (mm)

Pmax (kN)

Ds (mm)

Pun (kN)

Ds (mm)

220 190 180 160 140

4 4 4.7 4.5 4.5

270 240 220 200 170

3.5 3.6 3.6 3.6 3

280 250 Concrete crushed Concrete crushed Concrete crushed

14 13

250 230 200 180 160

52 50 56 56 55

Note: Pmax = Maximum load, Pun = Unloaded column.

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100 years in the strain-hardening region, ending the crushing of concrete. As shown in Table 2, for these three cases, the concrete is crushed before the reinforcement bars exceed the strain hardening region due to the loss in the moment capacities of each section. After the concrete reaches the maximum compressive strain, almost the same amount of slip is recorded for lateral forces due to corrosion effects. Once the corrosion phases begin, the effects of corrosion, which result in slip, are higher during the propagation period, which varies from the first cracking to the loss of the load-carrying capacity of the section. To accurately define the most effected time period of the performance level of the frame given the additional displacement due to slip as a function of time, the results were supported by IDA. The three major effects of corrosion combined were used to predict the time-dependent seismic performance level of the corroded frame, which is presented in the following section. 6. Incremental dynamic analysis The methodology presented in this study for the time-dependent corrosion model was also used to perform analysis with the IDA procedure. There are several methods to assess the performance level of structures under earthquake ground motions [53]. IDA involves performing a series of nonlinear dynamic analyses in which the intensity of the ground motion selected for the collapse investigation is incrementally increased until the global collapse capacity of the structure is reached [54,55]. It also involves plotting an intensity measure (i.e., the peak ground acceleration (PGA) and Sa at the fundamental natural period of the structure) against a damage measure (i.e., the maximum inter-story (MIDR) drift or roof drift). In addition, fragility curves can be obtained by IDA. The fragility curves represent expected damage (i.e., IO, LS and CP) as a function of the selected ground motion intensity, which were used here as a function of the corrosion rate for different time periods. The limit states at each performance level, defined by the multi-record IDA curves at 16%, 50% and 84% fragility obtained as a function of time, are summarised. The fragility curves of probabilistic structural damage estimation were obtained in terms of PGA for each performance level. In this study, the thresholds of the associated roof drift ratios corresponding to the performance levels of IO, LS and CP were assumed to be 0.48%, 1.34%, and 2%, respectively [56]. To perform the analysis, the NONLIN [57] software program was used. For IDA, the first-mode Sa (T1, 5%) for 5% damping was selected. The list of ground motion records used [58] is presented in Appendix A, where the earthquake moment magnitudes (M) ranged from 4.7 to 7.4, the PGA varied from 0.005 to 0.6 g and the peak ground velocity (PGV) ranged from 2 to 117 cm/s. 7. Discussion of incremental dynamic analyses results The results of the IDA obtained for the frame were compared as a function of the time-dependent damage in the reduction of the performance levels. Fig. 8a–c shows the three IDA curves of Sa versus the roof drift ratio of the frame as a function of time. As shown in Fig. 8, the roof drift ratio increases for the same amount of Sa with increasing time. To better understand the changes in the roof drift ratio, the cumulative distribution function (CDF) of the roof drift ratio must be constructed for each time period. Fig. 9 indicates the CDF of the roof drift ratios of each time period according to the design base earthquake hazard level (DBE). The lognormal CDF indicates that there is a serious increase in the roof drift ratios with increasing time due to the time-dependent effects of corrosion. For instance, in Fig. 9, the probability of exceeding 2% of the roof drift ratio (corresponded to the CP limit state) of the non-corroded frame is only 0.3%, but the probabilities of exceeding 2% of the roof drift ratio of 25, 50, 75 and 100 years are 14%, 16%, 34%, and 42%, respectively. Fig. 9 clearly shows that corrosion of a RC structure causes an increase in the probability of exceeding the roof drift ratio as a function of time and causes a decrease in the performance level of the frame. The probability of exceeding the roof drift ratio is also higher if it is compared with the maximum considered earthquake (MCE) hazard levels. Fig. 10a–e shows the multi-record IDA curves (16%, 50% and 84% fragility curves) of each time period. In Fig. 10a, for the non-corroded frame with an Sa of 0.75 g, 84% of the earthquake records caused a roof drift ratio greater than 0.46%, whilst 16% of the earthquake records caused a roof drift ratio greater than 1.01%. However, when the time period is equal to 25 years at the same Sa, 84% of the earthquake records caused a roof drift ratio greater than 0.75%, whilst 16% of the earthquake records caused a roof drift ratio greater than 1.93%. Thus, 25 years after construction, due to the time-dependent effects of corrosion, 84% of the earthquake records reduced the performance level from IO to LS, whilst 16% of the earthquake records reduced the performance level from LS to CP. At the same Sa after 50 years, 84% of the earthquake records caused a roof drift ratio greater than 0.98%, whilst 16% of the earthquake records caused a roof drift ratio greater than 1.99%. Thus, 50 years after construction, 84% of the earthquake records again reduced the performance level from IO to LS with a higher percentage of the roof drift ratio, whilst 16% of the earthquake records reduced the performance level almost to the collapse level based on the associated roof drift ratios corresponding to the performance levels. For the recorded roof drift ratios after 75 and 100 years at the same Sa (0.75 g), 84% of the earthquake records caused a roof drift ratio greater than 1.18% and 1.2%, respectively, whilst 16% of the earthquake records caused a roof drift ratio greater than 2.49% and 2.67%, respectively. These results clearly indicate the behaviour of the RC frame damaged by the effects of corrosion as a function of time. The summation of time-dependent reduction in the cross sectional area of the reinforcement bars, the reduced concrete strength and the slip provides a more accurate prediction of the performance level of RC structures subject to corrosion as a function of time. This phenomenon plays an important role in the evaluation of time to strengthening of structures un-

2

1.5 1.25 1 0.75 0.5 0.25 Non-corroded (T: 0)

0 0.00

1.00

2.00

(b)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

1.75

3.00

4.00

Spectral acceleration "Sa (T1, 5%)" (g)

(a)

H. Yalciner et al. / Engineering Failure Analysis 19 (2012) 109–122

Spectral acceleration "Sa (T1, 5%)" (g)

118

2

1.5 1.25 1

0.75 0.5 0.25 T: 25 years

0

0.00

1.00

Spectral acceleration "Sa (T1, 5%)" (g)

Roof drift ratio (%)

(c)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

1.75

2.00

3.00

4.00

Roof drift ratio (%)

2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

1.75 1.5 1.25 1 0.75 0.5 0.25 T: 50 years

0 0.00

1.00

2.00

3.00

4.00

Roof drift ratio (%)

Fig. 8. IDA curves: (a) non-corroded (t: 0), (b) t: 25 years, (c) t: 50 years.

Cumulative distribution function

der the expected seismic motions to prevent serious damage of structures. Fig. 11a–c shows the fragility curves in terms of PGA as a function of time to predict the performance level of the frame. Table 3 summarises the results of the fragility curves based on the probability of exceeding of limit states as IO, LS and CP of the assessed frame for different time periods in different seismic zones (through Z1–Z4) according to the recommended A0 given by the Turkish earthquake code [50]. As shown in Fig. 11 and Table 3, there is a high seismic risk for both the first seismic zone (Z1) and second seismic zone (Z2) due to time-dependent effects of corrosion. In the first seismic zone of the non-corroded frame, the probability of exceeding the limit state corresponding to IO is 58%, whilst this probability is 86% after 25 years. This probability of exceeding the limit state is increased to 91% after 50 years. For CP limit states of the first seismic zone, the probability of exceeding the limit state increases from 15% to 29% and 37% after 25 and 50 years, respectively. At the second seismic zone of the non-corroded frame, the calculated probability of exceeding the limit state corresponding to IO is 39%, and this probability

1 0.8 0.6 0.4 0.2 0 0

0.5

1

1.5

2

2.5

3

3.5

4

Roof drift ratio (%) Non-corroded (T: 0)

T: 75 years

T: 25 years

T: 100years

T: 50 years

Fig. 9. Cumulative distribution function of the roof drift ratio.

119

1.5 84% LS

1.25

(b)

84% CP 50% CP 50% LS

84% IO

1

50 % IO

0.75

16% CP 16% LS

0.5 16% IO

0.25 0 0

0.5

16% IDA IO

1

50% IDA LS

1.5

84% IDA CP

2

Spectral acceleration "Sa (T1, 5%)" (g)

(a)

Spectral acceleration "Sa (T1, 5%)" (g)

H. Yalciner et al. / Engineering Failure Analysis 19 (2012) 109–122

1.5 1.25 1 0.75 0.5 0.25 0

2.5

0

0.5

1.5

(d)

84% CP 84% LS

1.25 1

50% CP

50% LS

0.75 84% IO

0.5 0.25

16% IDA IO

16% IO

0

0

16% CP

16% LS

50 % IO

0.5

1

50% IDA LS

1.5

1.5

2

2.5

84% IDA CP

2

2

2.5

1.5 1.25 1 0.75 0.5 0.25 0

2.5

0

0.5

Roof drift ratio (%)

1

1.5

Roof drift ratio (%)

Spectral acceleration "Sa (T1, 5%)" (g)

(e)

1

Roof drift ratio (%)

Spectral acceleration "Sa (T1, 5%)" (g)

(c)

Spectral acceleration "Sa (T1, 5%)" (g)

Roof drift ratio (%)

1.5 1.25 1 0.75 0.5 0.25 0

0

0.5

1

1.5

2.5

2

Roof drift ratio (%)

(b)

0.8 0.6 0.4 0.2 IO

0 0

Non-corroded (T: 0) T: 25 years T: 50 years T: 75 years T: 100 years

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Cumulative distribution function

1

1 0.8 0.6

(c)

Non-corroded (T: 0)

0.4 0.2 LS

0 0

1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1 0.8 0.6 0.4

Non-corroded (T: 0)

0.2 CP

0 0

T: 25 years T: 50 years T: 75 years T: 100 years

Peak ground acceleration (g)

Peak ground acceleration (g) Cumulative distribution function

(a)

Cumulative distribution function

Fig. 10. IDA curves and corresponding performance level at 16%, 50% and 84% fragility: (a) non-corroded (t: 0), (b) t: 25 years, (c) t: 50 years, (d) t: 75 years, (e) t: 100 years.

T: 25 years T: 50 years T: 75 years T: 100 years

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

Peak ground acceleration (g) Fig. 11. Fragility curves of limit states: (a) immediate occupancy, (b) life safety, (c) collapse prevention.

1

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H. Yalciner et al. / Engineering Failure Analysis 19 (2012) 109–122 Table 3 Probability of exceeding of limit states of IO, LS and CP in different seismic zones. Frame

Non-corroded (t: 0)

t: 25 years

t: 50 years

t: 75 years

t: 100 years

Limit state

IO LS CP IO LS CP IO LS CP IO LS CP IO LS CP

PGA(g)-Seismic zone A0:0.4 Z1

A0:0.3 Z2

A0: 0.2 Z3

A0:0.1 Z4

58 25 15 86 40 29 91 49 37 94 55 45 95 58 48

39 13 5 70 23 12 78 33 18 86 43 25 89 45 28

17 4 0.65 39 8 2 50 17 4 63 27 8 74 28 10

1.7 0.19 0.0046 5 0.6 0.02 10 3 0.09 17 9 0.3 33 9 0.5

increases to 70% after 25 years. For the same seismic zone (Z2) of the non-corroded frame, the probability of exceeding the limit state corresponding to CP is 5%, and this probability is 12% after 25 years. According to the Turkish earthquake code 2007 [50], the minimum expected performance level for buildings with an importance factor of 1 (I = 1) is LS after an earthquake. According to the results in Table 3, in the first and second seismic zones, the probability of exceeding the limit state corresponding to LS is 40% and 23% after 25 years after construction, respectively. Therefore, it can be concluded that the structure will not show the expected performance level during an earthquake due to corrosion. Strong relationships were also found between the slip displacements and fragility curves (Figs. 7 and 11a–c). According to Fig. 7 and results in Table 2, during the propagation of corrosion phases, additional displacement due to slip has a serious effect in reducing the performance level of the frame. According to Table 3, the probabilities of exceeding the limit states corresponding to the performance levels increase sharply between the time periods of non-corroded (t: 0) and 25 years. However, for the subsequent time periods, these probabilities increase slightly, reaching their maximum values as a function of time. The same results were also obtained in Fig. 9, where the probabilities of exceeding 2% of the roof drift ratio increase rapidly for the same time periods of ranges (t: 0–25) and then continue to increase slightly for the subsequent time periods.

8. Conclusions In this study, the long-term corrosion process of a damaged RC frame was analysed as a function of time by using nonlinear IDA for 20 earthquake ground motion records. The seismic performance level of the frame was predicted as a function of the corrosion rate by taking into account three important corrosion effects. A relationship between the corrosion rate and the reduced concrete strength was developed. It was found that there are strong relationships between the reinforcement slip in concrete and the roof drift ratio of the frame. This study showed that the assessment of the structural performance of corroded RC structures requires a combination of different engineering disciplines with time-dependent models. Thus, the prediction of the performance levels of corroded RC structures can serve as a useful tool for engineers in decision making regarding the time for strengthening or maintenance. The effects of the corrosion rate include not only the loss of the cross sectional area of the reinforcement bars but also slippage, which must be taken into account for structural assessment. Therefore, the thresholds of corrosion rates must be redefined by considering the bond–slip relationship for time-dependent structural assessments. Additional studies are also required for more accurate performance assessment of multi-degree-of-freedom systems. Thus, further investigations are now in progress for defining the relationship between the plastic hinge properties and the slip under the effect of corrosion. It is believed that the methodology developed here can also be integrated with other time-dependent reasonable corrosion parameters for the assessment and strengthening of RC structures. Finally, this study presents a methodology to predict the timedependent performance level of corroded RC structures, which plays an important role in defining risk maps of seismic areas for structural safety decision making.

Acknowledgement The authors gratefully acknowledge Prof. Dr. A. Ghani Razaqpur at McMaster University for his collaboration on developing the methodology described above.

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Appendix A List of ground motion records [58] No

Event

Station

Angle (°)

M

Soil type

Epicentral distance (km)

PGA (g)

PGV (cm/s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Oroville 1975 Oroville 1975 Coalinga 1983 Dinar 1995 Duzce1999 Duzce1999 Duzce 1999 Erzincan 1992 Kocaeli 1999 Imperial Valley 1940 Kobe, Japan 1995 Kocaeli 1999 Kocaeli 1999 Kocaeli 1999 LomaPrietal989 Victoria, Mexico 1980 Kobe, Japan 1995 Kobe, Japan 1995 Sanfemando 1971 Kocaeli 1999

Oroville airport Broadbeck residence Coalinga Burdur Cekmece Center Sakarya Center Gebze El Centro Array #9 Takatori Aydin Tosya Usak Saratoga – Aloha Ave Cerro Prieto

180 270 90 180 180 270 180 90 90 180 90 180 90 270 90 180

4.79 4.7 4.89 6.4 7.2 7.2 7.2 6.69 7.4 6.5 6.9 7.4 7.4 7.4 6.9 6.3

Soft soil Soft soil Soft soil Soft soil Soft soil Soft soil Soft soil Soft soil Soft soil Alluvium Stiff soil Soft soil Soft soil Soft soil Alluvium Stiff soil

14 7 9 39 200 1 20 9 8 13 13 373 342 237 27 34

0.036 0.168 0.2 0.3 0.0153 0.535 0.45 0.515 0.244 0.37 0.611 0.0054 0.0091 0.014 0.376 0.5722

2.15 3.35 6.4 33.17 2.1 70.77 55.65 72.95 38.3 31.74 117.14 2.79 5.55 4.59 48.52 27.06

Nishi-Akashi Shin-Osaka Castaic – Old Ridge Route Yarimca

90 270 90 180

6.9 6.9 6.6 7.4

Stiff soil Stiff soil Alluvium Soft soil

9 46 25 19

0.4862 0.243 0.255 0.3055

35.73 32.82 29.8 60.51

17 18 19 20

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