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A yield curvature model considering axial compression ratio

Abstract

This study proposed a yield curvature prediction model considering axial compression ratio with exponential function which is improved on the basis of the specification effective yield curvature prediction model. Parametric moment–curvature curves approach was used to verify that the yield curvature is greatly affected by the section size, the yield strength of longitudinal steel bar and the axial compression ratio. On the basis, the yield curvature under different levels was obtained by Xtract and parametric moment–curvature curves approach, the result shows that with the increase of axial compression ratio, the yield curvature also increases, which is roughly a linear relationship. Subsequently, combined with the specification and considering the influence of axial compression ratio, a new yield curvature prediction model is proposed based on a massive sample space obtained by parametric moment–curvature curves approach. Moreover, by comparing with the experimental database of PEER, the accuracy of new prediction model is verified, and the result shows that the new prediction model is suitable for estimating yield curvature of square section columns.

1 Introduction

Bridge columns are structural elements that support the weight of the bridge. These columns are subject to various types of loads, including horizontal and vertical loads, and moments caused by bridge displacement. The design of the column is crucial to the safety and reliability of the structure, and the failure of the column will lead to catastrophic consequences (Cornell et al. 2002). Axial compression ratio is an important design parameter that significantly affects the seismic performance of columns. This is demonstrated in prediction models proposed by researchers. Ho (Ho and Pam 2010) proposed a prediction model of curvature in collapse damage state, in which the axial compression ratio is an important parameter. Moreover, in the specification, the axial compression ratio plays a crucial role in collapse damage state (Ministry  2020). However, for the effective yield curvature, the influence of axial compression ratio has not been considered by some researchers and specifications (Ministry  2020; Olivia and Mandal 2005; En 2005; ATC-40. 1996). The effective yield curvature is obtained from the actual moment–curvature curve equivalent to the ideal elastic–plastic moment–curvature curve, and the ideal elastic–plastic moment–curvature curve must pass through the point corresponding to the yield curvature, but it is different from the definition of yield curvature, moreover, some scholars have considered the influence of axial compression ratio in the yield curvature prediction model (Hernández-Montes and Aschleim 2003; Zhong et al. 2022a). In the prediction model proposed by Hernández (2003), the yield curvature increases with the increase of axial compression ratio. The yield curvature prediction model proposed by Zhong (Zhong et al. 2022a) also considers the influence of axial compression ratio, the yield and effective yield curvature prediction model proposed by scholars and specifications is shown in Table 1. Although the yield curvature prediction models proposed by Hernández (2003) and Zhong (2022a) have been verified, there are still the following problems: (1) it is inconvenient to remember; (2) prediction model is not applicable when the axial compression ratio is 0.

Table 1 Summary of some prediction models

Finite element analysis has become a popular choice among researchers for studying bridge columns due to its advantages in terms of resource efficiency and convenience, as compared to experimental methods. With the aid of finite element analysis software, scholars extensively investigate and optimize the design of bridge columns. Su (2019) obtained the yield curvature of bridge columns using Xtract and implemented it into a formula to calculate the displacement of steel reinforcement slip. Zhang (2020) studied the factors affecting the top displacement of high-strength column through ABAQUS. Aldabagh (2022) deduced the prediction model of drift ratio of different damage states by establishing samples with OpenSees. Therefore, Xtract was employed as a tool to validate the yield curvature in this study.

In this study, the yield curvature is first defined, and the section information of the columns is replaced by the expression by using the parametric moment–curvature (M-φ) curves approach (PMCA), and the M-φ curves can be obtained based on the plane hypothesis model and the stress–strain models of longitudinal reinforcement and concrete. On this basis, PMCA was employed to discuss the influence of section size (L), axial compression ratio (Rac), longitudinal reinforcement ratio (ρl), stirrup reinforcement ratio (ρs), concrete compressive strength (fco) and yield strength of longitudinal steel bar (fy) on yield curvature, and then remove the parameters that have little effect on yield curvature. On this basis, some levels under different L, fy and Rac were set, and the yield curvature was obtained by Xtract and PMCA and compared. Moreover, some columns whose failure form is flexural failure are selected and the experimental yield curvature is obtained. The yield curvature prediction model considering the influence of Rac was proposed based on a massive sample space obtained by PMCA and compared it with experiments.

2 Definition of yield curvature

The order of failure of the bridge column is as follows: the cracks first occur, then the first yielding of longitudinal steel bars is observed, followed by the spalling of the cover concrete, the crushing of the core concrete, and the fracture of the stirrup in the final stage. The section curvature corresponding to the first yielding of longitudinal steel bars is taken as the yield curvature (φy) of column in this study, as shown in Fig. 1. Strain can be used as an index to judge the damage state (Calvi and Kingsley 1995; Priestley et al. 1996). When the strain of the longitudinal steel bars reaches, it can be considered that the longitudinal steel bars has yielded for the first time, and the corresponding curvature is φy.

Fig. 1
figure 1

Definition of yield curvature

3 Parametric M-φ curves approach

Zhong (2022a) proposed a parametric moment–curvature (M-φ) curves approach (PMCA), which transformed discrete longitudinal steel bars into ‘steel loop’, the thickness of the ‘steel loop’ can be approximately represented to d0 = (ρlLW) / (2L + 2W-4C0), where L and W are the size of the bridge column section, C0 is cover concrete thickness, and so that three important parts (cover concrete, core concrete and longitudinal steel bars) are continuous sections. Each part can be represented by thickness information: Tuc, Tcc, and Ts, as shown in Fig. 2. Then, based on the plane hypothesis model and the stress–strain model of concrete (proposed by Mander et al. (1988)) and steel (steel01), the balance between the axial force and the reaction force of the column is established and moment is obtained. The stress–strain model is shown in Fig. 3, where εco, εcc and εcu are peak strain of cover concrete, peak strain of core concrete and ultimate strain of core concrete, fco and fcc are the compressive strength of cover and core concrete, b is strain-hardening ratio.

Fig. 2
figure 2

Parametric M-φ curves approach

Fig. 3
figure 3

a Concrete04; and b Steel01 model

The φy prediction model proposed by Zhong (2020) does not consider the influence of fy, and the φy cannot be calculated when the Rac is 0. Therefore, this study attempts to establish a φy prediction model of six parameters, and then remove the parameters that have little influence on the yield curvature. 96(531,441) levels are established to fit the prediction model through PMCA, and the parameters information is shown in the Table 2.

Table 2 Sample space parameter information

The exponential function is used for fitting to directly obtain the influence of each parameter on φy. The form of the expression is as follows:

$${\varphi }_{y}={aL}^{{a}_{1}}{\left(1-{R}_{ac}\right)}^{{a}_{2}}{\rho }_{l}^{{a}_{3}}{\rho }_{s}^{{a}_{4}}{f}_{co}^{{a}_{5}}{f}_{y}^{{a}_{6}}$$
(1)

where a, a1, a2, a3, a4, a5, a6 are coefficients of exponential function. The greater the absolute value of a1 to a6, the greater the influence of parameters on φy. The fitted expression is shown in Eq. 2.

$${\varphi }_{y}=7\times {10}^{-6}{L}^{-1.03}{\left(1-{R}_{ac}\right)}^{-0.96}{\rho }_{l}^{0.038}{\rho }_{s}^{-0.0015}{f}_{co}^{0.104}{f}_{y}^{0.98}$$
(2)

By comparing the fitted expression and PMCA in Fig. 4, the effect is not bad. From the fitted expression, φy is significantly influenced by L and fy, and as fy increases or L decreases, the φy increase accordingly, as reported in previous studies. Priestley ( 1998) reported that L and fy have a great influence on the curvature of the slight limit state, which is inversely proportional to L and proportional to fy. The coefficient of (1-Rac) is also high, therefore, based on the effective yield curvature prediction model combined with the specification, this study proposes a yield curvature prediction model considering Rac. Hernández ( 2003) studied that as Rac increases, the curvature of the slight limit state also increases, which is consistent with Eq. 2.

Fig. 4
figure 4

Comparison of fitted expression with PMCA

4 Comparison between numerical simulation and PMCA

4.1 Finite element model

Xtract was used in this study to verify the accuracy of PMCA and provide a control group for subsequent studies. According to the main influence parameters obtained by PMCA, some levels of different L, fy and Rac are set, as shown in Table 3.

Table 3 Parameters information

Xtract is an effective software for obtaining φy, which can calculate the moment–curvature curve of column section and output φy directly. Therefore, a square section column was established by Xtract, and the parameters of cover concrete, core concrete and longitudinal steel bars are defined. The cover and core concrete material model proposed by Mander et al. (Mander et al. 1988) are adopted in Xtract. In this study, the concrete grade is C50, the cover concrete strength is 32.4 MPa. The core concrete strength is 42.1 MPa in Test 1 and 42.8 MPa in Test 3. The yield strain of core concrete is 0.0035 in Test 1 and 0.00365 in Test 3. The elastic modulus of cover and core concrete is 3.45 × 104 MPa. The longitudinal reinforcement ratio is 1.13%, the yield strength of stirrup is 360 MPa, the stirrup ratio is 1%, and the thickness of cover concrete is 0.04 m, the other parameters are shown in Table 3, the units are divided according to the default length.

4.2 Comparison

By applying Xtract and PMCA, the yield curvature of all conditions in Table 3 is calculated and compared. On the one hand, the trend of yield curvature with the change of Rac can be seen. On the other hand, Xtract can be set as the control group to verify the accuracy of PMCA. The comparison results are shown in Fig. 5. The error rate = 100% × (PMCA—Xtract) / Xtract.

Fig. 5
figure 5

Comparison between specification and numerical simulation: a Test 1; b Test 2; and c Test 3

From the comparison of the two, the above two problems can be easily solved: (1) With the increase of Rac, the yield curvature also increases, which is roughly a linear relationship; (2) The calculation results of PMCA and Xtract are very close, the error between the two is about 3%, and the maximum is only 5%. Therefore, PMCA can replace Xtract as the main tool to obtain yield curvature in the follow study. In addition, considering that the influence of longitudinal steel bars into ‘steel loop’, the yield curvature of PMCA is always smaller than Xtract. However, this is beneficial to engineering design and can leave a certain safety space for the project.

5 Experimental data

The experiment of PEER database is integrated here (Nagasaka 1982; Imai and Yamamoto 1986; Zhou et al. 1987; Arakawa et al. 1989; Umehara 1983; Bett et al. 1985; Aboutaha et al. 1999; Iwasaki et al. 1985; Priestley et al. 1994; Pandey and Mutsuyoshi 2005; Yoshimura et al. 1991; Hassane 2002; Nakamura and Yoshimura 2002; Moehle 2000; Wight 1973; Lynn et al. 1996; Pandey and Mutsuyoshi 2005; Nagasaka 1982; Ohue et al. 1985; Ono and Shimizu 1985; Ono 1989; Amitsu et al. 1991; Wight 1973; Lynn et al. 1996; Xiao and Martirossyan 1998; Sezen and Moehle 2002; Iwasaki et al. 1985; Ikeda 1968; Umemura and Endo 1970; Hirosawa 1973; Yalcin 1997; Elwood and Moehle 2008; Saatcioglu and Ozcebe 1989; Esaki 1996; Lynn et al. 1996; Yoshimura et al. 2003; Yarandi 2007; Pandey and Mutsuyoshi 2005; Yoshimura and Yamanaka 2000; Gill 1979; Ang 1981; Soesianawati 1986; Zahn 1985; Watson 1989; Tanaka 1990; Park and Paulay 1990; Arakawa et al. 1982; Ohno and Nishioka 1984; Zhou et al. 1987; Kanda 1988; Muguruma et al. 1989; Sakai 1990; Atalay and Penzien 1975; Azizinamini et al. 1988; Saatcioglu and Ozcebe 1989; Galeota et al. 1996; Wehbe 1998; Xiao and Martirossyan 1998; Sugano 1996; Nosho et al. 1996; Bayrak and Sheikh 1996; Saatcioglu and Grira 1999; Matamoros 1999; Mo and Wang 2000; Aboutaha and Machado 1999; Thomson and Wallace 1994; Legeron and Paultre 2000; Paultre et al. 2001; Pujol 2002; Kono and Watanabe 2000; Harries et al. 2006; Melek and Wallace 2004). The distribution of L, Rac and fy are represented by the histogram and the cumulative probability, as shown in Fig. 6. It can be seen that L and Rac are roughly logarithmic normal distribution, with mean values of 0.317m and 0.242, respectively, while fy is roughly uniform distribution, with mean value of 429MPa.

Fig. 6
figure 6

The experimental columns parameter distribution of PEER database: a L; b Rac; c fy

The research object of this paper is mainly the bridge column with flexural failure. In order to ensure that the bridge column is flexural failure, only the shear span ratio not less than 2.5 (H/L ≥ 2.5) and the square section bridge column of ordinary reinforced concrete are retained. Therefore, the stacked bar charts for the column physical parameters are shown in Fig. 7, fyh is the yield strength of stirrups; H/L is the column aspect ratio.

Fig. 7
figure 7

Stacked bar chart of column physical parameters

According to the yield displacement method proposed by Priestley and Park (Eq. 3), the yield displacement of these experiments is marked in the hysteresis curve, and the results are shown in Fig. 8.

Fig. 8
figure 8

Yield displacement and yield curvature of experiment

$${\Delta }_{y}=\frac{{\varphi }_{y}{H}^{2}}{3}\stackrel{}{\Rightarrow }{\varphi }_{y}=\frac{{3\Delta }_{y}}{{H}^{2}}$$
(3)

6 Prediction model combined with Chinese specification

6.1 New prediction model

Considering that the effective yield curvature is close to the yield curvature, so the prediction model of yield curvature is derived based on the effective yield curvature prediction model of Chinese specification. Based on the accuracy of PMCA, and this study removes some less influential parameters to use easily, a new prediction model is proposed which combines the exponential function considering the influence of Rac with the Chinese specification. A large number of levels are obtained by PMCA, the parameters information is shown in Table 2. The new prediction model is not complex and is more suitable for researchers to use directly. The prediction model is as follows:

$${\varphi }_{y}=1.957\frac{{f}_{y}}{L\times {E}_{s}}\times {b}_{1}{\left(1-{R}_{ac}\right)}^{{b}_{2}}$$
(4)

where the first part is the Chinese specification effective yield curvature prediction model, b1 and b2 are the coefficients. The values of b1 and b2 are fitted by the least square method. Finally, the prediction model of φy combined with Chinese specification is Eq. 5. The experimental axial compression ratios of the retained PEER database are all brought into the new prediction model, and the average value of the coefficients is calculated, the coefficient is 1.82, it shows that the yield curvature is about 0.1 times smaller than the coefficient of effective yield curvature (1.957).

$${\varphi }_{y}=1.449\frac{{f}_{y}}{L\times {E}_{s}\times \left(1-{R}_{ac}\right)}$$
(5)

6.2 Application of the prediction model

In order to verify the accuracy of the new prediction model, the yield curvature obtained from the experiment is compared with the predicted, and the results are shown in the Table 4 and Fig. 9.

Table 4 The comparison between experiment and new model
Fig. 9
figure 9

Comparison between experiment and new model

From the comparison in Fig. 9 and Table 4, it can be seen that the results of the experiment and the prediction are very close, and the error rate is kept within -20% ~ 20%, and most of them are less than 0%. This shows that the predicted yield curvature is often smaller than the experiment, which also provides a certain safety space for practical projects. In addition, the reason why some errors are relatively large may be that the data source of the new prediction model is determined according to the set condition range. There will be some errors outside the range, but the error is still guaranteed to be within a relatively small range. Therefore, the prediction model can be used to predict the yield curvature of practical engineering.

7 Conclusions

The main purpose of this paper is to study the influence of axial compression ratio on yield curvature, and propose a prediction model considering the axial compression ratio based on the effective yield curvature prediction model of Chinese specification. To achieve this goal, parametric moment–curvature curves approach (PMCA) is adopted to verify that section size, the yield strength of longitudinal steel bar and the axial compression ratio have great influence on yield curvature. Then, some levels under different section size, the yield strength of longitudinal steel bar and the axial compression ratio were set, and the yield curvature was obtained by Xtract and PMCA and compared, the result shows that the yield curvature increases with the increase of the axial compression ratio. Besides, a new prediction model is proposed by combining the exponential function with effective yield curvature prediction model of Chinese specification, the yield curvature of the database of PEER is compared with the new prediction model. Through the above research, the following conclusions can be obtained:

  1. (1)

    The numerical simulation result shows that yield curvature increases with the increase of the axial compression ratio, and the growth trend is obvious, which is different from the specifications effective yield curvature prediction model.

  2. (2)

    The yield curvature prediction model proposed in this study can well predict the yield curvature of the experiment, and the error is between -20% and 20%, and most of them are concentrated near -10%. The negative error indicates that the prediction is smaller than the experiment, indicating that retaining a certain safety space and it is beneficial to the actual project.

In this paper, a simplified prediction model of yield curvature is proposed, which provides a convenient tool for the design of bridge columns in practical engineering. However, this paper only studies the square cross-section column and cannot predict the curvature of the limit state after the column yield. In the future research, we will make up for these deficiencies.

8 Appendix

#

Reference

ID

fc

(MPa)

fy

(MPa)

fyh

(MPa)

L

(m)

W

(m)

Rac

ρl

(%)

ρs

(%)

1

Nagasaka 1982)

HPRC10-63

21.6

371

344

0.20

0.20

0.17

1.27

0.80

2

Imai and Yamamoto 1986)

UNIT_1

27.1

318

336

0.50

0.40

0.07

2.66

0.40

3

Zhou et al. 1987)

No.104–08

19.8

341

559

0.16

0.16

0.80

2.22

0.70

4

Zhou et al. 1987)

No.114–08

19.8

341

559

0.16

0.16

0.80

2.22

0.70

5

Zhou et al. 1987)

No.124–08

19.8

341

559

0.16

0.16

0.80

2.22

1.80

6

Arakawa et al. 1989)

OA2

31.8

340

249

0.18

0.18

0.18

3.13

0.20

7

Arakawa et al. 1989)

OA5

33.0

340

249

0.18

0.18

0.45

3.13

0.20

8

Umehara 1983)

CUS

34.9

441

414

0.41

0.23

0.16

3.01

0.30

9

Umehara 1983)

CUW

34.9

441

414

0.23

0.41

0.16

3.01

0.30

10

Bett et al. 1985)

UNIT_1_1

29.9

462

414

0.31

0.31

0.10

2.44

0.30

11

Aboutaha et al. 1999)

SC3

21.9

434

400

0.46

0.91

0.00

1.88

0.27

12

Aboutaha et al. 1999)

SC9

16.0

434

400

0.91

0.46

0.00

1.88

0.20

13

Iwasaki et al. 1985)

I18

33.1

323

258

0.50

0.50

0.00

2.12

0.47

14

Iwasaki et al. 1985)

I21

31.7

323

258

0.50

0.50

0.00

2.12

0.47

15

Priestley et al. 1994)

UnitR3A

34.5

469

324

0.41

0.61

0.06

2.53

0.23

16

Priestley et al. 1994)

UnitR5A

32.4

469

324

0.41

0.61

0.06

2.53

0.23

17

Priestley et al. 1994)

Specimen_B1

32.5

380

396

0.30

0.30

0.03

2.68

0.18

18

Pandey and Mutsuyoshi 2005)

Specimen_CE

26.0

388

312

0.18

0.18

0.10

3.08

0.70

19

Yoshimura et al. 1991)

Specimen_BE

32.7

344

312

0.18

0.18

0.10

3.08

0.70

20

Yoshimura et al. 1991)

Specimen_LE

41.5

344

322

0.18

0.18

0.10

6.94

3.78

21

Yoshimura et al. 1991)

No.1

30.7

402

392

0.30

0.30

0.20

2.68

0.47

22

Yoshimura et al. 1991)

No.3

30.7

402

392

0.30

0.30

0.20

2.68

0.24

23

Yoshimura et al. 1991)

No.4

30.7

402

392

0.30

0.30

0.30

2.68

0.47

24

Yoshimura et al. 1991)

C1

13.5

340

587

0.30

0.30

0.30

1.69

0.20

25

Hassane 2002)

C4

13.5

340

587

0.30

0.30

0.30

1.69

0.69

26

Hassane 2002)

C8

18.0

340

384

0.30

0.30

0.30

1.69

0.69

27

Hassane 2002)

C12

18.0

340

384

0.30

0.30

0.20

1.69

0.69

28

Hassane 2002)

D1

27.7

447

398

0.30

0.30

0.22

1.69

1.03

29

Hassane 2002)

D11

28.1

447

398

0.30

0.30

0.21

2.25

0.34

30

Hassane 2002)

D12

28.1

447

398

0.30

0.30

0.21

2.25

0.34

31

Hassane 2002)

D13

26.1

447

398

0.30

0.30

0.23

2.25

1.03

32

Hassane 2002)

D14

26.1

447

398

0.30

0.30

0.23

2.25

1.03

33

Hassane 2002)

D16

26.1

447

398

0.30

0.30

0.23

1.69

1.03

34

Hassane 2002)

N-18 M

26.5

380

380

0.30

0.30

0.18

2.68

0.53

35

Nakamura and Yoshimura 2002)

N-27C

26.5

380

380

0.30

0.30

0.27

2.68

0.53

36

Nakamura and Yoshimura 2002)

N-27 M

26.5

380

380

0.30

0.30

0.27

2.68

0.53

37

Nakamura and Yoshimura 2002)

S-1

25.1

547

355

0.40

0.40

0.20

3.87

0.45

38

Moehle 2000)

WI_0_033E

32.0

496

345

0.31

0.15

0.00

2.45

0.33

39

Wight 1973)

3CLH18

26.9

331

400

0.46

0.46

0.09

3.03

0.16

40

Lynn et al. 1996)

A1

28.8

380

396

0.30

0.30

0.03

2.68

0.30

41

Pandey and Mutsuyoshi 2005)

HPRC19-32

21.0

371

344

0.20

0.20

0.35

1.27

1.40

42

Nagasaka 1982)

2D16RS

32.0

369

316

0.20

0.20

0.14

2.01

0.60

43

Ohue et al. 1985)

4D13RS

29.9

370

316

0.20

0.20

0.15

2.65

0.60

44

Ohue et al. 1985)

No.1007

34.0

336

341

0.08

0.08

0.70

1.77

0.50

45

Ono and Shimizu 1985)

No.204–08

21.1

341

559

0.16

0.16

0.80

2.22

0.70

46

Ono and Shimizu 1985)

No.223–09

21.1

341

559

0.16

0.16

0.90

2.22

1.80

47

Ono and Shimizu 1985)

No.302–07

28.8

341

559

0.16

0.16

0.70

2.22

0.70

48

Ono and Shimizu 1985)

No.312–07

28.8

341

559

0.16

0.16

0.70

2.22

0.70

49

Ono and Shimizu 1985)

CA025C

25.8

361

426

0.20

0.20

0.26

2.13

0.90

50

Ono 1989)

CA060C

25.8

361

426

0.20

0.20

0.62

2.13

0.90

51

Ono 1989)

CB060C

46.3

441

414

0.28

0.28

0.74

2.75

0.90

52

Amitsu et al. 1991)

WI_40_033aE

34.7

496

345

0.31

0.15

0.12

2.45

0.33

53

Wight 1973)

WI_40_033aW

34.7

496

345

0.31

0.15

0.12

2.45

0.33

54

Wight 1973)

WI_40_048E

26.1

496

345

0.31

0.15

0.15

2.45

0.48

55

Wight 1973)

WI_40_048W

26.1

496

345

0.31

0.15

0.15

2.45

0.48

56

Wight 1973)

WI_40_033_E

33.6

496

345

0.31

0.15

0.11

2.45

0.33

57

Wight 1973)

WI_40_033_W

33.6

496

345

0.31

0.15

0.11

2.45

0.33

58

Wight 1973)

WI_25_033_E

33.6

496

345

0.31

0.15

0.07

2.45

0.33

59

Wight 1973)

WI_25_033_W

33.6

496

345

0.31

0.15

0.07

2.45

0.33

60

Wight 1973)

WI_0_048W

25.9

496

345

0.31

0.15

0.00

2.45

0.48

61

Wight 1973)

WI_40_067_E

33.4

496

345

0.31

0.15

0.11

2.45

0.70

62

Wight 1973)

WI_40_067_W

33.4

496

345

0.31

0.15

0.11

2.45

0.70

63

Wight 1973)

WI_40_147_E

33.5

496

317

0.31

0.15

0.11

2.45

1.50

64

Wight 1973)

WI_40_147_W

33.5

496

317

0.31

0.15

0.11

2.45

1.50

65

Wight 1973)

WI_40_092_E

33.5

496

317

0.31

0.15

0.11

2.45

0.90

66

Wight 1973)

WI_40_092_W

33.5

496

317

0.31

0.15

0.11

2.45

0.90

67

Wight 1973)

2CLH18

33.1

331

400

0.46

0.46

0.07

1.94

0.16

68

Lynn et al. 1996)

2CMH18

25.5

331

400

0.46

0.46

0.28

1.94

0.16

69

Lynn et al. 1996)

2SLH18

33.1

331

400

0.46

0.46

0.07

1.94

0.16

70

Lynn et al. 1996)

3SMD12

25.5

331

400

0.46

0.46

0.28

3.03

0.41

71

Lynn et al. 1996)

HC4-0.1P

86.0

510

449

0.25

0.25

0.10

2.46

1.60

72

Xiao and Martirossyan 1998a)

HC4-0.2P

86.0

510

449

0.25

0.25

0.19

2.46

1.60

73

Xiao and Martirossyan 1998a)

Specimen_1

21.1

434

476

0.46

0.46

0.15

2.48

0.20

74

Sezen and Moehle 2002)

Specimen_2

21.1

434

476

0.46

0.46

0.61

2.48

0.20

75

Sezen and Moehle 2002)

Specimen_4

21.8

434

476

0.46

0.46

0.15

2.48

0.20

76

Sezen and Moehle 2002)

I_03

30.7

323

258

0.40

0.80

0.00

1.42

0.61

77

Iwasaki et al. 1985)

I_04

28.4

323

258

0.40

0.80

0.00

1.77

0.61

78

Iwasaki et al. 1985)

I_10

31.2

323

258

0.50

0.50

0.00

2.12

0.47

79

Iwasaki et al. 1985)

I_14

32.0

323

258

0.50

0.50

0.00

2.12

0.47

80

Iwasaki et al. 1985)

I_16

31.8

323

258

0.50

0.50

0.00

2.12

0.47

81

Iwasaki et al. 1985)

I_17

31.8

323

258

0.50

0.50

0.00

2.12

0.47

82

Iwasaki et al. 1985)

I_20

33.3

323

258

0.50

0.50

0.00

2.12

0.47

83

Iwasaki et al. 1985)

I_25

33.0

323

258

0.50

0.50

0.00

2.12

2.37

84

Iwasaki et al. 1985)

IK_43

19.6

434

559

0.20

0.20

0.10

1.99

0.66

85

Ikeda 1968)

IK_44

19.6

434

559

0.20

0.20

0.10

1.99

0.66

86

Ikeda 1968)

IK_45

19.6

434

559

0.20

0.20

0.20

1.99

0.66

87

Ikeda 1968)

IK_46

19.6

434

559

0.20

0.20

0.20

2.66

0.66

88

Ikeda 1968)

IK_62

19.6

345

476

0.20

0.20

0.10

1.97

0.67

89

Ikeda 1968)

IK_63

19.6

345

476

0.20

0.20

0.20

1.97

0.67

90

Ikeda 1968)

IK_64

19.6

345

476

0.20

0.20

0.20

1.97

0.67

91

Ikeda 1968)

UM_205

17.6

462

324

0.20

0.20

0.22

1.99

0.61

92

Umemura and Endo 1970)

UM_207

17.6

462

324

0.20

0.20

0.22

1.99

0.61

93

Umemura and Endo 1970)

UM_214

17.6

462

324

0.20

0.20

0.56

1.99

0.31

94

Umemura and Endo 1970)

UM_220

32.9

379

648

0.20

0.20

0.12

1.18

0.24

95

Umemura and Endo 1970)

UM_231

14.8

324

524

0.20

0.20

0.27

0.95

0.28

96

Umemura and Endo 1970)

UM_232

13.1

324

524

0.20

0.20

0.30

0.95

0.28

97

Umemura and Endo 1970)

UM_233

13.9

372

524

0.20

0.20

0.28

1.18

0.28

98

Umemura and Endo 1970)

UM_234

13.1

372

524

0.20

0.20

0.30

1.18

0.28

99

Umemura and Endo 1970)

KO_372

19.9

524

352

0.20

0.20

0.20

1.33

0.80

100

Hirosawa 1973)

KO_373

20.4

524

352

0.20

0.20

0.19

1.98

0.79

101

Hirosawa 1973)

KO_452

21.9

359

316

0.20

0.20

0.45

2.84

0.77

102

Hirosawa 1973)

KO_454

21.9

359

316

0.20

0.20

0.45

3.80

0.76

103

Hirosawa 1973)

BR-S1

45.0

445

425

0.55

0.55

0.13

1.98

0.30

104

Yalcin 1997)

Specimen1

24.5

479

718

0.23

0.23

0.10

1.94

0.45

105

Elwood and Moehle 2008)

Specimen2

23.9

479

718

0.23

0.23

0.24

1.94

0.45

106

Elwood and Moehle 2008)

UnitR1A

37.9

324

359

0.61

0.41

0.05

2.53

0.23

107

Saatcioglu and Ozcebe 1989)

U2

30.2

453

470

0.35

0.35

0.16

3.21

0.69

108

Esaki 1996)

H-2-1_3

23.0

362

364

0.20

0.20

0.35

2.65

1.62

109

Esaki 1996)

H-2-1_5

23.0

362

364

0.20

0.20

0.21

2.65

1.29

110

Esaki 1996)

HT-2-1_3

20.2

362

364

0.20

0.20

0.35

2.65

1.62

111

Esaki 1996)

HT-2-1_5

20.2

362

364

0.20

0.20

0.21

2.65

1.29

112

Lynn et al. 1996)

3CMH18

27.6

331

400

0.46

0.46

0.26

3.04

0.16

113

Lynn et al. 1996)

3CMD12

27.6

331

400

0.46

0.46

0.26

3.04

0.42

114

Lynn et al. 1996)

3SLH18

26.9

331

400

0.46

0.46

0.09

3.03

0.16

115

Yoshimura et al. 2003)

Unit_6

30.7

409

392

0.30

0.30

0.20

1.77

0.48

116

Yoshimura et al. 2003)

Unit_7

30.7

409

392

0.30

0.30

0.20

1.77

0.32

117

Yarandi 2007)

RRC

35.0

400

400

0.70

0.35

0.15

1.46

0.11

118

Yarandi 2007)

SRC

42.0

400

400

0.70

0.35

0.15

1.46

0.37

119

Pandey and Mutsuyoshi 2005)

A4

33.1

380

396

0.30

0.30

0.03

2.68

0.65

120

Pandey and Mutsuyoshi 2005)

C1

36.4

396

427

0.30

0.30

0.03

2.68

0.30

121

Yoshimura and Yamanaka 2000)

FS0

27.0

387

355

0.30

0.30

0.26

3.82

1.48

122

Yoshimura and Yamanaka 2000)

FS1

27.0

387

355

0.30

0.30

0.26

3.82

1.48

123

Gill 1979)

No.1

23.1

375

297

0.55

0.55

0.26

1.79

1.50

124

Gill 1979)

No.2

41.4

375

316

0.55

0.55

0.21

1.79

2.30

125

Gill 1979)

No.3

21.4

375

297

0.55

0.55

0.42

1.79

2.00

126

Gill 1979)

No.4

23.5

375

294

0.55

0.55

0.60

1.79

3.50

127

Ang 1981)

No.3

23.6

427

320

0.40

0.40

0.38

1.51

2.80

128

Ang 1981)

No.4

25.0

427

280

0.40

0.40

0.21

1.51

2.20

129

Soesianawati 1986)

No.1

46.5

446

364

0.40

0.40

0.10

1.51

0.90

130

Soesianawati 1986)

No.2

44.0

446

360

0.40

0.40

0.30

1.51

1.20

131

Soesianawati 1986)

No.3

44.0

446

364

0.40

0.40

0.30

1.51

0.80

132

Soesianawati 1986)

No.4

40.0

446

255

0.40

0.40

0.30

1.51

0.60

133

Zahn 1985)

No.7

28.3

440

466

0.40

0.40

0.22

1.51

1.60

134

Zahn 1985)

No.8

40.1

440

466

0.40

0.40

0.39

1.51

2.00

135

Watson 1989)

No.5

41.0

474

372

0.40

0.40

0.50

1.51

0.70

136

Watson 1989)

No.6

40.0

474

388

0.40

0.40

0.50

1.51

0.30

137

Watson 1989)

No.7

42.0

474

308

0.40

0.40

0.70

1.51

1.30

138

Watson 1989)

No.8

39.0

474

372

0.40

0.40

0.70

1.51

0.70

139

Watson 1989)

No.9

40.0

474

308

0.40

0.40

0.70

1.51

2.50

140

Tanaka 1990)

No1

25.6

474

333

0.40

0.40

0.20

1.57

2.50

141

Tanaka 1990)

No2

25.6

474

333

0.40

0.40

0.20

1.57

2.50

142

Tanaka 1990)

No3

25.6

474

333

0.40

0.40

0.20

1.57

2.50

143

Tanaka 1990)

No4

25.6

474

333

0.40

0.40

0.20

1.57

2.50

144

Tanaka 1990)

No5

32.0

511

325

0.55

0.55

0.10

1.25

1.70

145

Tanaka 1990)

No6

32.0

511

325

0.55

0.55

0.10

1.25

1.70

146

Tanaka 1990)

No7

32.0

511

325

0.55

0.55

0.30

1.25

2.10

147

Tanaka 1990)

No8

32.1

511

325

0.55

0.55

0.30

1.25

2.10

148

Park and Paulay 1990)

No9

26.9

432

305

0.60

0.40

0.10

1.89

1.88

149

Arakawa et al. 1982)

No.102

20.6

393

323

0.25

0.25

0.33

0.68

1.20

150

Ohno and Nishioka 1984)

L1

24.8

362

325

0.40

0.40

0.03

1.42

0.30

151

Ohno and Nishioka 1984)

L2

24.8

362

325

0.40

0.40

0.03

1.42

0.30

152

Ohno and Nishioka 1984)

L3

24.8

362

325

0.40

0.40

0.03

1.42

0.30

153

Zhou et al. 1987)

214–08

21.1

341

559

0.16

0.16

0.80

2.22

0.70

154

Kanda 1988)

85STC-1

27.9

374

506

0.25

0.25

0.11

1.62

0.40

155

Kanda 1988)

85STC-2

27.9

374

506

0.25

0.25

0.11

1.62

0.40

156

Kanda 1988)

85STC-3

27.9

374

506

0.25

0.25

0.11

1.62

0.40

157

Kanda 1988)

85PDC-1

24.8

374

352

0.25

0.25

0.12

1.62

0.40

158

Kanda 1988)

85PDC-2

27.9

374

506

0.25

0.25

0.11

1.62

0.40

159

Kanda 1988)

85PDC-3

27.9

374

506

0.25

0.25

0.11

1.62

0.40

160

Muguruma et al. 1989)

AL-1

85.7

399

328

0.20

0.20

0.40

3.17

1.60

161

Muguruma et al. 1989)

AH-1

85.7

399

792

0.20

0.20

0.40

3.80

1.60

162

Muguruma et al. 1989)

AL-2

85.7

399

328

0.20

0.20

0.63

3.80

1.60

163

Muguruma et al. 1989)

AH-2

85.7

399

792

0.20

0.20

0.63

3.80

1.60

164

Muguruma et al. 1989)

BL-1

115.8

399

328

0.20

0.20

0.25

3.80

1.60

165

Muguruma et al. 1989)

BH-1

115.8

399

792

0.20

0.20

0.25

3.80

1.60

166

Muguruma et al. 1989)

BL-2

115.8

399

328

0.20

0.20

0.42

3.80

1.60

167

Muguruma et al. 1989)

BH-2

115.8

399

792

0.20

0.20

0.42

3.80

1.60

168

Sakai 1990)

B1

99.5

379

774

0.25

0.25

0.35

2.43

0.50

169

Sakai 1990)

B2

99.5

379

774

0.25

0.25

0.35

2.43

0.70

170

Sakai 1990)

B3

99.5

379

344

0.25

0.25

0.35

2.43

0.60

171

Sakai 1990)

B4

99.5

379

1126

0.25

0.25

0.35

2.43

0.50

172

Sakai 1990)

B5

99.5

379

774

0.25

0.25

0.35

2.43

0.50

173

Sakai 1990)

B6

99.5

379

857

0.25

0.25

0.35

2.43

0.50

174

Sakai 1990)

B7

99.5

339

774

0.25

0.25

0.35

1.81

0.50

175

Atalay and Penzien 1975)

No.1S1

29.1

367

363

0.31

0.31

0.10

1.63

1.50

176

Atalay and Penzien 1975)

No.2S1

30.7

367

363

0.31

0.31

0.09

1.63

0.90

177

Atalay and Penzien 1975)

No.3S1

29.2

367

363

0.31

0.31

0.10

1.63

1.50

178

Atalay and Penzien 1975)

No.4S1

27.6

429

363

0.31

0.31

0.10

1.63

0.90

179

Atalay and Penzien 1975)

No.5S1

29.4

429

392

0.31

0.31

0.20

1.63

1.50

180

Atalay and Penzien 1975)

No.6S1

31.8

429

392

0.31

0.31

0.18

1.63

0.90

181

Atalay and Penzien 1975)

No.9

33.3

363

392

0.31

0.31

0.26

1.63

1.50

182

Atalay and Penzien 1975)

No.10

32.4

363

392

0.31

0.31

0.27

1.63

0.90

183

Atalay and Penzien 1975)

No.11

31.0

363

373

0.31

0.31

0.28

1.63

1.50

184

Atalay and Penzien 1975)

No.12

31.8

363

373

0.31

0.31

0.27

1.63

0.90

185

Azizinamini et al. 1988)

NC

39.3

439

454

0.46

0.46

0.21

1.94

2.20

186

Azizinamini et al. 1988)

NC

39.8

439

616

0.46

0.46

0.31

1.94

1.30

187

Saatcioglu and Ozcebe 1989)

U1

43.6

430

470

0.35

0.35

0.00

3.31

0.90

188

Saatcioglu and Ozcebe 1989)

U3

34.8

430

470

0.35

0.35

0.14

3.31

2.50

189

Saatcioglu and Ozcebe 1989)

U4

32.0

438

470

0.35

0.35

0.15

3.31

2.50

190

Saatcioglu and Ozcebe 1989)

U6

37.3

437

425

0.35

0.35

0.13

3.31

3.21

191

Saatcioglu and Ozcebe 1989)

U7

39.0

437

425

0.35

0.35

0.13

3.31

2.00

192

Galeota et al. 1996)

AA1

80.0

430

430

0.25

0.25

0.30

1.51

1.20

193

Galeota et al. 1996)

AA2

80.0

430

430

0.25

0.25

0.30

1.51

1.20

194

Galeota et al. 1996)

AA3

80.0

430

430

0.25

0.25

0.20

1.51

1.20

195

Galeota et al. 1996)

AA4

80.0

430

430

0.25

0.25

0.20

1.51

1.20

196

Galeota et al. 1996)

BA1

80.0

430

430

0.25

0.25

0.20

1.51

1.80

197

Galeota et al. 1996)

BA2

80.0

430

430

0.25

0.25

0.30

1.51

1.80

198

Galeota et al. 1996)

BA3

80.0

430

430

0.25

0.25

0.30

1.51

1.80

199

Galeota et al. 1996)

BA4

80.0

430

430

0.25

0.25

0.20

1.51

1.80

200

Galeota et al. 1996)

CA1

80.0

430

430

0.25

0.25

0.20

1.51

3.70

201

Galeota et al. 1996)

CA2

80.0

430

430

0.25

0.25

0.30

1.51

3.70

202

Galeota et al. 1996)

CA3

80.0

430

430

0.25

0.25

0.20

1.51

3.70

203

Galeota et al. 1996)

CA4

80.0

430

430

0.25

0.25

0.30

1.51

3.70

204

Galeota et al. 1996)

AB1

80.0

430

430

0.25

0.25

0.20

6.03

1.20

205

Galeota et al. 1996)

AB2

80.0

430

430

0.25

0.25

0.30

6.03

1.20

206

Galeota et al. 1996)

AB3

80.0

430

430

0.25

0.25

0.30

6.03

1.20

207

Galeota et al. 1996)

AB4

80.0

430

430

0.25

0.25

0.20

6.03

1.20

208

Galeota et al. 1996)

BB

80.0

430

430

0.25

0.25

0.20

6.03

1.80

209

Galeota et al. 1996)

BB1

80.0

430

430

0.25

0.25

0.20

6.03

1.80

210

Galeota et al. 1996)

BB4

80.0

430

430

0.25

0.25

0.30

6.03

1.80

211

Galeota et al. 1996)

BB4B

80.0

430

430

0.25

0.25

0.30

6.03

1.80

212

Galeota et al. 1996)

CB1

80.0

430

430

0.25

0.25

0.20

6.03

3.70

213

Galeota et al. 1996)

CB2

80.0

430

430

0.25

0.25

0.20

6.03

3.70

214

Galeota et al. 1996)

CB3

80.0

430

430

0.25

0.25

0.30

6.03

3.70

215

Galeota et al. 1996)

CB4

80.0

430

430

0.25

0.25

0.30

6.03

3.70

216

Wehbe 1998)

A1

27.2

448

428

0.61

0.38

0.10

2.22

0.40

217

Wehbe 1998)

A2

27.2

448

428

0.61

0.38

0.24

2.22

0.40

218

Wehbe 1998)

B1

28.1

448

428

0.61

0.38

0.09

2.22

0.50

219

Wehbe 1998)

B2

28.1

448

428

0.61

0.38

0.23

2.22

0.50

220

Xiao and Martirossyan 1998b)

HC4-0.1P

76.0

510

510

0.25

0.25

0.10

3.55

3.70

221

Xiao and Martirossyan 1998b)

HC4-0.2P

76.0

510

510

0.25

0.25

0.20

3.55

3.70

222

Xiao and Martirossyan 1998b)

HC4-0.1P

86.0

510

510

0.25

0.25

0.10

2.46

3.70

223

Xiao and Martirossyan 1998b)

HC4-0.2P

86.0

510

510

0.25

0.25

0.19

2.46

3.70

224

Sugano 1996)

UC10H

118.0

393

1415

0.23

0.23

0.60

1.86

3.18

225

Sugano 1996)

UC15H

118.0

393

1424

0.23

0.23

0.60

1.86

5.00

226

Sugano 1996)

UC20H

118.0

393

1424

0.23

0.23

0.60

1.86

5.00

227

Sugano 1996)

UC15L

118.0

393

1424

0.23

0.23

0.35

1.86

5.00

228

Sugano 1996)

UC20L

118.0

393

1424

0.23

0.23

0.35

1.86

5.00

229

Nosho et al. 1996)

No.1

40.6

407

351

0.28

0.28

0.34

1.01

2.18

230

Bayrak and Sheikh 1996)

ES-1HT

72.1

454

463

0.31

0.31

0.50

2.58

3.20

231

Bayrak and Sheikh 1996)

AS-2HT

71.7

454

542

0.31

0.31

0.36

2.58

2.80

232

Bayrak and Sheikh 1996)

AS-3HT

71.8

454

542

0.31

0.31

0.50

2.58

2.80

233

Bayrak and Sheikh 1996)

AS-4HT

71.9

454

463

0.31

0.31

0.50

2.58

5.10

234

Bayrak and Sheikh 1996)

AS-5HT

101.8

454

463

0.31

0.31

0.45

2.58

4.00

235

Bayrak and Sheikh 1996)

AS-6HT

101.9

454

463

0.31

0.31

0.46

2.58

6.70

236

Bayrak and Sheikh 1996)

AS-7HT

102.0

454

542

0.31

0.31

0.45

2.58

2.70

237

Bayrak and Sheikh 1996)

ES-8HT

102.2

454

463

0.31

0.31

0.47

2.58

4.30

238

Saatcioglu and Grira 1999)

BG-1

34.0

455

570

0.35

0.35

0.43

1.95

1.00

239

Saatcioglu and Grira 1999)

BG-2

34.0

455

570

0.35

0.35

0.43

1.95

2.00

240

Saatcioglu and Grira 1999)

BG-3

34.0

455

570

0.35

0.35

0.20

1.95

2.00

241

Saatcioglu and Grira 1999)

BG-4

34.0

455

570

0.35

0.35

0.46

2.93

1.30

242

Saatcioglu and Grira 1999)

BG-5

34.0

455

570

0.35

0.35

0.46

2.93

2.70

243

Saatcioglu and Grira 1999)

BG-6

34.0

478

570

0.35

0.35

0.46

2.29

2.70

244

Saatcioglu and Grira 1999)

BG-7

34.0

455

580

0.35

0.35

0.46

2.93

1.30

245

Saatcioglu and Grira 1999)

BG-8

34.0

455

580

0.35

0.35

0.23

2.93

1.30

246

Saatcioglu and Grira 1999)

BG-9

34.0

428

580

0.35

0.35

0.46

3.28

1.30

247

Saatcioglu and Grira 1999)

BG-10

34.0

428

570

0.35

0.35

0.46

3.28

2.70

248

Matamoros 1999)

C10-05N

69.6

586

407

0.20

0.20

0.05

1.93

1.00

249

Matamoros 1999)

C10-05S

69.6

586

407

0.20

0.20

0.05

1.93

1.00

250

Matamoros 1999)

C10-10N

67.8

572

514

0.20

0.20

0.10

1.93

1.00

251

Matamoros 1999)

C10-10S

67.8

573

515

0.20

0.20

0.10

1.93

1.00

252

Matamoros 1999)

C10-20N

65.5

572

514

0.20

0.20

0.21

1.93

1.00

253

Matamoros 1999)

C10-20S

65.5

573

515

0.20

0.20

0.21

1.93

1.00

254

Matamoros 1999)

C5-00N

37.9

572

514

0.20

0.20

0.00

1.93

1.00

255

Matamoros 1999)

C5-00S

37.9

573

515

0.20

0.20

0.00

1.93

1.00

256

Matamoros 1999)

C5-20N

48.3

586

407

0.20

0.20

0.14

1.93

1.00

257

Matamoros 1999)

C5-20S

48.3

587

408

0.20

0.20

0.14

1.93

1.00

258

Matamoros 1999)

C5-40N

38.0

572

514

0.20

0.20

0.36

1.93

1.00

259

Matamoros 1999)

C5-40S

38.0

573

515

0.20

0.20

0.36

1.93

1.00

260

Mo and Wang 2000)

C1-1

24.9

497

459

0.40

0.40

0.11

2.14

3.00

261

Mo and Wang 2000)

C1-2

26.7

497

459

0.40

0.40

0.16

2.14

3.00

262

Mo and Wang 2000)

C1-3

26.1

497

459

0.40

0.40

0.22

2.14

3.00

263

Mo and Wang 2000)

C2-1

25.3

497

459

0.40

0.40

0.11

2.14

3.00

264

Mo and Wang 2000)

C2-2

27.1

497

459

0.40

0.40

0.16

2.14

3.00

265

Mo and Wang 2000)

C2-3

26.8

497

459

0.40

0.40

0.21

2.14

3.00

266

Mo and Wang 2000)

C3-1

26.4

497

459

0.40

0.40

0.11

2.14

3.00

267

Mo and Wang 2000)

C3-2

27.5

497

459

0.40

0.40

0.15

2.14

3.00

268

Mo and Wang 2000)

C3-3

26.9

497

459

0.40

0.40

0.21

2.14

3.00

269

Aboutaha and Machado 1999)

ORC1

83.0

414

414

0.51

0.31

0.00

2.53

5.19

270

Aboutaha and Machado 1999)

ORC2

83.0

414

414

0.51

0.31

0.12

2.53

5.19

271

Aboutaha and Machado 1999)

ORC3

83.0

414

414

0.51

0.31

0.16

2.53

5.20

272

Thomson and Wallace 1994)

A1

102.7

517

793

0.15

0.15

0.00

2.45

1.44

273

Thomson and Wallace 1994)

A3

86.3

517

793

0.15

0.15

0.20

2.45

1.44

274

Thomson and Wallace 1994)

B1

87.5

455

793

0.15

0.15

0.00

2.45

1.63

275

Thomson and Wallace 1994)

B2

83.4

455

793

0.15

0.15

0.10

2.45

1.63

276

Thomson and Wallace 1994)

B3

90.0

455

793

0.15

0.15

0.20

2.45

1.63

277

Thomson and Wallace 1994)

C1

67.5

476

1262

0.15

0.15

0.00

2.45

1.63

278

Thomson and Wallace 1994)

C2

74.6

476

1262

0.15

0.15

0.10

2.45

1.63

279

Thomson and Wallace 1994)

C3

81.8

476

1262

0.15

0.15

0.20

2.45

1.63

280

Thomson and Wallace 1994)

D1

75.8

476

1262

0.15

0.15

0.20

2.45

1.63

281

Thomson and Wallace 1994)

D2

87.0

476

1262

0.15

0.15

0.20

2.45

1.63

282

Thomson and Wallace 1994)

D3

71.2

476

1262

0.15

0.15

0.20

2.45

1.63

283

Legeron and Paultre 2000)

1,006,015

92.4

451

391

0.31

0.31

0.14

2.57

9.97

284

Legeron and Paultre 2000)

1,006,025

93.3

430

391

0.31

0.31

0.28

2.57

9.97

285

Legeron and Paultre 2000)

1,006,040

98.2

451

418

0.31

0.31

0.39

2.57

9.97

286

Legeron and Paultre 2000)

10,013,015

94.8

451

391

0.31

0.31

0.14

2.57

9.97

287

Legeron and Paultre 2000)

10,013,025

97.7

430

391

0.31

0.31

0.26

2.57

9.97

288

Legeron and Paultre 2000)

10,013,040

104.3

451

418

0.31

0.31

0.37

2.57

9.97

289

Paultre et al. 2001)

806,040

78.7

446

438

0.31

0.31

0.40

2.57

9.97

290

Paultre et al. 2001)

1,206,040

109.2

446

438

0.31

0.31

0.41

2.57

9.97

291

Paultre et al. 2001)

1,005,540

109.5

446

825

0.31

0.31

0.35

2.57

7.04

292

Paultre et al. 2001)

1,008,040

104.2

446

825

0.31

0.31

0.37

2.57

7.04

293

Paultre et al. 2001)

1,005,552

104.5

446

744

0.31

0.31

0.53

2.57

9.84

294

Paultre et al. 2001)

1,006,052

109.4

446

492

0.31

0.31

0.51

2.57

9.97

295

Pujol 2002)

10–2-3N

33.7

453

411

0.30

0.15

0.09

2.45

0.60

296

Pujol 2002)

10–2-3S

33.7

453

411

0.30

0.15

0.09

2.45

0.60

297

Pujol 2002)

10–3-1.5N

32.1

453

411

0.30

0.15

0.09

2.45

1.96

298

Pujol 2002)

10–3-1.5S

32.1

453

411

0.30

0.15

0.09

2.45

1.96

299

Pujol 2002)

10–3-3N

29.9

453

411

0.30

0.15

0.10

2.45

1.96

300

Pujol 2002)

10–3-3S

29.9

453

411

0.30

0.15

0.10

2.45

1.96

301

Pujol 2002)

10–3-2.25N

27.4

453

411

0.30

0.15

0.10

2.45

1.96

302

Pujol 2002)

10–3-2.25S

27.4

453

411

0.30

0.15

0.10

2.45

1.96

303

Pujol 2002)

20–3-3N

36.4

453

411

0.30

0.15

0.16

2.45

1.96

304

Pujol 2002)

20–3-3S

36.4

453

411

0.30

0.15

0.16

2.45

1.96

305

Pujol 2002)

10–2-2.25N

34.9

453

411

0.30

0.15

0.08

2.45

1.96

306

Pujol 2002)

10–2-2.25S

34.9

453

411

0.30

0.15

0.08

2.45

1.96

307

Pujol 2002)

10–1-2.25N

36.5

453

411

0.30

0.15

0.08

2.45

1.96

308

Pujol 2002)

10–1-2.25S

36.5

453

411

0.30

0.15

0.08

2.45

1.96

309

Kono and Watanabe 2000)

D1N30

37.6

461

485

0.25

0.25

0.30

2.43

1.91

310

Kono and Watanabe 2000)

D1N60

37.6

461

485

0.25

0.25

0.60

2.43

1.91

311

Kono and Watanabe 2000)

L1D60

39.2

388

524

0.60

0.60

0.57

1.69

7.81

312

Kono and Watanabe 2000)

L1N60

39.2

388

524

0.60

0.60

0.57

1.69

7.55

313

Kono and Watanabe 2000)

L1N6B

32.2

388

524

0.56

0.56

0.59

1.94

7.55

314

Harries et al. 2006)

L0

24.6

460

438

0.46

0.46

0.25

1.48

0.20

315

Melek and Wallace 2004)

S10MI

36.2

510

481

0.46

0.46

0.07

1.94

0.16

316

Melek and Wallace 2004)

S20MI

36.2

510

481

0.46

0.46

0.14

1.94

0.16

317

Melek and Wallace 2004)

S30MI

36.2

510

481

0.46

0.46

0.21

1.94

0.16

318

Melek and Wallace 2004)

S20HI

35.3

510

481

0.46

0.46

0.14

1.94

0.16

319

Melek and Wallace 2004)

S20HIN

35.3

510

481

0.46

0.46

0.14

1.94

0.16

320

Melek and Wallace 2004)

S30XI

35.3

510

481

0.46

0.46

0.22

1.94

0.16

Availability of data and materials

The data and materials in the current study are available from the corresponding author on reasonable request.

References

  • Aboutaha RS, Machado RI (1999) Seismic resistance of steel-tubed high-strength reinforced-concrete columns. J Struct Eng 125(5):485–494

    Article  Google Scholar 

  • Aboutaha RS, Engelhardt MD, Jirsa JO et al (1999) Rehabilitation of shear critical concrete columns by use of rectangular steel jackets. Struct J 96(1):68–78

    Google Scholar 

  • Aldabagh S, Hossain F, Alam MS (2022) Simplified Predictive Expressions of Drift Limit States for Reinforced Concrete Circular Bridge Columns. J Struct Eng 148(3):04021285

    Article  Google Scholar 

  • Amitsu S, Shirai N, Adachi H et al (1991) Deformation of reinforced concrete column with high or fluctuating axial force. Transact Japan Concrete Institute 13:355–362

    Google Scholar 

  • Ang BG (1981) Ductility of reinforced concrete bridge piers under seismic loading.

  • Arakawa T, Arai Y, Egashira K et al (1982) Effects of the rate of cyclic loading on the load-carrying capacity and inelastic behavior of reinforced concrete columns. Transact Japan Concrete Institute 4:485–492

    Google Scholar 

  • Arakawa T, Arai Y, Mizoguchi M et al (1989) Shear resisting behavior of short reinforced concrete columns under biaxial bending-shear. Transact Japan Concrete Institute 11:317–324

    Google Scholar 

  • Atalay MB, Penzien J (1975) The seismic behavior of critical regions of reinforced concrete components as influenced by moment, shear and axial force. Earthquake Engineering Research Center, University of California, Berkeley, CA, USA

    Google Scholar 

  • ATC-40. (1996) Seismic evaluation and retrofit of concrete buildings.Applied Technology Council, Report No. ATC 40, also California Seismic Safety Commission, Report No SSC 96–01.

  • Azizinamini A, Johal L S, Hanson N W, et al (1988) Effects of transverse reinforcement on seismic performance of columns—A partial parametric investigation. Project No. CR, 9617.

  • Bayrak O, Sheikh S (1996) Confinement steel requirements for high strength concrete columns[C]//Proceedings of the 11th world conference on earthquake engineering.

  • Bett BJ, Jirsa JO, Klingner RE (1985) Behavior of strengthened and repaired reinforced concrete columns under cyclic deformations[M]. Phil M. Ferguson Structural Engineering Laboratory, University of Texas at Austin, Austin, TX, USA

  • Calvi GM, Kingsley GR (1995) Displacement-based seismic design of multi-degree-of-freedom bridge structures. Earthquake Eng Struct Dynam 24(9):1247–1266

    Article  Google Scholar 

  • Cornell CA, Jalayer F, Hamburger RO et al (2002) Probabilistic basis for 2000 SAC federal emergency management agency steel moment frame guidelines. J Struct Eng 128(4):526–533

    Article  Google Scholar 

  • Elwood KJ, Moehle JP (2008) Dynamic shear and axial-load failure of reinforced concrete columns. J Struct Eng 134(7):1189–1198

    Article  Google Scholar 

  • En C (2005) Eurocode 8: Design of Structures for Earthquake Resistance–Part 2 Bridges. Comit´e Europ´een de Normalisation: Brussels, 146.

  • Esaki F (1996) Reinforcing effect of steel plate hoops on ductility of R/C square columns[C]//Proc., 11th World Conf. on Earthquake Engineering. Pergamon, Elsevier Science 199.

  • Galeota D, Giammatteo MM, Marino R (1996) Seismic resistance of high strength concrete columns[C]//11th World Conf. on Earthquake Engineering.

  • Gill WD (1979) Ductility of rectangular reinforced concrete columns with axial load.

  • Harries KA, Ricles JR, Pessiki S et al (2006) Seismic retrofit of lap splices in nonductile square columns using carbon fiber-reinforced jackets. ACI Struct J 103(6):874

    Google Scholar 

  • Hassane O (2002) Experimental study on seismic behavior of reinforced concrete columns under constant and variable axial loadings. Proc Japan Concrete Institute 24(2):229–234

    Google Scholar 

  • Hernández-Montes E, Aschleim M (2003) Estimates of the yield curvature for design of reinforced concrete columns. Mag Concr Res 55(4):373–383

    Article  Google Scholar 

  • Hirosawa M. A list of past experimental results of reinforced concrete columns[M]. Building Research Institute; 1973.

  • Ho JCM, Pam HJ (2010) Deformability evaluation of high-strength reinforced concrete columns. Mag Concr Res 62(8):569–583

    Article  Google Scholar 

  • Ikeda A. Report of the training institute for engineering teachers[J]. Japan: Yokohama National University; 1968.

  • Imai H, Yamamoto Y (1986) A study on causes of earthquake damage of Izumi high school due to Miyagi-Ken-Oki earthquake in 1978. Transact Japan Concrete Institute 8(1):405–418

    Google Scholar 

  • Iwasaki T, Kawashima K, Hagiwara R et al (1985) Experimental investigation on hysteretic behavior of reinforced concrete bridge pier columns. Public Works Research Institute, Tsukuba, Japan

    Google Scholar 

  • Kanda M (1988) Analytical study on elasto-plastic hysteretic behavior of reinforced concrete members. Transact Japan Concrete Institute 10:257–264

    Google Scholar 

  • Kono S, Watanabe F (2000) Damage evaluation of reinforced concrete columns under multiaxial cyclic loadings[C]//The second US-Japan workshop on performance-based earthquake engineering methodology for reinforced concrete building structures 221–231.

  • Legeron F, Paultre P (2000) Behavior of high-strength concrete columns under cyclic flexure and constant axial load. Struct J 97(4):591–601

    Google Scholar 

  • Lynn AC, Moehle JP, Mahin SA et al (1996) Seismic evaluation of existing reinforced concrete building columns. Earthq Spectra 12(4):715–739

    Article  Google Scholar 

  • Mander JB, Priestley MJN, Park R (1988) Theoretical stress-strain model for confined concrete. J Struct Eng 114(8):1804–1826

    Article  Google Scholar 

  • Matamoros A B. Study of drift limits for high-strength concrete columns[M]. University of Illinois at Urbana-Champaign; 1999.

  • Melek M, Wallace JW (2004) Cyclic behavior of columns with short lap splices. Struct J 101(6):802–811

    Google Scholar 

  • Ministry of Transport of the People’s Republic of China. Specifications for Seismic Design of Highway Bridges (JTG/T 2231–01–2020). 2020.

  • Mo YL, Wang SJ (2000) Seismic behavior of RC columns with various tie configurations. J Struct Eng 126(10):1122–1130

    Article  Google Scholar 

  • Moehle JP. (2000) The Second US-Japan Workshop on Performance-Based Earthquake Engineering Methodology for Reinforced Concrete Building Structures. Pacific Earthquake Engineering Research Center (PEER) 2000(10).

  • Muguruma H, Watanabe F, Komuro T (1989) Applicability of high strength concrete to reinforced concrete ductile column. Transact Japan Concrete Institute 11(1):309–316

    Google Scholar 

  • Nagasaka T (1982) Effectiveness of steel fiber as web reinforcement in reinforced concrete columns. Transact Japan Concrete Institute 4(1):493–500

    Google Scholar 

  • Nakamura T, Yoshimura M (2002) Gravity load collapse of reinforced concrete columns with brittle failure modes. J Asian Archit Build Eng 1(1):21–27

    Article  Google Scholar 

  • Nosho K, Stanton J, MacRae G. (1996) Retrofit of rectangular reinforced concrete columns using tonen forca tow sheet carbon fiber wrapping. Report No. SGEM 96–2.

  • Ohno T, Nishioka T (1984) An experimental study on energy absorption capacity of columns in reinforced concrete structures. Doboku Gakkai Ronbunshu 1984(350):23–33

    Article  Google Scholar 

  • Ohue M, Morimoto H, Fujii S et al (1985) The behavior of RC short columns failing in splitting bond-shear under dynamic lateral loading. Transact Japan Concrete Institute 7(1):293–300

    Google Scholar 

  • Olivia M, Mandal P (2005) Curvature ductility of reinforced concrete beam. J Civ Eng 6(1):1–13

    Google Scholar 

  • Ono A (1989) Elasto-plastic Behavior of Reinforced Concrete Column with Fluctuating Axial Fore. Transact Japan Concrete Institute 11:239–246

    Google Scholar 

  • ONO A, SHIMIZU Y (1985) Behavior of reinforced concrete column under high axial load.

  • Pandey GR, Mutsuyoshi H (2005) Seismic performance of reinforced concrete piers with bond-controlled reinforcements. ACI Struct J 102(2):295

    Google Scholar 

  • Pantelides CP, Gergely J (2002) Carbon-fiber-reinforced polymer seismic retrofit of RC bridge bent: Design and in situ validation. J Compos Constr 6(1):52–60

    Article  Google Scholar 

  • Park R, Paulay T. Use of interlocking spirals for transverse reinforcement in bridge columns. Strength and ductility of concrete substructures of bridges, RRU (Road Research Unit) Bulletin, 1990, 84(1): 77–92.

  • Paultre P, Légeron F, Mongeau D (2001) Influence of concrete strength and transverse reinforcement yield strength on behavior of high-strength concrete columns. Struct J 98(4):490–501

    Google Scholar 

  • Priestley MJN (1998) Brief comments on elastic flexibility of reinforced concrete frames and significance to seismic design. Bulletin of the New Zealand National Society for Earthquake Engineering 31(4):246–259

  • Priestley MJN, Seible F, Xiao Y (1994) Steel jacket retrofitting of reinforced concrete bridge columns for enhanced shear strength–Part 2: Test results and comparison with theory. Structural Journal 91(5):537–551

    Google Scholar 

  • Priestley MJN, Seible F, Calvi GM. Seismic design and retrofit of bridges[M]. John Wiley & Sons; 1996.

  • Pujol S. Drift capacity of reinforced concrete columns subjected to displacement reversals[M]. Purdue University; 2002.

  • Saatcioglu M, Grira M (1999) Confinement of reinforced concrete columns with welded reinforced grids. Struct J 96(1):29–39

    Google Scholar 

  • Saatcioglu M, Ozcebe G (1989) Response of reinforced concrete columns to simulated seismic loading. Struct J 86(1):3–12

    Google Scholar 

  • Sakai Y. Experimental studies on flexural behavior of reinforced concrete columns using high-strength concrete. Japan Concrete Institute, 1990.

  • Sezen H, Moehle JP (2002) Seismic behavior of shear-critical reinforced concrete building columns[C]//Seventh US National Conference on Earthquake Engineering, Earthquake Engineering Research Institute, Boston, MA.

  • Sezen H, Moehle JP (2004) Shear strength model for lightly reinforced concrete columns. J Struct Eng 130(11):1692–1703

    Article  Google Scholar 

  • Soesianawati MT (1986) Limited ductility design of reinforced concrete columns.

  • Su J, Wang J, Li Z et al (2019) Effect of reinforcement grade and concrete strength on seismic performance of reinforced concrete bridge piers. Eng Struct 198:109512

    Article  Google Scholar 

  • Sugano S (1996) Seismic behavior of reinforced concrete columns which used ultra-high-strength concrete[C]//Eleventh World Conference on Earthquake Engineering, Paper (1383).

  • Tanaka H (1990) Effect of lateral confining reinforcement on the ductile behaviour of reinforced concrete columns.

  • Thomson JH, Wallace JW (1994) Lateral load behavior of reinforced concrete columns constructed using high-strength materials. Struct J 91(5):605–615

    Google Scholar 

  • Umehara H (1983) Shear strength and deterioration of short reinforced concrete columns under cyclic deformations.

  • Umemura H, Endo T. Report by Umemura Lab[J]. Tokyo University; 1970.

  • Watson S (1989) Design of reinforced concrete frames of limited ductility.

  • Wehbe N (1998) EERI Annual Student Paper Award Confinement of Rectangular Bridge Columns in Moderate Seismic Areas. Earthq Spectra 14(2):397–406

    Article  Google Scholar 

  • Wight JK. Shear strength decay in reinforced concrete columns subjected to large deflection reversals[M]. University of Illinois at Urbana-Champaign; 1973.

  • Xiao Y, Martirossyan A (1998) Seismic performance of high-strength concrete columns. J Struct Eng 124(3):241–251

    Article  Google Scholar 

  • Yalcin C. Seismic evaluation and retrofit of existing reinforced concrete bridge columns[J]. PhD Dessertation. Department of Civil Engineering, University of Ottawa; 1997.

  • Yarandi MS (2007) Seismic retrofit and repair of existing reinforced concrete bridge columns by transverse prestressing. University of Ottawa , Canada.

  • Yoshimura M, Yamanaka N (2000) Ultimate limit state of RC columns. PEER Report 10:313–326

    Google Scholar 

  • Yoshimura K, Kikcuri K, Kuroki M (1991) Seismic shear strengthening method for existing R/C short columns. Special Publication 128:1065–1080

    Google Scholar 

  • Yoshimura M, Takaine Y, Nakamura T (2003) Collapse drift of reinforced concrete columns. PEER Report 11:239–253

    Google Scholar 

  • Zahn FA (1985) Design of reinforced concrete bridge columns for strength and ductility.

  • Zhang J, Cai R, Li C et al (2020) Seismic behavior of high-strength concrete columns reinforced with high-strength steel bars. Eng Struct 218:110861

    Article  Google Scholar 

  • Zhong J, Ni M, Hu H et al (2022a) Uncoupled multivariate power models for estimating performance-based seismic damage states of column curvature ductility[C]//Structures. Elsevier 36:752–764

    Google Scholar 

  • Zhou X, Satoh T, Jiang W et al (1987) Behavior of reinforced concrete short column under high axial load. Transactions of the Japan Concrete Institute 9(6):541–548

    Google Scholar 

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Acknowledgements

This research was supported by the National Natural Science Foundation of China (52178135).

Funding

This research was funded by the National Natural Science Foundation of China (52178135).

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Yanyan Zhu: Software, Data curation, Validation, Writing-Original draft. Jian Zhong: Conceptualization, Methodology, Supervision, Writing-Review and Editing. All authors have read and agreed to the published version of the manuscript.

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Correspondence to Jian Zhong.

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Zhu, Y., Zhong, J. A yield curvature model considering axial compression ratio. ABEN 4, 19 (2023). https://doi.org/10.1186/s43251-023-00099-w

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