SEE6 / 1 / IIEES

A NEW PERIOD-BASED DAMAGE INDEX FOR SEISMIC ASSESSMENT OF RC FRAMES AND ITS VERIFICATION

E. Moshtagh, A. Massumi

Department of Civil Engineering, School of Engineering, Tarbiat Moallem University, Tehran, Iran

emaisl: ehs.moshtagh@tmu.ac.ir, massumi@tmu.ac.ir

ABSTRACT Nonlinear dynamic characteristics are appropriate indices to evaluate seismic behavior of damaged structures precisely. These characteristics reflect the effects of material properties, distribution of cracks and plastic hinges, construction quality and infill panels. Nonlinear characteristics may be extracted by some field tests like forced and/or ambient vibration methods. Recently a new damage index, based on nonlinear fundamental period of damaged structures, was represented by the authors to evaluate damage rate of reinforced concrete (RC) buildings after each moderate and/or severe earthquakes. This paper explains the procedure of finding the new period-based damage index and verifies the represented pattern of this damage index through some experimental data. This verification helps to trust and validate a pattern which estimates damage rates of RC buildings without modeling. As the proposed damage index is not depend on modeling, it could be more accurate than others, if it be calibrated using real data; because the modeling procedures which is depend on many known and unknown factors, could affect the results of analyses. Kywords: Period-Based Damage Index, Nonlinear Period, Reinforced Concrete Frames, Experimental Data, Seismic Behavior 1. INTRODUCTION Nonlinear dynamic characteristics are utilized for health monitoring of existing structures cheaply. Also the best dynamic parameter to evaluate structural integrity is natural period because of its sensitivity [1-2]. The effects of cracks and plastic hinges’ distribution, infill panels and architectural configuration (irregularity) are reflected by that too. Furthermore overall seismic behavior could be changed by the seismic behavior of each structural member which is represented by its dissipated energy and loading history (deformations). Therefore there is a useful correlation between these issues (natural period and seismic behavior of each member). This paper pursue the seismic behavior of RC structures while the lateral load increases and propose a new paradigm according to that correlation to evaluate damage rate of RC structures after each earthquake. The variation of natural period and seismic behavior of each element are considered to detect

Sixth International Conference of Seismology and Earthquake Engineering

16-18 May 2011 Tehran, Iran

SEE6 / 2 / IIEES

the logical correlation. A crucial damage index –Park-Ang– is utilized to pursue exact seismic behaviour of each element through using experimental data in modelling of hysteretic behavior model as following [3]:

m rh

u r y u

DI EM

θ θ βθ θ θ

−= +−

(1)

( ) ( ) ; ( ) istory i i component i componentcomponent

i component

EDI DIE

λ λ⎛ ⎞

= = ⎜ ⎟⎜ ⎟⎝ ⎠

∑ ∑ (2)

( ) ( ) ; ( ) ioverall i story i story i story

i story

EDI DIE

λ λ⎛ ⎞

= = ⎜ ⎟⎜ ⎟⎝ ⎠

∑ ∑ (3)

Where θm is the maximum rotation attained during the loading history; θu is the ultimate rotation capacity of the section; θy is the recoverable rotation when unloading; My is the yield moment, Eh is the dissipated energy in the section, β is the model constant parameter which was suggested 0.1 for nominal strength deterioration, λi is the energy weighting factor and Ei is the total absorbed energy by the component or story “i” [4-5]. 2. INCREMENTAL LOADING This stage does not mean that seismic assessment of existing RC buildings based on fundamental period elongation need to modeling and analysis. In this stage, the correlation between damage rate and variation percentage of nonlinear fundamental period has just been chased step by step to identify. Six flexural RC frames which are compatible with 3rd edition of Iranian Code of Practice for Seismic Resistant Design of Buildings [6] and Iranian National Building Codes (Part 9: Design and construction of reinforced concrete buildings) [7] have been studied. Also the configuration of frames is shown in Figure 1 with 3m stories’ height and 4m spans’ width. In this analytical process pushover analysis is carried out and its results are shown in Figure 2. Assessment shows that fundamental period is elongated in each step (with increasing of base shear coefficient) according to the damage rate (Park-Ang index). Also some of these steps are shown in Figure 3 for 10-Story frame (δ is fundamental period elongation). This procedure continues until fundamental period shift abruptly. This correlation is shown for each frame in Figure 4.

Figure 1. Frames’ configuration

SEE6 / 3 / IIEES

Figure 2. Capacity curves of moment resisting RC frames

Figure 3. Fundamental period elongation correspondence to the damage rate

Figure 4. Period elongation pursuit corresponding to the damage rate

SEE6 / 4 / IIEES

3. DETECTED CORRELATIONS It is common that structures are encountered with softening (period elongation) during damage increase. Assessments in each step show that after a specific step structures are encountered severe softening and they are beyond repair, therefore they are unreliable. Whereas they are considered such a repairable structure by assessments merely based on deformation and dissipated energy of elements [4]. Consideration of fundamental period causes this disparity. Seismic behavior of structures originates not only in hysteretic behavior of elements but also in configuration of structure and distribution of damage in structure. Thus if hysteretic behavior of elements is just considered in damage model, it would not seem a precise damage model. In this regard, fundamental period would contribute to complete damage model beside the hysteretic behavior of elements. Existing RC structures would be considered repairable in new pattern if the fundamental period elongation be less than δCritical because after this stage structures are encountered severe softening. This is noticeable in Figure 5 to Figure 10 that the damage curves have an asymptote near the percentage of critical elongation. It means that the stiffness of structure tend to the least value. Damage pattern of structures which are analyzed based on percentage of period elongation are shown in these figures. Steps which are pertained to severe softening are eliminated from the analysis process because this new pattern is valuable while the structures are repairable.

Figure 5. 2-Story damage pattern Figure 6. 4-Story damage pattern

Figure 7. 6-Story damage pattern Figure 8. 7-Story damage pattern

SEE6 / 5 / IIEES

Figure 9. 8-Story damage pattern Figure 10. 10-Story damage pattern

4. PROPOSED PATTERN A general damage pattern is proposed as a consequence of seismic damage assessment of these flexural RC frames (with no shear wall). This pattern is based on the percentage of non-linear fundamental period elongation (δ) which is calculated by Equation 4. Tplastic is the period of existing damaged RC buildings which is extracted by field tests. Telastic is the initial period of them when they are not damaged by earthquake and is calculated by experimental formula like which Iranian Code of Practice for Seismic Resistant Design of Buildings (3rd edition) suggested in Equation 5 [6]. Also H is the height of RC frames in meters.

( )plastic elastic

elastic

T TT

δ−

= (4)

3( )40.07elasticT H= (5)

New damage pattern is proposed in Equation 6. α and β are damage coefficient which are pertained to the initial elastic period of frames that is calculated by experimental formula. The correlation curves of damage coefficients with initial elastic period are presented in Figure 11 and Figure 12.

0.5

1DIα βδ

=−

(6)

Figure 11. Damage coefficient value of α Figure 12. Damage coefficient value of β

SEE6 / 6 / IIEES

Steps to seismic damage assessment of existing RC buildings based on new damage pattern: (a) Extract fundamental plastic period of existing damaged RC building by field tests [1] (b) Calculate fundamental elastic period of existing damaged RC building by experimental

or code period (usually for vital buildings this is available) (c) Calculate δ and read damage coefficient from correlation curves (d) Utilize new pattern (new pattern is valuable while δ ≤ δCritical)

δCritical is a new criteria to decide whether the damaged building is repairable or not. The buildings would be repairable if their period elongation be less than δCritical because they encounter sever softening afterward. This softening is occurred whereas some elements have been capable to load yet. This paradox originates from how the plastic hinges and cracks distribute throughout the structure that cause to change global stiffness matrix of structure abruptly. New damage pattern is represented in new format by changing Equation 6 to Equation 7. The value of δCritical is related to initial elastic period to which is correlated in Figure 13.

0.5 0.5

1( )

Critical

DIβ δ δ

=−

(7)

5. PATTERN’S PURVIEW & VERIFICATION In this pattern utilizing elastic and plastic experimental period is emphasized. However by some references which have assessed many RC frames empirically and analytically the disparity of experimental and analytical elastic period is mentioned at the most, less than 100 percent [3-8]. The disparity of experimental and analytical elastic periods for these five frames is represented in Table 1.

Figure 13. Value of δCritical

Table 1. Comparison of experimental and analytical elastic period

Number of Story Analytical Elastic Period

Experimental (Code) Elastic Period Disparity (%)

2 0.52 0.27 94 4 0.69 0.45 53 6 0.77 0.61 26 7 0.83 0.69 20 8 0.92 0.76 21

10 0.96 0.90 7 To inquire into this issue two case study of existing RC buildings are mentioned in this paper. The first one is an isolated 14 storey building which has been named Portela, founded on a thick gravel soil. It constructed in Lisbon in the 1970s. Seismic characteristics which were extracted by field tests and analyses are represented in Table 2 for Portela. Also its configuration is shown in Figure 14.

SEE6 / 7 / IIEES

Table 2. Portela building: Comparison of frequencies measured in-situ and computed with an analytical model (units: Hz) [9]

Vibration mode In-situ testing Analytical model Without infill walls With infill walls

1X direction 2.15 0.72 2.11 1Y direction 2.15 0.81 2.14

1Torsion 2.61 0.86 2.98 2X direction 7.03 1.94 6.36 2Y direction 7.03 2.23 6.61 XY direction 13.6 3.53 11.4

Figure 14. Portela building: a view; b plan and c and d 3-D analytical model with fundamental modes [9]

The second one is Solmar which is a 23 storeys RC building. Solmar comprises three cores which practically define the building behaviour to flexion and torsion. Therefore it could represent a guideline for tall and special buildings to whether use or not use analytical elastic period in seismic assessment based on fundamental period. Seismic characteristics of Solmar which are extracted by field test and modelling are represented in Table 3. Also the configuration of Solmar is shown in Figure 15. Table 3. Solmar building: comparison of frequencies measured in-situ and computed with an analytical

model (units: Hz) [9] Vibration mode In-situ testing Analytical model Error (%)

1Y direction 1.07 0.934 -12.7 1X direction 1.08 0.970 -10.1

1Torsion 1.43 1.521 6.4 2Y direction 3.6 3.401 -5.5 XY direction 3.6 3.642 1.2

2Torsion 4.6 4.758 3.4

SEE6 / 8 / IIEES

Figure 15. Solmar building: a plan; b view and c 3-D analytical model [9]

According to those references analytical elastic period could be utilized instead of experimental elastic period in this new damage pattern because it does not lead to large deviation. Therefore this new pattern is also useful for buildings that their initial elastic periods are not available. It should be further pointed out that plastic period of damaged buildings should be just extracted experimentally by field tests (Also new pattern is valuable whileδ ≤ δCritical). Regarding to this issue the value of damage coefficients and δCritical according to initial analytical period are represented in Figure 16, 17 and 18 too.

Figure 16. Damage coefficient value of α Figure 17. Damage coefficient value of β

Figure 18. Value of δCritical

SEE6 / 9 / IIEES

The best way for verification is using shaking tables and a full scale test. This is not possible for authors. Thus two series of experimental data from other references are selected for verification of proposed pattern. The first one is related to a 1 story RC frame with 415 cm high and its columns fixed in the lower spandrel beams. The configuration of frame and columns’ specifications are shown in Figure 19. Also the distance of the stirrups equals 15 cm at the 90 cm upper and lower sections of the columns and 30 cm in the mid-section. Furthermore, the initial seismic characteristics of this frame are presented in Table 4 and the plastic seismic characteristics correspondence to damage rate of that are presented in Table 5. The description of damage states are mentioned in Ref 10.

Figure 19. Configuration and specification of RC frame on shaking table [10]

Table 4. The initial seismic characteristics of RC frame [10]

Compressive concrete strength (MPa)

Young’s modulus of concrete (MPa)

f1 (Hz) direction x

f2 (Hz) direction y

f3 (Hz) torsion

36.65 31527 4.88 5.98 10.58

Table 5. The plastic seismic characteristics of RC frame correspondence to different damage level [10] Damage state f1 (Hz) f2 (Hz) f3 (Hz)

N 4.69 5.32 10.16 I 4.20 4.98 9.77 II 2.83 3.61 7.42 III 2.44 3.22 6.54 IV 2.09 2.54 5.47 V 1.76 2.15 4.69 VI 1.46 1.86 3.81

SEE6 / 10 / IIEES

Based on Table 5 and Ref 10 the RC frame encounters with the damage sate that small parts of concrete are falling and exposing the reinforcement in the upper parts of columns. Now to verify proposed pattern the DI is calculated in two directions as following: In X direction

2.341δ = 0.205 =142, =47, 9.14elastic CriticalT α β δ= ⇒ =

0.014DI = In Y direction

2.176δ = 0.167 =150, =50, 9.20elastic CriticalT α β δ= ⇒ =

0.013DI = Based on proposed pattern and description of Park-Ang damage index the frame must encounter with sporadic occurrence of cracking and partial crushing of concrete in some columns. This disparity of damage state in proposed pattern and observational situation originate in stirrups distance and columns’ dimension. According to columns’ dimension the stirrups’ distance should equal 8 cm at the 90 cm upper and lower sections of the columns and 16 cm in the mid-section based on Ref 7. Furthermore, none of the columns’ dimension should be less than 25 cm based on Ref 7. For these reasons the observational damages are more than anticipation. Therefore if RC structures satisfy the codes of practice for seismic resistant design of building, the proposed pattern could represent the damage state of them after each earthquake practically, cheaply and precisely. The second experimental data that are utilized relate to 4 stories, 2 bays and ¼ scaled model of RC frame which is without infill walls and design only for vertical loads in accordance with the Italian code before 1971. Thus the observational damage state should be more severe than proposed damage state reasonably. The initial fundamental period on shaking table is 0.48 second while it has elongated correspondence to increasing damage rates. The plastic period after the dynamic test is 0.83 second as a consequence of the moderate damage to many columns and, particularly, the heavy damage to some joints, as shown in Figure 20 whereas based on new pattern it should encounter with sporadic occurrence of cracking, if it satisfied the codes of practice for seismic resistant design of building.

Figure 20. Laboratory test: damage state in some beam-column joints at the end of tests [11]

6. CONCLUSION

Actual dynamic behavior is affected by dynamic behavior of elements, configuration of structures and infill panels. Furthermore, distribution of plastic hinges and cracks also damping ratio affect on dynamic behavior when the structure is on non-linear levels. Park-Ang damage

SEE6 / 11 / IIEES

index has just considered hysteretic behavior of each element as well as possible (dissipated energy and deformation). To complete this damage index and to assess real damage situation under seismic load fundamental period is considered which reflects the effects of configuration, infill panel and distribution of damage. Fortunately, pursuit of analysis’s steps detects a logical pattern between period elongation and damage rate [12]. Finally, it would be possible to precise seismic assessment of existing RC buildings by new damage pattern cheaply and expeditiously even there is not initial modal information of them but it should be noted that the new pattern needs to calibrate for each structural system by experimental data. 7. REFERENCES

1. Moshtagh, E. and Massumi, A. (2009). “Seismic assessment of RC buildings by estimation of effective parameters on seismic behavior using non-destructive tests”, The Structural Design of Tall and Special Buildings. (In Press). doi: 10.1002/tal.560.

2. Salawu, O. S. (1997). “Detection of structural damage through changes in frequency: a review”, Engineering Structures, 19(9): 718-723. doi: 10.1016/S0141-0296(96)00149-6.

3. Massumi, A. (2004). “Estimation of Response Modification Factors for RC-MRF Structures, Emphasizing on the Effect of Overstrength and Redundancy”, PhD Thesis of Structural Engineering. Dept. of Civil Engineering, Tarbiat Modarres University. (In Persian).

4. Park, Y. J., Ang, A. H.-S. and Wen, Y. K. (1987). “Damage-Limiting Aseismic Design of Buildings”, Earthquake Spectra, 3(1): 1-26. doi: 10.1193/1.1585416.

5. Park, Y. J., Reinhorn, A. M. and Kunnath, S. K. (1987). “IDARC: Inelastic Damage Analysis of Reinforced Concrete Frame - Shear-Wall Structures”, Technical Report NCEER-87-0008, State University of New York at Buffalo.

6. Building and Housing Research Center (BHRC). (2005) “Iranian Code of Practice for Seismic Resistant Design of Buildings”, Standard No. 2800-05, 3rd edition, Building and Housing Research Center: Tehran, Iran. (In Persian).

7. Ministry of Housing and Urban Development. (2005). “Iranian National Building Codes (Part 9: Design and Construction of Reinforced Concrete Buildings)”, Ministry of Housing and Urban Development, Tehran, Iran. (In Persian).

8. Tasnimi, A. A. and Massumi, A. (2006). “Estimation of Response Modification Factors for RC Moment Resisting Frames (Located in Low and Very High Seismicity Area)”, Building and Housing Research Center (BHRC), Publication No. R-436: Tehran, Iran. (In Persian).

9. Oliveira, C. S. and Navarro M. (2009). “Fundamental Period of Vibration of RC Buildings in Portugal In-Situ Experimental and Numerical Techniques”, Bulletin of Earthquake Engineering, 8(3): 609-642. doi: 10.1007/s10518-009-9162-1.

10. Zembaty, Z., Kowalski, M. and Pospisil, S. (2005). “Dynamic Identification of a Reinforced Concrete Frame in Progressive State of Damage”, Engineering Structures, 28(5): 668–681. doi:10.1016/j.engstruct.2005.09.025.

11. Masi, A. and Vona, M. (2009). “Experimental and Numerical Evaluation of The Fundamental Period of Undamaged and Damaged RC Framed Buildings”, Bulletin of Earthquake Engineering, 8(3): 643-656. doi: 10.1007/s10518-009-9136-3.

12. Massumi, A. and Moshtagh, E. (2010). “A New Damage Index for RC Buildings Based on Variations of Nonlinear Fundamental Period”, The Structural Design of Tall and Special Buildings. (In Press). doi: 10.1002/tal.656.