ON DRIFT LIMITS ASSOCIATED WITH DIFFERENT DAMAGE LEVELS Ahmed GHOBARAH ABSTRACT Performance objectives in performance-based design procedures have been described in several ways according to the operational status of the structure or the level of damage sustained up to collapse. The selection of the appropriate drift associated with different levels of damage for the design is significant in terms economy and safety. The identification of drift levels associated with different states of damage remains one of the unresolved issues in the development of performance objectives in performance-based design and assessment procedures. The objective of this study is to develop the approach to establish the drift of different structural systems that is associated with different definable levels of damage to use as performance objectives in the design of new structures and the evaluation of the seismic resistance of existing structures. Analytical and experimental data were used to examine the correlation between drift and damage of various structural elements and systems. The analytical procedures included time-history analysis, dynamic and static pushover analyses of various designs of reinforced concrete walls and moment resisting frames. Recently conducted tests as well as available experimental research results in the literature are reviewed for the appropriateness and consistency of the data. The experimental work included static and dynamic testing of walls and frame components. It was found that the drift associated with various damage levels of different reinforced concrete elements and structural systems vary significantly. Two main sets of drift limits were defined for ductile and nonductile structural systems. Keywords: Performance-based design, performance objectives, drift, damage, moment resisting frames, walls. INTRODUCTION Earthquakes continue to cause substantial damage and loss of life in many parts of the world. Although many buildings designed to current codes did not collapse during recent earthquakes, the level of damage to structures was unexpectedly high. In addition to the high cost of repairs, economic loss due to loss of use was significant. Department of Civil Engineering, McMaster University, Hamilton, Canada
Conventional methods of seismic design have the objectives to provide for life safety (strength and ductility) and damage control (serviceability drift limits). Current code design procedures succeeded in reducing loss of life during major seismic events. However, much remains to be done in the area of damage reduction. Performance-based design is a general design philosophy in which the design criteria are expressed in terms of achieving stated performance objectives when the structure is subjected to stated levels of seismic hazard. The performance targets may be a level of stress not to be exceeded, a load, a displacement, a limit state or a target damage state (Ghobarah 2). Specifying structural performance objectives in terms of drift limits has not been extensively studied. A set of performance objectives defined in terms of drift was given by several publications such as SEAOC (995) and FEMA (997). The definition of comprehensive and realistic drift limits that are associated with known damage states remains one of the important unresolved issues in performance-based design procedures. The relationship between performance objectives and damage is best illustrated by the typical performance curve shown in Figure. Vision 2 defined performance objectives are marked on the capacity curve. In addition, the states of damage of the structure are identified on the capacity curve. The structure is considered to suffer no damage or sustain very minor damage up to concrete cracking. Between concrete cracking and the first yield of steel, the crack sizes are normally < 2 mm and damage is considered to be repairable. Past steel yield, the cracks are wider than 2 mm and repair becomes difficult, impractical or costly, thus the irreparable damage classification. The described performance applies to ductile systems. However, nonductile systems may suffer brittle failure at any drift level that is associated with repairable or irreparable damage states. The structural response in terms of displacement can be related to strainbased limit state, which in turn is assumed related to damage. The defined performance of a structure in terms of a state of damage, strain or deformation gives better indicator of damage than stresses. However, relating displacement limits and drift of the structure to damage is an oversimplification since the level of damage is influenced by several other factors such as the structural system, the accumulation and distribution of structural damage, failure mode of the elements and components, the number of cycles and the duration of the earthquake and the acceleration levels in case of secondary systems. The objective of this investigation is to develop the approach to quantify the drift limits associated with different damage levels for some reinforced concrete structural systems such as moment resisting frames (MRF) and walls. 2
Behaviour Elastic Inelastic Collapse Damage Minor damage Repairable Irreparable Severe Extreme Vision 2 Immediate occupancy Operational Life safety Collapse prevention Near collapse Ultimate capacity Lateral load Yield of steel reinforcement Concrete cracking Drift Figure. Typical structural performance and associated damage states 2. DAMAGE An attempt to develop a procedure to correlate damage of various structural systems to drift taking into account various ground motion characteristics, was made through the use of a damage index (Ghobarah et al. 997). For effective design criteria, the correlation between damage and drift should be calibrated against experimental work as well as observed performance of structures during earthquakes when possible. Drift limits were found to vary and different sets should be developed for different structural systems such as nonductile and ductile moment resisting frame, moment resisting frame with infills, flexural structural walls and reinforced concrete squat shear walls. There have been several attempts to describe damage levels of various structural systems (Rossetto and Elnashai 23). The damage in terms of limits defined in this study (No damage, Repairable, Irreparable and Severe damage states) 3
associated with various performance levels of some structural systems such as nonductile and ductile moment resisting frames and frames with infills and walls, is described as follows: a) No damage No structural damage is observed. Some fine cracks in plaster may exist. b) Repairable damage Light damage. Initiation of hairline cracking in beams and columns near joints and in walls. Cracking at the interface between frame and infills and near corners of openings. Start of spalling in walls. Moderate damage. Flexural and shear cracking in beams, columns and walls. Some elements may reach yielding of steel. c) Irreparable damage Yielding of steel reinforcement occurs in several elements. Cracks are larger than 2 mm. Residual deflection may occur. Ultimate capacity is reached in some structural elements and walls. Failure of short columns may occur. Partial failure of infills and heavy damage to frame members may take place. Severe cracking and bucking of steel in boundary elements of walls occurs. d) Extreme Partial collapse of lateral and gravity load carrying elements of the structures is observed. Shear failure of columns. Shear failure of beams and columns causing complete failure of infills. Some reinforced concrete walls may fail. e) Collapse The structure may be on the verge of collapse or may experience total collapse. 3. DRIFT For the case of three performance levels (serviceability, damage control and life safety or collapse prevention), three corresponding structural characteristics (stiffness, strength and deformation capacity) dominate the performance. If more intermediate performance levels are selected, then it becomes difficult to define which structural characteristic dominate the performance. Different performance objectives may impose conflicting demands on strength and stiffness. The displacements or drift limits are also function of the structural system and its ability to deform (ductility). Design criteria may be established on the basis of observation and experimental data of deformation capacity. For example, near collapse the drift limits of ductile structural system are different from that of nonductle systems, which suggest that different drift limits will correspond to different damage levels for different structural systems. 4
3. Factors that affect drift The displacements or drift of a structure are functions of several factors such as the stiffness or strength and the ability of the structural system to deform (ductility). Other factors such as the applied load whether shear or flexure, confinement and shear span influence the structural deformations. An important factor in the behaviour of columns and walls is the effect of the axial load. The increase in the axial load increases the shear resistance of the member. In addition, it was found experimentally that the increase in axial load reduces the lateral drift. Although the performance objectives and the description of the associated damage may remain unchanged, it is clear that several sets of drift definitions are required to establish the limits for various structural systems and elements such as: Reinforced concrete moment resisting frame (MRF) a) Ductile well designed frames according to current codes. The established drift limits can be included in the code provisions. b) Existing frame with nonductile detailing designed to earlier codes. The established drift limits can be used in the evaluation of the lateral load carrying capacity of existing structures. c) Moment resisting frame with masonry infills. Structural walls a) Flexural structural walls of aspect ratio (height/length) >.5. b) Squat walls with predominantly shear behaviour of aspect ratio <.5. 3.2 Interstorey drift distribution The roof drift is a useful simple measure of the overall structural deformation that is routinely calculated. It can be determined from nonlinear dynamic analysis, pushover analysis or the equivalent single degree of freedom representation in response spectrum procedures. Roof drift calculated using the gross section inertia is almost half the drift calculated using the cracked section inertia. Roof drift can be related to damage. However, the roof drift does not reflect the distribution of damage along the height of the structure and does not identify weak elements or soft storeys. The interstorey drift can be directly used in the design and serviceability check for beams and columns of the frame and can be correlated to damage at the floor level. A welldesigned MRF structure according to current seismic code provisions would have an almost uniform interstorey drift distribution along its height. In this case, the relationship between the roof drift and the maximum interstorey drift is linear with near 45 o slope as shown in Figure 2. For existing nonductile structures and poorly designed frames such as those with a soft storey, the maximum interstorey drift of the soft storey may indicate collapse while the roof drift will correspond to lower damage level. Therefore, the damage to the MRF can be considered to be influenced by two drift parameters: a) the interstorey drift; and b) its distribution along the height of the structure. 5
6 5 Roof drift % 4 3 2 2 4 6 Maximum interstorey drift % 8 Figure 2. Relationship between maximum interstorey drift and roof drift of welldesigned 3, 6, 9 and 2 storey MRFs subjected to several ground motion records To take into account a measure of the storey drift distribution along the height of the structure, a representative factor is proposed. The factor is called the Storey Drift Factor (SDF) and can be calculated by the formula: SDF = ( n ) n n 2 ( Si S) 2 i= i= S ( S ) i 2 () where n is the number of storeys, S i is the maximum interstorey drift of floor i, and S is the mean value of the maximum interstorey drift ratios. The SDF includes a normalization factor such that it varies between and. The value of the interstorey drift factor of zero indicates equal interstorey drift along the different stories, and indicating that only one storey is the cause of the overall deformation. The formula given by equation () is the result of multiplying the normalized form of the standard deviation by the variation of S i from a specific value taken as zero. The normalization is to make the upper bound value of the factor as. 6
4. MOMENT RESISTING FRAMES 4. Ductile MRF The storey drift factor calculated using equation () for a number of ductile, welldesigned MRFs can be correlated with damage as shown in Figure 3. The damage index used is the final softening representing the effect of stiffness degradation following the application of the load. This damage index was arbitrarily selected because of its simplicity. Other damage indices could have been also used. In Figure 3, zero damage index indicates no damage while represents collapse. However in practical terms, the actual failure of the structure occurs at damage index values of.7 to.8. For ductile MRF, damage index values up to.2 represent repairable damage. The plot in Figure 3 using SDF on the horizontal axis can be compared with a similar damage plot using the maximum interstorey drift shown in Figure 4. The figures are similar but not identical. Comparison between the two horizontal axes of Figures 3 and 4 gives a rough relationship between the maximum interstorey drift and the SDF values. The SDF for the ductile reinforced concrete moment resisting frames is plotted with the ductility factor as shown in figure 5. For SDF values from to.2 the damage as measured by the final softening damage index is light. Moderate repairable damage is estimated for SDF values from.2 to.4. The start of yield as indicated by ductility > from figure 5 corresponds to SDF of.4, damage index of.5 and intersorey drift of.3. In the figure, the point marking the departure from ductility factor is well defined. Past the yield point, damage increases and is considered irreparable. When using a large sample of frames, the mean damage index at frame yield is closer to.2. The maximum interstorey drift limits corresponding to various damage states for a ductile MRF are listed in Table. Table. Drift ratio (%) limits associated with various damage levels State of damage Ductile MRF Nonductile MRF MRF with infills Ductile walls Squat walls No damage <.2 <. <. <.2 <. Repairable damage a) Light damage.4.2.2.4.2 b) Moderate damage <. <.5 <.4 <.8 <.4 Irreparable damage >. >.5 >.4 >.8 >.4 (>yield point) Severe damage - Life.8.8.7.5.7 safe - Partial collapse Collapse >3. >. >.8 >2.5 >.8 7
.8 Damage index.6.4.2.2.4.6.8 Storey drift factor (SDF) Figure 3. Correlation between the intersory drift factor and damage for a 3, 6, 9 and 2 storey MRFs. Damage index.8.6.4 3-storey frame 6-storey frame 9-storey frame 2 storey frame Data trend.2.5.5 2 2.5 3 3.5 4 Interstorey drift ratio % Figure 4. Damage at various drift levels of code designed 3, 6, 9 and 2 storey ductile MRFs 8
5 Ductility factor 4 3 2.2.4.6.8 Storey drift factor (SDF) Figure 5. Correlation between ductility and the storey drift factor 4.2 Nonductile MRF MRF designed to earlier codes or without seismic detailing often suffer from poor confinement of lap splices, lack of shear reinforcement in the beam-column joints and inadequate embedment length of the beam bottom reinforcement at the column. These frames behave in a nonductile manner and may fail in brittle failure modes. As an example of the data used, the maximum interstorey drift is plotted against the damage index in Figure 6. The behaviour of several frames when subjected to a number of ground motions contributed the data shown in the figure. For nonductile MRF, the damage index corresponding to repairable damage limit is.4. This damage level corresponds to maximum interstory drift limit of.5%, which is considered to be the limit of irreparable damage as suggested by experimental observation. The maximum interstorey drift limits corresponding to various damage states of a nonductile MRF are listed in Table. Damage index.8.6.4.2 Existing 3-storey frame Existing 9-storey frame Data trend.5.5 2 2.5 3 3.5 4 Interstorey drift ratio % Figure 6. Relationship between maximum interstorey drift and damage for existing nonductile frames 9
4.3 MRF with infills Several researchers have recently studied the behaviour of MRFs with infills (Lu 22). Quality experimental data is becoming available. An example illustrating the effect of infills on the relationship between damage and maximum interstorey drift is shown in Figure 7. The load carrying capacity of infilled frame is higher than that of a bare frame. A moment resisting frame with infills gives roughly half the interstorey drift of a bare frame (Chiou et al 999) with twice the damage index. For example,.35 damage index corresponds to interstorey drift of bare MRF of.8%. Interstorey drift ratio of.8% corresponds to a damage index of a MRF with infills of.7, which is near collapse. The behaviour of infilled frame may not return to the behaviour of a ductile MRF after the failure of the masonry infills. The apparent lack of ductility for MRF with infills is because the pattern of masonry failure may cause brittle failure of the frame elements. This may be the case even for a well-designed frame that is ductile when tested without the infills. The maximum interstorey drift limits corresponding to various damage states of MRF with infills are listed in Table..8.7.6 Damage index.5.4.3.2. Bare MRF MRF with infills 2 3 Interstorey drift ratio % Figure 7. Behaviour of bare portal MRF and MRF with infills 5. WALLS Structural walls may act predominantly in shear or flexure depending on their aspect ratio and the applied loads. Squat walls may fail abruptly by one of several brittle modes of failure. There is a comprehensive volume of experimental research and post earthquake observation on the behaviour of walls (Duffey et al. 994; Khalil and Ghobarah 23; Kowalsky 2; Wood 99).
5. Flexural Structural walls An example of the behaviour of flexural walls is shown in Figure 8. Initially the wall stiffness is high. Yielding of the steel reinforcement in ductile flexural walls occurs at drift values of approximately.8%. The drift limits corresponding to various damage states of ductile flexural walls are listed in Table. 5.2 Squat shear walls The relationship between damage and drift ratio for squat walls is shown in Figure 8. Initially under low levels of load, the behaviour of the squat wall is the same as ductile flexural walls. However, when shear cracks occur and are not arrested, the wall stiffness degrades rapidly reflecting a substantial increase in damage leading to abrupt failure. In the case of squat walls, it was experimentally observed that damage index of.3 represents the limit of repairable damage. This limit corresponds to relatively low drift ratio value of.4%. The steel yield point is normally not reached before shear failure occurs. The drift limit corresponding to various states of damage of squat shear walls are listed in Table. Damage index.9.8.7.6.5.4.3.2. Squat shear wall Flexural wall 2 3 Drift ratio % Figure 8. Shear and flexural behaviour of walls (Khalil and Ghobarah 23)
6. CONCLUSIONS Different sets of drift limits associated with various damage levels were defined for moment resisting frames (ductile, nonductile, with infills), flexural structural walls and squat shear walls. The defined performance levels were based on experimental data, field observations and measurements and theoretical analyses. At least two main sets of drift limits can be identified to represent various damage levels for the design of ductile systems and the assessment of the seismic resistance of nonductile ones. Currently available drift limits were found to be conservative for ductile structures and nonconservative for nonductile structures. Realistic drift calculations should be made using reduced gross inertia due to the cracked section properties. The proposed drift limits representing various performance objectives of the structure can be further refined as additional test and analysis data are included. REFERENCES Chiou, Y-J., J-C. Tzeng, and Y-W Liou (999). Experimental and analytical study of masonry infilled frames. Journal of Structural Engineering, 25():9-7. Duffey, T.A., C.R. Farrar and A. Goldman (994) Low-rise shear wall ultimate drift limits. Earthquake Spectra (4):655-674. FEMA (997) Guidelines for seismic rehabilitation of buildings. National Earthquake Hazard Reduction Program (NEHRP), Report FEMA 273, Federal Emergency Management Agency, Washington, DC. Ghobarah, A. (2). Performance-based design in earthquake engineering: state of development. Engineering Structures, 23:878-884. Ghobarah, A., N.M. Aly and M. El Attar (997). Performance level criteria and evaluation. In: Fajfar P., Krawinkler, H. editors. Seismic Design Methodologies for the Next Generation of Codes. AA Balkema, Rotterdam: 27-25. Khalil, A. and A. Ghobarah (23) Scale model testing of structural walls. Response of Structures to Extreme Loading, Toronto, Canada, Paper# 246, Elsevier, UK. Kowalsky, M. J. (2). RC structural walls designed according to UBC and displacement-based methods. Journal of Structural Engineering, 27(5):56-56. Lu, Y. (22). Comparative Study of Seismic Behavior of Multistory Reinforced concrete Framed Structures. Journal of Structural Engineering, 28(2):69 78. Rossetto, T. and A. Elnashai (23) Derivation of vulnerability functions for European type RC structures based on observed data. Engineering Structures 25:24-263. SEAOC (995). Vision 2, Performance based seismic engineering of buildings. Structural Engineers Association of California, Sacramento, CA. Wood, S. L. (99). Performance of reinforced concrete buildings during the 985 Chile earthquake: implications for the design of structural walls. Earthquake Spectra, 7(4):67-638. 2