A Forensic Study to Apportion Damage due to Multiple Sequential Earthquakes

Transcription

1 A Forensic Study to Apportion Damage due to Multiple Sequential Earthquakes Behnam ARYA Associate Weidlinger Associates Inc Marina del Rey, CA, USA Behnam Arya, born 1965, received his PhD in structural engineering from Tufts University at Medford, MA, USA. He works at Weidlinger Associates in Marina del Rey, USA. His main areas of expertise include: forensic investigation, failure analysis and earthquake engineering. Anurag JAIN Principal Weidlinger Associates Inc Marina del Rey, CA, USA Anurag Jain, born 1969, received his PhD in structural engineering from Johns Hopkins University at Baltimore, MD, USA. He works at Weidlinger Associates in Marina del Rey, USA. His main areas of expertise include: wind/ earthquake engineering and forensic investigation. Can C. SIMSIR Associate Weidlinger Associates Inc Marina del Rey, CA, USA Can Simsir, born 1977, received his PhD in structural engineering from University of Illinois at Urbana-Champaign, USA. He works at Weidlinger Associates in Marina del Rey, USA. His main areas of expertise include: forensic investigation, failure analysis and earthquake engineering. Summary This paper presents an analytical approach to isolate contribution of multiple earthquakes to the overall damage caused to a structure. In this study, the buildings lateral force resisting systems are idealized as a single degree of freedom (SDOF). The SDOF is defined using a nonlinear forcedeformation curve to represent the structures response to lateral earthquake loads. A nonlinear analysis was conducted using the SDOF model subjected to the sequential ground motion time history. The energy dissipated through hysteresis response loops was calculated at the end of each earthquake. The amount of dissipated energy directly correlates to the damage sustained by lateral load resisting system since earthquake energy is dissipated through the inelastic actions of the structure. This approach can quantify the relative contribution of multiple sequential earthquakes to the overall damage based on the energy dissipated by the building during each event. Keywords: Earthquake Engineering, Damage Allocation, Nonlinear Analysis, Forensic Investigation 1. Introduction The purpose of this paper is to introduce an approach to quantify the relative contribution of multiple earthquakes or major earthquakes and their aftershocks to damage to the buildings. Similar studies have attempted to quantify damage contribution from sequential earthquake events. These studies are performed to separate damages from major earthquakes and their aftershocks and to determine the residual capacity of the structure after each event. The New Zealand Earthquake Commission (EQC) [1] developed an apportionment methodology after the Canterbury earthquakes. A review of the EQC s methodology shows that it is simply a qualitative assessment based on visual observation of damage subsequent to each event or comparing the damage with other properties in the area where the extent of damage and when it occurred is known. Wilson, Bradley, Belliss [2] at the University of Canterbury developed a method to determine the cumulative ground motion effects of the Canterbury earthquake sequence on structures. This study uses a nonlinear singledegree-of-freedom (SDOF) model to represent the structure. A nonlinear time history analysis of the SDOF subject to Canterbury earthquake sequence ground motion determines the displacement demand for a range of structural periods and ductility. The displacement demand from each event is then used to determine relative contribution of each event to the overall damage of the structure. Brooke and Davidson [3] developed an analytical method for determining relative damage ratios for a series of earthquakes. In this method, the structure is represented by a linear SDOF. The contribution of each earthquake to damage is determined by proportioning of the calculated earthquake displacement demands that are larger than the prescribed damage threshold. Energy dissipated by the structure during earthquakes has been used as an indicator of the residual seismic capacity after major earthquakes (Kang and Maeda [4]) and (Nakano et al [5]). Park et al.,

2 [6], introduced a damage index (Park-Ang Damage Index, DPA) for structures based on a combination of displacement demand and the plastic energy dissipation demand during the ground motion. Johnson [7] used DPA index to demonstrate how the energy based earthquake demand differ from the building code based earthquake demand commonly used in structural engineering practice. This study showed that the energy based earthquake demand is a more realistic measure of building performance. 2. Quantitative Apportionment Approach 2.1 General The method presented in this paper is based on a nonlinear dynamic time-history analyses of a single degree of freedom (SDOF) representation of the structure subject to a sequential ground motion time history loading. Damage indicator is the energy dissipated by the SDOF system through cyclic hysteretic response to the earthquake ground motion. The methodology presented in this paper accounts for both stiffness and strength cyclic degradation as well as second order effects that are expected to occur during a nonlinear inelastic response of a structure during strong ground motions. The structural damage is directly linked to the energy dissipated by the lateral force resisting system through hysteretic behaviour in response to ground motion. The following steps are taken to quantify apportionment of damage using the proposed approach: 1. Develop site specific earthquake ground motion corresponding to each event. 2. Develop a force-deformation curve (capacity curve) for lateral load resisting system. 3. Perform a nonlinear response history analyses to compute building response to earthquake sequence. 4. Perform analysis to compute relative contribution of each of the major earthquakes to the overall damage to building s lateral load resisting systems. 2.2 Site-Specific Ground Motions In this study, major earthquakes of the Canterbury earthquake sequence in Christchurch, New Zealand and damage to the buildings in the vicinity of the epicentre of these earthquakes are considered to develop the proposed approach. The Canterbury earthquake sequence commenced with a magnitude 7.1 (M 7.1) earthquake, which occurred on September 4, 21. It initiated other significant earthquakes close to Christchurch including: M 5.1 October 19, 21; M 4.9 December 26, 21; M 6.3 February 22, 211; M 5., March 5, 211; M 4.9 March 2, 21; M 5.3 April 16, 211; M 6.4 June 13, 211; M 5.4 June ; M 4.9 Fig. 1: Locations of Canterbury earthquake epicentres September 2, 211 M 6.; December 23, 211 and M 5.3 January 7, 212 earthquakes. These events resulted in peak ground acceleration (PGA) in excess of.1g in the vicinity of Christchurch and caused significant damage to the buildings and infrastructure in the region. Figure 1 shows the location of the epicentres of significant Canterbury earthquakes on a vicinity map of Christchurch. A comparison of ground acceleration values at stations near Christchurch reveal that the February event was the most destructive earthquake of the Canterbury earthquake sequence. During the Canterbury earthquakes nearly fifty recording stations recorded the ground motion data in Christchurch and its vicinity according to the Geonet website [8] which makes all the New

3 Zealand seismograph data available to public. For each property under investigation, earthquake ground motion data from nearby recording stations (within 5 km of the building site) were used to estimate the magnitude of ground acceleration and displacement that occurred at the site during each of the earthquake events of the Canterbury earthquake sequence. Various techniques can be utilized to estimate site specific ground motion. Scaling of recorded ground acceleration to match the peak ground acceleration at the site or weighted average of the closest recoding station data are amongst these methods. For this paper, the ground motion at the building site was estimated by developing a weighted average of the recorded horizontal ground motion acceleration history of each of these events. The averaging technique takes into consideration the spatial distribution of the recording stations by using a weighted average approach that assigns higher weights to stations that are located closer to the building site. To determine the contribution of each of the earthquake events to the building s total damage, the estimated ground acceleration histories were combined to produce a single sequential event in the same order as they occurred from September 21 through January Capacity Curve To calculate the response of the building s lateral force resisting system to earthquake loading, the lateral force resisting system was idealized as a single-degree-of-freedom (SDOF) model. A capacity curve was developed for the SDOF model to represent the structure s displacement as a function of laterally applied earthquake load. The capacity curve is a force-deformation (spectral acceleration-spectral displacement) curve that incorporates characteristics of the building s structural system and mechanical properties of the materials used for the construction of the building. The capacity curve is commonly computed by conducting a performance-based analysis of a detailed three-dimensional computer model of a building which incorporates inelastic characteristics of load carrying elements of the model. While this method yields the most accurate representation of the building s response, it is time-consuming and expensive. For some buildings, the information required to create a detailed computer model or the budget to perform such detailed analysis may not be always available. In the absence of a detailed analysis of the building and for the purpose of this analysis, the capacity curve was obtained using the procedure outlined in the United States Federal Emergency Management Agency (FEMA) methodology for estimating potential losses from earthquakes. The methodology is implemented in a software tool called HAZUS-MH (abbreviation for HAZards United States Multi Hazard) [9]. Capacity curves for buildings with various types of structural systems and materials have been developed as part of the well accepted, HAZUS-MH database. Building types are listed with specific codes depending on the structural system and height in the HAZUS-MH database. These curves describe the horizontal displacement of different structure types and seismic design levels as a function of laterally-applied earthquake load. This is an adequate approach since the primary objective of this analysis is to determine the relative contribution of the various strong motion events to the overall damage sustained by the structure. The capacity curve defined in HAZUS-MH does not specify the post-peak (beyond the ultimate strength) response of the building. Therefore, the HAZUS-MH capacity curve was appended to incorporate the post-peak response of the building using the modelling parameters for strength loss and post-peak plastic rotations of structural components described in the ASCE 41-6 Standard [1]. Figure 2 shows a typical capacity curve used for this analysis. Fc and dc = Capping strength and displacement Fy and dy = Yield strength and displacement Fr and dr = Residual strength and displacement du = Ultimate deformation capacity; dp = Plastic displacement capacity for monotonic loading dpc = Post-capping displacement capacity Fig 2: Typical capacity curve for building s lateral force resisting system used in analysis

4 2.4 Nonlinear Dynamic Time-History To study the response of structuress to the Canterbury earthquake sequence, the SDOF model with characteristics shown in Figure 2 is subjected to the sequential ground acceleration history of the Canterbury earthquakes. The Interactive Interface for Incremental Dynamic Analysis Procedure (IIIDAP) [11] computer program was used to perform a nonlinear dynamic time-historseismic evaluation of deteriorating or non-deteriorating SDOF analysis. IIIDAP is an analysis software for systems. This software uses deteriorating hysteretic models that can capture the various strength and stiffness deterioration modes of structural components and is able to simulate the lateral force resisting system reaching its collapse limit state under seismic loading. The deterioration characteristic of the SDOF system used in IIIDAP is based on a modified version of Ibarra- Krawinkler model (Ibarra et al. [12]). Modifications are described in Lignos and Krawinkler [13]. Three types of hysteresis responsee shown in Figure 3 are available in IIIDAP: Bilinear; peak- for concrete, oriented and pinching hysteretic response. For this work, pinching model was used masonry and wood structures and peak-oriented model was used for steel structures. The analyses also include the second order effects (P-Delta). Fig 3: Hysteresis response models available in IIIDAP (Adopted from IIIDAP manual [11]) 2.5 Relative Contribution of Earthquake Events to Total Damage The inelastic response of the building s lateral load resisting system during cyclic earthquake loading results in energy dissipation in each cyclic loop (excursion). Elastic response of the building s lateral force resisting system occurs when the components remain within their elastic force-deformation capacity when little or no damage is expected. Inelastic responsee occurs when components exceed their linear response range and results in larger displacement of the structure. Large displacements commonly result in damage to building s structural components and architectural features such as cracking of concrete, yielding and buckling of steel and reinforcing steel bars, and yielding, shearing, and pullout of connectors, partition wall cracking and door and window racking. When the earthquake demand exceeds the yield capacity of the structure, most of the earthquake energy is dissipated through the inelastic actions of the structure. The energy dissipated through hysteresis can be calculated at the end of each earthquake using the SDOF model in IIIDAP software. A comparison of dissipated hysteresis energies at the end of each event reveals the relative contribution of each of each earthquake to the total hysteresis energy dissipated by the building during the Canterbury sequence. Energy dissipation through hysteresis loops is an indication of the contribution of each event to the overall damage to the building s lateral load resisting system. 3. Case Study This section present the application of the proposed method to determine the relative contribution of major earthquakes of the Canterbury earthquake sequence to damage to an eight-story residential building near the Christchurch Central Business District (CBD). The building s lateral force resisting system is comprised of a combination of reinforced concrete moment frames and reinforced concrete shear walls. Figure 4 shows typical shear wall cracks in this building during Canterbury earthquakes. Ground motion data from four recording stations were used to estimate the magnitude of ground acceleration and displacement that occurred at the site during the major earthquakes of the Canterbury earthquake sequence. Fig. 5 shows the ground motion recording stations located in the vicinity of the building site. The ground motion at the building site was estimated by developing a weighted average of the recorded horizontal ground motion acceleration time history as described above. The estimated ground acceleration histories were combined to

5 produce a single sequential event in the same order as they occurred from September 4, 21 through January 7, 211 (Fig. 6). Example Building Fig 4: Typical cracking of concrete shear wall Fig. 5: Recording stations within 5 km of site Fig. 6: Estimated ground motion in the transverse (direction 1) and longitudinal (direction 2) directions at the site for nine major Canterbury earthquakes The capacity curve for the building was developed using elasto-plastic curves in the HAZUS-MH software database for concrete shear walls and concrete frame. Since the building s lateral force resisting system is a combination of two structural systems, the capacity curve was estimated by developing a weighted average based on tributary area of each lateral force resisting system. The building has similar characteristic in both directions. The HAZUS-MH capacity curve was modified to incorporate the post-peak response of the building using the modelling parameters for strength loss and post-peak plastic rotation of concrete elements described in the ASCE 41-6 Standard. Figure 7 shows the modified HAZUS-MH capacity curve used for the building under investigation in both longitudinal and transverse directions of the building. The SDOF model shown in Figure 7 was subjected to the sequential ground motion time histories shown in Figure 6 using IIIDAP software. Figures 8 and 9 show the building s response in longitudinal and transverse directions. Figure 8 shows plots of the building s roof displacement history and Figure 9 shows plots of cyclic force-deformation (hysteresis) response of the building s lateral force resisting system during the Canterbury earthquake sequence. Figure 8 clearly indicates the contribution of P-Delta effect in increasing the lateral displacement of the SDOF model after the February earthquake. Figures 8 and 9 also indicate that the building experienced a maximum of 97 mm of displacement in the transverse direction and maximum of 71 mm of displacement in the longitudinal direction. Comparing the response curves to the capacity curve, it is clear that the building s response exceeded the elastic capacity range (yield point) and thus permanent

6 deformation is expected as shown in these Figures. Figure 8 show a permanent deformation of 45 mm in the transverse direction and 25 mm in the longitudinal direction, respectively. This is consistent with onsite investigation and verticality measurements reported for the property after the earthquakes. The energy dissipated through hysteresis in both directions of the building was calculated at the end of each earthquake using the output of IIIDAP software as shown in Figure 1. Results of the analysis indicates that September 4, 21, February 22, 211, June 13, 211 and December 23, 211 had the largest contribution to the hysteretic energy dissipated by the SDOF model of the building. Ratio of the hysteresis energy dissipated during each earthquake to the total hysteresis energy dissipated over the entire duration of the combined ground motion history yields the percent relative contribution of each earthquake to the total energy dissipated during the Canterbury earthquake sequence. Table 1 shows the contribution of each event to the total hysteretic energy dissipated by the building s lateral force resisting systems during the major Canterbury earthquakes. The percentages listed in these table are the expected contribution of each earthquake to the damage to the building s lateral force resisting system. The relative contributions to damage from these events as computed by our analysis are consistent with the extent of damage described for each event through eyewitness interviews and engineering reports (available for some events only) prepared after each event. This qualitative assessment of damage per event is similar to the EQC apportionment methodology and correlates well with our analytical and quantitative assessment of damage for each event. Table 1: Contribution of the nine major Canterbury earthquakes to the overall damage to the building s lateral force resisting system Earthquake Date Energy Absorbed Energy Absorbed Energy Absorbed (kn-mm) (kn-mm) (kn-mm) Transverse Longitudinal Total Event Contribution 4-Sep ,1% 19-Oct ,3% 26-Dec ,5% 22-Feb ,1% 16-Apr ,4% 13-Jun ,4% 21-Jun ,3% 23-Dec ,7% 7-Jan ,2% Fig7: Building s capacity curve developed using HAZUS- MH database and ASCE 41-6

7 Displacement (mm) 2-2 Displacement (mm) (a) -6-8 (b) Time (sec) Time (sec) Fig. 8: Displacement of the building s roof subjected to sequential ground motion in transverse direction, (a) transverse direction and (b) longitudinal direction Force (kn) -2 2 Force (kn) (a) Displacement (mm) Displacement (mm) Fig 9: Force-deformation (hysteresis) response of the building roof subjected to sequential ground motion in transverse direction, (a) transverse direction and (b) (b) 25 2 December 23, 211 June 13, 211 December 23, 211 Total Energy (kn-mm) 15 1 February 22, 211 June 13, 211 February 22, 211 Fig 1: Hysteretic energy dissipated by the building s lateral force resisting system during the major earthquakes of the Canterbury earthquake sequence 4. Conclusions 5 September 4, 21 Transverse Direction September 4, 21 Longitudinal Direction Time (sec) This paper proposes an analytical approach to isolate contribution of multiple earthquakes to the overall damage caused to a structure. The structural damage is directly linked to the energy

8 dissipated by the lateral force resisting system through hysteretic behaviour in response to ground motion. This method can be applied to any sequential earthquakes that occur within a relatively short period of time. The relative contributions to damage from these events as computed by this analysis are consistent with the extent of damage described for each event through eyewitness interviews and engineering reports prepared after each event. This analysis can be used to serve owners as well as the insurance industry to resolve disputes over insurance claims. In addition, it can be used to determine the residual capacity of buildings after major earthquakes and their aftershocks. This can also help both owners and authorities to identify the building s safety for future use and occupancy and to determine the feasibility of repairs for an earthquake damaged building. 5. References [1] NEW ZEALAND GOVERNMENT EARTHQUAKE COMMISSION (EQC) Apportionment Fact Sheet, Wellington, New Zealand, 213 [2] WILSON, N., BRADLEY, B., AND BELLISS, C., Cumulative ground Motion Effects on Structures in the Canterbury Earthquake Sequence, University of Canterbury, Department of Civil & natural Resources Engineering, Christchurch, New Zealand, 212. [3] BROOKE, N., DAVIDSON, B., The Allocation of Damage to Structures Resulting from an Earthquake Sequence, SESOC NZ Conference, 212. [4] KANG, D., MAEDA, M. AND YI, W.H. (24), Post-Earthquake Capacity Evaluation of Reinforced Concrete Buildings Based on Seismic Response Analysis, 13th World Conference on Earthquake Engineering, 24 ; Paper No. 1633, Vancouver, B.C., Canada. [5] NAKANO, Y., CHOI, H., AND TAKAHASHI, N., Residual Seismic Capacity Estimation of RC Frames with Concrete Block Infill Based on their Crack Widths, International Symposium on Seismic Risk Reduction (ISSR 27), Paper ID 85, The JICA Technical Cooperation Project, Bucharest, Romania. [6] PARK, Y.J. AND ANG, A.H.-S. (1985). Mechanistic seismic damage model for reinforced concrete, Journal of Structural Engineering ASCE, 1985; 111:4, [7] JOHNSON, J. G., (October 213), Energy Methods, What Does the Future Hold? Structure Magazine, A joint Publication of NCSEA, CASE and SEI, pp ; Fall River, WI. [8] An interactive, multi-layered map displaying the locations of New Zealand seismograph sites, strong-motion detection sites and tsunami gauge sites; [9] UNITED STATES DEPARTMENT OF HOMELAND SECURITY, FEDERAL EMERGENCY MANAGEMENT AGENCY, Multi-hazard Loss Estimation Methodology, Earthquake Model, Hazus MH 2.1, Computer program for Estimating Potential Losses from Disasters, Developed by the (FEMA), Mitigation Division, Washington D.C., 213. [1] AMERICAN SOCIETY OF CIVIL ENGINEERS, ASCE/SEI 41-6 Supplement 1, Seismic Rehabilitation of Existing Building, Reston, Virginia, 27. [11] LIGNOS, D.G., Interactive Interface for Incremental Dynamic Analysis Procedure (IIIDAP) using Deteriorating Single Degree of Freedom Systems, Version 1.1.5, Stanford University, Stanford, CA, 21. [12] IBARRA L. F., MEDINA R. A., AND KRAWINKLER H., Hysteretic models that incorporate strength and stiffness deterioration, Earthquake Engineering and Structural Dynamics 25; 34(12): [13] LIGNOS D. G., AND KRAWINKLER, H., Sidesway collapse of deteriorating structural systems under seismic excitations, John A. Blume Earthquake Engineering Center, Report No. TR 172, Stanford University, Stanford, CA, 29.