In this thesis, focus is given to develop methodologies for rapidly estimating specific components of loss and downtime functions. The thesis proposes methodologies for deriving loss functions by (i) considering individual component performance; (ii) grouping them as per their performance characteristics; and (iii) applying them to similar building usage categories. The degree of variation in building stock and understanding their characteristics are important factors to be considered in the loss estimation methodology and the field surveys carried out to collect data add value to the study. To facilitate developing ‘downtime’ functions, this study investigates two key components of downtime: (i) time delay from post-event damage assessment of properties; and (ii) time delay in settling the insurance claims lodged. In these two areas, this research enables understanding of critical factors that influence certain aspects of downtime and suggests approaches to quantify those factors. By scrutinising the residential damage insurance claims data provided by the Earthquake Commission (EQC) for the 2010- 2011 Canterbury Earthquake Sequence (CES), this work provides insights into various processes of claims settlement, the time taken to complete them and the EQC loss contributions to building stock in Christchurch city and Canterbury region. The study has shown diligence in investigating the EQC insurance claim data obtained from the CES to get new insights and build confidence in the models developed and the results generated. The first stage of this research develops contribution functions (probabilistic relationships between the expected losses for a wide range of building components and the building’s maximum response) for common types of claddings used in New Zealand buildings combining the probabilistic density functions (developed using the quantity of claddings measured from Christchurch buildings), fragility functions (obtained from the published literature) and cost functions (developed based on inputs from builders) through Monte Carlo simulations. From the developed contribution functions, glazing, masonry veneer, monolithic and precast concrete cladding systems are found to incur 50% loss at inter-storey drift levels equal to 0.027, 0.003, 0.005 and 0.011, respectively. Further, the maximum expected cladding loss for glazing, masonry veneer, monolithic, precast concrete cladding systems are found to be 368.2, 331.9, 365.0, and 136.2 NZD per square meter of floor area, respectively. In the second stage of this research, a detailed cost breakdown of typical buildings designed and built for different purposes is conducted. The contributions of structural and non- structural components to the total building cost are compared for buildings of different usages, and based on the similar ratios of non-structural performance group costs to the structural performance group cost, four-building groups are identified; (i) Structural components dominant group: outdoor sports, stadiums, parkings and long-span warehouses, (ii) non- structural drift-sensitive components dominant group: houses, single-storey suburban buildings (all usages), theatres/halls, workshops and clubhouses, (iii) non-structural acceleration- sensitive components dominant group: hospitals, research labs, museums and retail/cold stores, and (iv) apartments, hotels, offices, industrials, indoor sports, classrooms, devotionals and aquariums. By statistically analysing the cost breakdowns, performance group weighting factors are proposed for structural, and acceleration-sensitive and drift-sensitive non-structural components for all four building groups. Thus proposed building usage groupings and corresponding weighting factors facilitate rapid seismic loss estimation of any type of building given the EDPs at storey levels are known. A model for the quantification of post-earthquake inspection duration is developed in the third stage of this research. Herein, phase durations for the three assessment phases (one rapid impact and two rapid building) are computed using the number of buildings needing inspections, the number of engineers involved in inspections and a phase duration coefficient (which considers the median building inspection time, efficiency of engineer and the number of engineers involved in each assessment teams). The proposed model can be used: (i) by national/regional authorities to decide the length of the emergency period following a major earthquake, and estimate the number of engineers required to conduct a post-earthquake inspection within the desired emergency period, and (ii) to quantify the delay due to inspection for the downtime modelling framework. The final stage of this research investigates the repair costs and insurance claim settlement time for damaged residential buildings in the 2010-2011 Canterbury earthquake sequence. Based on the EQC claim settlement process, claims are categorized into three groups; (i) Small Claims: claims less than NZD15,000 which were settled through cash payment, (ii) Medium Claims: claims less than NZD100,000 which were managed through Canterbury Home Repair Programme (CHRP), and (iii) Large Claims: claims above NZD100,000 which were managed by an insurance provider. The regional loss ratio (RLR) for greater Christchurch for three events inducing shakings of approximate seismic intensities 6, 7, and 8 are found to be 0.013, 0.066, and 0.171, respectively. Furthermore, the claim duration (time between an event and the claim lodgement date), assessment duration (time between the claim lodgement day and the most recent assessment day), and repair duration (time between the most recent assessment day and the repair completion day) for the insured residential buildings in the region affected by the Canterbury earthquake sequence is found to be in the range of 0.5-4 weeks, 1.5- 5 months, and 1-3 years, respectively. The results of this phase will provide useful information to earthquake engineering researchers working on seismic risk/loss and insurance modelling.
In major seismic events, a number of plan-asymmetric buildings which experienced element failure or structural collapse had twisted significantly about their vertical axis during the earthquake shaking. This twist, known as “building torsion”, results in greater demands on one side of a structure than on the other side. The Canterbury Earthquakes Royal Commission’s reports describe the response of a number of buildings in the February 2011 Christchurch earthquakes. As a result of the catastrophic collapse of one multi-storey building with significant torsional irregularity, and significant torsional effects also in other buildings, the Royal Commission recommended that further studies be undertaken to develop improved simple and effective guides to consider torsional effects in buildings which respond inelastically during earthquake shaking. Separately from this, as building owners, the government, and other stakeholders, are planning for possible earthquake scenarios, they need good estimates of the likely performance of both new and existing buildings. These estimates, often made using performance based earthquake engineering considerations and loss estimation techniques, inform decision making. Since all buildings may experience torsion to some extent, and torsional effects can influence demands on building structural and non-structural elements, it is crucial that demand estimates consider torsion. Building seismic response considering torsion can be evaluated with nonlinear time history analysis. However, such analysis involves significant computational effort, expertise and cost. Therefore, from an engineers’ point of view, simpler analysis methods, with reasonable accuracy, are beneficial. The consideration of torsion in simple analysis methods has been investigated by many researchers. However, many studies are theoretical without direct relevance to structural design/assessment. Some existing methods also have limited applicability, or they are difficult to use in routine design office practice. In addition, there has been no consensus about which method is best. As a result, there is a notable lack of recommendations in current building design codes for torsion of buildings that respond inelastically. There is a need for building torsion to be considered in yielding structures, and for simple guidance to be developed and adopted into building design standards. This study aims to undertaken to address this need for plan-asymmetric structures which are regular over their height. Time history analyses are first conducted to quantify the effects of building plan irregularity, that lead to torsional response, on the seismic response of building structures. Effects of some key structural and ground motion characteristics (e.g. hysteretic model, ground motion duration, etc.) are considered. Mass eccentricity is found to result in rather smaller torsional response compared to stiffness/strength eccentricity. Mass rotational inertia generally decreases the torsional response; however, the trend is not clearly defined for torsionally restrained systems (i.e. large λty). Systems with EPP and bilinear models have close displacements and systems with Takeda, SINA, and flag-shaped models yield almost the same displacements. Damping has no specific effect on the torsional response for the single-storey systems with the unidirectional eccentricity and excitation. Displacements of the single-storey systems subject to long duration ground motion records are smaller than those for short duration records. A method to consider torsional response of ductile building structures under earthquake shaking is then developed based on structural dynamics for a wide range of structural systems and configurations, including those with low and high torsional restraint. The method is then simplified for use in engineering practice. A novel method is also proposed to simply account for the effects of strength eccentricity on response of highly inelastic systems. A comparison of the accuracy of some existing methods (including code-base equivalent static method and model response spectrum analysis method), and the proposed method, is conducted for single-storey structures. It is shown that the proposed method generally provides better accuracy over a wide range of parameters. In general, the equivalent static method is not adequate in capturing the torsional effects and the elastic modal response spectrum analysis method is generally adequate for some common parameters. Record-to-record variation in maximum displacement demand on the structures with different degrees of torsional response is considered in a simple way. Bidirectional torsional response is then considered. Bidirectional eccentricity and excitation has varying effects on the torsional response; however, it generally increases the weak and strong edges displacements. The proposed method is then generalized to consider the bidirectional torsion due to bidirectional stiffness/strength eccentricity and bidirectional seismic excitation. The method is shown to predict displacements conservatively; however, the conservatism decreases slightly for cases with bidirectional excitation compared to those subject to unidirectional excitation. In is shown that the roof displacement of multi-storey structures with torsional response can be predicted by considering the first mode of vibration. The method is then further generalized to estimate torsional effects on multi-storey structure displacement demands. The proposed procedure is tested multi-storey structures and shown to predict the displacements with a good accuracy and conservatively. For buildings which twist in plan during earthquake shaking, the effect of P-Δλ action is evaluated and recommendations for design are made. P-Δλ has more significant effects on systems with small post- yield stiffness. Therefore, system stability coefficient is shown not to be the best indicator of the importance of P-Δλ and it is recommended to use post-yield stiffness of system computed with allowance for P-Δλ effects. For systems with torsional response, the global system stability coefficient and post- yield stiffness ration do not reflect the significance of P-Δλ effects properly. Therefore, for torsional systems individual seismic force resisting systems should be considered. Accuracy of MRSA is investigated and it is found that the MRSA is not always conservative for estimating the centre of mass and strong edge displacements as well as displacements of ductile systems with strength eccentricity larger than stiffness eccentricity. Some modifications are proposed to get the MRSA yields a conservative estimation of displacement demands for all cases.
A buckling-restrained braced frame (BRBF) is a structural bracing system that provides lateral strength and stiffness to buildings and bridges. They were first developed in Japan in the 1970s (Watanabe et al. 1973, Kimura et al. 1976) and gained rapid acceptance in the United States after the Northridge earthquake in 1994 (Bruneau et al. 2011). However, it was not until the Canterbury earthquakes of 2010/2011, that the New Zealand construction market saw a significant uptake in the use of buckling-restrained braces (BRBs) in commercial buildings (MacRae et al. 2015). In New Zealand there is not yet any documented guidance or specific instructions in regulatory standards for the design of BRBFs. This makes it difficult for engineers to anticipate all the possible stability and strength issues within a BRBF system and actively mitigate them in each design. To help ensure BRBF designs perform as intended, a peer review with physical testing are needed to gain building compliance in New Zealand. Physical testing should check the manufacturing and design of each BRB (prequalification testing), and the global strength and stability of each BRB its frame (subassemblage testing). However, the financial pressures inherent in commercial projects has led to prequalification testing (BRB only testing) being favoured without adequate design specific subassemblage testing. This means peer reviewers have to rely on BRB suppliers for assurances. This low regulation environment allows for a variety of BRBF designs to be constructed without being tested or well understood. The concern is that there may be designs that pose risk and that issues are being overlooked in design and review. To improve the safety and design of BRBFs in New Zealand, this dissertation studies the behaviour of BRBs and how they interact with other frame components. Presented is the experimental test process and results of five commercially available BRB designs (Chapter 2). It discusses the manufacturing process, testing conditions and limitations of observable information. It also emphasises that even though subassemblage testing is impractical, uniaxial testing of the BRB only is not enough, as this does not check global strength or stability. As an alternative to physical testing, this research uses computer simulation to model BRB behaviour. To overcome the traditional challenges of detailed BRB modelling, a strategy to simulate the performance of generic BRB designs was developed (Chapter 3). The development of nonlinear material and contact models are important aspects of this strategy. The Chaboche method is employed using a minimum of six backstress curves to characterize the combined isotropic and kinematic hardening exhibited by the steel core. A simplified approach, adequate for modelling the contact interaction between the restrainer and the core was found. Models also capture important frictional dissipation as well as lateral motion and bending associated with high order constrained buckling of the core. The experimental data from Chapter 2 was used to validate this strategy. As BRBs resist high compressive loading, global stability of the BRB and gusseted connection zone need to be considered. A separate study was conducted that investigated the yielding and buckling strength of gusset plates (Chapter 4). The stress distribution through a gusset plate is complex and difficult to predict because the cross-sectional area of gusset plate is not uniform, and each gusset plate design is unique in shape and size. This has motivated design methods that approximate yielding of gusset plates. Finite element modelling was used to study the development of yielding, buckling and plastic collapse behaviour of a brace end bolted to a series of corner gusset plates. In total 184 variations of gusset plate geometries were modelled in Abaqus®. The FEA modelling applied monotonic uniaxial load with an imperfection. Upon comparing results to current gusset plate design methods, it was found that the Whitmore width method for calculating the yield load of a gusset is generally un-conservative. To improve accuracy and safety in the design of gusset plates, modifications to current design methods for calculating the yield area and compressive strength for gusset plates is proposed. Bolted connections are a popular and common connection type used in BRBF design. Global out-of-plane stability tends to govern the design for this connection type with numerous studies highlighting the risk of instability initiated by inelasticity in the gussets, neck of the BRB end and/or restrainer ends. Subassemblage testing is the traditional method for evaluating global stability. However, physical testing of every BRBF variation is cost prohibitive. As such, Japan has developed an analytical approach to evaluate out-of-plane stability of BRBFs and incorporated this in their design codes. This analytical approach evaluates the different BRB components under possible collapse mechanisms by focusing on moment transfer between the restrainer and end of the BRB. The approach have led to strict criteria for BRBF design in Japan. Structural building design codes in New Zealand, Europe and the United States do not yet provide analytical methods to assess BRB and connection stability, with prototype/subassemblage testing still required as the primary means of accreditation. Therefore it is of interest to investigate the capability of this method to evaluate stability of BRBs designs and gusset plate designs used in New Zealand (including unstiffened gusset connection zones). Chapter 5 demonstrates the capability of FEA to study to the performance of a subassemblage test under cyclic loading – resembling that of a diagonal ground storey BRBF with bolted connections. A series of detailed models were developed using the strategy presented in Chapter 3. The geometric features of BRB 6.5a (Chapter 2) were used as a basis for the BRBs modelled. To capture the different failure mechanisms identified in Takeuchi et al. (2017), models varied the length that the cruciform (non-yielding) section inserts into the restrainer. Results indicate that gusset plates designed according to New Zealand’s Steel Structures Standard (NZS 3404) limit BRBF performance. Increasing the thickness of the gusset plates according to modifications discussed in Chapter 4, improved the overall performance for all variants (except when Lin/ Bcruc = 0.5). The effect of bi-directional loading was not found to notably affect out-of-plane stability. Results were compared against predictions made by the analytical method used in Japan (Takeuchi method). This method was found to be generally conservative is predicting out-of-plane stability of each BRBF model. Recommendations to improve the accuracy of Takeuchi’s method are also provided. The outcomes from this thesis should be helpful for BRB manufacturers, researchers, and in the development of further design guidance of BRBFs.
