This study investigates the uncertainty of simulated earthquake ground motions for smallmagnitude events (Mw 3.5 – 5) in Canterbury, New Zealand. 148 events were simulated with specified uncertainties in: event magnitude, hypocentre location, focal mechanism, high frequency rupture velocity, Brune stress parameter, the site 30-m time-averaged shear wave velocity (Vs30), anelastic attenuation (Q) and high frequency path duration. In order to capture these uncertainties, 25 realisations for each event were generated using the Graves and Pitarka (2015) hybrid broadband simulation approach. Monte-Carlo realisations were drawn from distributions for each uncertainty, to generate a suite of simulation realisations for each event and site. The fit of the multiple simulation realisations to observations were assessed using linear mixed effects regression to generate the systematic source, path and site effects components across all ground motion intensity measure residuals. Findings show that additional uncertainties are required in each of the three source, path, and site components, however the level of output uncertainty is promising considering the input uncertainties included.
The overarching goal of this dissertation is to improve predictive capabilities of geotechnical seismic site response analyses by incorporating additional salient physical phenomena that influence site effects. Specifically, multidimensional wave-propagation effects that are neglected in conventional 1D site response analyses are incorporated by: (1) combining results of 3D regional-scale simulations with 1D nonlinear wave-propagation site response analysis, and (2) modelling soil heterogeneity in 2D site response analyses using spatially-correlated random fields to perturb soil properties. A method to combine results from 3D hybrid physics-based ground motion simulations with site-specific nonlinear site response analyses was developed. The 3D simulations capture 3D ground motion phenomena on a regional scale, while the 1D nonlinear site response, which is informed by detailed site-specific soil characterization data, can capture site effects more rigorously. Simulations of 11 moderate-to-large earthquakes from the 2010-2011 Canterbury Earthquake Sequence (CES) at 20 strong motion stations (SMS) were used to validate simulations with observed ground motions. The predictions were compared to those from an empirically-based ground motion model (GMM), and from 3D simulations with simplified VS30- based site effects modelling. By comparing all predictions to observations at seismic recording stations, it was found that the 3D physics-based simulations can predict ground motions with comparable bias and uncertainty as the GMM, albeit, with significantly lower bias at long periods. Additionally, the explicit modelling of nonlinear site-response improves predictions significantly compared to the simplified VS30-based approach for soft-soil or atypical sites that exhibit exceptionally strong site effects. A method to account for the spatial variability of soils and wave scattering in 2D site response analyses was developed and validated against a database of vertical array sites in California. The inputs required to run the 2D analyses are nominally the same as those required for 1D analyses (except for spatial correlation parameters), enabling easier adoption in practice. The first step was to create the platform and workflow, and to perform a sensitivity study involving 5,400 2D model realizations to investigate the influence of random field input parameters on wave scattering and site response. Boundary conditions were carefully assessed to understand their effect on the modelled response and select appropriate assumptions for use on a 2D model with lateral heterogeneities. Multiple ground-motion intensity measures (IMs) were analyzed to quantify the influence from random field input parameters and boundary conditions. It was found that this method is capable of scattering seismic waves and creating spatially-varying ground motions at the ground surface. The redistribution of ground-motion energy across wider frequency bands, and the scattering attenuation of high-frequency waves in 2D analyses, resemble features observed in empirical transfer functions (ETFs) computed in other studies. The developed 2D method was subsequently extended to more complicated multi-layer soil profiles and applied to a database of 21 vertical array sites in California to test its appropriate- ness for future predictions. Again, different boundary condition and input motion assumptions were explored to extend the method to the in-situ conditions of a vertical array (with a sensor embedded in the soil). ETFs were compared to theoretical transfer functions (TTFs) from conventional 1D analyses and 2D analyses with heterogeneity. Residuals of transfer-function- based IMs, and IMs of surface ground motions, were also used as validation metrics. The spatial variability of transfer-function-based IMs was estimated from 2D models and compared to the event-to-event variability from ETFs. This method was found capable of significantly improving predictions of median ETF amplification factors, especially for sites that display higher event-to-event variability. For sites that are well represented by 1D methods, the 2D approach can underpredict amplification factors at higher modes, suggesting that the level of heterogeneity may be over-represented by the 2D random field models used in this study.
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.
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.
