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.
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.
Low Damage Seismic Design (LDSD) guidance material being developed by Engineering NZ is considering a design drift limit for multi-storey buildings of 0.5% at a new damage control limit state (DCLS). The impact of this new design requirement on the expected annual loss due to repair costs is investigated for a four-storey office building with reinforced concrete walls located in Christchurch. The LDSD guidance material aims to reduce the expected annual loss of complying buildings to below 0.1% of building replacement cost. The research tested this expectation. Losses were estimated in accordance with FEMA P58, using building responses from non-linear time history analyses (performed with OpenSees using lumped plasticity models). The equivalent static method, in line with NZS 1170.5 and NZS 3101, was used to design the building to LDSD specifications, representing a future state-of-practice design. The building designed to low-damage specification returned an expected annual loss of 0.10%, and the building designed conventionally returned an expected annual loss of 0.13%. Limitations with the NZS 3101 method for determining wall stiffness were identified, and a different method acknowledging the relationship between strength and stiffness was used to redesign the building. Along with improving this design assumption, the study finds that LDSD design criteria could be an effective way of limiting damage and losses.
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.
Advanced seismic effective-stress analysis is used to scrutinize the liquefaction performance of 55 well-documented case-history sites from Christchurch. The performance of these sites during the 2010-2011 Canterbury earthquake sequence varied significantly, from no liquefaction manifestation at the ground surface (in any of the major events) to severe liquefaction manifestation in multiple events. For the majority of the 55 sites, the simplified liquefaction evaluation procedures, which are conventionally used in engineering practice, could not explain these dramatic differences in the manifestation. Detailed geotechnical characterization and subsequent examination of the soil profile characteristics of the 55 sites identified some similarities but also important differences between sites that manifested liquefaction in the two major events of the sequence (YY-sites) and sites that did not manifest liquefaction in either event (NN-sites). In particular, while the YY-sites and NN-sites are shown to have practically identical critical layer characteristics, they have significant differences with regard to their deposit characteristics including the thickness and vertical continuity of their critical zones and liquefiable materials. A CPT-based effective stress analysis procedure is developed and implemented for the analyses of the 55 case history sites. Key features of this procedure are that, on the one hand, it can be fully automated in a programming environment and, on the other hand, it is directly equivalent (in the definition of cyclic resistance and required input data) to the CPT-based simplified liquefaction evaluation procedures. These features facilitate significantly the application of effective-stress analysis for simple 1D free-field soil-column problems and also provide a basis for rigorous comparisons of the outcomes of effective-stress analyses and simplified procedures. Input motions for the analyses are derived using selected (reference) recordings from the two major events of the 2010-2011 Canterbury earthquake sequence. A step-by-step procedure for the selection of representative reference motions for each site and their subsequent treatment (i.e. deconvolution and scaling) is presented. The focus of the proposed procedure is to address key aspects of spatial variability of ground motion in the near-source region of an earthquake including extended-source effects, path effects, and variation in the deeper regional geology.
To reduce seismic vulnerability and the economic impact of seismic structural damage, it is important to protect structures using supplemental energy dissipation devices. Several types of supplemental damping systems can limit loads transferred to structures and absorb significant response energy without sacrificial structural damage. Lead extrusion dampers are one type of supplemental energy dissipation devices. A smaller volumetric size with high force capacities, called high force to volume (HF2V) devices, have been employed in a large series of scaled and full-scaled experiments, as well as in three new structures in Christchurch and San Francisco. HF2V devices have previously been designed using very simple models with limited precision. They are then manufactured, and tested to ensure force capacities match design goals, potentially necessitating reassembly or redesign if there is large error. In particular, devices with a force capacity well above or below a design range can require more testing and redesign, leading to increased economic and time cost. Thus, there is a major need for a modelling methodology to accurately estimate the range of possible device force capacity values in the design phase – upper and lower bounds. Upper and lower bound force capacity estimates are developed from equations in the metal extrusion literature. These equations consider both friction and extrusion forces between the lead and the bulged shaft in HF2V devices. The equations for the lower and upper bounds are strictly functions of device design parameters ensuring easy use in the design phase. Two different sets of estimates are created, leading to estimates for the lower and upper bounds denoted FLB,1, FUB,1, FUB,2, respectively. The models are validated by comparing the bounds with experimental force capacity data from 15 experimental HF2V device tests. All lower bound estimates are below or almost equal to the experimental device forces, and all upper bound estimates are above. Per the derivation, the (FLB,1, FUB,1) pair provide narrower bounds. The (FLB,1, FUB,1) pair also had a mean lower bound gap of -34%, meaning the lower bound was 74% of device force on average, while the mean upper bound gap for FUB,1 was +23%. These are relatively tight bounds, within ~±2 SE of device manufacture, and can be used as a guide to ensure device forces are in range for the actual design use when manufactured. Therefore, they provide a useful design tool.
