New Zealand has a long tradition of using light timber frame for construction of its domestic dwellings. After the most recent earthquakes (e.g. Canterbury earthquakes sequence), wooden residential houses showed satisfactory life safety performance. However, poor performance was reported in terms of their seismic resilience. Although numerous innovative methods to mitigate damage have been introduced to the New Zealand community in order to improve wooden house performance, these retrofit options have not been readily taken up. The low number of retrofitted wooden-framed houses leads to questions about whether homeowners are aware of the necessity of seismic retrofitting their houses to achieve a satisfactory seismic performance. This study aims to explore different retrofit technologies that can be applied to wooden-framed houses in Wellington, taking into account the need of homeowners to understand the risk, likelihood and extent of damage expected after an event. A survey will be conducted in Wellington about perceptions of homeowners towards the expected performance of their wooden-framed houses. The survey questions were designed to gain an understanding of homeowners' levels of safety and awareness of possible damage after a seismic event. Afterwards, a structural review of a sample of the houses will be undertaken to identify common features and detail potential seismic concerns. The findings will break down barriers to making improvements in the performance of wooden-framed houses and lead to enhancements in the confidence of homeowners in the event of future seismic activity. This will result in increased understanding and contribute towards an accessible knowledge base, which will possibly increase significantly the use of these technologies and avoid unnecessary economic and social costs after a seismic event.
This thesis presents an assessment of historic seismic performance of the New Zealand stopbank network from the 1968 Inangahua earthquake through to the 2016 Kaikōura earthquake. An overview of the types of stopbanks and the main aspects of the design and construction of earthen stopbanks was presented. Stopbanks are structures that are widely used on the banks of rivers and other water bodies to protect against the impact of flood events. Earthen stopbanks are found to be the most used for such protection measures. Different stopbank damage or failure modes that may occur due to flooding or earthquake excitation were assessed with a focus on past earthquakes internationally, and examples of these damage and failure modes were presented. Stopbank damage and assessment reports were collated from available reconnaissance literature to develop the first geospatial database of stopbank damage observed in past earthquakes in New Zealand. Damage was observed in four earthquakes over the past 50 years, with a number of earthquakes resulting in no stopbank damage. The damage database therefore focussed on the Edgecumbe, Darfield, Christchurch and Kaikōura earthquakes. Cracking of the crest and liquefaction-induced settlement were the most common forms of damage observed. To understand the seismic demand on the stopbank network in past earthquakes, geospatial analyses were undertaken to approximate the peak ground acceleration (PGA) across the stopbank network for ten large earthquakes that have occurred in New Zealand over the past 50 years. The relationship between the demand, represented by the peak ground acceleration (PGA) and damage is discussed and key trends identified. Comparison of the seismic demand and the distribution of damage suggested that the seismic performance of the New Zealand stopbank network has been generally good across all events considered. Although a significant length of the stopbank networks were exposed to high levels of shaking in past events, the overall damage length was a small percentage of this. The key aspect controlling performance was the performance of the underlying foundation soils and the effect of this on the stopbank structure and stability.
Nowadays the telecommunication systems’ performance has a substantial impact on our lifestyle. Their operationality becomes even more substantial in a post-disaster scenario when these services are used in civil protection and emergency plans, as well as for the restoration of all the other critical infrastructure. Despite the relevance of loss of functionality of telecommunication networks on seismic resilience, studies on their performance assessment are few in the literature. The telecommunication system is a distributed network made up of several components (i.e. ducts, utility holes, cabinets, major and local exchanges). Given that these networks cover a large geographical area, they can be easily subjected to the effects of a seismic event, either the ground shaking itself, or co-seismic events such as liquefaction and landslides. In this paper, an analysis of the data collected after the 2010-2011 Canterbury Earthquake Sequence (CES) and the 2016 Kaikoura Earthquake in New Zealand is conducted. Analysing these data, information gaps are critically identified regarding physical and functional failures of the telecommunication components, the timeline of repair/reconstruction activities and service recovery, geotechnical tests and land planning maps. Indeed, if these missing data were presented, they could aid the assessment of the seismic resilience. Thus, practical improvements in the post-disaster collection from both a network and organisational viewpoints are proposed through consultation of national and international researchers and highly experienced asset managers from Chorus. Finally, an outline of future studies which could guide towards a more resilient seismic performance of the telecommunication network is presented.
The operation of telecommunication networks is critical during business as usual times, and becomes most vital in post-disaster scenarios, when the services are most needed for restoring other critical lifelines, due to inherent interdependencies, and for supporting emergency and relief management tasks. In spite of the recognized critical importance, the assessment of the seismic performance for the telecommunication infrastructure appears to be underrepresented in the literature. The FP6 QuakeCoRE project “Performance of the Telecommunication Network during the Canterbury Earthquake Sequence” will provide a critical contribution to bridge this gap. Thanks to an unprecedented collaboration between national and international researchers and highly experienced asset managers from Chorus, data and evidences on the physical and functional performance of the telecommunication network after the Canterbury Earthquakes 2010-2011 have been collected and collated. The data will be processed and interpreted aiming to reveal fragilities and resilience of the telecommunication networks to seismic events
Unreinforced masonry churches in New Zealand, similarly to everywhere else in the word have proven to be highly vulnerable to earthquakes, because of their particular construction features. The Canterbury (New Zealand) earthquake sequence, 2010-2011 caused an invaluable loss of local architectural heritage and of churches, as regrettably, some of them were demolished instead of being repaired. It is critical for New Zealand to advance the data collection, research and understanding pertaining to the seismic performance and protection of church buildings, with the aim to:
Existing unreinforced masonry (URM) buildings are often composed of traditional construction techniques, with poor connections between walls and diaphragms that results in poor performance when subjected to seismic actions. In these cases the application of the common equivalent static procedure is not applicable because it is not possible to assure “box like” behaviour of the structure. In such conditions the ultimate strength of the structure relies on the behaviour of the macro-elements that compose the deformation mechanisms of the whole structure. These macroelements are a single or combination of structural elements of the structure which are bonded one to each other. The Canterbury earthquake sequence was taken as a reference to estimate the most commonly occurring collapse mechanisms found in New Zealand URM buildings in order to define the most appropriate macroelements.
This thesis describes the strategies for earthquake strengthening vintage clay bricks unreinforced masonry (URM) buildings. URM buildings are well known to be vulnerable to damage from earthquake-induced lateral forces that may result in partial or full building collapse. The 2010/2011 Canterbury earthquakes are the most recent destructive natural disaster that resulted in the deaths of 185 people. The earthquake events had drawn people’s attention when URM failure and collapse caused about 39 of the fatality. Despite the poor performance of URM buildings during the 2010/2011 Canterbury earthquakes, a number of successful case study buildings were identified and their details research in-depth. In order to discover the successful seismic retrofitting techniques, two case studies of retrofitted historical buildings located in Christchurch, New Zealand i.e. Orion’s URM substations and an iconic Heritage Hotel (aka Old Government Building) was conducted by investigating and evaluating the earthquake performance of the seismic retrofitting technique applied on the buildings prior to the 2010/2011 Canterbury earthquakes and their performance after the earthquakes sequence. The second part of the research reported in this thesis was directed with the primary aim of developing a cost-effective seismic retrofitting technique with minimal interference to the vintage clay-bricks URM buildings. Two retrofitting techniques, (i) near-surface mounted steel wire rope (NSM-SWR) with further investigation on URM wallettes to get deeper understanding the URM in-plane behaviour, and (ii) FRP anchor are reported in this research thesis.
Introduction This poster presents the inferred initial performance and recovery of the water supply network of Christchurch following the 22 February 2011 Mw 6.2 earthquake. Results are presented in a geospatial and temporal fashion. This work strengthens the current understanding of the restoration of such a system after a disaster and quantifies the losses caused by this earthquake in respect with the Christchurch community. Figure 1 presents the topology of the water supply network as well as the spatial distribution of the buildings and their use.
Asset management in power systems is exercised to improve network reliability to provide confidence and security for customers and asset owners. While there are well-established reliability metrics that are used to measure and manage business-as-usual disruptions, an increasing appreciation of the consequences of low-probability high-impact events means that resilience is increasingly being factored into asset management in order to provide robustness and redundancy to components and wider networks. This is particularly important for electricity systems, given that a range of other infrastructure lifelines depend upon their operation. The 2010-2011 Canterbury Earthquake Sequence provides valuable insights into electricity system criticality and resilience in the face of severe earthquake impacts. While above-ground assets are relatively easy to monitor and repair, underground assets such as cables emplaced across wide areas in the distribution network are difficult to monitor, identify faults on, and repair. This study has characterised in detail the impacts to buried electricity cables in Christchurch resulting from seismically-induced ground deformation caused primarily by liquefaction and lateral spread. Primary modes of failure include cable bending, stretching, insulation damage, joint braking and, being pulled off other equipment such as substation connections. Performance and repair data have been compiled into a detailed geospatial database, which in combination with spatial models of peak ground acceleration, peak ground velocity and ground deformation, will be used to establish rigorous relationships between seismicity and performance. These metrics will be used to inform asset owners of network performance in future earthquakes, further assess component criticality, and provide resilience metrics.
Natural catastrophes are increasing worldwide. They are becoming more frequent but also more severe and impactful on our built environment leading to extensive damage and losses. Earthquake events account for the smallest part of natural events; nevertheless seismic damage led to the most fatalities and significant losses over the period 1981-2016 (Munich Re). Damage prediction is helpful for emergency management and the development of earthquake risk mitigation projects. Recent design efforts focused on the application of performance-based design engineering where damage estimation methodologies use fragility and vulnerability functions. However, the approach does not explicitly specify the essential criteria leading to economic losses. There is thus a need for an improved methodology that finds the critical building elements related to significant losses. The here presented methodology uses data science techniques to identify key building features that contribute to the bulk of losses. It uses empirical data collected on site during earthquake reconnaissance mission to train a machine learning model that can further be used for the estimation of building damage post-earthquake. The first model is developed for Christchurch. Empirical building damage data from the 2010-2011 earthquake events is analysed to find the building features that contributed the most to damage. Once processed, the data is used to train a machine-learning model that can be applied to estimate losses in future earthquake events.
Eccentrically Braced Frames (EBFs) are a widely used seismic resisting structural steel system. Since their inception in the late 1970s, they have been a viable option with an available stiffness that is between simple braced systems and moment resisting systems. A similar concept, the linked column frame (LCF), uses shear links between two closely spaced columns. In both cases, the key component is the active link or the shear link, and this component is the objective of this study. The performance of high rise EBF buildings in the 2010 and 2011 Christchurch earthquakes was beyond that which was expected, especially considering the very high accelerations recorded. As the concrete high-rises were torn down, two EBF buildings remained standing and only required some structural repair. These events prompted a renewed interest in bolted shear links, as well as their performance. While some research into replaceable shear links had already been done (Mansour, 2011), the objectives of this study were to improve on the shear link itself, with the consideration that links built in the future are likely to be bolted. The main components of this study were to: 1. Reduce or eliminate the requirements for intermediate web stiffeners, as they were suspected of being detrimental to performance. Furthermore, any reduction in stiffening requirements is a direct fabrication cost saving. Links with low web aspect ratios were found to achieve exceptional ductilities when no stiffeners were included, prompting new design equations. 2. Ensure that the stresses in the ends of links are adequately transferred into the endplates without causing fractures. Although most of the experimental links had web doubler plates included, four had varied lengths of such doubler plates from 0.0 in. to 8.0 in. The link without any doubler plates performed to a similar level to its peers, and thus it is likely that links with quality end details may not need web doubler plates at all. 3. Evaluate the performance of a link with double sided stiffeners without the use of web welds, as opposed to conventional single sided, welded stiffeners. This link performed well, and web-weld-less double sided stiffeners may be an economical alternative to conventional stiffeners for deeper sections of links. 4. Evaluate the performance of a link with thin endplates that are made efficient with the use of gusset plates. This link performed to an acceptable level and provides evidence for a cost effective alternative to thick endplates, especially considering the high overstrength end moments in links, typically requiring 16-bolt connections. 5. Examine the potential use of an alternative EBF arrangement where the collector beam is over sized, and the link section is formed by cutting out parts of the beam's web. After running a series of finite element models each with a unique variation, a number of approximate design rules were derived such that future research could develop this idea further experimentally. 6. Ensure that during testing, the secondary elements (members that are not the shear link), do not yield and are not close to yielding. None of the instrumented elements experienced any unexpected yielding, however the concerns for high stresses in the collector beam panel zone during design were warranted. The use of an existing New Zealand design equation is recommended as an extra check for design codes worldwide. The above objectives were mainly conducted experimentally, except: the data set for item 1 was greatly expanded through the use of a calibrated numerical model which was then used in an extensive parametric study; item 5 was purely finite element based; and, a small parametric study was included for item 3 in an attempt to expand on the trends found there.
This thesis presents the application of data science techniques, especially machine learning, for the development of seismic damage and loss prediction models for residential buildings. Current post-earthquake building damage evaluation forms are developed for a particular country in mind. The lack of consistency hinders the comparison of building damage between different regions. A new paper form has been developed to address the need for a global universal methodology for post-earthquake building damage assessment. The form was successfully trialled in the street ‘La Morena’ in Mexico City following the 2017 Puebla earthquake. Aside from developing a framework for better input data for performance based earthquake engineering, this project also extended current techniques to derive insights from post-earthquake observations. Machine learning (ML) was applied to seismic damage data of residential buildings in Mexico City following the 2017 Puebla earthquake and in Christchurch following the 2010-2011 Canterbury earthquake sequence (CES). The experience showcased that it is readily possible to develop empirical data only driven models that can successfully identify key damage drivers and hidden underlying correlations without prior engineering knowledge. With adequate maintenance, such models have the potential to be rapidly and easily updated to allow improved damage and loss prediction accuracy and greater ability for models to be generalised. For ML models developed for the key events of the CES, the model trained using data from the 22 February 2011 event generalised the best for loss prediction. This is thought to be because of the large number of instances available for this event and the relatively limited class imbalance between the categories of the target attribute. For the CES, ML highlighted the importance of peak ground acceleration (PGA), building age, building size, liquefaction occurrence, and soil conditions as main factors which affected the losses in residential buildings in Christchurch. ML also highlighted the influence of liquefaction on the buildings losses related to the 22 February 2011 event. Further to the ML model development, the application of post-hoc methodologies was shown to be an effective way to derive insights for ML algorithms that are not intrinsically interpretable. Overall, these provide a basis for the development of ‘greybox’ ML models.
Validation is an essential step to assess the applicability of simulated ground motions for utilization in engineering practice, and a comprehensive analysis should include both simple intensity measures (PGA, SA, etc), as well as the seismic response of a range of complex systems obtained by response history analysis. In order to enable a spectrum of complex structural systems to be considered in systematic validation of ground motion simulations in a routine fashion, an automated workflow was developed. Such a workflow enables validation of simulated ground motions in terms of different complex model responses by considering various ground motion sets and different ground motion simulation methods. The automated workflow converts the complex validation process into a routine one by providing a platform to perform the validation process promptly as a built-in process of simulation post-processing. As a case study, validation of simulated ground motions was investigated via the automated workflow by comparing the dynamic responses of three steel special moment frame (SMRF) subjected to the 40 observed and 40 simulated ground motions of 22 February 2011 Christchurch earthquake. The seismic responses of the structures are principally quantified via the peak floor acceleration and maximum inter-storey drift ratio. Overall, the results indicate a general agreement in seismic demands obtained using the recorded and simulated ensembles of ground motions and provide further evidence that simulated ground motions can be used in code-based structural performance assessments in-place of, or in combination with, ensembles of recorded ground motions.
The full scale, in-situ investigations of instrumented buildings present an excellent opportunity to observe their dynamic response in as-built environment, which includes all the real physical properties of a structure under study and its surroundings. The recorded responses can be used for better understanding of behavior of structures by extracting their dynamic characteristics. It is significantly valuable to examine the behavior of buildings under different excitation scenarios. The trends in dynamic characteristics, such as modal frequencies and damping ratios, thus developed can provide quantitative data for the variations in the behavior of buildings. Moreover, such studies provide invaluable information for the development and calibration of realistic models for the prediction of seismic response of structures in model updating and structural health monitoring studies. This thesis comprises two parts. The first part presents an evaluation of seismic responses of two instrumented three storey RC buildings under a selection of 50 earthquakes and behavioral changes after Ms=7.1 Darfield (2010) and Ms=6.3 Christchurch (2011) earthquakes for an instrumented eight story RC building. The dynamic characteristics of the instrumented buildings were identified using state-of-the-art N4SID system identification technique. Seismic response trends were developed for the three storey instrumented buildings in light of the identified frequencies and the peak response accelerations (PRA). Frequencies were observed to decrease with excitation level while no trends are discernible for the damping ratios. Soil-structure interaction (SSI) effects were also determined to ascertain their contribution in the seismic response. For the eight storey building, it was found through system identification that strong nonlinearities in the structural response occurred and manifested themselves in all identified natural frequencies of the building that exhibited a marked decrease during the strong motion duration compared to the pre-Darfield earthquakes. Evidence of foundation rocking was also found that led to a slight decrease in the identified modal frequencies. Permanent stiffness loss was also observed after the strong motion events. The second part constitutes developing and calibrating finite element model (FEM) of the instrumented three storey RC building with a shear core. A three dimensional FEM of the building is developed in stages to analyze the effect of structural, non-structural components (NSCs) and SSI on the building dynamics. Further to accurately replicate the response of the building following the response trends developed in the first part of the thesis, sensitivity based model updating technique was applied. The FEMs were calibrated by tuning the updating parameters which are stiffnesses of concrete, NSCs and soil. The updating parameters were found to generally follow decreasing trends with the excitation level. Finally, the updated FEM was used in time history analyses to assess the building seismic performance at the serviceability limit state shaking. Overall, this research will contribute towards better understanding and prediction of the behavior of structures subjected to ground motion.
Results from a series of 1D seismic effective stress analyses of natural soil deposits from Christchurch are summarized. The analysed soil columns include sites whose performance during the 2010-2011 Canterbury earthquakes varied significantly, from no liquefaction manifestation at the ground surface to very severe liquefaction, in which case a large area of the site was covered by thick soil ejecta. Key soil profile characteristics and response mechanisms affecting the severity of surface liquefaction manifestation and subsequent damage are explored. The influence of shaking intensity on the triggering and contribution of these mechanisms is also discussed. Careful examination of the results highlights the importance of considering the deposit as a whole, i.e. a system of layers, including interactions between layers in the dynamic response and through pore water pressure redistribution and water flow.
High demolition rates were observed in New Zealand after the 2010-2011 Canterbury Earthquake Sequence despite the success of modern seismic design standards to achieve required performance objectives such as life safety and collapse prevention. Approximately 60% of the multi-storey reinforced concrete (RC) buildings in the Christchurch Central Business District were demolished after these earthquakes, even when only minor structural damage was present. Several factors influenced the decision of demolition instead of repair, one of them being the uncertainty of the seismic capacity of a damaged structure. To provide more insight into this topic, the investigation conducted in this thesis evaluated the residual capacity of moderately damaged RC walls and the effectiveness of repair techniques to restore the seismic performance of heavily damaged RC walls. The research outcome provided insights for developing guidelines for post-earthquake assessment of earthquake-damaged RC structures. The methodology used to conduct the investigation was through an experimental program divided into two phases. During the first phase, two walls were subjected to different types of pre-cyclic loading to represent the damaged condition from a prior earthquake, and a third wall represented a repair scenario with the damaged wall being repaired using epoxy injection and repair mortar after the pre-cyclic loading. Comparisons of these test walls to a control undamaged wall identified significant reductions in the stiffness of the damaged walls and a partial recovery in the wall stiffness achieved following epoxy injection. Visual damage that included distributed horizontal and diagonal cracks and spalling of the cover concrete did not affect the residual strength or displacement capacity of the walls. However, evidence of buckling of the longitudinal reinforcement during the pre-cyclic loading resulted in a slight reduction in strength recovery and a significant reduction in the displacement capacity of the damaged walls. Additional experimental programs from the literature were used to provide recommendations for modelling the response of moderately damaged RC walls and to identify a threshold that represented a potential reduction in the residual strength and displacement capacity of damaged RC walls in future earthquakes. The second phase of the experimental program conducted in this thesis addressed the replacement of concrete and reinforcing steel as repair techniques for heavily damaged RC walls. Two walls were repaired by replacing the damaged concrete and using welded connections to connect new reinforcing bars with existing bars. Different locations of the welded connections were investigated in the repaired walls to study the impact of these discontinuities at the critical section. No significant changes were observed in the stiffness, strength, and displacement capacity of the repaired walls compared to the benchmark undamaged wall. Differences in the local behaviour at the critical section were observed in one of the walls but did not impact the global response. The results of these two repaired walls were combined with other experimental programs found in the literature to assemble a database of repaired RC walls. Qualitative and quantitative analyses identified trends across various parameters, including wall types, damage before repair, and repair techniques implemented. The primary outcome of the database analysis was recommendations for concrete and reinforcing steel replacement to restore the strength and displacement capacity of heavily damaged RC walls.
The 2010-2011 Canterbury earthquake sequence, and the resulting extensive data sets on damaged buildings that have been collected, provide a unique opportunity to exercise and evaluate previously published seismic performance assessment procedures. This poster provides an overview of the authors’ methodology to perform evaluations with two such assessment procedures, namely the P-58 guidelines and the REDi Rating System. P-58, produced by the Federal Emergency Management Agency (FEMA) in the United States, aims to facilitate risk assessment and decision-making by quantifying earthquake ground shaking, structural demands, component damage and resulting consequences in a logical framework. The REDi framework, developed by the engineering firm ARUP, aids stakeholders in implementing resilience-based earthquake design. Preliminary results from the evaluations are presented. These have the potential to provide insights on the ability of the assessment procedures to predict impacts using “real-world” data. However, further work remains to critically analyse these results and to broaden the scope of buildings studied and of impacts predicted.
Buildings subject to earthquake shaking will tend to move not only horizontally but also rotate in plan. In-plan rotation is known as “building torsion” and it may occur for a variety of reasons, including stiffness and strength eccentricity and/or torsional effects from ground motions. Methods to consider torsion in structural design standards generally involve analysis of the structure in its elastic state. This is despite the fact that the structural elements can yield, thereby significantly altering the building response and the structural element demands. If demands become too large, the structure may collapse. While a number of studies have been conducted into the behavior of structures considering inelastic building torsion, there appears to be no consensus that one method is better than another and as a result, provisions within current design standards have not adopted recent proposals in the literature. However, the Canterbury Earthquakes Royal Commission recently made the recommendation that provisions to account for inelastic torsional response of buildings be introduced within New Zealand building standards. Consequently, this study examines how and to what extent the torsional response due to system eccentricity may affect the seismic performance of a building and considers what a simple design method should account for. It is concluded that new methods should be simple, be applicable to both the elastic and inelastic range of response, consider bidirectional excitation and include guidance for multi-story systems.
Reinforced concrete buildings that satisfied modern seismic design criteria generally behaved as expected during the recent Canterbury and Kaikoura earthquakes in New Zealand, forming plastic hinges in intended locations. While this meant that life-safety performance objectives were met, widespread demolition and heavy economic losses took place in the aftermath of the earthquakes.The Christchurch central business district was particularly hard hit, with over 60% of the multistorey reinforced concrete buildings being demolished. A lack of knowledge on the post-earthquake residual capacity of reinforced concrete buildings was a contributing factor to the mass demolition.Many aspects related to the assessment of earthquake-damaged reinforced concrete buildings require further research. This thesis focusses on improving the state of knowledge on the post earthquakeresidual capacity and reparability of moderately damaged plastic hinges, with an emphasis on plastic hinges typical of modern moment frame structures. The repair method focussed on is epoxy injection of cracks and patching of spalled concrete. A targeted test program on seventeen nominally identical large-scale ductile reinforced concrete beams, three of which were repaired by epoxy injection following initial damaging loadings, was conducted to support these objectives. Test variables included the loading protocol, the loading rate, and the level of restraint to axial elongation.The information that can be gleaned from post-earthquake damage surveys is investigated. It is shown that residual crack widths are dependent on residual deformations, and are not necessarily indicative of the maximum rotation demands or the plastic hinge residual capacity. The implications of various other types of damage typical of beam and column plastic hinges are also discussed.Experimental data are used to demonstrate that the strength and deformation capacity of plastic hinges with modern seismic detailing are often unreduced as a result of moderate earthquake induced damage, albeit with certain exceptions. Special attention is given to the effects of prior yielding of the longitudinal reinforcement, accounting for the low-cycle fatigue and strain ageing phenomena. A material-level testing program on the low-cycle fatigue behaviour of grade 300E reinforcing steel was conducted to supplement the data available in the literature.A reduction in stiffness, relative to the initial secant stiffness to yield, occurs due to moderate plastic hinging damage. This reduction in stiffness is shown to be correlated with the ductility demand,and a proposed model gives a conservative lower-bound estimate of the residual stiffness following an arbitrary earthquake-type loading. Repair by epoxy injection is shown to be effective in restoring the majority of stiffness to plastic hinges in beams. Epoxy injection is also shown to have implications for the residual strength and elongation characteristics of repaired plastic hinges.
