The performance of buildings in recent New Zealand earthquakes (Canterbury, Seddon and Kaikōura), delivered stark lessons on seismic resilience. Most of our buildings, with a few notable exceptions, performed as our Codes intended them to, that is, to safeguard people from injury. Many buildings only suffered minor structural damage but were unable to be reused and occupied for significant periods of time due to the damage and failure of non-structural elements. This resulted in substantial economic losses and major disruptions to our businesses and communities. Research has attributed the damage to poor overall design coordination, inadequate or lack of seismic restraints for non structural elements and insufficient clearances between building components to cater for the interaction of non structural elements under seismic actions. Investigations have found a clear connection between the poor performance of non-structural elements and the issues causing pain in the industry (procurement methods, risk aversion, the lack of clear understanding of design and inspection responsibility and the need for better alignment of the design codes to enable a consistent integrated design approach). The challenge to improve the seismic performance of non structural elements in New Zealand is a complex one that cuts across a diverse construction industry. Adopting the key steps as recommended in this paper is expected to have significant co-benefits to the New Zealand construction industry, with improvements in productivity alongside reductions in costs and waste, as the rework which plagues the industry decreases.
A magnitude 6.3 earthquake struck the city of Christchurch at 12:51pm on Tuesday 22 February 2011. The earthquake caused 182 fatalities, a large number of injuries, and resulted in widespread damage to the built environment, including significant disruption to the lifelines. The event created the largest lifeline disruption in a New Zealand city in 80 years, with much of the damage resulting from extensive and severe liquefaction in the Christchurch urban area. The Christchurch earthquake occurred when the Canterbury region and its lifelines systems were at the early stage of recovering from the 4 September 2010 Darfield (Canterbury) magnitude 7.1 earthquake. This paper describes the impact of the Christchurch earthquake on lifelines by briefly summarising the physical damage to the networks, the system performance and the operational response during the emergency management and the recovery phase. Special focus is given to the performance and management of the gas, electric and road networks and to the liquefaction ejecta clean-up operations that contributed to the rapid reinstatement of the functionality of many of the lifelines. The water and wastewater system performances are also summarized. Elements of resilience that contributed to good network performance or to efficient emergency and recovery management are highlighted in the paper.
The focus of the study presented herein is an assessment of the relative efficacy of recent Cone Penetration Test (CPT) and small strain shear wave velocity (Vs) based variants of the simplified procedure. Towards this end Receiver Operating Characteristic (ROC) analyses were performed on the CPT- and Vs-based procedures using the field case history databases from which the respective procedures were developed. The ROC analyses show that Factors of Safety (FS) against liquefaction computed using the most recent Vs-based simplified procedure is better able to separate the “liquefaction” from the “no liquefaction” case histories in the Vs liquefaction database than the CPT-based procedure is able to separate the “liquefaction” from the “no liquefaction” case histories in the CPT liquefaction database. However, this finding somewhat contradicts the assessed predictive capabilities of the CPT- and Vs-based procedures as quantified using select, high quality liquefaction case histories from the 20102011 Canterbury, New Zealand, Earthquake Sequence (CES), wherein the CPT-based procedure was found to yield more accurate predictions. The dichotomy of these findings may result from the fact that different liquefaction field case history databases were used in the respective ROC analyses for Vs and CPT, while the same case histories were used to evaluate both the CPT- and Vs-based procedures.
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This paper describes the pounding damage sustained by buildings in the February 2011 Christchurch earthquake. Approximately 6% of buildings in Christchurch CBD were observed to have suffered some form of serious pounding damage. Typical and exceptional examples of building pounding damage are presented and discussed. Almost all building pounding damage occurred in unreinforced masonry buildings, highlighting their vulnerability to this phenomenon. Modern buildings were found to be vulnerable to pounding damage where overly stiff and strong ‘flashing’ components were installed in existing building separations. Soil variability is identified as a key aspect that amplifies the relative movement of buildings, and hence increases the likelihood of pounding damage. Building pounding damage is compared to the predicted critical pounding weaknesses that have been identified in previous analytical research.
This paper describes the pounding damage sustained by buildings in the February 2011 Christchurch earthquake. Approximately 6% of buildings in Christchurch CBD were observed to have suffered some form of serious pounding damage. Typical and exceptional examples of building pounding damage are presented and discussed. Almost all building pounding damage occurred in unreinforced masonry buildings, highlighting their vulnerability to this phenomenon. Modern buildings were found to be vulnerable to pounding damage where overly stiff and strong ‘flashing’ components were installed in existing building separations. Soil variability is identified as a key aspect that amplifies the relative movement of buildings, and hence increases the likelihood of pounding damage. Building pounding damage is compared to the predicted critical pounding weaknesses that have been identified in previous analytical research.
The University of Canterbury has initialized a research program focusing on the seismic sustainability of structures. As part of this program, the relative seismic sustainability of various structures will be assessed to identify those with the highest sustainability for the Christchurch rebuild and general use in New Zealand. This preliminary case study assesses one reinforced concrete (RC) frame structure and one RC wall structure. The scenario loss is evaluated for two earthquake records considering direct losses only in order to explain and illustrate the methodology.
The Canterbury earthquake and aftershock sequence in New Zealand during 2010-2011 subjected the city’s structures to a significant accumulated cyclic demand and raised significant questions regarding the low-cycle fatigue demands imposed upon the structures. There is a significant challenge to quantify the level of cumulative demand imposed on structures and to assess the percentage of a structure's fatigue life that has been consumed as a result of this earthquake sequence. It is important to be able to quantify the cumulative demand to determine how a building will perform in a subsequent large earthquake and inform repair and re-occupancy decisions. This paper investigates the cumulative fatigue demand for a structure located within the Christchurch Central Business District (CBD). Time history analysis and equivalent cycle counting methods are applied across the Canterbury earthquake sequence, using key events from September 4th 2010 and February 22nd , 2011 main shocks. The estimate of the cumulative fatigue demand is then compared to the expected capacity of a case study reinforced concrete bridge pier, to undertake a structure-specific fatigue assessment. The analysis is undertaken to approximate the portion of the structural fatigue capacity that has been consumed, and how much residual capacity remains. Results are assessed for recordings at the four Christchurch central city strong motion recording sites installed by the GeoNet programme, to provide an estimate of variation in results. The computed cyclic demand results are compared to code-based design methods and as assessment of the inelastic displacement demand of the reinforcing steel. Results are also presented in a fragility context where a de minimis (inconsequential), irreparable damage and full fatigue fracture are defined to provide a probabilistic assessment of the fatigue damage incurred. This methodology can provide input into the overall assessment of fatigue demands and residual capacity.
The 22nd February 2011, Mw 6.3 Christchurch earthquake in New Zealand caused major damage to critical infrastructure, including the healthcare system. The Natural Hazard Platform of NZ funded a short-term project called “Hospital Functions and Services” to support the Canterbury District Health Board’s (CDHB) efforts in capturing standardized data that describe the effects of the earthquake on the Canterbury region’s main hospital system. The project utilised a survey tool originally developed by researchers at Johns Hopkins University (JHU) to assess the loss of function of hospitals in the Maule and Bío-Bío regions following the 27th February 2010, Mw 8.8 Maule earthquake in Chile. This paper describes the application of the JHU tool for surveying the impact of Christchurch earthquake on the CDHB Hospital System, including the system’s residual capacity to deliver emergency response and health care. A short summary of the impact of the Christchurch earthquake on other CDHB public and private hospitals is also provided. This study demonstrates that, as was observed in other earthquakes around the world, the effects of damage to non-structural building components, equipment, utility lifelines, and transportation were far more disruptive than the minor structural damage observed in buildings (FEMA 2007). Earthquake related complications with re-supply and other organizational aspects also impacted the emergency response and the healthcare facilities’ residual capacity to deliver services in the short and long terms.
Over 900 buildings in the Christchurch central business district and 10,000 residential homes were demolished following the 22nd of February 2011 Canterbury earthquake, significantly disrupting the rebuild progress. This study looks to quantify the time required for demolitions during this event which will be useful for future earthquake recovery planning. This was done using the Canterbury Earthquake Recovery Authority (CERA) demolition database, which allowed an in-depth look into the duration of each phase of the demolition process. The effect of building location, building height, and the stakeholder which initiated the demolition process (i.e. building owner or CERA) was investigated. The demolition process comprises of five phases; (i) decision making, (ii) procurement and planning, (iii) demolition, (iv) site clean-up, and (v) completion certification. It was found that the time required to decide to demolish the building made up majority of the total demolition duration. Demolition projects initiated by CERA had longer procurement and planning durations, but was quicker in other phases. Demolished buildings in the suburbs had a longer decision making duration, but had little effect on other phases of the demolition process. The decision making and procurement and planning phases of the demolition process were shorter for taller buildings, though the other phases took longer. Fragility functions for the duration of each phase in the demolition process are provided for the various categories of buildings for use in future studies.
The paper presents preliminary findings from comprehensive research studies on the liquefaction-induced damage to buildings and infrastructure in Christchurch during the 2010-2011 Canterbury earthquakes. It identifies key factors and mechanisms of damage to road bridges, shallow foundations of CBD buildings and buried pipelines, and highlights the implications of the findings for the seismic analysis and design of these structures.
Recurrent liquefaction in Christchurch during the 2010-2011 Canterbury earthquake sequence created a wealth of shallow subsurface intrusions with geometries and orientations governed by (1) strong ground motion severity and duration, and (2) intrinsic site characteristics including liquefaction susceptibility, lateral spreading severity, geomorphic setting, host sediment heterogeneity, and anthropogenic soil modifications. We present a suite of case studies that demonstrate how each of these characteristics influenced the geologic expressions of contemporary liquefaction in the shallow subsurface. We compare contemporary features with paleo-features to show how geologic investigations of recurrent liquefaction can provide novel insights into the shaking characteristics of modern and paleo-earthquakes, the influence of geomorphology on liquefaction vulnerability, and the possible controls of anthropogenic activity on the geologic record. We conclude that (a) sites of paleo-liquefaction in the last 1000-2000 years corresponded with most severe liquefaction during the Canterbury earthquake sequence, (b) less vulnerable sites that only liquefied in the strongest and most proximal contemporary earthquakes are unlikely to have liquefied in the last 1000-2000 years or more, (c) proximal strong earthquakes with large vertical accelerations favoured sill formation at some locations, (d) contemporary liquefaction was more severe than paleoliquefaction at all study sites, and (e) stratigraphic records of successive dike formation were more complete at sites with severe lateral spreading, (f) anthropogenic fill suppressed surface liquefaction features and altered subsurface liquefaction architecture.
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature. Prediction of building collapse due to significant seismic motion is a principle objective of earthquake engineers, particularly after a major seismic event when the structure is damaged and decisions may need to be made rapidly concerning the safe occupation of a building or surrounding areas. Traditional model-based pushover analyses are effective, but only if the structural properties are well understood, which is not the case after an event when that information is most useful. This paper combines hysteresis loop analysis (HLA) structural health monitoring (SHM) and incremental dynamic analysis (IDA) methods to identify and then analyse collapse capacity and the probability of collapse for a specific structure, at any time, a range of earthquake excitations to ensure robustness. This nonlinear dynamic analysis enables constant updating of building performance predictions following a given and subsequent earthquake events, which can result in difficult to identify deterioration of structural components and their resulting capacity, all of which is far more difficult using static pushover analysis. The combined methods and analysis provide near real-time updating of the collapse fragility curves as events progress, thus quantifying the change of collapse probability or seismic induced losses very soon after an earthquake for decision-making. Thus, this combination of methods enables a novel, higher-resolution analysis of risk that was not previously available. The methods are not computationally expensive and there is no requirement for a validated numerical model, thus providing a relatively simpler means of assessing collapse probability immediately post-event when such speed can provide better information for critical decision-making. Finally, the results also show a clear need to extend the area of SHM toward creating improved predictive models for analysis of subsequent events, where the Christchurch series of 2010–2011 had significant post-event aftershocks.
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A wide range of reinforced concrete (RC) wall performance was observed following the 2010/2011 Canterbury earthquakes, with most walls performing as expected, but some exhibiting undesirable and unexpected damage and failure characteristics. A comprehensive research programme, funded by the Building Performance Branch of the New Zealand Ministry of Business, Innovation and Employment, and involving both numerical and experimental studies, was developed to investigate the unexpected damage observed in the earthquakes and provide recommendations for the design and assessment procedures for RC walls. In particular, the studies focused on the performance of lightly reinforced walls; precast walls and connections; ductile walls; walls subjected to bi-directional loading; and walls prone to out-of-plane instability. This paper summarises each research programme and provides practical recommendations for the design and assessment of RC walls based on key findings, including recommended changes to NZS 3101 and the NZ Seismic Assessment Guidelines.
The ultimate goal of this study is to develop a model representing the in-plane behaviour of plasterboard ceiling diaphragms, as part of the efforts towards performance-based seismic engineering of low-rise light timber-framed (LTF) residential buildings in New Zealand (NZ). LTF residential buildings in NZ are constructed according to a prescriptive standard – NZS 3604 Timberframed buildings [1]. With regards to seismic resisting systems, LTF buildings constructed to NZS3604 often have irregular bracing arrangements within a floor plane. A damage survey of LTF buildings after the Canterbury earthquake revealed that structural irregularity (irregular bracing arrangement within a plane) significantly exacerbated the earthquake damage to LTF buildings. When a building has irregular bracing arrangements, the building will have not only translational deflections but also a torsional response in earthquakes. How effectively the induced torsion can be resolved depends on the stiffness of the floors/roof diaphragms. Ceiling and floor diaphragms in LTF buildings in NZ have different construction details from the rest of the world and there appears to be no information available on timber diaphragms typical of NZ practice. This paper presents experimental studies undertaken on plasterboard ceiling diaphragms as typical of NZ residential practice. Based on the test results, a mathematical model simulating the in-plane stiffness of plasterboard ceiling diaphragms was developed, and the developed model has a similar format to that of plasterboard bracing wall elements presented in an accompany paper by Liu [2]. With these two models, three-dimensional non-linear push-over studies of LTF buildings can be undertaken to calculate seismic performance of irregular LTF buildings.
By closely examining the performance of a 22-storey steel framed building in Christchurch subject to various earthquakes over the past seven years, it is shown that a number of lessons can be learnt regarding the cost-effective consideration of non-structural elements. The first point in this work is that non-structural elements significantly affected the costs associated with repairing steel eccentrically braced frame (EBF) links. The decommissioning or rerouting of non-structural elements in the vicinity of damaged links in the case study building attributed to approximately half the total cost of their repair. Such costs could be significantly reduced if the original positioning of non-structural elements took account of the potential need to repair the EBF links. The second point highlighted is the role that pre-cast cladding apparently played on the distribution and type of damage in the building. Loss estimates obtained following the FEMA P-58 framework vary considerably when cladding is or isnt modelled, both because of changes to drift demands up the height of the building and because certain types of subsequent damage are likely to be cheaper to repair than others. Finally, costly repairs to non-structural partition walls were required not only after the moment magnitude 7.1 earthquake in 2010 but also in multiple aftershocks in the years that followed. Repair costs associated with aftershock events exceeded those from the main event, emphasizing the need to consider aftershocks within modern performance-based earthquake engineering and also the opportunity that exists to make more cost-effective repair strategies following damaging earthquakes.
This paper presents on-going challenges in the present paradigm shift of earthquakeinduced ground motion prediction from empirical to physics-based simulation methods. The 2010-2011 Canterbury and 2016 Kaikoura earthquakes are used to illustrate the predictive potential of the different methods. On-going efforts on simulation validation and theoretical developments are then presented, as well as the demands associated with the need for explicit consideration of modelling uncertainties. Finally, discussion is also given to the tools and databases needed for the efficient utilization of simulated ground motions both in specific engineering projects as well as for near-real-time impact assessment.
In practice, several competing liquefaction evaluation procedures (LEPs) are used to compute factors of safety against soil liquefaction, often for use within a liquefaction potential index (LPI) framework to assess liquefaction hazard. At present, the influence of the selected LEP on the accuracy of LPI hazard assessment is unknown, and the need for LEP-specific calibrations of the LPI hazard scale has never been thoroughly investigated. Therefore, the aim of this study is to assess the efficacy of three CPT-based LEPs from the literature, operating within the LPI framework, for predicting the severity of liquefaction manifestation. Utilising more than 7000 liquefaction case studies from the 2010–2011 Canterbury (NZ) earthquake sequence, this study found that: (a) the relationship between liquefaction manifestation severity and computed LPI values is LEP-specific; (b) using a calibrated, LEP-specific hazard scale, the performance of the LPI models is essentially equivalent; and (c) the existing LPI framework has inherent limitations, resulting in inconsistent severity predictions against field observations for certain soil profiles, regardless of which LEP is used. It is unlikely that revisions of the LEPs will completely resolve these erroneous assessments. Rather, a revised index which more adequately accounts for the mechanics of liquefaction manifestation is needed.
A one story, two bays, approximately half scaled, perimeter moment frame containing precastprestressed floor units was built and tested at the University of Canterbury to investigate the effect of precastprestressed floor units on the seismic performance of reinforced concrete moment resisting frame. This paper gives an overview of the experimental set up and summarizes the results obtained from the test. The results show that elongation in the beam plastic hinges is partially restrained by the prestressed floor, which increases the strength of the beams much more than that being specified in the codes around the world.
A seismic financial risk analysis of typical New Zealand reinforced concrete buildings constructed with topped precast concrete hollow-core units is performed on the basis of experimental research undertaken at the University of Canterbury over the last five years. An extensive study that examines seismic demands on a variety of multi-storey RC buildings is described and supplemented by the experimental results to determine the inter-storey drift capacities of the buildings. Results of a full-scale precast concrete super-assemblage constructed and tested in the laboratory in two stages are used. The first stage investigates existing construction and demonstrates major shortcomings in construction practice that would lead to very poor seismic performance. The second stage examines the performance of the details provided by Amendment No. 3 to the New Zealand Concrete Design Code NZS 3101:1995. This paper uses a probabilistic financial risk assessment framework to estimate the expected annual loss (EAL) from previously developed fragility curves of RC buildings with precast hollow core floors connected to the frames according to the pre-2004 standard and the two connection details recommended in the 2004 amendment. Risks posed by different levels of damage and by earthquakes of different frequencies are examined. The structural performance and financial implications of the three different connection details are compared. The study shows that the improved connection details recommended in the 2004 amendment give a significant economic payback in terms of drastically reduced financial risk, which is also representative of smaller maintenance cost and cheaper insurance premiums.
In order to provide information related to seismic vulnerability of non-ductile reinforced concrete (RC) frame buildings, and as a complementary investigation on innovative feasible retrofit solutions developed in the past six years at the University of Canterbury on pre-19170 reinforced concrete buildings, a frame building representative of older construction practice was tested on the shake table. The specimen, 1/2.5 scale, consists of two 3-storey 2-bay asymmetric frames in parallel, one interior and one exterior, jointed together by transverse beams and floor slabs. The as-built (benchmark) specimen was first tested under increasing ground motion amplitudes using records from Loma Prieta Earthquake (California, 1989) and suffered significant damage at the upper floor, most of it due to lap splices failure. As a consequence, in a second stage, the specimen was repaired and modified by removing the concrete in the lap splice region, welding the column longitudinal bars, replacing the removed concrete with structural mortar, and injecting cracks with epoxy resin. The modified as-built specimen was then tested using data recorded during Darfield (New Zealand, 2010) and Maule (Chile, 2010) Earthquakes, with whom the specimen showed remarkably different responses attributed to the main variation in frequency content and duration. In this contribution, the seismic performance of the three series of experiments are presented and compared.
An as-built reinforced concrete (RC) frame building designed and constructed according to pre-1970s code design construction practice has been recently tested on the shake table at the University of Canterbury. The specimen, 1/2.5 scaled version of the original prototype, consists of two 3-storey 2-bay asymmetric frames in parallel, one interior and one exterior, jointed together by transverse beams and floor slabs. Following the benchmark test, a retrofit intervention has been proposed to rehabilitate the tested specimen. In this paper, detailed information on the assessment and design of the seismic retrofit procedure using GFRP (glass fibre reinforced polymer) materials is given for the whole frame. Hierarchy of strength and sequence of events (damage mechanisms) in the panel zone region are evaluated using a moment-axial load (M-N) interaction performance domain, according to a performance-based retrofit philosophy. Specific limit states or design objectives are targeted with attention given to both strength and deformation limits. In addition, an innovative retrofit solution using FRP anchor dowels for the corner beam-column joints with slabs is proposed. Finally, in order to provide a practical tool for engineering practice, the retrofit procedure is provided in a step-by step flowchart fashion.
Recent advances in timber design at the University of Canterbury have led to new structural systems that are appropriate for a wide range of building types, including multi-storey commercial office structures. These buildings are competitive with more traditional construction materials in terms of cost, sustainability and structural performance. This paper provides seismic design recommendations and analytical modelling approaches, appropriate for the seismic design of post-tensioned coupled timber wall systems. The models are based on existing seismic design theory for precast post-tensioned concrete, modified to more accurately account for elastic deformation of the timber wall systems and the influence of the floor system. Experimental test data from a two storey post-tensioned timber building, designed, constructed and tested at the University of Canterbury is used to validate the analytical models.
This paper discusses the seismic performance of the standard RC office building in Christchurch that is given as a structural design example in NZS3101, the concrete structures seismic standard in New Zealand. Firstly the push-over analysis was carried out to evaluate the lateral load carrying capacity of the RC building and then to compare that carrying capacity with the Japanese standard law. The estimated figures showed that the carrying capacity of the New Zealand standard RC office building of NZS3101:2006 was about one third of Japanese demanded carrying capacity. Secondly, time history analysis of the multi-mass system was performed to estimate the maximum response story drift angle using recorded ground motions. Finally, a three-dimensional analysis was carried out to estimate the response of the building to the 22nd February, 2011 Canterbury earthquake. The following outcomes were obtained. 1) The fundamental period of the example RC building is more than twice that of Japanese simplified calculation, 2) The example building’s maximum storey drift angle reached 2.5% under the recorded ground motions. The main purpose of this work is to provide background information of seismic design practice for the reconstruction of Christchurch.
The objective of this project is to collect perishable seismic response data from the baseisolated Christchurch Women's Hospital. The strong and continuing sequence of aftershocks presents a unique opportunity to capture high-fidelity data from a modern base-isolated facility. These measurements will provide quantitative information required to assess the mechanisms at play in this and in many other seismically-isolated structures.
The seismic response of unreinforced masonry (URM) buildings, in both their as-built or retrofitted configuration, is strongly dependent on the characteristics of wooden floors and, in particular, on their in-plane stiffness and on the quality of wall-to-floor connections. As part of the development of alternative performance-based retrofit strategies for URM buildings, experimental research has been carried out by the authors at the University of Canterbury, in order to distinguish the different elements contributing to the whole diaphragm's stiffness. The results have been compared to the ones predicted through the use of international guidelines in order to highlight shortcomings and qualities and to propose a simplified formulation for the evaluation of the stiffness properties.
The performance of conventionally designed reinforced concrete (RC) structures during the 2011 Christchurch earthquake has demonstrated that there is greater uncertainty in the seismic performance of RC components than previously understood. RC frame and wall structures in the Christchurch central business district were observed to form undesirable cracks patterns in the plastic hinge region while yield penetration either side of cracks, and into development zones, were less than theoretical predictions. The implications of this unexpected behaviour: (i) significantly less available ductility; (ii) less hysteretic energy dissipation; and (iii) the localization of peak reinforcement strains, results in considerable doubt for the residual capacity of RC structures. The significance of these consequences has prompted a review of potential sources of uncertainty in seismic experimentation with the intention to improve the current confidence level for newly designed conventional RC structures. This paper attempts to revisit the principles of RC mechanics, in particular, to consider the influence of loading history, concrete tensile strength, and reinforcement ratio on the performance of ‘real’ RC structures compared to experimental test specimens.
Rapid, accurate structural health monitoring (SHM) assesses damage to optimise decision-making. Many SHM methods are designed to track nonlinear stiffness changes as damage. However, highly nonlinear pinched hysteretic systems are problematic in SHM. Model-based SHM often fails as any mismatch between model and measured response dynamics leads to significant error. Thus, modelfree methods of hysteresis loop tracking methods have emerged. This study compares the robustness and accuracy in the presence of significant measurement noise of the proven hysteresis loop analysis (HLA) SHM method with 3 emerging model-free methods and 2 further novel adaptations of these methods using a highly nonlinear, 6-story numerical structure to provide a known ground-truth. Mean absolute errors in identifying a known nonlinear stiffness trajectory assessed at four points over two successive ground motion inputs from September 2010 and February 2011 in Christchurch range from 1.71-10.52%. However, the variability is far wider with maximum errors ranging from 3.90-49.72%, where the second largest maximum absolute error was still 19.74%. The lowest mean and maximum absolute errors were for the HLA method. The next best method had mean absolute error of 2.92% and a maximum of 10.51%. These results show the clear superiority of the HLA method over all current emerging model-free methods designed to manage the highly nonlinear pinching responses common in reinforced concrete structures. These results, combined with high robustness and accuracy in scaled and fullscale experimental studies, provide further validation for using HLA for practical implementation.
