We present ground motion simulations of the Porters Pass (PP) fault in the Canterbury region of New Zealand; a major active source near Christchurch city. The active segment of the PP fault has an inferred length of 82 km and a mostly strike-slip sense of movement. The PP fault slip makes up approximately 10% of the total 37 mm/yr margin-parallel plate motion and also comprises a significant proportion of the total strain budget in regional tectonics. Given that the closest segment of the fault is less than 45 km from Christchurch city, the PP fault is crucial for accurate earthquake hazard assessment for this major population centre. We have employed the hybrid simulation methodology of Graves and Pitarka (2010, 2015), which combines low (f<1 Hz) and high (f>1 Hz) frequencies into a broadband spectrum. We have used validations from three moderate magnitude events (šš¤4.6 Sept 04, 2010; šš¤4.6 Nov 06, 2010; šš¤4.9 Apr 29, 2011) to build confidence for the šš¤ > 7 PP simulations. Thus far, our simulations include multiple rupture scenarios which test the impacts of hypocentre location and the finite-fault stochastic rupture representation of the source itself. In particular, we have identified the need to use location-specific 1D šš /šš models for the high frequency part of the simulations to better match observations.
The need for a simple but rigorous seismic assessment procedure to predict damage to reinforced concrete buildings during a seismic event has been highlighted following the Canterbury Earthquake sequence. Such simplified assessment procedure, applied to individual structure or large building inventory, should not only have low requirement in terms of input information and involve straightforward analyses, but also should be capable to provide reliable predictive results within short timeframe. This research provides a general overview and critical comparison of alternative simplified assessment procedures adopted in NZSEE 2006 Guidelines (Assessment and Improvement of the Structural Performance of Buildings in Earthquakes), ASCE 41-13 (Seismic Evaluation and Retrofit of Existing Buildings), and EN: 1998-3: 2005 (Assessment and Retrofitting of Buildings). Particular focus is given to the evaluation of the capability of Simplified Lateral Mechanism Analysis (SLaMa), which is an analytical pushover method adopted in NZSEE 2006 Guidelines. The predictive results from SLaMa are compared to damages observed for a set of reinforced concrete buildings in Christchurch, as well as the results from more detailed assessment procedure based on numerical modelling. This research also suggests improvements to SLaMa, together with validation of the improvements, to include assessment of local mechanism by strength hierarchy evaluation, as well as to develop assessment of global mechanism including post-yield mechanism sequence based on local mechanism.
This thesis addresses the topic of local bond behaviour in RC structures. The mechanism of bond refers to the composite action between deformed steel reinforcing bars and the surrounding concrete. Bond behaviour is an open research topic with a wide scope, particularly because bond it is such a fundamental concept to structural engineers. However, despite many bond-related research findings having wide applications, the primary contribution of this research is an experimental evaluation of the prominent features of local bond behaviour and the associated implications for the seismic performance of RC structures. The findings presented in this thesis attempt to address some structural engineering recommendations made by the Canterbury Earthquakes Royal Commission following the 2010-2011 Canterbury (New Zealand) earthquake sequence. A chapter of this thesis discusses the structural behaviour of flexure-dominated RC wall structures with an insufficient quantity of longitudinal reinforcement, among other in situ conditions, that causes material damage to predominantly occur at a single crack plane. In this particular case, the extent of concrete damage and bond deterioration adjacent to the crack plane will influence the ductility capacity that is effectively provided by the reinforcing steel. As a consequence of these in situ conditions, some lightly reinforced wall buildings in Christchurch lost their structural integrity due to brittle fracture of the longitudinal reinforcement. With these concerning post-earthquake observations in mind, there is the underlying intention that this thesis presents experimental evidence of bond behaviour that allows structural engineers to re-assess their confidence levels for the ability of lightly reinforced concrete structures to achieve the life-safety seismic performance objective the ultimate limit state. Three chapters of this thesis are devoted to the experimental work that was conducted as the main contribution of this research. Critical details of the experimental design, bond testing method and test programme are reported. The bond stress-slip relationship was studied through 75 bond pull-out tests. In order to measure the maximum local bond strength, all bond tests were carried out on deformed reinforcing bars that did not yield as the embedded bond length was relatively short. Bond test results have been presented in two separate chapters in which 48 monotonic bond tests and 27 cyclic bond tests are presented. Permutations of the experiments include the loading rate, cyclic loading history, concrete strength (25 to 70 MPa), concrete age, cover thickness, bar diameter (16 and 20 mm), embedded length, and position of the embedded bond region within the specimen (close or far away to the free surface). The parametric study showed that the concrete strength significantly influences the maximum bond strength and that it is reasonable to normalise the bond stress by the square-root of the concrete compressive strength, ā(f'c). The generalised monotonic bond behaviour is described within. An important outcome of the research is that the measured bond strength and stiffness was higher than stated by the bond stress-slip relationship in the fib Model Code 2010. To account for these observed differences, an alternative model is proposed for the local monotonic bond stress-slip relationship. Cyclic bond tests showed a significant proportion of the total bond degradation occurs after the loading cycle in the peak bond strength range, which is when bond slip has exceeded 0.5 mm. Subsequent loading to constant slip values showed a linear relationship between the amount of bond strength degradation and the log of the number of cycles that were applied. To a greater extent, the cyclic bond deterioration depends on the bond slip range, regardless of whether the applied load cycling is half- or fully-reversed. The observed bond deterioration and hysteretic energy dissipated during cyclic loading was found to agree reasonably well between these cyclic tests with different loading protocols. The cyclic bond deterioration was also found to be reasonably consistent exponential damage models found in the literature. This research concluded that the deformed reinforcing bars used in NZ construction, embedded in moderate to high strength concrete, are able to develop high local bond stresses that are mobilised by a small amount of local bond slip. Although the relative rib geometry was not varied within this experimental programme, a general conclusion of this thesis is that deformed bars currently available in NZ have a relative rib bearing area that is comparatively higher than the test bars used in previous international research. From the parametric study it was found that the maximum monotonic bond strength is significant enhanced by dynamic loading rates. Experimental evidence of high bond strength and initial bond stiffness generally suggests that only a small amount of local bond slip that can occur when the deformed test bar was subjected to large tension forces. Minimal bond slip and bond damage limits the effective yielding length that is available for the reinforcing steel to distribute inelastic material strains. Consequently, the potential for brittle fracture of the reinforcement may be a more problematic and widespread issue than is apparent to structural engineers. This research has provided information that improve the reliability of engineering predictions (with respect to ductility capacity) of maximum crack widths and the extent of bond deterioration that might occur in RC structures during seismic actions.
This project was initiated by ENGEO Limited and KiwiRail Holdings Limited to assess the stability of Slovens Creek Viaduct (specifically its western abutment) and a 3km section of rail corridor between Slovens Creek Viaduct and Avoca on the Midland Line (MDL). Commonly known as the scenic TranzAlpine rail journey (through Arthurs Pass National Park) the MDL connects Greymouth to Christchurch via Rolleston, where the MDL meets the Main South Line into Christchurch. The project area is approximately 40km southeast of Arthurs Pass Township, in the eastern extension of the Castle Hill Basin which is part of the Waimakariri Catchment and Canterbury Foothills. The field area is underlain by Rakaia Terrane, which is part of the Torlesse Composite Terrane forming the basement rock unit for the field area. Cretaceous-Tertiary rocks of the Castle Hill Basin overlie the basement strata and record a transgression-regression sequence, as well as mid-Oligocene submarine volcanism. The stratigraphic sequence in the Castle Hill Basin, and its eastern extension to Avoca, comprises two formations of the Eyre group, the older Broken River Formation and the younger Iron Creek Formation. Deep marine Porter Group limestones, marls, and tuffs of Oligocene age succeed the Iron Creek Formation of the Eyre Group, and probably records the maximum of the transgression. The Enys Formation lies disconformably on the Porter Group and is overlain unconformably by Late Pleistocene glacifluvial and glacial deposits. The Tertiary strata in the Slovens-Avoca rail corridor are weak, and the clay-rich tuff derived from mid-Oligocene volcanism is particularly prone to slaking. Extensive mapping carried out for this project has identified that some 90 percent of the surface along the length of the Slovens-Avoca corridor has been subject to mass movement. The landslides of the Slovens-Avoca rail corridor are clearly younger than the Last Glaciation, and Slovens Creek has been downcutting, with associated faulting and uplift, to form the present day geomorphology of the rail corridor. Deep-seated landslides in the rail corridor extend to Slovens Creek, locally deflecting the stream course, and a generic ground failure model for the rail corridor has been developed. Exploratory geotechnical investigations, including core drilling, installation of an inclinometer and a piezometer, enabled the construction of a simple ground model and cross section for the Slovens Creek Viaduct western abutment. Limit-equilibrium and pseudo-static slope stability analyses using both circular and block critical slip surface search methods were applied to the ground model for the western abutment of Slovens Creek Viaduct. Piezometric and strength data obtained during laboratory testing of core material have been used to constrain the western abutment stability assessment for one representative section line (C-Cā). Prior to pseudo-static sensitivity analyses peak ground acceleration (PGA) for various Ultimate Limit State (ULS) design return periods, defined by an equation given in NZS1170.5:2004, were calculated and have been used as a calibration technique to find and compare specific PGA values for pseudo-static analyses in the Slovens Creek Viaduct area. The main purpose has been to provide an indication of how railway infrastructure could be affected by seismic events of various return periods defined by ULS design standards for the area. Limit equilibrium circular slip surface search methods, both grid search and auto refine search, indicated the slope is stable with a FoS greater than 1.0 returned from each, although one particular surface returned the lowest FoS in each. This surface is in the lower portion of the slope, adjacent to Slovens Stream and northeast of the MDL. As expected, pseudo-static analyses returned a lower FoS overall when compared to limit equilibrium analyses. The PGA analyses suggest that partial ground failure at the Slovens Creek Viaduct western abutment could occur in a 1 in 25-year return period event within materials on the slower slope beyond the immediate rail corridor. A ULS (1 in 500-year) event in the Slovens Creek Viaduct area would likely produce a PGA of ~0.9g, and the effects on the western abutment and rail infrastructure would most likely be catastrophic. Observed ground conditions for the western abutment of the Slovens Creek Viaduct suggest there is no movement within the landslide at depth within the monitoring timeframe of this project (22 May 2015 ā 4 August 2015). Slope stability monitoring is recommended to be continued in two parts: (1) the inclinometer in BH1 is to be monitored on a six monthly basis for one year following completion of this thesis, and then annually unless ground movements become evident; and (2) surface movement monitoring should be installed using a fixed datum on the stable eastern abutment. Long-term stability management strategies for the Slovens Creek Viaduct western abutment are dependent upon future observed changes and ongoing monitoring. Hazard and risk assessment using the KiwiRail Qualitative Risk Assessment Framework (QRA) is recommended, and if slope stability becomes problematic for operation of the Midland Line consideration should be given to deep slope drainage. In the event of a large magnitude or high PGA earthquake all monitoring should be reviewed.
Validating dynamic responses of engineered systems subjected to simulated ground motions is essential in scrutinising the applicability of simulated ground motions for engineering demand analyses. This paper compares the responses of two 3D building models subjected to recorded and simulated ground motions scaled to the NZS1170.5 design response spectrum, in order to evaluate the applicability of simulated ground motions for use in conventional engineering practice in New Zealand. The buildings were designed according to the NZS1170.5 and physically constructed in Christchurch prior to the 2010-2011 Canterbury earthquakes. 40 recorded ground motions from the 22 February 2011 Christchurch earthquake, along with the simulated ground motions for this event from Razafindrakoto et al. (2018) are considered. 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 using state-of-the-art methods can be used in code-based structural performance assessments inplace of, or in combination with, ensembles of recorded ground motions.
This paper investigates the effects of variability in source rupture parameters on site-specific physics-based simulated ground motions, ascertained through the systematic analysis of ground motion intensity measures. As a preliminary study, we consider simulations of the 22 February 2011 Christchurch earthquake using the Graves and Pitarka (2015) methodology. The effects of source variability are considered via a sensitivity study in which parameters (hypocentre location, earthquake magnitude, average rupture velocity, fault geometry and the Brune stress parameter) are individually varied by one standard deviation. The sensitivity of simulated ground motion intensity measures are subsequently compared against observational data. The preliminary results from this study indicate that uncertainty in the stress parameter and the rupture velocity have the most significant effect on the high frequency amplitudes. Conversely, magnitude uncertainty was found to be most influential on the spectral acceleration amplitudes at low frequencies. Further work is required to extend this preliminary study to exhaustively consider more events and to include parameter covariance. The ultimate results of this research will assist in the validation of the overall simulation methodās accuracy in capturing various rupture parameters, which is essential for the use of simulated ground motion models in probabilistic seismic hazard analysis.
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.
One of the failure modes that got the attention of researchers in the 2011 February New Zealand earthquake was the collapse of a key supporting structural wall of Grand Chancellor Hotel in Christchurch which failed in a brittle manner. However, until now this failure mode has been still a bit of a mystery for the researchers in the field of structural engineering. Moreover, there is no method to identify, assess and design the walls prone to such failure mode. Following the recent break through regarding the mechanism of this failure mode based on experimental observations (out-of-plane shear failure), a numerical model that can capture this failure was developed using the FE software DIANA. A comprehensive numerical parametric study was conducted to identify the key parameters contributing to the development of out-of-plane shear failure in reinforced concrete (RC) walls. Based on the earthquake observations, experimental and numerical studies conducted by the authors of this paper, an analytical method to identify walls prone to out-of-plane shear failure that can be used in practice by engineers is proposed. The method is developed based on the key parameters affecting the seismic performance of RC walls prone to out-of-plane shear failure and can be used for both design and assessment purposes
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.
This paper presents a methodology by which both site-specific and spatially distributed ground motion intensity can be obtained immediately following an earthquake event. The methodology makes use of both prediction models for ground motion intensity and its correlation over spatial distances. A key benefit of the methodology is that the ground motion intensity at a given location is not a single value but a distribution of values. The distribution is comprised of both a mean and also standard deviation, with the standard deviation being a function of the distance to nearby strong motion stations. The methodology is illustrated for two applications. Firstly, maps of conditional peak ground acceleration (PGA) have been developed for the major events in the Canterbury earthquake sequence. It is illustrated how these conditional maps can be used for post-event evaluation of liquefaction triggering criteria which have been adopted by the Department of Building and Housing (DBH). Secondly, the conditional distribution of response spectral ordinates is obtained at a specific location for the purposes of determining appropriate ground motion records for use in seismic response analyses of important structures at locations where direct recordings are absent.
This paper presents site-specific and spatially-distributed ground-motion intensity estimates which have been utilized in the aftermath of the 2010-2011 Canterbury, New Zealand earthquakes. The methodology underpinning the ground motion intensity estimation makes use of both prediction models for ground motion intensity and its within-event spatial correlation. A key benefit of the methodology is that the estimated ground motion intensity at a given location is not a single value but a distribution of values. The distribution is comprised of both a mean and standard deviation, with the standard deviation being a function of the distance to nearby observations at strong motion stations. The methodology is illustrated for two applications. Firstly, maps of conditional peak ground acceleration (PGA) have been developed for the major events in the Canterbury earthquake sequence, which among other things, have been utilized for assessing liquefaction triggering susceptibility of land in residential areas. Secondly, the conditional distribution of response spectral ordinates is obtained at the location of the Canterbury Television building (CTV), which catastrophically collapsed in the 22 February 2011 earthquake. The conditional response spectra provide insight for the selection of ground motion records for use in forensic seismic response analyses of important structures at locations where direct recordings are absent.
A major hazard accompanying earthquake shaking in areas of steep topography is the detachment of rocks from bedrock outcrops that subsequently slide, roll, or bounce downslope (i.e. rockfalls). The 2010-2011 Canterbury earthquake sequence caused recurrent and severe rockfall in parts of southern Christchurch. Coseismic rockfall caused five fatalities and significant infrastructural damage during the 2011 Mw 6.2 Christchurch earthquake. Here we examine a rockfall site in southern Christchurch in detail using geomorphic mapping, lidar analysis, geochronology (cosmogenic 3He dating, radiocarbon dating, optically stimulated luminescence (OSL) from quartz, infrared stimulated luminescence from K-feldspar), numerical modeling of rockfall boulder trajectories, and ground motion prediction equations (GMPEs). Rocks fell from the source cliff only in earthquakes with interpolated peak ground velocities exceeding ~10 cm/s; hundreds of smaller earthquakes did not produce rockfall. On the basis of empirical observations, GMPEs and age chronologies we attribute paleo-rockfalls to strong shaking in prehistoric earthquakes. We conclude that earthquake shaking of comparable intensity to the strongest contemporary earthquakes in Christchurch last occurred at this site approximately 5000 to 7000 years ago, and that in some settings, rockfall deposits provide useful proxies for past strong ground motions.
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 2010ā2011 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.
The lateral capacity of a conventional CLT shear wall is often governed by the strength and stiffness of its connections, which do not significantly utilize the in-plane strength of the CLT. Therefore, CLT shear walls are not yet being used efficiently in the construction of mass timber buildings due to a lack of research on high-capacity connections and alternative wall configurations. In this study, cyclic experiments were completed on six full-scale, 5-ply cantilever CLT shear walls with high-capacity hold-downs using mixed angle screws and bolts. All specimens exhibited significantly higher strength and stiffness than previously tested conventional CLT shear walls in the literature. The base connections demonstrated ductile failure modes through yielding of the hold-down connections. Based on the experimental results, numerical models were calibrated to investigate the seismic behaviour of CLT shear walls for prototype buildings of 3 and 6-storeys in Christchurch, NZ. As an alternative to cantilever (single) shear walls, a type of coupled wall with steel link beams between adjacent CLT wall piers was investigated. Effective coupling requires the link beam-to-wall connections to have adequate strength to ensure ductile link beam responses and adequate stiffness to yield the link beams at a relatively low inter-storey drift level. To this end, three beam-to-wall connection types were developed and cyclically tested to investigate their behaviour and feasibility. Based on the test results of the critical connection, a 3-storey, 2/3-scale coupled CLT wall specimen with three steel link beams and mixed angle screwed hold-downs was cyclically tested to evaluate its performance and experimentally validate the system concept. The test results showed a relatively high lateral strength compared to conventional CLT shear walls, as well as a high system ductility ratio of 7.6. Failure of the system was characterised by combined bending and withdrawal of the screws in the mixed angle screw hold-downs, yielding and eventual inelastic buckling of the steel link beams, CLT toe crushing, and local CLT delamination. Following the initial test, the steel link beams, mixed angle screw hold-downs, and damaged CLT regions were repaired, then the wall specimen was re-tested. The repaired wall behaved similarly to the original test and exhibited slightly higher energy dissipation and peak strength, but marginally more rapid strength deterioration under cyclic loading. Several hybrid coupled CLT shear walls were numerically modelled and calibrated based on the results of the coupled wall experiments. Pushover analyses were conducted on a series of configurations to validate a capacity design method for the system and to investigate reasonable parameter values for use in the preliminary design of the system. Additionally, an iterative seismic design method was proposed and used to design sample buildings of 6, 8, and 10-storeys using both nonlinear pushover and nonlinear time history analyses to verify the prototype designs. Results of the sample building analyses demonstrated adequate seismic behaviour and the proposed design parameters were found to be appropriate. In summary, high-capacity CLT shear walls can be used for the resistance of earthquakes by using stronger base connections and coupled wall configurations. The large-scale experimental testing in this study has demonstrated that both cantilever and coupled CLT shear walls are feasible LLRSs which can provide significantly greater lateral strength, stiffness, and energy dissipation than conventional CLT shear wall configurations.
8-pages Due to the extreme damage seen in several recent earthquakes, several passive energy dissipation devices have been developed with different mechanisms of energy dissipation. Response spectra analysis across multiple earthquake suites is used to investigate the reductions in structural response and base shear forces to probabilistically assess the impact of these devices using suites of ground motions from the SAC project. Single-degree-of-freedom spectral analysis structures are used with nonlinear models of the sliding hinge joint (SHJ) and HF2V devices. Reduction factors are computed for each device compared to a linear, no-device structure. Force capacity for SHJ and HF2V devices are equivalent. Results are presented as 5th, 25th, median (50th), 75th and 95th percentile responses at each period (0.1-5.0s by 0.1s increments). Both devices show significant reductions in displacement at all spectral periods of 30- 60% (at median). Both increase base shear forces. However, SHJ systems show both a broader 5-95th percentile range, as well as larger increases in base shear due to their different velocity dependence in dissipating energy. The results provide initial design trade-off information in a probabilistic, performance-based framework for these devices.
Seismic isolation is an effective technology for significantly reducing damage to buildings and building contents. However, its application to light-frame wood buildings has so far been unable to overcome cost and technical barriers such as susceptibility to movement during high-wind loading. The precursor to research in the field of isolation of residential buildings was the 1994 Northridge Earthquake (6.7 MW) in the United States and the 1995 Kobe Earthquake (6.9 MW) in Japan. While only a small number of lives were lost in residential buildings in these events, the economic impact was significant with over half of earthquake recovery costs given to repair and reconstruction of residential building damage. A value case has been explored to highlight the benefits of seismically isolated residential buildings compared to a standard fixed-base dwellings for the Wellington region. Loss data generated by insurance claim information from the 2011 Christchurch Earthquake has been used by researchers to determine vulnerability functions for the current light-frame wood building stock. By further considering the loss attributed to drift and acceleration sensitive components, and a simplified single degree of freedom (SDOF) building model, a method for determining vulnerability functions for seismic isolated buildings was developed. Vulnerability functions were then applied directly in a loss assessment using the GNS developed software, RiskScape. Vulnerability was shown to dramatically reduce for isolated buildings compared to an equivalent fixed-base building and as a result, the monetary savings in a given earthquake scenario were significant. This work is expected to drive further interest for development of solutions for the seismic isolation of residential dwellings, of which one option is further considered and presented herein.
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.
Designing a structure for higher- than-code seismic performance can result in significant economic and environmental benefits. This higher performance can be achieved using the principles of Performance-Based Design, in which engineers design structures to minimize the probabilistic lifecycle seismic impacts on a building. Although the concept of Performance-Based Design is not particularly new, the initial capital costs associated with designing structures for higher performance have historically hindered the widespread adoption of performance-based design practices. To overcome this roadblock, this research is focused on providing policy makers and stakeholders with evidence-based environmental incentives for designing structures in New Zealand for higher seismic performance. In the first phase of the research, the environmental impacts of demolitions in Christchurch following the Canterbury Earthquakes were quantified to demonstrate the environmental consequences of demolitions following seismic events. That is the focus here. A building data set consisting of 142 concrete buildings that were demolished following the earthquake was used to quantify the environmental impacts of the demolitions in terms of the embodied carbon and energy in the building materials. A reduced set of buildings was used to develop a material takeoff model to estimate material quantities in the entire building set, and a lifecycle assessment tool was used to calculate the embodied carbon and energy in the materials. The results revealed staggering impacts in terms of the embodied carbon and energy in the materials in the demolished buildings. Ongoing work is focused developing an environmental impact framework that incorporates all the complex factors (e.g. construction methodologies, repair methodologies (if applicable), demolition methodologies (if applicable), and waste management) that contribute to the environmental impacts of building repair and demolition following earthquakes.
Liquefaction is a phenomenon that results in a loss of strength and stability of a saturated soil mass due to dynamic excitation such as that imposed by an earthquake. The granular nature of New Zealand soils and the location of many of our cities and towns on fluvial foundations are such that the effects of liquefaction can be very important. Research was undertaken to build on the past work undertaken at the University of Canterbury studying the effects of the 1929 Murchison earthquake, the 1968 Inangahua earthquake and the 1991 Hawks Crag earthquakes on the West Coast. Additional archival information has been gathered from newspapers and reports and from discussions with people who experienced one or all of these large earthquakes that occurred on the West Coast during the 20th Century. Further, some twenty Cone Penetrometer Tests were carried out, with varying success, in Greymouth and Karamea using the Department of Civil Engineering's Drilling Rig. These, combined with the basic site investigation information, consolidate and add to the liquefaction case history data bank at the University of Canterbury. Many of the sites have liquefied in some but not all of the three earthquakes and thus provide both upper and lower bounds for the calibration of empirical models. While a lack of knowledge of the 1929 source location reduces the value of information from that event, the data form a useful set of liquefaction case histories and will become more so as further earthquakes occur. A list of critical sites for checking of the future earthquakes is provided and recommendations are made for the installation of downhole arrays of accelerometers and pore water pressure transducers at a number of sites.
This paper provides a summary of initial research results investigating systematic site effects from the prediction residuals of empirical- and physics-based ground-motion models (GMMs) for small magnitude (i.e., 3.5 ā¤ MW ā¤ 5) active shallow crustal earthquakes in New Zealand (NZ). Advancing ground-motion predictability through physics-based GMMs is an iterative process and requires addressing fundamental questions like: Is there salient physics which has been overlooked? Which geographic regions have predictions that significantly deviate from observations and why? Which sites exhibit systematic prediction residuals and how can the attributes influencing them be identified? This preliminary study examines these questions by classifying 171 sites from the Canterbury and Wellington regions into four geomorphic categories: basin, basin-edge, hill, and valley, following the categorisation by Nweke et al. (2022). Trends in the site-to-site residuals for each geomorphic category indicate apparent differences between the four categories, with residuals for valley sites illustrating a clear dependence with the inferred fundamental site period. Computed residuals from both empirical- and physics-based GMMs also provided insight into the role of site-specific attributes vs. the different prediction methods, assisting to understand the salient causes of these residuals.
In this paper we introduce CityViewAR, a mobile outdoor Augmented Reality (AR) application for providing AR information visualization on a city scale. The CityViewAR application was developed to provide geographical information about the city of Christchurch, which was hit by several major earthquakes in 2010 and 2011. The application provides information about destroyed buildings and historical sites that were affected by the earthquakes. The geo-located content is provided in a number of formats including 2D map views, AR visualization of 3D models of buildings on-site, immersive panorama photographs, and list views. The paper describes the iterative design and implementation details of the application, and gives one of the first examples of a study comparing user response to AR and non-AR viewing in a mobile tourism application. Results show that making such information easily accessible to the public in a number of formats could help people to have richer experience about cities. We provide guidelines that will be useful for people developing mobile AR applications for city-scale tourism or outdoor guiding, and discuss how the underlying technology could be used for applications in other areas.
In this dissertation it is argued that the Canterbury Earthquake Recovery Act 2011 and the Canterbury Earthquake Recovery Authority were both necessary and inevitable given the trends and traditions of civil defence emergency management (CDEM) in New Zealand. The trends and traditions of civil defence are such that principles come before practice, form before function, and change is primarily brought about through crisis and criticism. The guiding question of the research was why were a new governance system and law made after the Canterbury earthquakes in 2010 and 2011? Why did this outcome occur despite the establishment of a modern emergency management system in 2002 which included a recovery framework that had been praised by international scholars as leading edge and a model for other countries? The official reason was the unprecedented scale and demands of the recovery ā but a disaster of such scale is the principle reason for having a national emergency management system. Another explanation is the lack of cooperation among local authorities ā but that raises the question of whether the CDEM recovery framework would have been successful in another locality. Consequentially, the focus of this dissertation is on the CDEM recovery framework and how New Zealand came to find itself making disaster law during a disaster. Recommendations include a review of emergency powers for recovery, a review of the capabilities needed to fulfil the mandate of Recovery Managers, and the establishment of a National Recovery Office with a cadre of Recovery Managers that attend every recovery to observe, advise, or assume control as needed. CDEM Group Recovery Managers would be seconded to the National Recovery Office which would allow for experience in recovery management to be developed and institutionalised through regular practice.
Timber has experienced renewed interests as a sustainable building material in recent times. Although traditionally it has been the prime choice for residential construction in New Zealand and some other parts of the world, its use can be increased significantly in the future through a wider range of applications, particularly when adopting engineered wood material, Research has been started on the development of innovative solutions for multi-storey non-residential timber buildings in recent years and this study is part of that initiative. Application of timber in commercial and office spaces posed some challenges with requirements of large column-free spaces. The current construction practice with timber is not properly suited for structures with the aforementioned required characteristics and new type of structures has to be developed for this type of applications. Any new structural system has to have adequate capacity for carry the gravity and lateral loads due to occupancy and the environmental effects. Along with wind loading, one of the major sources of lateral loads is earthquakes. New Zealand, being located in a seismically active region, has significant risk of earthquake hazard specially in the central region of the country and any structure has be designed for the seismic loading appropriate for the locality. There have been some significant developments in precast concrete in terms of solutions for earthquake resistant structures in the last decade. The āHybridā concept combining post-tensioning and energy dissipating elements with structural members has been introduced in the late 1990s by the precast concrete industry to achieve moment-resistant connections based on dry jointed ductile connections. Recent research at the University of Canterbury has shown that the concept can be adopted for timber for similar applications. Hybrid timber frames using post-tensioned beams and dissipaters have the potential to allow longer spans and smaller cross sections than other forms of solid timber frames. Buildings with post-tensioned frames and walls can have larger column-free spaces which is a particular advantage for non-residential applications. While other researchers are focusing on whole structural systems, this research concentrated on the analysis and design of individual members and connections between members or between member and foundation. This thesis extends existing knowledge on the seismic behaviour and response of post-tensioned single walls, columns under uni-direction loads and small scale beam-column joint connections into the response and design of post-tensioned coupled walls, columns under bi-directional loading and full-scale beam-column joints, as well as to generate further insight into practical applications of the design concept for subassemblies. Extensive experimental investigation of walls, column and beam-column joints provided valuable confirmation of the satisfactory performance of these systems. In general, they all exhibited almost complete re-centering capacity and significant energy dissipation, without resulting into structural damage. The different configurations tested also demonstrated the flexibility in design and possibilities for applications in practical structures. Based on the experimental results, numerical models were developed and refined from previous literature in precast concrete jointed ductile connections to predict the behaviour of post-tensioned timber subassemblies. The calibrated models also suggest the values of relevant parameters for applications in further analysis and design. Section analyses involving those parameters are performed to develop procedures to calculate moment capacities of the subassemblies. The typical features and geometric configurations the different types of subassemblies are similar with the only major difference in the connection interfaces. With adoption of appropriate values representing the corresponding connection interface and incorporation of the details of geometry and configurations, moment capacities of all the subassemblies can be calculated with the same scheme. That is found to be true for both post-tensioned-only and hybrid specimens and also applied for both uni-directional and bi-directional loading. The common section analysis and moment capacity calculation procedure is applied in the general design approach for subassemblies.
The Avon-Heathcote Estuary, located in Christchurch, New Zealand, experienced coseismic deformation as a result of the February 22nd 2011 Christchurch Earthquake. The deformation is reflected as subsidence in the northern area and uplift in the southern area of the Estuary, in addition to sand volcanoes which forced up sediment throughout the floor of the Estuary altering estuary bed height and tidal flow. The first part of the research involved quantifying the change in the modern benthic foraminifera distribution as a result of the coseismic deformation caused by the February 22nd 2011 earthquake. By analysing the taxa present immediately post deformation and then the taxa present 2 years post deformation a comparison of the benthic foraminifera distribution can be made of the pre and post deformation. Both the northern and the southern areas of the Estuary were sampled to establish whether foraminifera faunas migrated landward or seaward as a result of subsidence and uplift experienced in different areas. There was no statistical change in overall species distribution in the two year time period since the coseismic deformation occurred, however, there were some noticeable changes in foraminifera distribution at BSNS-Z3 showing a landward migration of taxa. The changes that were predicted to occur as a result of the deformation of the Estuary are taking longer than expected to show up in the foraminiferal record and a longer time period is needed to establish these changes. The second stage involved establishing the modern distribution of foraminifera at Settlers Reserve in the southern area of the Avon-Heathcote Estuary by detailed sampling along a 160 m transect. Foraminifera are sensitive to environmental parameters, tidal height, grainsize, pH and salinity were recorded to evaluate the effect these parameters have on distribution. Bray-Curtis two-way cluster analysis was primarily used to assess the distribution pattern of foraminifera. The modern foraminifera distribution is comparable to that of the modern day New Zealand brackish-water benthic foraminifera distribution and includes species not yet found in other studies of the Avon-Heathcote Estuary. Differences in sampling techniques and the restricted intertidal marshland area where the transect samples were collected account for some of the differences seen between this model and past foraminifera studies. xiii The final stage involved sampling a 2.20 m core collected from Settlers Reserve and using the modern foraminiferal distribution to establish a foraminiferal history of Settlers Reserve. As foraminifera are sensitive to tidal height they may record past coseismic deformation events and the core was used to ascertain whether record of past coseismic deformation is preserved in Settlers Reserve sediments. Sampling the core for foraminifera, grainsize, trace metals and carbon material helped to build a story of estuary development. Using the modern foraminiferal distribution and the tidal height information collected, a down core model of past tidal heights was established to determine past rates of change. Foraminifera are not well preserved throughout the core, however, a sudden relative rise in sea level is recorded between 0.25 m and 0.85 m. Using trace metal and isotope analysis to develop an age profile, this sea level rise is interpreted to record coseismic subsidence associated with a palaeoseismic event in the early 1900ās. Overall, although the Avon-Heathcote Estuary experienced clear coseismic deformation as a result of the 22nd of February 2011 earthquake, modern changes in foraminiferal distribution cannot yet be tracked, however, past seismic deformation is identified in a core. The modern transect describes the foraminifera distribution which identifies species that have not been identified in the Avon-Heathcote Estuary before. This thesis enhances the current knowledge of the Avon-Heathcote Estuary and is a baseline for future studies.
Seismically vulnerable buildings constitute a major problem for the safety of human beings. In many parts of the world, reinforced concrete (RC) frame buildings designed and constructed with substandard detailing, no consideration of capacity design principles, and improper or no inclusion of the seismic actions, have been identified. Amongst those vulnerable building, one particular typology representative of the construction practice of the years previous to the 1970ās, that most likely represents the worst case scenario, has been widely investigated in the past. The deficiencies of that building typology are related to non-ductile detailing in beam column joints such as the use of plain round bars, the lack of stirrups inside the joint around the longitudinal reinforcement of the column, the use of 180Ā° end hooks in the beams, the use of lap splices in potential āplastic hingeā regions, and substandard quality of the materials. That type of detailing and the lack of a capacity design philosophy create a very fragile fuse in the structure where brittle inelastic behaviour is expected to occur, which is the panel zone region of exterior beam column joints. The non-ductile typology described above was extensively investigated at the University of Canterbury in the context of the project āRetrofit Solutions for New Zealand Multi-Storey Buildingsā (2004-2011), founded by the āFoundation for Research, Science and Technologyā TÅ«Äpapa Rangahau PÅ«taiao. The experimental campaign prior to the research carried out by the author consisted of quasi-static tests of beam column joint subassemblies subjected to lateral loading regime, with constant and varying axial load in the column. Most of those specimens were representative of a plane 2D frame (knee joint), while others represented a portion of a space 3D frame (corner joints), and only few of them had a floor slab, transverse beams, and lap splices. Using those experiments, several feasible, cost-effective, and non-invasive retrofit techniques were developed, improved, and refined. Nevertheless, the slow motion nature of those experiments did not take into account the dynamical component inherent to earthquake related problems. Amongst the set of techniques investigated, the use of FRP layers for strengthening beam column joints is of particular interest due to its versatility and the momentum that its use has gained in the current state of the practice. That particular retrofit technique was previously used to develop a strengthening scheme suitable for plane 2D and space 3D corner beam column joints, but lacking of floor slabs. In addition, a similar scheme was not developed for exterior joints of internal frames, referred here as ācruciformā. In this research a 2/5 scale RC frame model building comprising of two frames in parallel (external and internal) joined together by means of floor slabs and transverse beams, with non-ductile characteristics identical to those of the specimens investigated previously by others, and also including lap splices, was developed. In order to investigate the dynamic response of that building, a series of shake table tests with different ground motions were performed. After the first series of tests, the specimen was modified by connecting the spliced reinforcement in the columns in order to capture a different failure mode. Ground motions recorded during seismic events that occurred during the initial period of the experimental campaign (2010) were used in the subsequent experiments. The hierarchy of strengths and sequence of events in the panel zone region were evaluated in an extended version of the bending moment-axial load (M-N) performance domain developed by others. That extension was required due to the asymmetry in the beam cross section introduced by the floor slab. In addition, the effect of the torsion resistance provided by the spandrel (transverse beam) was included. In order to upgrade the brittle and unstable performance of the as-built/repaired specimen, a practical and suitable ad-hoc FRP retrofit intervention was developed, following a partial retrofit strategy that aimed to strengthen exterior beam column joints only (corner and cruciform). The ability of the new FRP scheme to revert the sequence of events in the panel zone region was evaluated using the extended version of the M-N performance domain as well as the guidelines for strengthening plane joints developed by others. Weakening of the floor slab in a novel configuration was also incorporated with the purpose of reducing the flexural capacity of the beam under negative bending moment (slab in tension), enabling the damage relocation from the joint into the beam. The efficacy of the developed retrofit intervention in upgrading the seismic performance of the as-built specimen was investigated using shake table tests with the input motions used in the experiments of the as-built/repaired specimen. Numerical work aimed to predict the response of the model building during the most relevant shake table tests was carried out. By using a simple numerical model with concentrated plasticity elements constructed in Ruaumoko2D, the results of blind and post-experimental predictions of the response of the specimen were addressed. Differences in the predicted response of the building using the nominal and the actual recorded motions of the shake table were investigated. The dependence of the accuracy of the numerical predictions on the assumed values of the parameters that control the hysteresis rules of key structural members was reviewed. During the execution of the experimental campaign part of this thesis, two major earthquakes affected the central part of Chile (27 of February 2010 Maule earthquake) and the Canterbury region in New Zealand (22 February 2011 Canterbury earthquake), respectively. As the author had the opportunity to experience those events and investigate their consequences in structures, the observations related to non-ductile detailing and drawbacks in the state of the practice related to reinforced concrete walls was also addressed in this research, resulting in preliminary recommendations for the refinement of current seismic code provisions and assessment guidelines. The investigations of the ground motions recorded during those and other earthquakes were used to review the procedures related to the input motions used for nonlinear dynamic analysis of buildings as required by most of the current code provisions. Inelastic displacement spectra were constructed using ground motions recorded during the earthquakes mentioned above, in order to investigate the adequacy of modification factors used to obtain reduced design spectra from elastic counterparts. Finally a simplified assessment procedure for RC walls that incorporates capacity compatible spectral demands is proposed.
School travel is a major aspect of a young personās everyday activity. The relationship between the built environment that youth experience on their way to and from school, influences a number of factors including their development, health and wellbeing. This is especially important in low income areas where the built environment is often poorer, but the need for it to be high quality and accessible is greater. This study focusses on the community of Aranui, a relatively low income suburb in Christchurch, New Zealand. It pays particular attention to Haeata Community Campus, a state school of just under 800 pupils from year one through to year thirteen (ages 5-18). The campus opened in 2017 following the closure of four local schools (three primary and one secondary), as part of the New Zealand Governmentās Education Renewal scheme following the Christchurch earthquakes of 2010/11. Dedicated effort toward understanding the local built environment, and subsequent travel patterns has been argued to be insufficiently considered. The key focus of this research was to understand the importance of the local environment in encouraging active school travel. The present study combines geospatial analysis, quantitative survey software Maptionnaire, and statistical models to explore the features of the local environment that influence school travel behaviour. Key findings suggest that distance to school and parental control are the most significant predictors of active transport in the study sample. Almost 75% of students live within two kilometres of the school, yet less than 40% utilise active transport. Parental control may be the key contributing factor to the disproportionate private vehicle use. However, active school travel is acknowledged as a complex process that is the product of many individual, household, and local environment factors. To see increased active transport uptake, the local environment needs to be of greater quality. Meaning that the built environment should be improved to be youth friendly, with greater walkability and safe, accessible cycling infrastructure.
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.
Observations of out-of-plane (OOP) instability in the 2010 Chile earthquake and in the 2011 Christchurch earthquake resulted in concerns about the current design provisions of structural walls. This mode of failure was previously observed in the experimental response of some wall specimens subjected to in-plane loading. Therefore, the postulations proposed for prediction of the limit states corresponding to OOP instability of rectangular walls are generally based on stability analysis under in-plane loading only. These approaches address stability of a cracked wall section when subjected to compression, thereby considering the level of residual strain developed in the reinforcement as the parameter that prevents timely crack closure of the wall section and induces stability failure. The New Zealand code requirements addressing the OOP instability of structural walls are based on the assumptions used in the literature and the analytical methods proposed for mathematical determination of the critical strain values. In this study, a parametric study is conducted using a numerical model capable of simulating OOP instability of rectangular walls to evaluate sensitivity of the OOP response of rectangular walls to variation of different parameters identified to be governing this failure mechanism. The effects of wall slenderness (unsupported height-to-thickness) ratio, longitudinal reinforcement ratio of the boundary regions and length on the OOP response of walls are evaluated. A clear trend was observed regarding the influence of these parameters on the initiation of OOP displacement, based on which simple equations are proposed for prediction of OOP instability in rectangular walls.
The Canterbury region of New Zealand experienced a sequence of strong earthquakes during 2010-2011. Responses included government acquisition of many thousands of residential properties in the city of Christchurch in areas with severe earthquake effects. A large and contiguous tract of this āred zonedā land lies in close proximity to the ÅtÄkaro / Avon River and is known as the Avon-ÅtÄkaro Red Zone (AORZ). The focus of this study was to provide an overview of the floodplain characteristics of the AORZ and review of international experience in ecological restoration of similar river margin and floodplain ecosystems to extract restoration principles and associated learnings. Compared to pre-earthquake ground levels, the dominant trend in the AORZ is subsidence, together with lateral movement especially in the vicinity of waterway. An important consequence of land subsidence in the lower ÅtÄkaro / Avon River is greater exposure to flooding and the effects of sea level rise. Scenario modelling for sea level rise indicates that much of the AORZ is exposed to inundation within a 100 year planning horizon based on a 1 m sea level rise. As with decisions on built infrastructure, investments in nature-based āgreen infrastructureā also require a sound business case including attention to risks posed by climate change. Future-proofing of the expected benefits of ecological restoration must therefore be secured by design. Understanding and managing the hydrology and floodplain dynamics are vital to the future of the AORZ. However, these characteristics are shared by other floodplain and river restoration projects worldwide. Identifying successful approaches provides a useful a source of useful information for floodplain planning in the AORZ. This report presents results from a comparative case study of three international examples to identify relevant principles for large-scale floodplain management at coastal lowland sites.
The Canterbury earthquakes, which started with the 7.1 magnitude event on September 4, 2010, caused significant damage in the region. The September 4 earthquakes brought substantial damage to land, buildings, and infrastructure, while the 6.3 magnitude earthquake on February 22, 2011 (and its subsequent aftershocks), brought even greater property damage, but also significant loss of life in addition to the region. Thousands were injured, and 185 persons died. A national State of Emergency was declared and remained in effect until April 30, 2011. A significant number of people required immediate assistance and support to deal with loss, injury, trauma experiences, and property damages. Many had to find alternate accommodation as their houses were too damaged to stay in. Of those affected, many were already vulnerable, and others had been too traumatized by the events to effectively deal with the challenges they were faced with. A number of human service organizations in the region, from both government and non-government sectors, joined forces to be able to more effectively and efficiently help those in need. This was the start of what would become known as the Earthquake Support Coordination Service. The aim of this report is to present an evaluation of the Earthquake Support Coordination Service and its collaborative organization, based on documentation and interviews with key stakeholders of the service. The aim is also to evaluate the service based on perspectives gathered among the clients as well as the coordinators working in the service. The final aim is to offer a reflection on the service model, and on what factors enabled the service, as well as recommendations regarding aspects of the service which may require review, and aspects which may be useful in other contexts.
