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.
The collapse of Redcliffs’ cliff in the 22 February 2011 and 13 June 2011 earthquakes were the first times ever a major failure incident occurred at Redcliffs in approximately 6000 years. This master’s thesis is a multidisciplinary engineering geological investigation sought to study these particular failure incidents, focusing on collecting the data necessary to explain the cause and effect of the cliff collapsing in the event of two major earthquakes. This study provides quantitative and qualitative data about the geotechnical attributes and engineering geological nature of the sea-cut cliff located at Redcliffs. Results from surveying the geology of Redcliffs show that the exposed lithology of the cliff face is a variably jointed rock body of welded and (relatively intact) unwelded ignimbrite, a predominantly massive unit of brecciated tuff, and a covering of wind-blown loess and soil deposit (commonly found throughout Canterbury) on top of the cliff. Moreover, detailing the external component of the slope profile shows that Redcliffs’ cliff is a 40 – 80 m cliff with two intersecting (NE and SE facing) slope aspects. The (remotely) measured geometry of the cliff face comprises of multiple outstanding gradients, averaging a slope angle of ~67 degrees (post-13 June 2011), where the steepest components are ~80 degrees, whereas the gentle sloping sections are ~44 degrees. The physical structure of Redcliffs’ cliff drastically changed after each collapse, whereby seismically induced alterations to the slope geometry resulted in material deposited on the talus at the base of the cliff. Prior to the first collapse, the variance of the gradient down the slope was minimal, with the SE Face being the most variable with up to three major gradients on one cross section. However, after each major collapse, the variability increased with more parts of the cliff face having more than one major gradient that is steeper or gentler than the remainder of the slope. The estimated volume of material lost as a result of the gradient changes was 28,267 m³ in February and 11,360 m³ in June 2011. In addition, surveys of the cliff top after the failure incidents revealed the development of fissures along the cliff edge. Monitoring 10 fissures over three months indicated that fissured by the cliff edge respond to intense seismicity (generally ≥ Mw 4) by widening. Redcliffs’ cliff collapsed on two separate occasions as a result of an accumulated amount of damage of the rock masses in the cliff (caused by weathering and erosion over time), and two Mw 6.2 trigger earthquakes which shook the Redcliffs and the surrounding area at a Peak Ground Acceleration (PGA) estimated to be around 2 g. The results of the theoretical study suggests that PGA levels felt on-site during both instances of failure are the result of three major factors: source of the quake and the site affected; topographic amplification of the ground movement; the short distance between the source and the cliff for both fault ruptures; the focus of seismic energy in the direction of thrust faulting along a path that intercepts Redcliffs (and the Port Hills). Ultimately, failure on the NE and SE Faces of Redcliffs’ cliff was concluded to be global as every part of the exposed cliff face deposited a significant volume of material on the talus at the base of the cliff, with the exception of one section on the NE Face. The cliff collapses was a concurrent process that is a single (non-monotonic) event that operated as a complex series of (primarily) toppling rock falls, some sliding of blocks, and slumping of the soil mantle on top of the cliff. The first collapse had a mixture of equivalent continua slope movement of the heavily weathered / damaged surface of the cliff face, and discontinuous slope movement of the jointed inner slope (behind the heavily weathered surface); whereas the second collapse resulted in only discontinuous slope movement on account of the freshly exposed cliff face that had damage to the rock masses, in the form of old and (relatively) new discontinuous fractures, induced by earthquakes and aftershocks leading up to the point of failure.
Following the 2010/2011 Canterbury earthquakes, approximately 60% of multi-story buildings with reinforced concrete walls required demolition. Both practitioners and researchers have increasingly realized that low-damage structural systems could be an alternative to improve the seismic behaviour of concrete buildings and to reduce the economic and social impact of structural damage in future earthquakes. To verify the seismic response of a low-damage concrete wall building representing state-of-art design practice, a shake table test on a two-story concrete building was recently conducted as part of an ILEE-QuakeCoRE collaborative research program. The building utilized flexible wall-to-floor connections in the long span direction and isolating wall-to-floor devices in the short span direction to provide a comparison of their respective behaviour. Additionally, the wall-to-floor interaction such as effects of wall uplift on the link slab, and force transfer mechanism from floor to the wall will be discussed in this paper.
In the period between September 2010 and December 2011, Christchurch was shaken by a series of strong earthquakes including the MW7.1 4 September 2010, Mw 6.2 22 February 2011, MW6.2 13 June 2011 and MW6.0 23 December 2011 earthquakes. These earthquakes produced very strong ground motions throughout the city and surrounding areas that resulted in soil liquefaction and lateral spreading causing substantial damage to buildings, infrastructure and the community. The stopbank network along the Kaiapoi and Avon River suffered extensive damage with repairs projected to take several years to complete. This presented an opportunity to undertake a case-study on a regional scale of the effects of liquefaction on a stopbank system. Ultimately, this information can be used to determine simple performance-based concepts that can be applied in practice to improve the resilience of river protection works. The research presented in this thesis draws from data collected following the 4th September 2010 and 22nd February 2011 earthquakes. The stopbank damage is categorised into seven key deformation modes that were interpreted from aerial photographs, consultant reports, damage photographs and site visits. Each deformation mode provides an assessment of the observed mechanism of failure behind liquefaction-induced stopbank damage and the factors that influence a particular style of deformation. The deformation modes have been used to create a severity classification for the whole stopbank system, being ‘no or low damage’ and ‘major or severe damage’, in order to discriminate the indicators and factors that contribute to ‘major to severe damage’ from the factors that contribute to all levels of damage a number of calculated, land damage, stopbank damage and geomorphological parameters were analysed and compared at 178 locations along the Kaiapoi and Avon River stopbank systems. A critical liquefiable layer was present at every location with relatively consistent geotechnical parameters (cone resistance (qc), soil behaviour type (Ic) and Factor of Safety (FoS)) across the study site. In 95% of the cases the critical layer occurred within two times the Height of the Free Face (HFF,). A statistical analysis of the geotechnical factors relating to the critical layer was undertaken in order to find correlations between specific deformation modes and geotechnical factors. It was found that each individual deformation mode involves a complex interplay of factors that are difficult to represent through correlative analysis. There was, however, sufficient data to derive the key factors that have affected the severity of deformation. It was concluded that stopbank damage is directly related to the presence of liquefaction in the ground materials beneath the stopbanks, but is not critical in determining the type or severity of damage, instead it is merely the triggering mechanism. Once liquefaction is triggered it is the gravity-induced deformation that causes the damage rather than the shaking duration. Lateral spreading and specifically the depositional setting was found to be the key aspect in determining the severity and type of deformation along the stopbank system. The presence or absence of abandoned or old river channels and point bar deposits was found to significantly influence the severity and type of deformation. A review of digital elevation models and old maps along the Kaiapoi River found that all of the ‘major to severe’ damage observed occurred within or directly adjacent to an abandoned river channel. Whilst a review of the geomorphology along the Avon River showed that every location within a point bar deposit suffered some form of damage, due to the depositional environment creating a deposit highly susceptible to liquefaction.
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.
The Mw 6.2 February 22nd 2011 Christchurch earthquake (and others in the 2010-2011 Canterbury sequence) provided a unique opportunity to study the devastating effects of earthquakes first-hand and learn from them for future engineering applications. All major events in the Canterbury earthquake sequence caused widespread liquefaction throughout Christchurch’s eastern suburbs, particularly extensive and severe during the February 22nd event. Along large stretches of the Avon River banks (and to a lesser extent along the Heathcote) significant lateral spreading occurred, affecting bridges and the infrastructure they support. The first stage of this research involved conducting detailed field reconnaissance to document liquefaction and lateral spreading-induced damage to several case study bridges along the Avon River. The case study bridges cover a range of ages and construction types but all are reinforced concrete structures which have relatively short, stiff decks. These factors combined led to a characteristic deformation mechanism involving deck-pinning and abutment back-rotation with consequent damage to the abutment piles and slumping of the approaches. The second stage of the research involved using pseudo-static analysis, a simplified seismic modelling tool, to analyse two of the bridges. An advantage of pseudo-static analysis over more complicated modelling methods is that it uses conventional geotechnical data in its inputs, such as SPT blowcount and CPT cone resistance and local friction. Pseudo-static analysis can also be applied without excessive computational power or specialised knowledge, yet it has been shown to capture the basic mechanisms of pile behaviour. Single pile and whole bridge models were constructed for each bridge, and both cyclic and lateral spreading phases of loading were investigated. Parametric studies were carried out which varied the values of key parameters to identify their influence on pile response, and computed displacements and damages were compared with observations made in the field. It was shown that pseudo-static analysis was able to capture the characteristic damage mechanisms observed in the field, however the treatment of key parameters affecting pile response is of primary importance. Recommendations were made concerning the treatment of these governing parameters controlling pile response. In this way the future application of pseudo-static analysis as a tool for analysing and designing bridge pile foundations in liquefying and laterally spreading soils is enhanced.
Results from a series of 1D seismic effective stress analyses of natural soil deposits from Christchurch are summarized. The analysed soil columns include sites whose performance during the 2010-2011 Canterbury earthquakes varied significantly, from no liquefaction manifestation at the ground surface to very severe liquefaction, in which case a large area of the site was covered by thick soil ejecta. Key soil profile characteristics and response mechanisms affecting the severity of surface liquefaction manifestation and subsequent damage are explored. The influence of shaking intensity on the triggering and contribution of these mechanisms is also discussed. Careful examination of the results highlights the importance of considering the deposit as a whole, i.e. a system of layers, including interactions between layers in the dynamic response and through pore water pressure redistribution and water flow.
This report presents the simplified seismic assessment of a case study reinforced concrete (RC) building following the newly developed and refined NZSEE/MBIE guidelines on seismic assessment (NZSEE/MBIE, semi-final draft 26 October 2016). After an overview of the step-by-step ‘diagnostic’ process, including an holistic and qualitative description of the expected vulnerabilities and of the assessment strategy/methodology, focus is given, whilst not limited, to the implementation of a Detailed Seismic Assessment (DSA) (NZSEE/MBIE, 2016c). The DSA is intended to provide a more reliable and consistent outcome than what can be provided by an initial seismic assessment (ISA). In fact, while the Initial Seismic Assessment (ISA), of which the Initial Evaluation Procedure is only a part of, is the more natural and still recommended first step in the overall assessment process, it is mostly intended to be a coarse evaluation involving as few resources as reasonably possible. It is thus expected that an ISA will be followed by a Detailed Seismic Assessment (DSA) not only where the threshold of 33%NBS is not achieved but also where important decisions are intended that are reliant on the seismic status of the building. The use of %NBS (% New Building Standard) as a capacity/demand ratio to describe the result of the seismic assessment at all levels of assessment procedure (ISA through to DSA) is deliberate by the NZSEE/MBIE guidelines (Part A) (NZSEE/MBIE 2016a). The rating for the building needs only be based on the lowest level of assessment that is warranted for the particular circumstances. Discussion on how the %NBS rating is to be determined can be found in Section A3.3 (NZSEE/MBIE 2016a), and, more specifically, in Part B for the ISA (NZSEE/MBIE 2016b) and Part C for the DSA (NZSEE/MBIE 2016c). As per other international approaches, the DSA can be based on several analysis procedures to assess the structural behaviour (linear, nonlinear, static or dynamic, force or displacement-based). The significantly revamped NZSEE 2016 Seismic Assessment Guidelines strongly recommend the use of an analytical (basically ‘by hand’) method, referred to the Simple Lateral Mechanism Analysis (SLaMA) as a first phase of any other numerically-based analysis method. Significant effort has thus been dedicated to provide within the NZSEE 2016 guidelines (NZSEE/MBIE 2016c) a step-by-step description of the procedure, either in general terms (Chapter 2) or with specific reference to Reinforced Concrete Buildings (Chapter 5). More specifically, extract from the guidelines, NZSEE “recommend using the Simple Lateral Mechanism Analysis (SLaMA) procedure as a first step in any assessment. While SLaMA is essentially an analysis technique, it enables assessors to investigate (and present in a simple form) the potential contribution and interaction of a number of structural elements and their likely effect on the building’s global capacity. In some cases, the results of a SLaMA will only be indicative. However, it is expected that its use should help assessors achieve a more reliable outcome than if they only carried out a detailed analysis, especially if that analysis is limited to the elastic range For complex structural systems, a 3D dynamic analysis may be necessary to supplement the simplified nonlinear Simple Lateral Mechanism Analysis (SLaMA).” This report presents the development of a full design example for the the implementation of the SLaMA method on a case study buildings and a validation/comparison with a non-linear static (pushover) analysis. The step-by-step-procedure, summarized in Figure 1, will be herein demonstrated from a component level (beams, columns, wall elements) to a subassembly level (hierarchy of strength in a beam-column joint) and to a system level (frame, C-Wall) assuming initially a 2D behaviour of the key structural system, and then incorporating a by-hand 3D behaviour (torsional effects).
This paper presents preliminary results of an experimental campaign on three beam-column joint subassemblies extracted from a 22-storey reinforced concrete frame building constructed in late 1980s at the Christchurch’s Central Business District (CBD) area, damaged and demolished after the 2010-2011 Canterbury earthquakes sequence (CES). The building was designed following capacity design principles. Column sway (i.e., soft storey) mechanisms were avoided, and the beams were provided with plastic hinge relocation details at both beam-ends, aiming at developing plastic hinges away from the column faces. The specimens were tested under quasi-static cyclic displacement controlled lateral loading. One of the specimens, showing no visible residual cracks was cyclically tested in its as-is condition. The other two specimens which showed residual cracks varying between hairline and 1.0mm in width, were subjected to cyclic loading to simulate cracking patterns consistent with what can be considered moderate damage. The cracked specimens were then repaired with an epoxy injection technique and subsequently retested until reaching failure. The epoxy injection techniques demonstrated to be quite efficient in partly, although not fully, restoring the energy dissipation capacities of the damaged specimens at all beam rotation levels. The stiffness was partly restored within the elastic range and almost fully restored after the onset of nonlinear behaviour.
The NMIT Arts & Media Building is the first in a new generation of multistorey timber structures. It employs an advanced damage avoidance earthquake design that is a world first for a timber building. Aurecon structural engineers are the first to use this revolutionary Pres-Lam technology developed at the University of Canterbury. This technology marks a fundamental change in design philosophy. Conventional seismic design of multi-storey structures typically depends on member ductility and the acceptance of a certain amount of damage to beams, columns and walls. The NMIT seismic system relies on pairs of coupled LVL shear walls that incorporate high strength steel tendons post-tensioned through a central duct. The walls are centrally fixed allowing them to rock during a seismic event. A series of U-shaped steel plates placed between the walls form a coupling mechanism, and act as dissipators to absorb seismic energy. The design allows the primary structure to remain essentially undamaged while readily replaceable connections act as plastic fuses. In this era where sustainability is becoming a key focus, the extensive use of timber and engineered-wood products such as LVL make use of a natural resource all grown and manufactured within a 100km radius of Nelson. This project demonstrates that there are now cost effective, sustainable and innovative solutions for multi-story timber buildings with potential applications for building owners in seismic areas around the world.
Earthquake Engineering is facing an extraordinarily challenging era, the ultimate target being set at increasingly higher levels by the demanding expectations of our modern society. The renewed challenge is to be able to provide low-cost, thus more widely affordable, high-seismic-performance structures capable of sustaining a design level earthquake with limited or negligible damage, minimum disruption of business (downtime) or, in more general terms, controllable socio-economical losses. The Canterbury earthquakes sequence in 2010-2011 has represented a tough reality check, confirming the current mismatch between societal expectations over the reality of seismic performance of modern buildings. In general, albeit with some unfortunate exceptions, modern multi-storey buildings performed as expected from a technical point of view, in particular when considering the intensity of the shaking (higher than new code design) they were subjected to. As per capacity design principles, plastic hinges formed in discrete regions, allowing the buildings to sway and stand and people to evacuate. Nevertheless, in many cases, these buildings were deemed too expensive to be repaired and were consequently demolished. Targeting life-safety is arguably not enough for our modern society, at least when dealing with new building construction. A paradigm shift towards damage-control design philosophy and technologies is urgently required. This paper and the associated presentation will discuss motivations, issues and, more importantly, cost-effective engineering solutions to design buildings capable of sustaining low-level of damage and thus limited business interruption after a design level earthquake. Focus will be given to the extensive research and developments in jointed ductile connections based upon controlled rocking & dissipating mechanisms for either reinforced concrete and, more recently, laminated timber structures. An overview of recent on-site applications of such systems, featuring some of the latest technical solutions developed in the laboratory and including proposals for the rebuild of Christchurch, will be provided as successful examples of practical implementation of performance-based seismic design theory and technology.
The effects of soil-foundation-structure interaction (SFSI) have been a topic of discussion amongst the structural and geotechnical community for many decades. The complexity of the mechanisms, as well as the need for inter-disciplinary knowledge of geotechnical and structural dynamics has plagued the advancement and the consequent inclusion of SFSI effects in design. A rigorous performance-based design methodology should not just consider the performance of the superstructure but the supporting foundation system as well. Case studies throughout history (eg. Kobe 1995, Kocaeli 1999 and Christchurch earthquakes 2010-2011) have demonstrated that a poor performance at the foundation level can result in a full demolition of the structure and, in general terms, that the extent of damage to, and repairability of, the building system as a whole, is given by the combination of the damage to the soil, foundation and superstructure. The lack of consideration of the modifying factors of SFSI and an absence of intuitive performance levels for controlling foundation and soil behaviour under seismic loads has resulted in inadequate designs for buildings sited on soft soil. For engineers to be satisfied that their designs meet the given performance levels they must first, understand how SFSI affects the overall system performance and secondly have tools available to adequately account for it in their design/assessment. This dissertation presents an integrated performance-based design procedure for buildingfoundation systems that considers all of the major mechanisms of SFSI. A new soil-foundation macro-element model was implemented into a nonlinear finite element software and validated against several experimental tests. The numerical model was used to provide insights in to the mechanisms of SFSI and statistical analysis on the results yielded simple expressions that allow the behaviour to be quantified. Particular attention was paid to the effects of shear force on the foundation response and the quantification of the rocking mode of response. The residual deformations of the superstructure and distribution of forces up the structure were also investigated. All of the major SFSI mechanisms are discussed in detail and targeted numerical studies are used to explain and demonstrate concepts. The design procedure was validated through the design and assessment of a series of concrete buildings that were designed to account for the effects of SFSI.
In most design codes, infill walls are considered as non-structural elements and thus are typically neglected in the design process. The observations made after major earthquakes (Duzce 1999, L’Aquila 2009, Christchurch 2011) have shown that even though infill walls are considered to be non-structural elements, they interact with the structural system during seismic actions. In the case of heavy infill walls (i.e. clay brick infill walls), the whole behaviour of the structure may be affected by this interaction (i.e. local or global structural failures such as soft storey mechanism). In the case of light infill walls (i.e. non-structural drywalls), this may cause significant economical losses. To consider the interaction of the structural system with the ‘non-structural ’infill walls at design stage may not be a practical approach due to the complexity of the infill wall behaviour. Therefore, the purpose of the reported research is to develop innovative technological solutions and design recommendations for low damage non-structural wall systems for seismic actions by making use of alternative approaches. Light (steel/timber framed drywalls) and heavy (unreinforced clay brick) non-structural infill wall systems were studied by following an experimental/numerical research programme. Quasi-static reverse cyclic tests were carried out by utilizing a specially designed full scale reinforced concrete frame, which can be used as a re-usable bare frame. In this frame, two RC beams and two RC columns were connected by two un-bonded post tensioning bars, emulating a jointed ductile frame system (PRESSS technology). Due to the rocking behaviour at the beam-column joint interfaces, this frame was typically a low damage structural solution, with the post-tensioning guaranteeing a linear elastic behaviour. Therefore, this frame could be repeatedly used in all of the tests carried out by changing only the infill walls within this frame. Due to the linear elastic behaviour of this structural bare frame, it was possible to extract the exact behaviour of the infill walls from the global results. In other words, the only parameter that affected the global results was given by the infill walls. For the test specimens, the existing practice of construction (as built) for both light and heavy non-structural walls was implemented. In the light of the observations taken during these tests, modified low damage construction practices were proposed and tested. In total, seven tests were carried out: 1) Bare frame , in order to confirm its linear elastic behaviour. 2) As built steel framed drywall specimen FIF1-STFD (Light) 3) As built timber framed drywall specimen FIF2-TBFD (Light) 4) As built unreinforced clay brick infill wall specimen FIF3-UCBI (Heavy) 5) Low damage steel framed drywall specimen MIF1-STFD (Light) 6) Low damage timber framed drywall specimen MIF2-TBFD (Light) 7) Low damage unreinforced clay brick infill wall specimen MIF5-UCBI (Heavy) The tests of the as built practices showed that both drywalls and unreinforced clay brick infill walls have a low serviceability inter-storey drift limit (0.2-0.3%). Based on the observations, simple modifications and details were proposed for the low damage specimens. The details proved to be working effectively in lowering the damage and increasing the serviceability drift limits. For drywalls, the proposed low damage solutions do not introduce additional cost, material or labour and they are easily applicable in real buildings. For unreinforced clay brick infill walls, a light steel sub-frame system was suggested that divides the infill panel zone into smaller individual panels, which requires additional labour and some cost. However, both systems can be engineered for seismic actions and their behaviour can be controlled by implementing the proposed details. The performance of the developed details were also confirmed by the numerical case study analyses carried out using Ruaumoko 2D on a reinforced concrete building model designed according to the NZ codes/standards. The results have confirmed that the implementation of the proposed low damage solutions is expected to significantly reduce the non-structural infill wall damage throughout a building.
Floor systems with precast concrete hollow-core units have been largely used in concrete buildings built in New Zealand during the 1980’s. Recent earthquakes, such as the Canterbury sequence in 2010-2011 and the Kaikoura earthquake in 2016, highlighted that this floor system can be highly vulnerable and potentially lead to the floor collapse. A series of research activities are in progress to better understand the seismic performance of floor diaphragms, and this research focuses on examining the performance of hollow core units running parallel to the walls of wall-resisting concrete structures. This study first focused on the development of fragility functions, which can be quickly used to assess likelihood of the hollow-core being able to survive given the buildings design drift, and secondly to determine the expected performance of hollow-core units that run parallel to walls, focusing on the alpha unit running by the wall. Fragility functions are created for a range of different parameters for both vertical dislocation and crack width that can be used as the basis of a quick analysis or loss estimation for the likely impact of hollow-core floors on building vulnerability and risk. This was done using past experimental tests, and the recorded damage. Using these results and the method developed by Baker fragility curves were able to be created for varying crack widths and vertical dislocations. Current guidelines for analysis of hollow-core unit incompatible displacements are based on experimental vertical displacement results from concrete moment resisting frame systems to determine the capacity of hollow-core elements. To investigate the demands on hollow-core units in a wall-based structure, a fibre-element model in the software Seismostruct is created and subject to quasi-static cyclic loading, using elements which are verified from previous experimental tests. It is shown that for hollow-core units running by walls that the 10 mm displacement capacity used for hollow-core units running by a beam is insufficient for members running by walls and that shear analysis should be used. The fibre-element model is used to simulate the seismic demand induced on the floor system and has shown that the shear demand is a function of drift, wall length, hollow-core span, linking slab length and, to a minor extent, wall elongation.
Recent severe earthquakes, such as the 2010-2011 Christchurch earthquake series, have put emphasis on building resilience all over the world. To achieve such resilience, procedures for low damage seismic design have been developed to satisfy both life safety requirements and the need to minimize undesirable economic effects of required building repair or structural member replacement following a major earthquake. Seismic resisting systems following this concept are expected to withstand severe earthquakes without requiring major post-earthquake repairs, using isolating mechanisms or sacrificial systems that either do not need repair or are readily repairable or replaceable. These include the sliding hinge joint with asymmetric friction connections (SHJAFCs) in beam-to-column connections of the moment resisting steel frames (MRSFs) and symmetric friction connections (SFCs) in braces of the braced frames. A 9 m tall, configurable three-storey steel framed composite floor building incorporating frictionbased connections is to be tested using two linked bi-directional shake tables at the International joint research Laboratory of Earthquake Engineering (ILEE) facilities, Shanghai, China. The structural systems are configurable, allowing different moment and braced frame structural systems tested in two horizontal directions. The structure is designed and detailed to undergo, at worst, minor damage under a planned series of severe earthquakes.
To this extent, modern buildings generally demonstrated good resistance to collapse during the recent earthquakes in New Zealand. However, damage to non-structural elements (NSE) has been persistent during these events. NSEs include secondary systems or components attached to the floors, roofs, and walls of a building or industrial facility that are not explicitly designed to participate in the main vertical or lateral load-bearing mechanism of the structure. They play a major role in the operational and functional aspects of buildings and contribute a major portion of the building’s overall cost. Therefore, they are expected to accommodate the effects of seismic actions such as drifts and accelerations. Typical examples of NSEs include internal non-loadbearing partitions, suspended ceilings, sprinkler piping systems, architectural claddings, building contents, mechanical/electrical equipment, and furnishings. The main focus of this thesis is the drift sensitive NSEs: precast concrete cladding panels and internal partition walls. Even though most precast concrete cladding panels performed well from a life-safety point of view during recent earthquakes in NZ, some collapsed panels posed a significant threat to life safety. It is, therefore, important that the design and detailing of the panel-to-structure connections ensure that their strength and displacement capacity are adequate to meet the corresponding seismic demands, at least during design level earthquakes. In contrast, the partition wall is likely to get damaged and lose serviceability at a low inter-story drift unless designed to accommodate the relative deformations between them and the structure. Partition walls suffered wide-ranging damage such as screw failures, diagonal cracking, detachments to the gypsum linings, and anchorage failures during the 2011 Canterbury Earthquake Sequence in NZ. Therefore, the thesis is divided into two parts. Part I of the thesis focuses on developing novel low-damage precast concrete cladding panel connections, i.e. “rocking” connection details comprising vertically slotted steel embeds and weld plates. The low-damage seismic performance of novel “rocking” connection details is verified through experimental tests comprising uni-directional, bi-directional, and multi-storey scaled quasi-static cyclic tests. Comparison with the seismic performance of traditional panel connections reported in the literature demonstrated the system’s significantly improved seismic resilience. Furthermore, the finite element models of panel connections and sealants are developed in ABAQUS. The force-drift responses of the “rocking” panel system modelled in SAP2000 is compared with the experimental results to evaluate their accuracy and validity. Part II of the thesis focuses on a) understanding the seismic performance of traditional rigid timber-framed partition wall, b) development and verification of low-damage connections (i.e. “rocking” connection details comprising of dual-slot tracks), and c) seismic evaluation of partition walls with a novel “bracketed and slotted” connections (comprising of innovative fastener and plastic bracket named Flexibracket) under uni-directional and bidirectional quasi-static cyclic loadings. Moreover, parametric investigation of the partition walls was conducted through several experimental tests to understand better the pros and cons of the rocking connection details. The experimental results have confirmed that the implementation of the proposed low damage solutions of precast cladding panels and internal partition walls can significantly reduce their damage in a building.
Following the Mw 6.2 Christchurch Earthquake on 22 February 2011, extensive ground cracking in loessial soils was reported in some areas of the Port Hills, southeast of central Christchurch. This study was undertaken to investigate the mechanisms of earthquake-induced ground damage on the eastern side of the Hillsborough Valley. A zone of extensional cracking up to 40m wide and 600m long was identified along the eastern foot-slope, accompanied by compression features and spring formation at the toe of the slope. An engineering geological and geomorphological model was developed for the eastern Hillsborough Valley that incorporates geotechnical investigation data sourced from the Canterbury Geotechnical Database (CGD), the findings of trenching and seismic refraction surveying carried out for this research, and interpretation of historical aerial photographs. The thickness and extent of a buried peat swamp at the base of the slope was mapped, and found to coincide with significant compression features. Ground cracking was found to have occurred entirely within loess-colluvium and to follow the apices of pre-1920s tunnel-gully fan debris at the southern end of the valley. The ground-cracking on the eastern side of the Hillsborough Valley is interpreted to have formed through tensile failure of the loess-colluvium. Testing was carried out to determine the tensile strength of Port Hills loess colluvium as a function of water content and density, in order to better understand the occurrence and distribution of the observed ground cracking. A comprehensive review of the soil tensile strength testing literature was undertaken, from which a test methodology was developed. Results show remoulded loess-colluvium to possess tensile strength of 7 - 28 kPa across the range of tested moisture contents (10-15%) and dry densities (1650-1900kg/m3). A positive linear relationship was observed between tensile strength and dry density, and a negative linear relationship between moisture content and tensile strength. The observed ground damage and available geotechnical information (inclinometer and piezometer records provided by the Earthquake Commission) were together used to interpret the mechanism(s) of slope movement that occurred in the eastern Hillsborough Valley. The observed ground damage is characteristic of translational movement, but without the development of lateral release scarps, or a basal sliding surface - which was not located during drilling. It is hypothesised that shear displacement has been accommodated by multiple slip surfaces of limited extent within the upper 10m of the slope. Movement has likely occurred within near-saturated colluvial units that have lost strength during earthquake shaking. The eastern Hillsborough Valley is considered to be an ‘incipient translational slide’, as both the patterns of damage and shearing are consistent with the early stages of such slide development. Sliding block analysis was utilised to understand how the eastern Hillsborough Valley may perform in a future large magnitude earthquake. Known cumulative displacements of ~0.3m for eastern Hillsborough Valley during the 2010-2011 Canterbury Earthquake Sequence were compared with modelled slope displacements to back-analyse a lower-bound yield acceleration of 0.2 - 0.25g. Synthetic broadband modelling for future Alpine and Hope Fault earthquakes indicates PGAs of approximately 0.08g for soil sites in the Christchurch area, as such, slope movement is unlikely to be reactivated by an Alpine Fault or Hope Fault earthquake. This does not take into account the possible role of strength loss due to excess pore pressure that may occur during these future events.
The 14 November 2016 Kaikōura earthquake had major impacts on New Zealand's transport system. Road, rail and port infrastructure was damaged, creating substantial disruption for transport operators, residents, tourists, and business owners in the Canterbury, Marlborough and Wellington regions, with knock-on consequences elsewhere. During both the response and recovery phases, a large amount of information and data relating to the transport system was generated, managed, analysed, and exchanged within and between organisations to assist decision making. To improve information and data exchanges and related decision making in the transport sector during future events and guide new resilience strategies, we present key findings from a recent post-earthquake assessment. The research involved 35 different stakeholder groups and was conducted for the Ministry of Transport. We consider what transport information was available, its usefulness, where it was sourced from, mechanisms for data transfer between organisations, and suggested approaches for continued monitoring.
The recent earthquakes in Christchurch have made it clear that issues exist with current RC frame design in New Zealand. In particular, beam elongation in RC frame buildings was widespread and resulted in numerous buildings being rendered irreparable. Design solutions to overcome this problem are clearly needed, and the slotted beam is one such solution. This system has a distinct advantage over other damage avoidance design systems in that it can be constructed using current industry techniques and conventional reinforcing steel. As the name suggests, the slotted beam incorporates a vertical slot along part of the beam depth at the beam-column interface. Geometric beam elongation is accommodated via opening and closing of these slots during seismically induced rotations, while the top concrete hinge is heavily reinforced to prevent material inelastic elongation. Past research on slotted beams has shown that the bond demand on the bottom longitudinal reinforcement is increased compared with equivalent monolithic systems. Satisfying this increased bond demand through conventional means may yield impractical and economically less viable column dimensions. The same research also indicated that the joint shear mechanism was different to that observed within monolithic joints and that additional horizontal reinforcement was required as a result. Through a combination of theoretical investigation, forensic analysis, and database study, this research addresses the above issues and develops design guidelines. The use of supplementary vertical joint stirrups was investigated as a means of improving bond performance without the need for non-standard reinforcing steel or other hardware. These design guidelines were then validated experimentally with the testing of two 80% scale beam-column sub-assemblies. The revised provisions for bond within the bottom longitudinal reinforcement were found to be adequate while the top longitudinal reinforcement remained nominally elastic throughout both tests. An alternate mechanism was found to govern joint shear behaviour, removing the need for additional horizontal joint reinforcement. Current NZS3101:2006 joint shear reinforcement provisions were found to be more than adequate given the typically larger column depths required rendering the strut mechanism more effective. The test results were then used to further refine design recommendations for practicing engineers. Finally, conclusions and future research requirements were outlined.
During the 2010 - 2011 Canterbury earthquake sequence, extensive liquefaction was observed in many areas of Christchurch city and its surroundings, causing widespread damage to buildings and infrastructure. While existing simplified methods were found to work well in some areas of the city, there were also large areas where these methods did not perform satisfactorily. In some of these cases, researchers have proposed that layers of fine grained material within the soil profile may be responsible for preventing the manifestation of liquefaction. This paper presents preliminary findings on the mechanisms at play when pressure differentials exist across a clay layer. It is found that if the clay layer is unable to distort, then pore fluid is unable to break-through the layer even with relatively high pressures, resulting in dissipation of excess pore pressures by seepage. If the layers are however able to distort, then it is possible for the pore fluid to break through the clay layer, potentially resulting in adverse effects in terms of the severity of liquefaction.
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.
Seismic behaviour of typical unreinforced masonry (URM) brick houses, that were common in early last century in New Zealand and still common in many developing countries, is experimentally investigated at University of Canterbury, New Zealand in this research. A one halfscale model URM house is constructed and tested under earthquake ground motions on a shaking table. The model structure with aspect ratio of 1.5:1 in plan was initially tested in the longitudinal direction for several earthquakes with peak ground acceleration (PGA) up to 0.5g. Toppling of end gables (above the eaves line) and minor to moderate cracking around window and door piers was observed in this phase. The structure was then rotated 90º and tested in the transverse (short) direction for ground motions with PGA up to 0.8g. Partial out-of-plane failure of the face loaded walls in the second storey and global rocking of the model was observed in this phase. A finite element analysis and a mechanism analysis are conducted to assess the dynamic properties and lateral strength of the model house. Seismic fragility function of URM houses is developed based on the experimental results. Damping at different phases of the response is estimated using an amplitude dependent equivalent viscous damping model. Financial risk of similar URM houses is then estimated in term of expected annual loss (EAL) following a probabilistic financial risk assessment framework. Risks posed by different levels of damage and by earthquakes of different frequencies are then examined.
In recent years, rocking isolation has become an effective approach to improve seismic performance of steel and reinforced concrete structures. These systems can mitigate structural damage through rigid body displacement and thus relatively low requirements for structural ductility, which can significantly improve seismic resilience of structures and reduce repairing costs after strong earthquakes. A number of base rocking structural systems with only a single rocking interface have been proposed. However, these systems can have significant high mode effect for high rise structures due to the single rocking interface. This RObust BUilding SysTem (ROBUST) project is a collaborative China-New Zealand project sponsored by the International Joint Research Laboratory of Earthquake Engineering (ILEE), Tongji University, and a number of agencies and universities within New Zealand including the BRANZ, Comflor, Earthquake Commission, HERA, QuakeCoRE, QuakeCentre, University of Auckland, and the University of Canterbury. A number of structural configurations will be tested [1, 2], and non-structural elements including ceilings, infilling walls, glazed curtain walls, precast concrete panels, piping system will also be tested in this project [3]. Within this study, a multiple rocking column steel structural system was proposed and investigated mainly by Tongji team with assistance of NZ members. The concept of rocking column system initiates from the structure of Chinese ancient wooden pagoda. In some of Chinese wooden pagodas, there are continuous core columns hanged only at the top of each pagoda, which is not connected to each stories. This core column can effectively avoid collapse of the whole structure under large storey drifts. Likewise, there are also central continuous columns in the newly proposed steel rocking column system, which can avoid weak story failure mechanism and make story drifts more uniform. In the proposed rocking column system, the structure can switch between an elastic rigidly connected moment resisting frame and a controlled rocking column system when subjected to strong ground motion excitations. The main seismic energy can be dissipated by asymmetric friction beam–column connections, thereby effectively reducing residual displacement of the structure under seismic loading without causing excessive damage to structural members. Re–centering of the structure is provided not only by gravity load carried by rocking columns, but also by mould coil springs. To investigate dynamic properties of the proposed system under different levels of ground excitations, a full-scale threestory steel rocking column structural system with central continuous columns is to be tested using the International joint research Laboratory of Earthquake Engineering (ILEE) facilities, Shanghai, China and an analytical model is established. A finite element model is also developed using ABAQUS to simulate the structural dynamic responses. The rocking column system proposed in this paper is shown to produce resilient design with quick repair or replacement.
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, √(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.
Reinforced concrete structures designed in pre-1970s are vulnerable under earthquakes due to lack of seismic detailing to provide adequate ductility. Typical deficiencies of pre-1970s reinforced concrete structures are (a) use of plain bars as longitudinal reinforcement, (b) inadequate anchorage of beam longitudinal reinforcement in the column (particularly exterior column), (c) lack of joint transverse reinforcement if any, (d) lapped splices located just above joint, and (e) low concrete strength. Furthermore, the use of infill walls is a controversial issue because it can help to provide additional stiffness to the structure on the positive side and on the negative side it can increase the possibility of soft-storey mechanisms if it is distributed irregularly. Experimental research to investigate the possible seismic behaviour of pre-1970s reinforced concrete structures have been carried out in the past. However, there is still an absence of experimental tests on the 3-D response of existing beam-column joints under bi-directional cyclic loading, such as corner joints. As part of the research work herein presented, a series of experimental tests on beam-column subassemblies with typical detailing of pre-1970s buildings has been carried out to investigate the behaviour of existing reinforced concrete structures. Six two-third scale plane frame exterior beam-column joint subassemblies were constructed and tested under quasi-static cyclic loading in the Structural Laboratory of the University of Canterbury. The reinforcement detailing and beam dimension were varied to investigate their effect on the seismic behaviour. Four specimens were conventional deep beam-column joint, with two of them using deformed longitudinal bars and beam bars bent in to the joint and the two others using plain round longitudinal bars and beam bars with end hooks. The other two specimens were shallow beam-column joint, one with deformed longitudinal bars and beam bars bent in to the joint, the other with plain round longitudinal bars and beam bars with end hooks. All units had one transverse reinforcement in the joint. The results of the experimental tests indicated that conventional exterior beam-column joint with typical detailing of pre-1970s building would experience serious diagonal tension cracking in the joint panel under earthquake. The use of plain round bars with end hooks for beam longitudinal reinforcement results in more severe damage in the joint core when compared to the use of deformed bars for beam longitudinal reinforcement bent in to the joint, due to the combination of bar slips and concrete crushing. One interesting outcome is that the use of shallow beam in the exterior beam-column joint could avoid the joint cracking due to the beam size although the strength provided lower when compared with the use of deep beam with equal moment capacity. Therefore, taking into account the low strength and stiffness, shallow beam can be reintroduced as an alternative solution in design process. In addition, the presence of single transverse reinforcement in the joint core can provide additional confinement after the first crack occurred, thus delaying the strength degradation of the structure. Three two-third scale space frame corner beam-column joint subassemblies were also constructed to investigate the biaxial loading effect. Two specimens were deep-deep beam-corner column joint specimens and the other one was deep-shallow beam-corner column joint specimen. One deep-deep beam-corner column joint specimen was not using any transverse reinforcement in the joint core while the two other specimens were using one transverse reinforcement in the joint core. Plain round longitudinal bars were used for all units with hook anchorage for the beam bars. Results from the tests confirmed the evidences from earthquake damage observations with the exterior 3-D (corner) beam-column joint subjected to biaxial loading would have less strength and suffer higher damage in the joint area under earthquake. Furthermore, the joint shear relation in the two directions is calibrated from the results to provide better analysis. An analytical model was used to simulate the seismic behaviour of the joints with the help of Ruaumoko software. Alternative strength degradation curves corresponding to different reinforcement detailing of beam-column joint unit were proposed based on the test results.
Post-tensioned timber technology was originally developed and researched at the University of Canterbury (UC) in New Zealand in 2005. It can provide a low-damage seismic design solution for multi-storey mass timber buildings. Since mass timber products, such as cross-laminated timber (CLT), have high in-plane stiffness, a post-tensioned timber shear wall will deform mainly in a rocking mechanism. The moment capacity of the wall at the base is commonly determined using the elastic form of the Modified Monolithic Beam Analogy (MMBA). In the calculation of the moment capacity at the wall base, it is critical to accurately predict the location of the neutral axis and the timber compressive stress distribution. Three 2/3 scale 8.6m tall post-tensioned CLT walls were experimentally tested under quasi-static cyclic loading – both uni-directional and bi-directional- in this study. These specimens included a single wall, a coupled wall, and a C-shaped core-wall. The main objective was to develop post-tensioned C-shaped timber core-walls for tall timber buildings with enhanced lateral strength and stiffness. To better understand the timber compressive stress distributions at the wall base, particle tracking technology (PTT) technology was applied for the first time to investigate the behaviour of the compression toe. Previous post-tensioned timber testing primarily used the displacement measurements to determine the timber compressive behavior at the wall base or rocking interfaces. However, by using PTT technology, the timber strain measurements in the compression zone can be much more accurate as PTT is able to track the movement of many particles on the timber surface. This paper presents experimental testing results of post-tensioned CLT walls with a focus on capturing timber compressive behavior using PTT. The PTT measurements were able to better capture small base rotations which occurred at the onset of gap opening and capture unexpected phenomena in core-wall tests. The single wall test result herein presented indicates that while the MMBA could predict the moment rotation behavior with reasonable accuracy, the peak strain response was under predicted in the compression toe. Further detailed study is required to better understand the complex strain fields generated reflective of the inherent cross-thickness inhomogeneity and material variability of CLT.
Supplemental energy dissipation devices are increasingly used to protect structures, limit loads transferred to structural elements and absorbing significant response energy without sacrificial structural damage. Lead extrusion dampers are supplemental energy dissipation devices, where recent development of smaller volumetric size with high force capacities, called high force to volume (HF2V) devices, has seen deployment in a large series of scaled and full-scaled experiments, as well as in three new structures in Christchurch, NZ and San Francisco, USA. HF2V devices have previously been designed using limited precision models, so there is variation in force prediction capability. Further, while the overall resistive force is predicted, the knowledge of the relative contributions of the different internal reaction mechanisms to these overall resistive forces is lacking, limiting insight and predictive accuracy in device design. There is thus a major need for detailed design models to better understand force generation, and to aid precision device design. These outcomes would speed the overall design and implementation process for uptake and use, reducing the need for iterative experimental testing. Design parameters from 17 experimental HF2V device tests are used to create finite element models using ABAQUS. The analysis is run using ABAQUS Explicit, in multiple step times of 1 second with automatic increments, to balance higher accuracy and computational time. The output is obtained from the time- history output of the contact pressure forces including the normal and friction forces on the lead along the shaft. These values are used to calculate the resistive force on the shaft as it moves through the lead, and thus the device force. Results of these highly nonlinear, high strain analyses are compared to experimental device force results. Model errors compared to experimental results for all 17 devices ranged from 0% to 20% with a mean absolute error of 6.4%, indicating most errors were small. In particular, the standard error in manufacturing is SE = ±14%. In this case, 15 of 17 devices (88%) are within ±1SE (±14%) and 2 of 17 devices (12%) are within ±2SE (±28). These results show low errors and a distribution of errors compared to experimental results that are within experimental device construction variability. The overall modelling methodology is objective and repeatable, and thus generalizable. The exact same modelling approach is applied to all devices with only the device geometry changing. The results validate the overall approach with relatively low error, providing a general modelling methodology for accurate design of HF2V devices.
