The influence of nonlinear soil-foundation-structure interaction (SFSI) on the performance of multi-storey buildings during earthquake events has become increasingly important in earthquake resistant design. For buildings on shallow foundations, SFSI refers to nonlinear geometric effects associated with uplift of the foundation from the supporting soil as well as nonlinear soil deformation effects. These effects can potentially be beneficial for structural performance, reducing forces transmitted from ground shaking to the structure. However, there is also the potential consequence of residual settlement and rotation of the foundation. This Thesis investigates the influence of SFSI in the performance of multi-storey buildings on shallow foundations through earthquake observations, experimental testing, and development of spring-bed numerical models that can be incorporated into integrated earthquake resistant design procedures. Observations were made following the 22 February 2011 Christchurch Earthquake in New Zealand of a number of multi-storey buildings on shallow foundations that performed satisfactorily. This was predominantly the case in areas where shallow foundations, typically large raft foundations, were founded on competent gravel and where there was no significant manifestation of liquefaction at the ground surface. The properties of these buildings and the soils they are founded on directed experimental work that was conducted to investigate the mechanisms by which SFSI may have influenced the behaviour of these types of structure-foundation systems. Centrifuge experiments were undertaken at the University of Dundee, Scotland using a range of structure-foundation models and a layer of dense cohesionless soil to simulate the situation in Christchurch where multi-storey buildings on shallow foundations performed well. Three equivalent single degree of freedom (SDOF) models representing 3, 5, and 7 storey buildings with identical large raft foundations were subjected to a range of dynamic Ricker wavelet excitations and Christchurch Earthquake records to investigate the influence of SFSI on the response of the equivalent buildings. The experimental results show that nonlinear SFSI has a significant influence on structural response and overall foundation deformations, even though the large raft foundations on competent soil meant that there was a significant reserve of bearing capacity available and nonlinear deformations may have been considered to have had minimal effect. Uplift of the foundation from the supporting soil was observed across a wide range of input motion amplitudes and was particularly significant as the amplitude of motion increased. Permanent soil deformation represented by foundation settlement and residual rotation was also observed but mainly for the larger input motions. However, the absolute extent of uplift and permanent soil deformation was very small compared to the size of the foundation meaning the serviceability of the building would still likely be maintained during large earthquake events. Even so, the small extent of SFSI resulted in attenuation of the response of the structure as the equivalent period of vibration was lengthened and the equivalent damping in the system increased. The experimental work undertaken was used to validate and enhance numerical modelling techniques that are simple yet sophisticated and promote interaction between geotechnical and structural specialists involved in the design of multi-storey buildings. Spring-bed modelling techniques were utilised as they provide a balance between ease of use, and thus ease of interaction with structural specialists who have these techniques readily available in practice, and theoretically rigorous solutions. Fixed base and elastic spring-bed models showed they were unable to capture the behaviour of the structure-foundation models tested in the centrifuge experiments. SFSI spring-bed models were able to more accurately capture the behaviour but recommendations were proposed for the parameters used to define the springs so that the numerical models closely matched experimental results. From the spring-bed modelling and results of centrifuge experiments, an equivalent linear design procedure was proposed along with a procedure and recommendations for the implementation of nonlinear SFSI spring-bed models in practice. The combination of earthquake observations, experimental testing, and simplified numerical analysis has shown how SFSI is influential in the earthquake performance of multi-storey buildings on shallow foundations and should be incorporated into earthquake resistant design of these structures.
This thesis is a creative and critical exploration of how transmedia storytelling meshes with political documentary’s nature of representing social realities and goals to educate and promote social change. I explore this notion through Obrero (“worker”), my independently produced transmedia and transjournalistic documentary project that explores the conditions and context of the Filipino rebuild workers who migrated to Christchurch, New Zealand after the earthquake in 2011. While the project should appeal to New Zealanders, it is specifically targeted at an audience from the Philippines. Obrero began as a film festival documentary that co-exists with strategically refashioned Web 2.0 variants, a social network documentary and an interactive documentary (i-doc). Using data derived from the production and circulation of Obrero, I interrogate how the documentary’s variants engage with differing audiences and assess the extent to which this engagement might be effective. This thesis argues that contemporary documentary needs to re-negotiate established film aesthetics and practices to adapt in the current period of shifting technologies and fragmented audiences. Documentary’s migration to new media platforms also creates a demand for filmmakers to work with a transmedia state of mind—that is, the capacity to practise the old canons of documentary making while comfortably adjusting to new media production praxis, ethics, and aesthetics. Then Obrero itself, as the creative component of this thesis, becomes an instance of research through creative practice. It does so in two respects: adding new knowledge about the context, politics, and experiences of the Filipino workers in New Zealand; and offering up a broader model for documentary engagement, which I analyse for its efficacy in the digital age.
This article is a critical commentary of how political documentary embodies the traits and functions of alternative journalism. I explore this notion through Obrero (‘worker’) my independent documentary project about the labour migration of Filipino workers to Christchurch, Aotearoa New Zealand, after the earthquake in 2011. This article maps out the points at where the theories and practices of alternative media and documentary intersect. Analysing political documentary as a format of alternative journalism has links to the long tradition of film and video production as a tool for social critique. As a form of practice-based research, Obrero falls under the rubric of alternative journalism—able to represent the politically marginal sectors of the polity and report on issues underreported in the mainstream press. This article concludes that a distribution plan that is responsive to fragmenting audiences works best when alternative journalism no longer targets a niche but transborder audiences.
To address the provocation provided by the editors I wish to reflect upon the ongoing civic and artistic responses to the earthquakes in Christchurch, New Zealand, 2010-11, in which 185 people lost their lives (largely due to poor engineering and construction practices). Whilst the example is very different in character from that of efforts to memorialize July 22, 2011, I wish to use the case to briefly respond to the issue of temporality as raised by Jacques Rancière in his critique of the ‘endless work of mourning’ produced by testimonial art. The orientation of this mourning, he argues, is always backward-looking, characterized by, ‘a reversal of the flow of time: the time turned towards an end to be accomplished – progress, emancipation or the Other – is replaced by that turned towards the catastrophe behind us.’ How might memorial practices divide their gaze between remembered pasts and possible futures? AM - Accepted Manuscript
This research is a creative exploration of transmedia’s ability to offer up a model of distribution and audience engagement for political documentary. Transmedia, as is well known, is a fluid concept. It is not restricted to the activities of the entertainment industry and its principles also reverberate in the practice of political and activist documentary projects. This practice-led research draws on data derived from the production and circulation of Obrero, an independent transmedia documentary. The project explores the conditions and context of the Filipino rebuild workers who migrated to Christchurch, New Zealand after the earthquake in 2011. Obrero began as a film festival documentary that co-exists with two other new media iterations, each reaching its respective target audience: a web documentary, and a Facebook-native documentary. This study argues that relocating the documentary across new media spaces not only expands the narrative but also extends the fieldwork and investigation, forms like-minded publics, and affords the creation of an organised hub of information for researchers, academics and the general public. Treating documentary as research can represent a novel pathway to knowledge generation and the present case study, overall, provides an innovative model for future scholarship.
New Zealand’s stock of unreinforced masonry (URM) bearing wall buildings was principally constructed between 1880 and 1935, using fired clay bricks and lime or cement mortar. These buildings are particularly vulnerable to horizontal loadings such as those induced by seismic accelerations, due to a lack of tensile force-resisting elements in their construction. The poor seismic performance of URM buildings was recently demonstrated in the 2011 Christchurch earthquake, where a large number of URM buildings suffered irreparable damage and resulted in a significant number of fatalities and casualties. One of the predominant failure modes that occurs in URM buildings is diagonal shear cracking of masonry piers. This diagonal cracking is caused by earthquake loading orientated parallel to the wall surface and typically generates an “X” shaped crack pattern due to the reversed cyclic nature of earthquake accelerations. Engineered Cementitious Composite (ECC) is a class of fiber reinforced cement composite that exhibits a strain-hardening characteristic when loaded in tension. The tensile characteristics of ECC make it an ideal material for seismic strengthening of clay brick unreinforced masonry walls. Testing was conducted on 25 clay brick URM wallettes to investigate the increase in shear strength for a range of ECC thicknesses applied to the masonry wallettes as externally bonded shotcrete reinforcement. The results indicated that there is a diminishing return between thickness of the applied ECC overlay and the shear strength increase obtained. It was also shown that, the effectiveness of the externally bonded reinforcement remained constant for one and two leaf wallettes, but decreased rapidly for wall thicknesses greater than two leafs. The average pseudo-ductility of the strengthened wallettes was equal to 220% of that of the as-built wallettes, demonstrating that ECC shotcrete is effective at enhancing both the in-plane strength and the pseudo-ductility of URM wallettes. AM - Accepted Manuscript
This section considers forms of collaboration in situated and community projects embedded in important spatial transformation processes in New Zealand cities. It aims to shed light on specific combinations of material and semantic aspects characterising the relation between people and their environment. Contributions focus on participative urban transformations. The essays that follow concentrate on the dynamics of territorial production of associations between multiple actors belonging both to civil society and constituted authority. Their authors were directly engaged in the processes that are reported and conceptualised, thereby offering evidence gained through direct hands-on experience. Some of the investigations use case studies that are conspicuous examples of the recent post-traumatic urban development stemming from the Canterbury earthquakes of 2010-2011. More precisely, these cases belong to the early phases of the programmes of the Christchurch recovery or the Wellington seismic prevention. The relevance of these experiences for the scope of this study lies in the unprecedented height of public engagement at local, national and international levels, a commitment reached also due to the high impact, both emotional and concrete, that affected the entire society.
Background: Up to 6 years after the 2011 Christchurch earthquakes, approximately one-third of parents in the Christchurch region reported difficulties managing the continuously high levels of distress their children were experiencing. In response, an app named Kākano was co-designed with parents to help them better support their children’s mental health. Objective: The objective of this study was to evaluate the acceptability, feasibility, and effectiveness of Kākano, a mobile parenting app to increase parental confidence in supporting children struggling with their mental health. Methods: A cluster-randomized delayed access controlled trial was carried out in the Christchurch region between July 2019 and January 2020. Parents were recruited through schools and block randomized to receive immediate or delayed access to Kākano. Participants were given access to the Kākano app for 4 weeks and encouraged to use it weekly. Web-based pre- and postintervention measurements were undertaken. Results: A total of 231 participants enrolled in the Kākano trial, with 205 (88.7%) participants completing baseline measures and being randomized (101 in the intervention group and 104 in the delayed access control group). Of these, 41 (20%) provided full outcome data, of which 19 (18.2%) were for delayed access and 21 (20.8%) were for the immediate Kākano intervention. Among those retained in the trial, there was a significant difference in the mean change between groups favoring Kākano in the brief parenting assessment (F1,39=7, P=.012) but not in the Short Warwick-Edinburgh Mental Well-being Scale (F1,39=2.9, P=.099), parenting self-efficacy (F1,39=0.1, P=.805), family cohesion (F1,39=0.4, P=.538), or parenting sense of confidence (F1,40=0.6, P=.457). Waitlisted participants who completed the app after the waitlist period showed similar trends for the outcome measures with significant changes in the brief assessment of parenting and the Short Warwick-Edinburgh Mental Well-being Scale. No relationship between the level of app usage and outcome was found. Although the app was designed with parents, the low rate of completion of the trial was disappointing. Conclusions: Kākano is an app co-designed with parents to help manage their children’s mental health. There was a high rate of attrition, as is often seen in digital health interventions. However, for those who did complete the intervention, there was some indication of improved parental well-being and self-assessed parenting. Preliminary indications from this trial show that Kākano has promising acceptability, feasibility, and effectiveness, but further investigation is warranted. Trial Registration: Australia New Zealand Clinical Trials Registry ACTRN12619001040156; https://www.anzctr.org.au/Trial/Registration/TrialReview.aspx?id=377824&isReview=true
A dramatic consequence of the Christchurch, New Zealand, earthquakes of 2010 and 2011 was the widespread liquefaction in the city. Part of the central business district (CBD) was badly affected by liquefaction but elsewhere large volumes of ejecta were not evident for those parts of the CBD where the upper layers in the soil profile are sandy gravel and gravelly sand. The purpose of the paper is to investigate the effect of the gravel permeability on the rise and dissipation of excess pore water pressure during cyclic loading of a soil profile idealised from Christchurch data. The Cyclic1D software, which performs one-dimensional non-linear effective stress site response analysis, was used. Permeability values associated with gravel were found to suppress the cyclic accumulation of excess pore water pressure in gravel layers. Given that there has not been any systematic measurement of the in situ permeability of the gravels in Christchurch, the modelling in the paper suggests that likely values for the bulk permeability of the gravel layers are within the range suggested in the geotechnical literature. However, the work reported is of wider application than Christchurch and emphasises the controlling influence of permeability on the accumulation and dissipation of cyclic pore pressures. VoR - Version of Record
Following the 2010/2011 Canterbury (New Zealand) earthquakes the seismic design of buildings with precast concrete panels has received significant attention. Although this form of construction generally performed adequately in Christchurch, there were a considerable number of precast concrete panel connection failures. This observation prompted a review of more than 4700 panel details to establish representative details used in both existing and new multi-storey and low rise industrial precast concrete buildings. The detailing and quantity of each reviewed connection type in the sampled data is reported, and advantages and potential deficiencies of each connection type are discussed. Following the Canterbury earthquakes, it was observed that brittle failure had occurred in some grouted metal duct connections used for precast concrete wall panels, resulting in recommendations for more robust detailing of this connection type. A set of experimental tests was subsequently performed to investigate the in-plane seismic behaviour of precast concrete wall panel connections. This testing comprised of seven reversed cyclic in-plane tests of fullscale precast concrete wall panels having wall-to-foundation grouted metal duct connections. Walls with existing connection detailing were found to perform adequately when carrying low axial loads, but performance was found to be less satisfactory as the axial load and wall panel length increased. The use of new recommended detailing was observed to prevent brittle connection response and to improve the robustness of the reinforcement splice. A parametric investigation was conducted using the finite element method to predict the failure mode of metal duct connections. From the results of the parametric study on metal duct connections it was identified that there were three possible failure modes, being reinforcement fracture, concrete spalling without metal duct pull out, and concrete spalling with metal duct pull-out. An alternative simple analytical method was proposed in order to determine the type of connection failure without using a time-consuming finite element method. Grouted sleeves inserts are an alternative connector that is widely used to connect wall panels to the foundations. The two full-scale wall panels were subjected to reversed cyclic in-plane demands until failure of either the connection or the wall panel. Wall panel failure was due to a combination of connection reinforcement pulling-out from the coupler and reinforcement fracture. In addition, non-embedded grouted sleeve tests filled with different quality of grout were conducted by subjecting these coupler assemblages to cyclic and monotonic forces.
A number of field testing techniques, such as standard penetration test (SPT), cone penetration test (CPT), and Swedish weight sounding (SWS), are popularly used for in-situ characterisation. The screw driving sounding (SDS) method, which has been recently developed in Japan, is an improved version of the SWS technique and measures more parameters, including the required torque, load, speed of penetration and rod friction; these provide more robust way of characterising soil stratigraphy. It is a cost-efficient technique which uses a machine-driven and portable device, making it ideal for testing in small-scale and confined areas. Moreover, with a testing depth of up to 10-15m, it is suitable for liquefaction assessment. Thus, the SDS method has great potential as an in-situ testing method for geotechnical site characterisation, especially for residential house construction. In this paper, the results of SDS tests performed at a variety of sites in New Zealand are presented. The soil database was employed to develop a soil classification chart based on SDS-derived parameters. Moreover, using the data obtained following the 2010-2011 Christchurch Earthquake Se-quence, a methodology was established for liquefaction potential evaluation using SDS data. http://www.isc5.com.au/wp-content/uploads/2016/09/1345-2-ORENSE.pdf
Axial elongation of reinforced concrete (RC) plastic hinges has previously been observed in a range of laboratory experiments, and more recently was observed in several Christchurch buildings following the 2010/2011 Canterbury earthquakes. Axial restraint to plastic hinges is provided by adjacent structural components such as floors as the plastic hinges elongate, which can significantly alter the performance of the plastic hinge and potentially invalidate the capacity design strength hierarchy of the building. Coupling beams in coupled wall systems are particularly susceptible to axial restraint effects due to their importance in the strength hierarchy, the high ductility demands that they experience, and the large stiffness of bounding walls. From computational modelling it has been found that ignoring axial restraint effects when designing coupled walls can result in significantly increased strength, reduced ductility and reduced energy dissipation capacity. The complexity of the topic merits further research to better account for realistic restraint effects when designing coupled walls.
This study is a qualitative investigation into the decision-making behaviour of commercial property owners (investors and developers) who are rebuilding in a city centre after a major disaster. In 2010/2011, Christchurch, the largest city in the South Island of New Zealand, was a site of numerous earthquakes. The stronger earthquakes destroyed many buildings and public infrastructure in the commercial inner city. As a result, affected property owners lost all or most of their buildings, a significant proportion of which were old and in the last phase of their life span. They had to negotiate pay-outs with insurance companies and decide, once paid out, whether they should rebuild in Christchurch or sell up and invest elsewhere. The clear majority of those who decided to reinvest in and rebuild the city are ‘locals’, almost all of whom had no prior experience of property development. Thus, in a post-disaster environment, most of these property owners have transitioned from being just being passive investors to active property developers. Their experience was interpreted using primary data gathered from in-depth and semi-structured interviews with twenty-one “informed property people” who included commercial property owners; property agents or consultants; representatives of public-sector agencies and financial institutions. The study findings showed that the decision-making behaviour of property investors and developers rebuilding after a major disaster did not necessarily follow a strict financial or profit motive as prescribed in the mainstream or neo-classical economics property literature. Rather, their decision-making behaviour has been largely shaped by emotional connections and external factors associated with their immediate environment. The theoretical proposition emerging from this study is that after a major disaster, local urban property owners are faced with two choices “to stay” or “to go”. Those who decide to stay and rebuild are typically very committed individuals who have a feeling of ownership, belonging and attachment to the city in which they live and work. These are people who will often take the lead in commercial property development, proactively making decisions and seeking positive investment outcomes for themselves which in turn result in revitalised commercial urban precincts.
Critical infrastructure networks are highly relied on by society such that any disruption to service can have major social and economic implications. Furthermore, these networks are becoming increasingly dependent on each other for normal operation such that an outage or asset failure in one system can easily propagate and cascade across others resulting in widespread disruptions in terms of both magnitude and spatial reach. It is the vulnerability of these networks to disruptions and the corresponding complexities in recovery processes which provide direction to this research. This thesis comprises studies contributing to two areas (i) the modelling of national scale in-terdependent infrastructure systems undergoing major disruptions, and (ii) the tracking and quantification of infrastructure network recovery trajectories following major disruptions. Firstly, methods are presented for identifying nationally significant systemic vulnerabilities and incorporating expert knowledge into the quantification of infrastructure interdependency mod-elling and simulation. With application to the interdependent infrastructures networks across New Zealand, the magnitudes and spatial extents of disruption are investigated. Results high-light the importance in considering interdependencies when assessing disruptive risks and vul-nerabilities in disaster planning applications and prioritising investment decisions for enhancing resilience of national networks. Infrastructure dependencies are further studied in the context of recovery from major disruptions through the analysis of curves measuring network functionality over time. Continued studies into the properties of recovery curves across a database of global natural disasters produce statistical models for predicting the trajectory and expected recovery times. Finally, the use of connectivity based metrics for quantifying infrastructure system functionality during recovery are considered with a case study application to the Christchurch Earthquake (February 22, 2011) wastewater network response.
During the 2010/2011 Canterbury earthquakes, several reinforced concrete (RC) walls in multi-storey buildings formed a single crack in the plastic hinge region as opposed to distributed cracking. In several cases the crack width that was required to accommodate the inelastic displacement of the building resulted in fracture of the vertical reinforcing steel. This type of failure is characteristic of RC members with low reinforcement contents, where the area of reinforcing steel is insufficient to develop the tension force required to form secondary cracks in the surrounding concrete. The minimum vertical reinforcement in RC walls was increased in NZS 3101:2006 with the equation for the minimum vertical reinforcement in beams also adopted for walls, despite differences in reinforcement arrangement and loading. A series of moment-curvature analyses were conducted for an example RC wall based on the Gallery Apartments building in Christchurch. The analysis results indicated that even when the NZS 3101:2006 minimum vertical reinforcement limit was satisfied for a known concrete strength, the wall was still susceptible to sudden failure unless a significant axial load was applied. Additionally, current equations for minimum reinforcement based on a sectional analysis approach do not adequately address the issues related to crack control and distribution of inelastic deformations in ductile walls.
Soil-structure interaction (SSI) has been widely studied during the last decades. The influence of the properties of the ground motion, the structure and the soil have been addressed. However, most of the studies in this field consider a stand-alone structure. This assumption is rarely justifiable in dense urban areas where structures are built close to one another. The dynamic interaction between adjacent structures has been studied since the early 1970s, mainly using numerical and analytical models. Even though the early works in this field have significantly contributed to understanding this problem, they commonly consider important simplifications such as assuming a linear behaviour of the structure and the soil. Some experimental works addressing adjacent structures have recently been conducted using geotechnical centrifuges and 1g shake tables. However, further research is needed to enhance the understanding of this complex phenomenon. A particular case of SSI is that of structures founded in fine loose saturated sandy soil. An iconic example was the devastating effects of liquefaction in Christchurch, New Zealand, during the Canterbury earthquake in 2011. In the case of adjacent structures on liquefiable soil, the experimental evidence is even scarcer. The present work addresses the dynamic interaction between adjacent structures by performing multiple experimental studies. The work starts with two-adjacent structures on a small soil container to expose the basics of the problem. Later, results from tests considering a more significant number of structures on a big laminar box filled with sand are presented. Finally, the response of adjacent structures on saturated sandy soil is addressed using a geotechnical centrifuge and a large 1g shake table. This research shows that the acceleration, lateral displacement, foundation rocking, damping ratio, and fundamental frequency of the structure of focus are considerably affected by the presence of neighbouring buildings. In general, adjacent buildings reduced the dynamic response of the structure of focus on dry sand. However, the acceleration was amplified when the structures had a similar fundamental frequency. In the case of structures on saturated sand, the presence of adjacent structures reduced the liquefaction potential. Neighbouring structures on saturated sand also presented larger rotation of the footing and lateral displacement of the top mass than that of the stand-alone case.
Eccentrically Braced Frames (EBFs) are a widely used seismic resisting structural steel system. Since their inception in the late 1970s, they have been a viable option with an available stiffness that is between simple braced systems and moment resisting systems. A similar concept, the linked column frame (LCF), uses shear links between two closely spaced columns. In both cases, the key component is the active link or the shear link, and this component is the objective of this study. The performance of high rise EBF buildings in the 2010 and 2011 Christchurch earthquakes was beyond that which was expected, especially considering the very high accelerations recorded. As the concrete high-rises were torn down, two EBF buildings remained standing and only required some structural repair. These events prompted a renewed interest in bolted shear links, as well as their performance. While some research into replaceable shear links had already been done (Mansour, 2011), the objectives of this study were to improve on the shear link itself, with the consideration that links built in the future are likely to be bolted. The main components of this study were to: 1. Reduce or eliminate the requirements for intermediate web stiffeners, as they were suspected of being detrimental to performance. Furthermore, any reduction in stiffening requirements is a direct fabrication cost saving. Links with low web aspect ratios were found to achieve exceptional ductilities when no stiffeners were included, prompting new design equations. 2. Ensure that the stresses in the ends of links are adequately transferred into the endplates without causing fractures. Although most of the experimental links had web doubler plates included, four had varied lengths of such doubler plates from 0.0 in. to 8.0 in. The link without any doubler plates performed to a similar level to its peers, and thus it is likely that links with quality end details may not need web doubler plates at all. 3. Evaluate the performance of a link with double sided stiffeners without the use of web welds, as opposed to conventional single sided, welded stiffeners. This link performed well, and web-weld-less double sided stiffeners may be an economical alternative to conventional stiffeners for deeper sections of links. 4. Evaluate the performance of a link with thin endplates that are made efficient with the use of gusset plates. This link performed to an acceptable level and provides evidence for a cost effective alternative to thick endplates, especially considering the high overstrength end moments in links, typically requiring 16-bolt connections. 5. Examine the potential use of an alternative EBF arrangement where the collector beam is over sized, and the link section is formed by cutting out parts of the beam's web. After running a series of finite element models each with a unique variation, a number of approximate design rules were derived such that future research could develop this idea further experimentally. 6. Ensure that during testing, the secondary elements (members that are not the shear link), do not yield and are not close to yielding. None of the instrumented elements experienced any unexpected yielding, however the concerns for high stresses in the collector beam panel zone during design were warranted. The use of an existing New Zealand design equation is recommended as an extra check for design codes worldwide. The above objectives were mainly conducted experimentally, except: the data set for item 1 was greatly expanded through the use of a calibrated numerical model which was then used in an extensive parametric study; item 5 was purely finite element based; and, a small parametric study was included for item 3 in an attempt to expand on the trends found there.
