Following the 2010–2011 Canterbury earthquakes, a renewed focus has been directed across New Zealand to the hazard posed by the country‘s earthquake-vulnerable buildings, namely unreinforced masonry (URM) and reinforced concrete (RC) buildings with potentially nonductile components that have historically performed poorly in large earthquakes. The research reported herein was pursued with the intention of addressing several recommendations made by the Canterbury Earthquakes Royal Commission of Inquiry which were classified into the following general categories: Identification and provisional vulnerability assessment of URM and RC buildings and building components; Testing, assessment, and retrofitting of URM walls loaded out-of-plane, with a particular focus on highly vulnerable URM cavity walls; Testing and assessment of RC frame components, especially those with presumably non-ductile reinforcement detailing; Portfolio management considering risks, regulations, and potential costs for a portfolio that includes several potentially earthquake-vulnerable buildings; and Ongoing investigations and proposed research needs. While the findings from the reported research have implications for seismic assessments of buildings across New Zealand and elsewhere, an emphasis was placed on Auckland given this research program‘s partnership with the Auckland Council, the Auckland region accounting for about a third each of the country‘s population and economic production, and the number and variety of buildings within the Auckland building stock. An additional evaluation of a historic building stock was carried out for select buildings located in Hawke‘s Bay, and additional experimental testing was carried out for select buildings located in Hawke‘s Bay and Christchurch.
This thesis describes the strategies for earthquake strengthening vintage clay bricks unreinforced masonry (URM) buildings. URM buildings are well known to be vulnerable to damage from earthquake-induced lateral forces that may result in partial or full building collapse. The 2010/2011 Canterbury earthquakes are the most recent destructive natural disaster that resulted in the deaths of 185 people. The earthquake events had drawn people’s attention when URM failure and collapse caused about 39 of the fatality. Despite the poor performance of URM buildings during the 2010/2011 Canterbury earthquakes, a number of successful case study buildings were identified and their details research in-depth. In order to discover the successful seismic retrofitting techniques, two case studies of retrofitted historical buildings located in Christchurch, New Zealand i.e. Orion’s URM substations and an iconic Heritage Hotel (aka Old Government Building) was conducted by investigating and evaluating the earthquake performance of the seismic retrofitting technique applied on the buildings prior to the 2010/2011 Canterbury earthquakes and their performance after the earthquakes sequence. The second part of the research reported in this thesis was directed with the primary aim of developing a cost-effective seismic retrofitting technique with minimal interference to the vintage clay-bricks URM buildings. Two retrofitting techniques, (i) near-surface mounted steel wire rope (NSM-SWR) with further investigation on URM wallettes to get deeper understanding the URM in-plane behaviour, and (ii) FRP anchor are reported in this research thesis.
The research presented in this thesis investigated the environmental impacts of structural design decisions across the life of buildings located in seismic regions. In particular, the impacts of expected earthquake damage were incorporated into a traditional life cycle assessment (LCA) using a probabilistic method, and links between sustainable and resilient design were established for a range of case-study buildings designed for different seismic performance objectives. These links were quantified using a metric herein referred to as the seismic carbon risk, which represents the expected environmental impacts and resource use indicators associated with earthquake damage during buildings’ life. The research was broken into three distinct parts: (1) a city-level evaluation of the environmental impacts of demolitions following the 2010/2011 Canterbury earthquake sequence in New Zealand, (2) the development of a probabilistic framework to incorporate earthquake damage into LCA, and (3) using case-study buildings to establish links between sustainable and resilient design. The first phase of the research focused on the environmental impacts of demolitions in Christchurch, New Zealand following the 2010/2011 Canterbury Earthquake Sequence. This large case study was used to investigate the environmental impact of the demolition of concrete buildings considering the embodied carbon and waste stream distribution. The embodied carbon was considered here as kilograms of CO2 equivalent that occurs on production, construction, and waste management stage. The results clearly demonstrated the significant environmental impacts that can result from moderate and large earthquakes in urban areas, and the importance of including environmental considerations when making post-earthquake demolition decisions. The next phase of the work introduced a framework for incorporating the impacts of expected earthquake damage based on a probabilistic approach into traditional LCA to allow for a comparison of seismic design decisions using a carbon lens. Here, in addition to initial construction impacts, the seismic carbon risk was quantified, including the impacts of seismic repair activities and total loss scenarios assuming reconstruction in case of non-reparability. A process-based LCA was performed to obtain the environmental consequence functions associated with structural and non-structural repair activities for multiple environmental indicators. In the final phase of the work, multiple case-study buildings were used to investigate the seismic consequences of different structural design decisions for buildings in seismic regions. Here, two case-study buildings were designed to multiple performance objectives, and the upfront carbon costs, and well as the seismic carbon risk across the building life were compared. The buildings were evaluated using the framework established in phase 2, and the results demonstrated that the seismic carbon risk can significantly be reduced with only minimal changes to the upfront carbon for buildings designed for a higher base shear or with seismic protective systems. This provided valuable insight into the links between resilient and sustainable design decisions. Finally, the results and observations from the work across the three phases of research described above were used to inform a discussion on important assumptions and topics that need to be considered when quantifying the environmental impacts of earthquake damage on buildings. These include: selection of a non-repairable threshold (e.g. a value beyond which a building would be demolished rather than repaired), the time value of carbon (e.g. when in the building life the carbon is released), the changing carbon intensity of structural materials over time, and the consideration of deterministic vs. probabilistic results. Each of these topics was explored in some detail to provide a clear pathway for future work in this area.
This thesis presents the application of data science techniques, especially machine learning, for the development of seismic damage and loss prediction models for residential buildings. Current post-earthquake building damage evaluation forms are developed for a particular country in mind. The lack of consistency hinders the comparison of building damage between different regions. A new paper form has been developed to address the need for a global universal methodology for post-earthquake building damage assessment. The form was successfully trialled in the street ‘La Morena’ in Mexico City following the 2017 Puebla earthquake. Aside from developing a framework for better input data for performance based earthquake engineering, this project also extended current techniques to derive insights from post-earthquake observations. Machine learning (ML) was applied to seismic damage data of residential buildings in Mexico City following the 2017 Puebla earthquake and in Christchurch following the 2010-2011 Canterbury earthquake sequence (CES). The experience showcased that it is readily possible to develop empirical data only driven models that can successfully identify key damage drivers and hidden underlying correlations without prior engineering knowledge. With adequate maintenance, such models have the potential to be rapidly and easily updated to allow improved damage and loss prediction accuracy and greater ability for models to be generalised. For ML models developed for the key events of the CES, the model trained using data from the 22 February 2011 event generalised the best for loss prediction. This is thought to be because of the large number of instances available for this event and the relatively limited class imbalance between the categories of the target attribute. For the CES, ML highlighted the importance of peak ground acceleration (PGA), building age, building size, liquefaction occurrence, and soil conditions as main factors which affected the losses in residential buildings in Christchurch. ML also highlighted the influence of liquefaction on the buildings losses related to the 22 February 2011 event. Further to the ML model development, the application of post-hoc methodologies was shown to be an effective way to derive insights for ML algorithms that are not intrinsically interpretable. Overall, these provide a basis for the development of ‘greybox’ ML models.
High demolition rates were observed in New Zealand after the 2010-2011 Canterbury Earthquake Sequence despite the success of modern seismic design standards to achieve required performance objectives such as life safety and collapse prevention. Approximately 60% of the multi-storey reinforced concrete (RC) buildings in the Christchurch Central Business District were demolished after these earthquakes, even when only minor structural damage was present. Several factors influenced the decision of demolition instead of repair, one of them being the uncertainty of the seismic capacity of a damaged structure. To provide more insight into this topic, the investigation conducted in this thesis evaluated the residual capacity of moderately damaged RC walls and the effectiveness of repair techniques to restore the seismic performance of heavily damaged RC walls. The research outcome provided insights for developing guidelines for post-earthquake assessment of earthquake-damaged RC structures. The methodology used to conduct the investigation was through an experimental program divided into two phases. During the first phase, two walls were subjected to different types of pre-cyclic loading to represent the damaged condition from a prior earthquake, and a third wall represented a repair scenario with the damaged wall being repaired using epoxy injection and repair mortar after the pre-cyclic loading. Comparisons of these test walls to a control undamaged wall identified significant reductions in the stiffness of the damaged walls and a partial recovery in the wall stiffness achieved following epoxy injection. Visual damage that included distributed horizontal and diagonal cracks and spalling of the cover concrete did not affect the residual strength or displacement capacity of the walls. However, evidence of buckling of the longitudinal reinforcement during the pre-cyclic loading resulted in a slight reduction in strength recovery and a significant reduction in the displacement capacity of the damaged walls. Additional experimental programs from the literature were used to provide recommendations for modelling the response of moderately damaged RC walls and to identify a threshold that represented a potential reduction in the residual strength and displacement capacity of damaged RC walls in future earthquakes. The second phase of the experimental program conducted in this thesis addressed the replacement of concrete and reinforcing steel as repair techniques for heavily damaged RC walls. Two walls were repaired by replacing the damaged concrete and using welded connections to connect new reinforcing bars with existing bars. Different locations of the welded connections were investigated in the repaired walls to study the impact of these discontinuities at the critical section. No significant changes were observed in the stiffness, strength, and displacement capacity of the repaired walls compared to the benchmark undamaged wall. Differences in the local behaviour at the critical section were observed in one of the walls but did not impact the global response. The results of these two repaired walls were combined with other experimental programs found in the literature to assemble a database of repaired RC walls. Qualitative and quantitative analyses identified trends across various parameters, including wall types, damage before repair, and repair techniques implemented. The primary outcome of the database analysis was recommendations for concrete and reinforcing steel replacement to restore the strength and displacement capacity of heavily damaged RC walls.
The 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 investigates life-safety risk in earthquakes. The first component of the thesis utilises a dataset of earthquake injuries and deaths from recent earthquakes in New Zealand to identify cause, context, and risk factors of injury and death in the 2011 MW6.3 Christchurch earthquake and 2016 MW7.8 Kaikōura earthquake. Results show that nearly all deaths occurred from being hit by structural elements from buildings, while most injuries were caused by falls, strains and being hit by contents or non-structural elements. Statistical analysis of injured cases compared to an uninjured control group found that age, gender, building damage, shaking intensity, and behaviour during shaking were the most significant risk factors for injury during these earthquakes. The second part of the thesis uses the empirical findings from the first section to develop two tools for managing life-safety risk in earthquakes. The first tool is a casualty estimation model for health system and emergency response planning. An existing casualty model used in New Zealand was validated against observed data from the 2011 Christchurch earthquake and found to underestimate moderate and severe injuries by an order of magnitude. The model was then updated to include human behaviour such as protective actions, falls and strain type injuries that are dependent on shaking intensity, as well as injuries and deaths outside buildings. These improvements resulted in a closer fit to observed casualties for the 2011 Christchurch earthquake. The second tool that was developed is a framework to set seismic loading standards for design based on fatality risk targets. The proposed framework extends the risk-targeted hazard method, by moving beyond collapse risk targets, to fatality risk targets for individuals in buildings and societal risk in cities. The framework also includes treatment of epistemic uncertainty in seismic hazard to allow this uncertainty to be used in risk-based decision making. The framework is demonstrated by showing how the current New Zealand loading standards could be revised to achieve uniform life-safety risk across the country and how the introduction of a new loading factor can reduce risk aggregation in cities. Not on Alma, moved and emailed. 1/02/2023 ce
The connections between walls of unreinforced masonry (URM) buildings and flexible timber diaphragms are critical building components that must perform adequately before desirable earthquake response of URM buildings may be achieved. Field observations made during the initial reconnaissance and the subsequent damage surveys of clay brick URM buildings following the 2010/2011 Canterbury, New Zealand earthquakes revealed numerous cases where anchor connections joining masonry walls or parapets with roof or floor diaphragms appeared to have failed prematurely. These observations were more frequent for the case of adhesive anchor connections than for the case of through-bolt connections (i.e. anchorages having plates on the exterior façade of the masonry walls). Subsequently, an in-field test program was undertaken in an attempt to evaluate the performance of adhesive anchor connections between unreinforced clay brick URM walls and roof or floor diaphragm. The study consisted of a total of almost 400 anchor tests conducted in eleven existing URM buildings located in Christchurch, Whanganui and Auckland. Specific objectives of the study included the identification of failure modes of adhesive anchors in existing URM walls and the influence of the following variables on anchor load-displacement response: adhesive type, strength of the masonry materials (brick and mortar), anchor embedment depth, anchor rod diameter, overburden level, anchor rod type, quality of installation and the use of metal foil sleeve. In addition, the comparative performance of bent anchors (installed at an angle of minimum 22.5o to the perpendicular projection from the wall surface) and anchors positioned horizontally was investigated. Observations on the performance of wall-to-diaphragm connections in the 2010/2011 Canterbury earthquakes and a snapshot of the performed experimental program and the test results are presented herein. http://hdl.handle.net/2292/21050
Reinforced concrete buildings that satisfied modern seismic design criteria generally behaved as expected during the recent Canterbury and Kaikoura earthquakes in New Zealand, forming plastic hinges in intended locations. While this meant that life-safety performance objectives were met, widespread demolition and heavy economic losses took place in the aftermath of the earthquakes.The Christchurch central business district was particularly hard hit, with over 60% of the multistorey reinforced concrete buildings being demolished. A lack of knowledge on the post-earthquake residual capacity of reinforced concrete buildings was a contributing factor to the mass demolition.Many aspects related to the assessment of earthquake-damaged reinforced concrete buildings require further research. This thesis focusses on improving the state of knowledge on the post earthquakeresidual capacity and reparability of moderately damaged plastic hinges, with an emphasis on plastic hinges typical of modern moment frame structures. The repair method focussed on is epoxy injection of cracks and patching of spalled concrete. A targeted test program on seventeen nominally identical large-scale ductile reinforced concrete beams, three of which were repaired by epoxy injection following initial damaging loadings, was conducted to support these objectives. Test variables included the loading protocol, the loading rate, and the level of restraint to axial elongation.The information that can be gleaned from post-earthquake damage surveys is investigated. It is shown that residual crack widths are dependent on residual deformations, and are not necessarily indicative of the maximum rotation demands or the plastic hinge residual capacity. The implications of various other types of damage typical of beam and column plastic hinges are also discussed.Experimental data are used to demonstrate that the strength and deformation capacity of plastic hinges with modern seismic detailing are often unreduced as a result of moderate earthquake induced damage, albeit with certain exceptions. Special attention is given to the effects of prior yielding of the longitudinal reinforcement, accounting for the low-cycle fatigue and strain ageing phenomena. A material-level testing program on the low-cycle fatigue behaviour of grade 300E reinforcing steel was conducted to supplement the data available in the literature.A reduction in stiffness, relative to the initial secant stiffness to yield, occurs due to moderate plastic hinging damage. This reduction in stiffness is shown to be correlated with the ductility demand,and a proposed model gives a conservative lower-bound estimate of the residual stiffness following an arbitrary earthquake-type loading. Repair by epoxy injection is shown to be effective in restoring the majority of stiffness to plastic hinges in beams. Epoxy injection is also shown to have implications for the residual strength and elongation characteristics of repaired plastic hinges.
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.
This thesis revisits the topic of earthquake recovery in Christchurch City more than a decade after the Canterbury earthquakes. Despite promising visions of a community reconnected and a sustainable and liveable city, significant portions of the city’s core – the Red Zone – remain dilapidated and “eerily empty”. At the same time, new developments in other areas have proven to be alienated or underutilised. Currently, the Canterbury Earthquake Recovery Authority’s plans for the rebuilding highlight the delivery of more residential housing to re-populate the city centre. However, prevalent approaches to housing development in Christchurch are ineffective for building an inclusive and active community. Hence, the central inquiry of the thesis is how the development of housing complexes can revitalise the Red Zone within the Christchurch city centre. The inquiry has been carried out through a research-through-design methodology, recognising the importance of an in-depth investigation that is contextualised and combined with the intuition and embodied knowledge of the designer. The investigation focuses on a neglected site in the Red Zone in the heart of Christchurch city, with significant Victorian and Edwardian Baroque heritage buildings, including Odeon Theatre, Lawrie & Wilson Auctioneers, and Sol Square, owned by The Regional Council Environment Canterbury. The design inquiry argues, develops, and is carried through a place-assemblage lens to housing development for city recovery, which recognizes the significance of socially responsive architecture that explores urban renewal by forging connections within the social network. Therefore, place-assemblage criteria and methods for developing socially active and meaningful housing developments are identified. Firstly, this thesis argues that co-living housing models are more focused on people relations and collective identity than the dominant developer-driven housing rebuilds, as they prioritise conduits for interaction and shared social meaning and practices. Secondly, the adaptive reuse of derelict heritage structures is proposed to reinvigorate the urban fabric, as heritage is seen to be conceived as and from a social assemblage of people. The design is realised by the principles outlined in the ICOMOS charter, which involves incorporating the material histories of existing structures and preserving the intangible heritage of the site by ensuring the continuity of cultural practices. Lastly, design processes and methods are also vital for place-sensitive results, which pay attention to the site’s unique characteristics to engage with local stakeholders and communities. The research explores place-assemblage methods of photographic extraction, the drawing of story maps, precedent studies, assemblage maps, bricolages, and paper models, which show an assembly of layers that piece together the existing heritage, social conduits, urban commons and housing to conceptualise the social network within its place.
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.
