Fire Conditions Research Articles

Drought triggers and sustains overnight fires in North America.

Overnight fires are emerging in North America with previously unknown drivers and implications. This notable phenomenon challenges the traditional understanding of the 'active day, quiet night' model of the diurnal fire cycle1-3 and current fire management practices4,5. Here we demonstrate that drought conditions promote overnight burning, which is a key mechanism fostering large active fires. We examined the hourly diurnal cycle of 23,557 fires and identified 1,095 overnight burning events (OBEs, each defined as a night when a fire burned through the night) in North America during 2017-2020 using geostationary satellite data and terrestrial fire records. A total of99% of OBEs were associated with large fires (>1,000 ha) and at least one OBE was identified in 20% of these large fires. OBEs were early onset after ignition and OBE frequency was positively correlated with fire size. Although warming is weakening the climatological barrier to night-time fires6, we found that the main driver of recent OBEs in large fires was the accumulated fuel dryness and availability (that is, drought conditions), which tended to lead to consecutive OBEs in a single wildfire for several days and even weeks. Critically, we show that daytime drought indicators can predict whether an OBE will occur the following night, which could facilitate early detection and management of night-time fires. We also observed increases in fire weather conditions conducive to OBEs over recentdecades, suggesting an accelerated disruption of the diurnal fire cycle.

The use and production of black Mn‐based pigments for painting late (c. 900–1450) and Inca (c. 1450–1600) periods ceramic vessels in Northwestern Argentina: a multi‐analytical approach using μRaman, FT‐IR, and XRD

AbstractLate and Inca period pottery in the Northwestern Argentine region present two or three characteristic prefiring colors (red, black, and white or cream) in their decoration. Sanagasta and Belén vessels from Late Period are characterized by a bichrome black‐on‐red/cream and black‐on‐red painted decoration, respectively, whereas Inca vessels exhibit a black‐on‐red painted decoration. Analytical results obtained by μRaman, FT‐IR, and XRD analyses on a relatively large number of samples show that the pre‐Hispanic potters during Late and Inca periods used a manganese‐based technique to obtain black colours in these large vessels fired in an oxidising atmosphere. Black paints were produced by the systematic use of different mineral complex mixtures of Mn (pyrolusite, bixbyte, and hausmannite) and hematite. As a result, spinel phases like jacobsite (a Fe‐Mn compound) and magnetite were formed at different firing temperatures. Red paints were obtained using the mineral hematite. A detailed discussion is presented concerning the firing conditions to obtain these black hues.

Investigation of sensing performances of thick-film resistors sintered on fluorophlogopite glass-ceramic substrates

Strain gauges made of thick-film resistors (TFRs) offer a promising solution for monitoring the structural health of civil engineering projects, owing to their exceptional durability and stability. To address the issue of strain mismatch between alumina substrates and concrete materials, fluorophlogopite glass-ceramic (FGC), which has a low elastic modulus and good machinability, was utilized as a substrate for thick-film resistors. Compatibility between resistor pastes and substrates should be considered, as the substrate can significantly impact the performance of thick-film resistors. TFRs with varying concentrations of RuO2 were screen printed and fired at different temperatures on both FGC and 96% Al2O3 (as a control) substrates. The sheet resistivity, temperature coefficient of resistance (TCR), and gauge factor (GF) of TFRs were evaluated. The strain sensing performances of TFRs on FGC evaluated under compressive loading. The results indicate that TFRs on FGC substrates exhibit higher hot TCRs, lower sheet resistivities, and lower gauge factors than those on Al2O3 substrates under typical firing conditions of 850°C for 10 minutes. As the concentration of RuO2 increases, the differences in properties between TFRs on the two substrates become less pronounced. Microstructural analyses of the interface between the resistor layer and substrate indicate that changes in properties of TFRs on FGC substrates are primarily attributed to variations in RuO2 concentration and glass phase composition, which result from interactions between the resistor layer and FGC substrate. The interaction between the FGC substrate and the resistor layer can be significantly alleviated by lowering the firing temperature from 850°C to 750°C, resulting in TFRs on FGC substrates with properties comparable to those on alumina substrates. The TFRs on FGC exhibit favorable sensitivity, linearity, repeatability, and hysteresis within the input compression strain range of 0–3043με, thus showcasing significant potential for application in structural health monitoring (SHM) in civil engineering.

The effect of firing conditions on the characteris-tics of thick-film resistors for temperature sensors

The effect of firing conditions on the characteris-tics of thick-film resistors for temperature sensors

A NUMERICAL INVESTIGATION ON FIRE PERFORMANCE OF INDUSTRIAL STEEL WAREHOUSES PROTECTED WITH GYPSUM‐BASED BOARDS

AbstractThis paper studies the fire performance of steel warehouse with their main elements insulated with fire protection boards composed of gypsum‐based mortars with perlite using the heat transfer and thermomechanical analysis in finite element (FE) software. The primary aim is to identify the optimal thickness of the fire protections boards based on the assigned fire model in thermal analysis. Besides that, a parametric study is also conducted by considering various factors that are often overlooked or not explicitly mentioned in fire design guidelines, such as EN 1991‐1‐2. The findings facilitate the development of optimized fire design approaches, ensuring the structural integrity and safety of steel warehouses under fire conditions.

Some results of petrographic study of Neolithic ceramics from the Luzhki II site

The presented article introduces into scientific circulation the first results of the petrographic study of the Neolithic ceramics of the Luzhki II site. A total of 22 samples from vessels decorated with punctures (8 units), impressions of a comb stamp (9 units), their combination (1 unit), nail-like notches (2 units), as well as only belts of pitted impressions under the cut of the rim (2 units) were analyzed. Petrographic analysis of ceramics allows to establish the mineralogical composition of clays and thickeners, to identify the formulation of ceramic dough, to determine the temperature and firing conditions, as well as to suggest possible sources of raw materials. According to the results of a micromorphological study, two groups of dishes are distinguished in the collection of the Luzhki II site. The first is characterized by the use of sand and chamotte as a cleaner, and for the second, consisting of two samples, only sand. In general, it can be summarized that all the vessels considered are made of thin clays, mainly hydrosluidic with a content of clastic material from 18% to 35%. Sand has always acted as a cleaner, mainly its share is about 45%, the concentration of chamotte does not exceed 20%, its size is 0,7–1,3 mm. The conditions of long-term firing of vessels are stable at a temperature of mainly +700…+800°C in an oxidizing environment.

New beam-based models for fire-induced buckling analysis of class 4 steel columns

Steel cross-sections with thin walls are vulnerable to fire-induced buckling instability, which reduces their load-bearing capacity. Eurocode 3 design provisions have been found inadequate, leading to alternative methods such as effective design strategies and advanced structural models built mostly with shell FE, which can be complex. For Class 4 steel beam-columns subjected to fire conditions, beam-type modelling to predict the Flexural-Torsional Buckling (FTB) strength has been proposed as an alternative approach, but it has not yielded satisfactory results for large compressive load eccentricities. This paper presents two new low computational cost modelling strategies based on Timoshenko's beam FE to address this issue: the Single beam-column Model (SbcM) and the Cruciform beam-column Model (CbcM). The first consists of a single line of beam FE, while the second uses a grid of beam FE for more flexibility. Both strategies effectively simulate the FTB behaviour in Class 4 steel beam-column during a fire, offering quicker computations compared to shell models. Still, the single-line model is favoured for its simplicity, making it more efficient in analysing complex fire engineering problems.

Post-earthquake fire resistance of self-centering concrete beam-column joint: An experimental investigation

Fire is an accidental disaster resulting in disastrous consequences for building. Post-earthquake fire is a secondary disaster induced by earthquake, triggering off larger destruction in a higher probability of occurrence. The potential severity of consequences to structures makes fire and post-earthquake fire safety imperative in the design of any new structures. Self-centering concrete joints are introduced as a promoting alternative to traditional reinforced concrete (RC) joints. They always exhibit excellent seismic performance and self-centering capacity, available in high-seismic zone. However, the current lack of experimental data on fire response of self-centering concrete joints means that they remain an open issue in current design codes. In this paper, full-scale quasi-static cyclic test and fire tests were conducted on two self-centering concrete joints connected with bolted angles and posttensioned (PT) tendons. The experiments aimed to explore the performance of self-centering joint in fire situations, and the impact of post-earthquake damages on fire response of self-centering joint. The deformation patterns and thermal responses of self-centering joints including temperature distribution, prestress force of PT tendons, displacements at beam ends and duration were recorded and analyzed. The results show that both self-centering joints exhibited satisfactory fire resistance with endurance over 170 min. Generally, the bolted angles and PT tendons in self-centering concrete joints showed acceptable working performance in fire. The findings unveil the actual response of self-centering concrete joints during the fire and post-earthquake fire conditions, providing experimental data for further numerical simulation and analysis. It can be used to calibrate the design approach for self-centering joints under fire and seismic-induced fire exposure.

Tensile Tests for Material Characterisation of High- and Ultra-High-Strength Steels S690QL and S960QL under Natural Fire Conditions

The mechanical material behavior of mild steels is reversible in the cooling phase of natural fires, which is proven by experimental evidence. For the material behavior of high-strength steels during cooling, no results are yet available. The paper provides the first comprehensive test program on the constitutive material behavior of high-strength steels S690QL and S960QL as well as mild steel S355 J2 + N in the case of natural fires. It is elaborated that the mechanical material behavior of high-strength steels in the cooling phase differs from the behavior in the heating phase and is not reversible due to phase changes of the microstructure. A constitutive material model for structural fire design purposes is developed on the basis of experimental data and the soundness and reliability of the model are proven by a statistical study that systematically evaluates the deviation of the model prediction from the test data.

Simulation analysis on the synergistic effect of vegetation ashes and charged particles on the gap electric field distortion

Hill fires, a sort of ultra-natural disaster that poses a severe threat to the safe and stable operation of transmission lines, have become more frequent in recent years. Currently, the modeling research on the transmission line gap electric field distortion under hill fire conditions does not consider the synergistic effect of charged particles and ash particles, which would lead to the imperfect gap electric field distortion mechanism. Herein, a coupled multi-physics field simulation model of electric, thermal, fluid, chemical field and particle motion was constructed to analyze the electric field distribution and particle motion. Compared to the related simulation models, this study improves the simulation accuracy by around 407% by optimizing the structure and parameters of the simulation model. The FEM software COMSOL Multiphysics simulation results show that the percentage of ash entering the examined region of the AC conductor was 34.1% higher, and the percentage of connected ash was 45% higher, increasing the likelihood of gap breakdown compared to the DC conductor; the charge of ash (10−14 to 10−11) is significantly less than the saturation charge of ash (⩾10−3). Therefore, the charged particles change the motion characteristics of the ash primarily through the electric field force and dielectrophoresis force, while the ash-induced distortion of the electric field affects the spatial distribution of the charged particles, eventually, the background electric field undergoes significant distortion by the synergistic effect of the two. The results examine the inherent mechanism of gap electric field distortion at the microscopic level, which can provide theoretical support for understanding the transition phase of transmission line gaps from insulation to break down under hill fire conditions.

Initial stiffness, ultimate capacity and failure mechanisms of tubular X-joints with external ring or plates at fire conditions

ABSTRACT This research work evaluates the effect of the ring, the plate and the joint geometry on the initial stiffness, ultimate strength and failure mechanisms of tubular X-joints subjected to axially compressive load at different fire conditions. At the first step, a finite element model was generated and verified by 19 experimental tests and 8 numerical models carried out by the present first author and other researchers. At the next step, 1170 numerical models were conducted. Using the generated FE models, the structural behaviour under different fire conditions (200°C, 400°C, 600°C and 800°C) was evaluated and compared to the corresponding behaviour at normal temperature (20°C). Results showed that both of the external ring and plate can notably increase the initial stiffness and ultimate capacity at all different elevated temperatures. Also, the use of these methods significantly improves the failure mechanisms at fire conditions. Two theoretical design formulas with high accuracy were proposed, based on the yield volume model, to determine the ultimate capacity in ring reinforced X-joints and plate reinforced X-joints at elevated temperatures.

НАУЧНЫЕ ОСНОВЫ ПРЕДУПРЕЖДЕНИЯ ВОЗГОРАНИЯ АВТОМОБИЛЬНЫХ НЕЙТРАЛИЗАТОРОВ В ЭКСПЛУАТАЦИИ

The issue of physical and mathematical representation of the thermal dynamics (kinetics) of the process of conversion of exhaust gases in a catalytic converter in dangerous, from the point of view of fire, uncontrolled emergency operating modes of its operation
 is considered. Modern automobile engines are required to ensure fire safety. On engines with converters, this conflicts with stringent international environmental standards, the satisfaction of which requires the dangerously heated converter to be placed in the engine compartment next to flammable combustible materials. It is proposed to solve the problematic issue by monitoring and diagnosing fire and emergency operating conditions of neutralizers in an in-place method, scientifically substantiated on an interdisciplinary basis – by analyzing the composition of the exhaust gases. The method has been positively tested under real operating conditions.

The Effect of Climate Change on Forest Fire Danger and Severity in the Canadian Boreal Forests for the Period 1976–2100

AbstractRecent climatic trends have increased forest fire activity in Canada. This study aimed to evaluate how forest fire conditions might evolve across the Canadian boreal forests in the future and to inform discussions about the impact of climate change on fire danger and severity. I generated surfaces of daily climate conditions using daily observational data from meteorological stations across Canada from 1976 to 2014. Simulated daily values of the same climatic variables were obtained from four earth system models of the Coupled Model Intercomparison Project Phase 5 project (CMIP5) for the historical period 1976–2005. Daily climate values for 2006–2100, forced by three climate change scenarios, Representative Concentration Pathway (RCP) 2.6, RCP 4.5, and RCP 8.5, were also simulated by the models. The simulated data were bias‐corrected and delta‐downscaled to project future trends in fire activity to assess the spatiotemporal variations of the potential impacts of climate change on forest fires. My results suggest fire danger and severity would increase in many Canadian boreal forests under RCP 8.5. The changes in fire conditions under RCP 2.6 were the least noteworthy; RCP 4.5 was associated with medium‐level changes.

Simplified analytical model for prediction of collapse resistance of restrained steel beam-column substructure exposed to fire

This paper provides a simplified analytical model for the restrained steel beam-column substructure under a fire-induced progressive collapse scenario, which is applied to predict the collapse resistance of substructures under fire. The simplified model is formulated for axially and rotationally restrained two-span steel beam-column substructures under column-loss scenarios and involves rigid and semi-rigid connections. The response characteristics of restrained substructures exposed to fire under column-loss scenarios in each response stage are elaborately analyzed. A “negative” catenary stage, in consideration of the unique negative axial force effects induced by the temperature thermal expansion, was first introduced in the five-stage simplified model for restrained substructures exposed to fire against progressive collapse. Subsequently, the explicit calculation formulas for determining the vertical loads and deflection of both rigid and semi-rigid joint substructures exposed to fire were derived in a quantified way, based on rigid-plastic mechanisms and restraint coefficient methods. In addition, the corresponding numerical simulation analysis on a restrained two-span steel beam-column substructure with different end constraints and fire conditions was carried out to verify the applicability and reliability of established theoretical formulas. Comparisons of vertical load-deflection relationships between the calculation formulas and corresponding numerical simulation shows good accuracy. For more accurate prediction results, the error analysis was further conducted, and several theoretical formulas were modified, which were verified to be accurate and reliable after correction. With derived resistance functions, the resistance of steel beam-column substructures in fire-induced progressive collapse scenarios can be predicted.

Computational Analysis for the Evaluation of Fire Resistance in Constructive Wooden Elements with Protection

Wood is a material whose properties vary depending on different conditions, being particularly vulnerable to changes induced by high temperatures. When exposed to a fire situation, the wood properties suffer degradation, causing a char layer formation. Despite ensuring the protection of the inner core of the wood, the char layer reduces its resistant section. The evaluation of wood behavior under fire conditions is possible through experimental tests, simplified analytical models, and numerical models. To overcome difficulties in the development of experimental tests and in the approximations made to analytical methods, numerical models allow the evaluation of the fire resistance in a parametric way. First, this study will present a numerical model validated with an experimental test, using the finite element method. The validation of the results is based on the evolution of the temperature field, the char layer formation on the wooden elements, and its residual section, as well as the application of the thermal insulation criterion. The second part of the study evaluates the influence of geometric parameters, associated with different wooden constructive models with gypsum board exposed to fire. Different numerical tests are presented to evaluate the thermal and transient analysis of different wooden constructive elements with gypsum board. This type of constructive element presents cavities, making the numerical analysis in the study complex when approaching real models. The methodology applied allowed us to conclude that, at the same time, a smaller distance between wooden centers, a greater dimension of the wooden beam in height and width, as well as a greater thickness of gypsum board guarantee a better performance of the constructive wooden model.

Performance of recycled aggregate concrete composite metal decks under elevated temperatures: a comprehensive review

ABSTRACT This comprehensive review explores the performance of composite metal decks and structural elements incorporating recycled aggregate concrete (RAC) at elevated temperatures. Despite the acknowledged environmental benefits of using recycled aggregates in concrete production, there is a notable gap in the literature regarding their behaviour under fire conditions. The investigation delves into studies encompassing fire resistance, physio-thermal properties, mechanical attributes, and structural performance of composite metal decks constructed with RAC. The analysis reveals that the inclusion of recycled aggregates has both positive and negative impacts on these elements when exposed to high temperatures. The fire resistance of metal decking composite slabs is significantly influenced by material properties, composition, and RAC mix design. Experimental findings indicate that RAC slabs showed larger midspan deflection under load and fire exposure compared to their counterpart NC slabs. After 120 min. of duration, the mid-span deflection of RAC-0 was recorded to be 19 % higher than the corresponding deflection of NC-0 slab. While temperature-time curves show comparable performance between RAC and natural concrete (NC) slabs, RAC slabs exhibit a notably lower ratio of soffit temperature to the upper surface temperature, resulting in increased spalling. In conclusion, this study advocates for the broader utilization of RAC in constructing structural elements, particularly composite slabs facing extreme temperatures. However, it emphasizes the need for additional research to optimize fire resistance and gain a comprehensive understanding of their behaviour. The findings provide essential guidance for structural engineers and researchers involved in the design of sustainable and fire-resistant structures.

Insights into ancient ceramic technology: a comprehensive analysis of mineralogy, chemistry and firing conditions

The intensive integration of Azerbaijan into the global economy, mainly through international gas and oil pipeline construction, has led to significant archaeological research in the past two decades. The construction of the Baku-Tbilisi-Ceyhan oil pipeline (BTC) and the Southern Caucasus Pipeline gas pipeline (SCP) prompted a four-year archaeological fieldwork program, followed by a six-year post-excavation program. The current work applied an interdisciplinary approach using various instrumental methods for studying ancient artifacts found during those projects. The thermogravimetric method and differential thermal analysis were employed to obtain insights into the production technology of the ancient pottery and information about the mineralogy of the ceramic sherds. The complex processes involved in firing the ceramic paste have been studied extensively, and patterns in mass loss ratios during different temperature ranges have been established. In total, 15 samples were investigated, and the thermogravimetric analysis of ceramic shards revealed that the firing temperature of the samples was in the range of 700 °C. XRD analysis confirmed the presence of quartz, feldspar, and clay minerals in the ceramic samples. The presence of calcite and other specific minerals is subject to the origin of the ceramic materials. The results obtained from this multidisciplinary approach provide insights into the firing technology and the origin of the ceramic samples.

Forest thinning and prescribed burning treatments reduce wildfire severity and buffer the impacts of severe fire weather

BackgroundThe capacity of forest fuel treatments to moderate the behavior and severity of subsequent wildfires depends on weather and fuel conditions at the time of burning. However, in-depth evaluations of how treatments perform are limited because encounters between wildfires and areas with extensive pre-fire data are rare. Here, we took advantage of a 1200-ha randomized and replicated experiment that burned almost entirely in a subsequent wildfire under a wide range of weather conditions. We compared the impacts of four fuel treatments on fire severity, including two thin-only, a thin-burn, a burn-only, and an untreated control. We evaluated four fire severity metrics—tree mortality, average bole char height, percent crown volume consumed (PCVC), and percent crown volume affected (PCVA)—and leveraged data from pre-fire surface and canopy fuels to better understand the mechanisms driving differences in wildfire severity among treatments and how they changed with fire weather.ResultsWe found strong mitigating effects of treatments on fire behavior and tree mortality, despite 20 years having elapsed since mechanical thinning and 10 years since the second entry of prescribed fire. The thin-burn treatment resulted in the lowest fire severity across all four metrics and the untreated control the highest. All four fire severity metrics were positively associated with pre-fire canopy and surface fuel loads, with the exception that PCVC (a fire severity metric related to crown fire behavior) was not associated with surface fuel load. The fire weather conditions under which fuel treatment was most effective varied among fire severity metrics. Fuel treatment benefit was maximized at intermediate burning index values for tree mortality, intermediate to high burning index values for PCVA, and high burning index for bole char height and PCVC.ConclusionsWe conclude that reducing canopy bulk density via mechanical thinning treatments can help to limit crown fire behavior for 20 years or more. However, reducing surface fuels is necessary to limit scorching and the total crown impacts associated with tree mortality. Further, while fuel treatment effectiveness may decline under the most severe fire weather conditions for fire severity metrics associated with tree mortality, it is maximized under severe fire weather conditions for fire severity metrics associated with crown fire behavior (bole charring and torching). Our results provide strong evidence for the use of fuel treatments to mitigate fire behavior and resulting fire severity even under extreme fire weather conditions.

Adaptation of the Coniferous Forests to Natural Fire Disturbances in the Altai Mountains, Xinjiang, China

The Altai Mountains, located in the northwesternmost part of China, have a harsh climate and little human activity, making it an excellent location to study forest ecology undisturbed by human interference. The forest is frequently struck by lightning and experiences long-term natural fire disturbances, leading to the evolution of unique fire adaptation traits in the major conifer species. To explore the role of natural fire disturbances in the Altai Mountain forest ecosystem, we conducted a study on the fire adaptation traits of Larix sibirica, Pinus sibirica, Picea obovata, and Abies sibirica, and reconstructed the fire history of the forest area over the past 100 years. We investigated three representative forest areas with varying fire disturbance conditions and habitats in the Altai Mountains. Data on fire disturbance conditions, relative air humidity, and species composition were collected in these areas. Basal diameter to diameter at breast height, relative bark thickness, and under-crown heights were measured and counted for each of the four species, and litter, bark, and wood layers were sampled and analyzed for physicochemical properties (ash, fat, and higher heating value) for each of the four species in the plots examined. We conducted a count of the four conifer species in the forest for each fire adaptation index and analyzed the differences in fire adaptation traits among the species. Larix sibirica showed fire-tolerant traits, Pinus sibirica displayed fire-embracer traits, and Picea obovata and Abies sibirica exhibited fire-avoider traits. Through the analysis of stand composition and exposure to fire disturbance in the different forest areas, we were able to correlate the fire-adaptive strategies of the four conifers with stand characteristics under varying fire disturbances and habitats. The interaction between forests and fires, and their adaptation to each other, ultimately create the current ecosystems in the Altai Mountains.

Application of Composite Bars in Wooden, Full-Scale, Innovative Engineering Products-Experimental and Numerical Study.

The commercialization of modular timber products as cost-effective and lightweight components has resulted in innovative engineering products, e.g., glued laminated timber, laminated veneer lumber, I-beams, cross-laminated timber and solid timber joined with wedge joints. With the passage of time, timber structures can deteriorate, or new structural elements are required to increase the stiffness or load-bearing capacity in newly built structures, e.g., lintels over large-scale glazing or garages, or to reduce cross-sectional dimensions or save costly timber material while still achieving low weight. It is in such cases that repair or correct reinforcement is required. In this experimental and numerical study, the static performance of flexural timber beams reinforced with prestressed basalt BFRP, glass GFRP and hybrid glass-basalt fiber bars is shown. The experimental tests resulted in an increase in the load-carrying capacity of BFRP (44%), GFRP (33%) and hybrid bars (43%) and an increase in the stiffness of BFRP (28%), GFRP (24%) and hybrid bars (25%). In addition to this, glued laminated timber beams reinforced with prestressed basalt rods subjected to biological degradation, 7 years of weathering and prolonged exposure to various environmental conditions were examined, and an increase in the load-bearing capacity of 27% and an increase in stiffness of 28% were obtained. In addition, full-size laminated timber beams reinforced with prestressed basalt bars were investigated in the field as an exploratory test under fire conditions at elevated temperatures, and the effect of the physical-mechanical properties during the fire was examined via an analysis of these properties after the fire. In addition, a satisfactory correlation of the numerical simulations with the experimental studies was obtained. The differences were between 1.1% and 5.5%. The concordance was due to the fact that, in this study, the Young, Poisson and shear moduli were determined for all quality classes of sawn timber. Only a significant difference resulted in the numerical analysis for the beams exposed to fire under fire conditions. The experimental, theoretical and numerical analyses in this research were exploratory and will be expanded as directions for future research.