Critical Load Estimates Research Articles

Fracture Load Estimations for U-Notched and V-Notched 3D Printed PLA and Graphene-Reinforced PLA plates using the ASED Criterion

This paper addresses the estimation of critical loads in FFF (Fused Filament Fabrication) printed polymers and composites containing notches. Particularly, the analysis is focused on the fracture load estimations of 39 PLA (polylactic acid) and 39 graphene reinforced PLA (PLA-Gr) printed plates containing two different types of notches (U- and V-notches) and combining different plate thicknesses and defect length to plate width (a/W) ratios. The addition of graphene (1 wt.%) increases both the yield stress and the ultimate tensile strength, also reducing the strain at rupture and, thus, generating a material whose behavior is closer to linear elasticity. Among the different assessment tools that may be used to estimate critical loads, this work applies the well-known Averaged Strain Energy Density (ASED) criterion, which compares the averaged strain energy over a certain control volume at the notch tip with the corresponding critical value, the latter being a material property. This approach has a linear-elastic nature, so its application to non-fully linear materials may require the use of specific corrections or calibrations. For the two materials analyzed here, PLA and PLA-Gr, it has been observed that the ordinary linear-elastic ASED criterion provides good estimations for the PLA-Gr material, whereas the pristine PLA, with more evident non-linear behavior, the obtainment of accurate results requires a previous specific calibration of the ASED material parameters

Dexterity, Workspace and Performance Analysis of the Conceptual Design of a Novel Three-legged, Redundant, Lightweight, Compliant, Serial-parallel Robot

In this article, the mechanical design and analysis of a novel three-legged, agile robot with passively compliant 4-degrees-of-freedom legs, comprising a hybrid topology of serial, planar and spherical parallel structures, is presented. The design aims to combine the established principle of the Spring Loaded Inverted Pendulum model for energy efficient locomotion with the accuracy and strength of parallel mechanisms for manipulation tasks. The study involves several kinematics and Jacobian based analyses that specifically evaluate the application of a non-overconstrained spherical parallel manipulator as a robot hip joint, decoupling impact forces and actuation torques, suitable for the requirements of legged locomotion. The dexterity is investigated with respect to joint limits and workspace boundary contours, showing that the mechanism stays well conditioned and allows for a sufficient range of motion. Based on the functional redundancy of the constrained serial-parallel architecture it is furthermore revealed that the robot allows for the exploitation of optimal leg postures, resulting in the possible optimization of actuator load distribution and accuracy improvements. Consequently, the workspace of the robot torso as additional end-effector is investigated for the possible application of object manipulation tasks. Results reveal the existence of a sufficient volume applicable for spatial motion of the torso in the statically stable tripodal posture. In addition, a critical load estimation is derived, which yields a posture dependent performance index that evaluates the risks of overload situations for the individual actuators.

Atmospheric deposition of reactive nitrogen to a deciduous forest in the southern Appalachian Mountains.

Assessing nutrient critical load exceedances requires complete and accurate atmospheric deposition budgets for reactive nitrogen (Nr). The exceedance is the total amount of Nr deposited to the ecosystem in excess of the critical load, which is the amount of Nr input below which harmful effects do not occur. Total deposition includes all forms of Nr (i.e., organic and inorganic) deposited to the ecosystem by wet and dry pathways. Here we present results from the Southern Appalachian Nitrogen Deposition Study (SANDS), in which a combination of measurements and field-scale modeling was used to develop a complete annual Nr deposition budget for a deciduous forest at the Coweeta Hydrologic Laboratory. Wet deposition of ammonium, nitrate, nitrite, and bulk organic N were measured directly. The dry deposited Nr fraction was estimated using a bidirectional resistance-based model driven with speciated measurements of Nr air concentrations (e.g., ammonia, ammonium aerosol, nitric acid, nitrate aerosol, bulk organic N in aerosol, total alkyl nitrates, and total peroxy nitrates), micrometeorology, canopy structure, and biogeochemistry. Total annual deposition was ~6.7 kg N ha-1 yr-1, which is on the upper end of Nr critical load estimates recently developed for similar ecosystems in the nearby Great Smoky Mountains National Park. Of the total (wet + dry) budget, 51.1% was contributed by reduced forms of Nr , with oxidized and organic forms contributing ~41.3% and 7.6%, respectively. Our results indicate that reductions in deposition would be needed to achieve the lowest estimates (~3.0 kg N ha-1 yr-1) of Nr critical loads in southern Appalachian forests.

Fracture testing and estimation of critical loads in a PMMA-based dental material with nonlinear behavior in the presence of notches

The goal of the present investigation is twofold: first, to provide new experimental data on the fracture behavior of biopolymer specimens containing notches, and second, to validate new fracture criteria to predict the corresponding experimental fracture loads. For this purpose, nine fracture experiments are conducted on U-notched rectangular specimens with different notch tip radii made of polymer-based dental material under monotonic tension. As the main outcomes of the experimental program, the fracture loads of the specimens, as well as the corresponding load-displacement curves, were recorded. Due to the nonlinear behavior of the dental material being tested, considerable plastic deformations are developed in the U-notch vicinity and, hence, the use of linear elastic notch fracture mechanics (LENFM) criteria (e.g., the maximum tangential stress (MTS) and mean stress (MS) criteria) for fracture (critical) load predictions provides inaccurate results. Consequently, the Equivalent Material Concept (EMC), which equates the nonlinear biopolymer material with a virtual brittle material having perfectly linear elastic behavior, is combined with the MTS and the MS criteria, allowing the use of LENFM for fracture load predictions of the U-notched biopolymer specimens being tested. It is observed that the two resulting criteria, EMC-MTS and EMC-MS, provide very good predictions of the experimental results. From the viewpoint of mechanical design, the EMC-MTS criterion may be preferred to the EMC-MS criterion, given its inherent simplicity.

Geometrically nonlinear analysis of the stability of the stiffened plate taking into account the interaction of eigenforms of buckling

The aims of this work are a detailed consideration in a geometrically nonlinear formulation of the stages of the equilibrium behavior of a compressed stiffened plate, taking into account the interaction of the general form of buckling and local forms of wave formation in the plate or in the reinforcing ribs, comparison of the results of the semi-analytical solution of the system of nonlinear equations with the results of the numerical solution on the Patran-Nastran FEM complex of the problem of subcritical and postcritical equilibrium of a compressed stiffened plate. Methods. Geometrically-nonlinear analysis of displacement fields, deformations and stresses, calculation of eigenforms of buckling and construction of bifurcation solutions and solutions for equilibrium curves with limit points depending on the initial imperfections. An original method is proposed for determining critical states and obtaining bilateral estimates of critical loads at limiting points. Results. An algorithm for studying the equilibrium states of a stiffened plate near critical points is described in detail and illustrated by examples, using the first nonlinear (cubic terms) terms of the potential energy expansion, the coordinates of bifurcation points and limit points, as well as the corresponding values of critical loads. The curves of the critical load sensitivity are plotted depending on the value of the initial imperfections of the total deflection. Equilibrium curves with characteristic bifurcation points of local wave formation are constructed using a numerical solution. For the case of action of two initial imperfections, an algorithm is proposed for obtaining two-sided estimates of critical loads at limiting points.

Coupling Finite Element Analysis and the Theory of Critical Distances to Estimate Critical Loads in Al6060-T66 Tubular Beams Containing Notches

This paper validates a methodology for the estimation of critical loads in tubular beams containing notch-type defects. The methodology is particularized for the case of Al6060-T66 tubular cantilever beams containing U-shaped notches. It consists in obtaining the stress field at the notch tip using finite element analysis (FEA) and the subsequent application of the theory of critical distances (TCD) to derive the corresponding critical load (or load-bearing capacity). The results demonstrate that this methodology provides satisfactory predictions of fracture loads.

Methodological Considerations for the Determination of the Critical Load for the Deadlift.

Moss, AC, Dinyer, TK, Abel, MG, and Bergstrom, HC. Methodological considerations for the determination of the critical load for the deadlift. J Strength Cond Res 35(2S): S31-S37, 2021-This study determined whether performance method during conventional deadlifting affects critical load (CL) estimates derived from the linear work limit (Wlim) vs. repetitions relationship. Eleven subjects completed 1-repetition maximum (1RM) deadlift testing followed by separate visits, to determine the number of repetitions to failure at 50, 60, 70, and 80% 1RM for both reset (RS) and touch-and-go (TG) methods. The CL was the slope of the line of total work completed (load [kg] × repetitions) vs. total repetitions for 4 intensities (50-80% 1RM). The number of repetitions to failure were determined at CLRS and CLTG. The kg values and repetitions to failure at CLRS and CLTG, and total repetitions at each intensity (50-80%) for each method (RS and TG) were compared. There were no significant mean differences (±SD) in kg values (-0.4 ± 7.9 kg, range = -8.8 to 17 kg, p = 0.856), %1RM (-1.2 ± 5.6%, p = 0.510), or total repetitions completed (2.8 ± 15.7 reps, range = -15 to 37 reps, p = 0.565) for CLRS and CLTG. These findings indicated that performance method did not affect mean estimation of CL or number of repetitions completed at submaximal loads. Thus, the estimates of CL from the modeling of total work vs. repetitions were relatively robust to variations in deadlifting methodologies. However, individual variability (range of scores) in kg values and repetition to failure at CLRS and CLTG indicated that deadlifting methods may differ in anatomical region of fatigue. The CL is an individually derived threshold that may be used to examine and describe performance capabilities.

A dynamic model to evaluate the critical loads of heavy metals in agricultural soil.

Estimation of critical load (CL) is important for soil environmental management and pollution prevention. We developed a mass balance-based dynamic critical load (DCL) model, which improved the model performance, applicability and functionality compared with the traditional one. Paddy soils in two typical fields in central south China and two scenarios were chosen as case studies. The result of case study showed that atmospheric deposition was the main source of Cd, Cu, Pb, and Zn in the soils, with percentage contributions ranging from 59.9 to 79.8%. Crop uptake, particularly the rice straw harvest, was the primary output pathway, accounting for 35.1-71.2% of the total output flux. The critical loads also known as annual input limits (Imax) of heavy metals in the paddy soils were calculated by the developed DCL model. For example, the Imax of Cd was recommended as 0.05kgha-1 in the paddy soils under the default scenario for a protection period of 40 years, and that became 0.12kgha-1 and 0.17kgha-1 under the straw removal scenario in the two typical fields, respectively. The scenario simulation suggested that the straw removal strategy reduced the total concentrations of heavy metals (Ct) in the soils and notably increased the Imax. Meanwhile, the sensitivity analysis indicated that the changes of Ct and Imax can be controlled by adjusting the partition coefficient (Kd), plant uptake factor (PUF) and input flux. The mass balance-based DCL model provides a reference method to establish the standard for controlling heavy metal inputs to agricultural soil, this will be helpful to develop strategies for the prevention of soil contamination.

Shaping of Axially Compressed Bipolarly Prestressed Closely Spaced Built-Up Members

Abstract The paper presents a method of shaping and describing the geometry of bipolarly prestressed closely spaced built-up member with symmetrical supports and a bisymmetrical cross-section. The following has been defined as a function dependant on the position along the length of the x section of the closely spaced built-up member with determined geometrical parameters: intial elastic y 0 (x) of the closely spaced built-up member chord in the prestressing zone, distance between the chords in the clear s i (x), moment of inertia J i (x) relative to main axes and eccentricity e i (x) of compressive force in a single chord. The length of the extreme section L 1 and the prestressing zone L 2, the maximum distance between chords s max in the clear and the geometric characteristics of a single chord section were assumed. A full and correct description of the geometry of bipolarly prestressed closely spaced built-up members is necessary to start the static and stress analysis. As a result of the introduction of a bipolar displacement prestressing into the closely spaced built-up member, the moment of inertia increases in the middle part with respect to the non-material axis z. It allows predicting the increase of the critical load bearing capacity of the closely spaced built-up member. The load bearing capacity of bipolarly prestressed closely spaced built-up members was estimated using the modified Engesser’s formula for two-chord closely spaced built-up member with rigid battens. For selected pair of channel sections, the analytical critical load estimation results were verified using FEM.

Estimating mineral surface area and base cation weathering rates of Spodosols under forest in British Columbia, Canada

Soil mineral surface area is regarded as a key uncertainty in the estimation of base cation weathering rates, yet is rarely measured. Acidification studies rely heavily on pedotransfer functions (PTFs) that use widely available soil data to estimate mineral surface area. This study examined the relationship between soil properties and mineral surface area in soils (n = 25) from Kitimat, British Columbia, an area that is receiving elevated sulphur (S) deposition due to recent modernization of an aluminum (Al) smelter. Mineral surface area was measured on bulk soil samples using BET (Brunaeur, Emmett and Teller) gas-adsorption. Previously published particle size-based PTFs were a poor predictor of surface area in Kitimat soils (R2 between 0.42 and 0.66). Instead, mineral surface area was best predicted using a regionally-specific PTF (R2 = 0.81), which used particle size as well as the concentration of kaolinite, the most abundant clay mineral in the region. Surface area values estimated using the regionally-specific PTF were applied to the PROFILE model to calculate weathering rates for critical load estimates. These estimates predicted that none of the sites received S deposition in exceedance of their critical load for acidity. However, as surface area is largely related to kaolinite content (a mineral that does not largely contribute to weathering rates), the applicability of using surface area functions for weathering rates is questionable. Further, the texture-based PTF developed for Kitimat did not provide accurate estimates of measured surface area for other soils in Canada, particularly at surface area values exceeding 2.5 m2 g−1.

Efficient global optimization and modal strain energy coefficient-based algorithm for fast prediction of dynamic aeroelastic loads

Design optimization of airframes is conventionally conducted employing a deterministic set of critical load cases defined through performing a sheer number of aeroelastic analyses spanning the aircrafts’ design space. Due to its large computational cost, the latter process cannot be integrated within the structural optimization cycle, hindering the development of a multidisciplinary design optimization (MDO) framework. In this paper, we present an algorithm for the efficient estimation of critical dynamic aeroelastic loads, as a first step towards the development of an integrated MDO platform. The method is based on the Kriging metamodeling technique along with the Latin hypercube scheme for initial sampling, and the expected improvement function for subsequent selection of sample points, known together as the efficient global optimization (EGO) algorithm. Furthermore, the use of the element modal strain energy coefficient (MSEC) is investigated as an inexpensive indicator to determine if a substantial change in the loads is expected after structural modification, thus triggering the necessity for the re-exploration of the loads’ design space. A case study is presented to evaluate the performance of the proposed methodology versus a stand-alone Kriging interpolation; a reduction of over 40% was achieved in the total time of execution employing the proposed algorithm.

Eigenfrequency and Euler's Critical Load Evaluation of Transversely Cracked Beams with a Linear Variation of Widths

For a truthful evaluation of the mechanical response of structures reliable and adequate computational models are essential. Consequently, various researches have been devoted to the mathematical representation of cracked structures. This paper studies the performance of the simplified crack model in estimations of fundamental eigenfrequency as well as elastic Euler's critical load for transversely cracked beams of rectangular cross-sections with linearly-varying widths. To obtain these solutions for different beams with diverse boundary conditions Rayleigh’s energy method which requires an assumed transverse displacement function can be applied. After the appropriate displacement function is being selected, kinetic and strain energy, as well as the work done by an external axial compressive force P are evaluated. From these values, the estimations of the fundamental eigenfrequency, as well as the critical load, are assessed. To obtain these preliminary estimates, static deflection functions were applied initially. These functions represent a wide group of suitable functions since they automatically satisfy the required kinematic boundary conditions. Afterwards, alternative functions constructed from a dedicated polynomial solution were applied. Since this mathematical form offers straightforward integration, the genuinely applied displacement functions were further upgraded, separately for eigenfrequency as well as for critical load estimation. All obtained simplified model’s solutions were afterwards compared to the results from equivalent and more detailed 3D finite models of the examined structures. The comparisons of the results demonstrated very fine agreements with the results from 3D FE models for all performed analyses. The considered simplified model thus clearly yields a suitable alternative in modelling of cracked beams with a linear variation of width in those situations, where cracks have to be considered within the analysis.

Estimates of exceedances of critical loads for acidifying deposition in Alberta and Saskatchewan

Abstract. Estimates of potential harmful effects on ecosystems in the Canadian provinces of Alberta and Saskatchewan due to acidifying deposition were calculated, using a 1-year simulation of a high-resolution implementation of the Global Environmental Multiscale-Modelling Air-quality and Chemistry (GEM-MACH) model, and estimates of aquatic and terrestrial ecosystem critical loads. The model simulation was evaluated against two different sources of deposition data: total deposition in precipitation and total deposition to snowpack in the vicinity of the Athabasca oil sands. The model captured much of the variability of observed ions in wet deposition in precipitation (observed versus model sulfur, nitrogen and base cation R2 values of 0.90, 0.76 and 0.72, respectively), while being biased high for sulfur deposition, and low for nitrogen and base cations (slopes 2.2, 0.89 and 0.40, respectively). Aircraft-based estimates of fugitive dust emissions, shown to be a factor of 10 higher than reported to national emissions inventories (Zhang et al., 2018), were used to estimate the impact of increased levels of fugitive dust on model results. Model comparisons to open snowpack observations were shown to be biased high, but in reasonable agreement for sulfur deposition when observations were corrected to account for throughfall in needleleaf forests. The model–observation relationships for precipitation deposition data, along with the expected effects of increased (unreported) base cation emissions, were used to provide a simple observation-based correction to model deposition fields. Base cation deposition was estimated using published observations of base cation fractions in surface-collected particles (Wang et al., 2015).Both original and observation-corrected model estimates of sulfur, nitrogen, and base cation deposition were used in conjunction with critical load data created using the NEG-ECP (2001) and CLRTAP (2017) methods for calculating critical loads, using variations on the Simple Mass Balance model for terrestrial ecosystems, and the Steady State Water Chemistry and First-order Acidity Balance models for aquatic ecosystems. Potential ecosystem damage was predicted within each of the regions represented by the ecosystem critical load datasets used here, using a combination of 2011 and 2013 emissions inventories. The spatial extent of the regions in exceedance of critical loads varied between 1 × 104 and 3.3 × 105 km2, for the more conservative observation-corrected estimates of deposition, with the variation dependent on the ecosystem and critical load calculation methodology. The larger estimates (for aquatic ecosystems) represent a substantial fraction of the area of the provinces examined.Base cation deposition was shown to be sufficiently high in the region to have a neutralizing effect on acidifying deposition, and the use of the aircraft and precipitation observation-based corrections to base cation deposition resulted in reasonable agreement with snowpack data collected in the oil sands area. However, critical load exceedances calculated using both observations and observation-corrected deposition suggest that the neutralization effect is limited in spatial extent, decreasing rapidly with distance from emissions sources, due to the rapid deposition of emitted primary dust particles as a function of their size. We strongly recommend the use of observation-based correction of model-simulated deposition in estimating critical load exceedances, in future work.

Numerical Study on the Ultimate Behavior of Elastomeric Bearings under Combined Compression and Shear

Predicting the ultimate behavior of elastomeric bearings subjected to combined compression-shear loading is an indispensable part of quantitatively evaluating the performance of seismic isolated structures during earthquakes. In this paper, the initial critical load derived from three different approximations for bending modulus are analyzed and evaluated by existing experimental data. Then, Finite Element (FE) models of bearings are developed and validated by critical load results. Based on that, a parametric FE study is performed to investigate the failure mode of bearings under this combined loading. It is demonstrated that the bending modulus based on the pressure solution and further simplification provides a more reasonable estimate of initial critical load. The predicting capacity of the overlapping area method for the general trend of critical load is improved with the increasing of external diameter. The dividing line between stability limit and shear failure is dominated by the second shape factor. Furthermore, as the first shape factor increases, the ultimate shear deformation corresponding to shear failure slightly increases.

Bryophytes and Organic layers Control Uptake of Airborne Nitrogen in Low-N Environments.

The effects of atmospheric nitrogen (N) deposition on ecosystem functioning largely depend on the retention of N in different ecosystem compartments, but accumulation and partitioning processes have rarely been quantified in long-term field experiments. In the present study we analysed for the first time decadal-scale flows and allocation patterns of N in a heathland ecosystem that has been subject to airborne N inputs over decades. Using a long-term 15N tracer experiment, we quantified N retention and flows to and between ecosystem compartments (above-ground/below-ground vascular biomass, moss layer, soil horizons, leachate). After 9 years, about 60% of the added 15N-tracer remained in the N cycle of the ecosystem. The moss layer proved to be a crucial link between incoming N and its allocation to different ecosystem compartments (in terms of a short-term capture, but long-term release function). However, about 50% of the 15N captured and released by the moss layer was not compensated for by a corresponding increase in recovery rates in any other compartment, probably due to denitrification losses from the moss layer in the case of water saturation after rain events. The O-horizon proved to be the most important long-term sink for added 15N, as reflected by an increase in recovery rates from 18 to 40% within 8 years. Less than 2.1% of 15N were recovered in the podzol-B-horizon, suggesting that only negligible amounts of N were withdrawn from the N cycle of the ecosystem. Moreover, 15N recovery was low in the dwarf shrub above-ground biomass (<3.9% after 9 years) and in the leachate (about 0.03% within 1 year), indicating still conservative N cycles of the ecosystem, even after decades of N inputs beyond critical load thresholds. The continuous accumulation of reactive forms of airborne N suggests that critical load-estimates need to account for cumulative effects of N additions into ecosystems.

Atmospheric nitrogen deposition to China: A model analysis on nitrogen budget and critical load exceedance

We present a national-scale model analysis on the sources and processes of inorganic nitrogen deposition over China using the GEOS-Chem model at 1/2° × 1/3° horizontal resolution. Model results for 2008–2012 are evaluated with an ensemble of surface measurements of wet deposition flux and gaseous ammonia (NH3) concentration, and satellite measurements of tropospheric NO2 columns. Annual total inorganic nitrogen deposition fluxes are simulated to be generally less than 10 kg N ha−1 a−1 in western China (less than 2 kg N ha−1 a−1 over Tibet), 15–50 kg N ha−1 a−1 in eastern China, and 16.4 kg N ha−1 a−1 averaged over China. Annual total deposition to China is 16.4 Tg N, with 10.2 Tg N (62%) from reduced nitrogen (NHx) and 6.2 Tg N from oxidized nitrogen (NOy). Domestic anthropogenic sources contribute 86% of the total deposition; foreign anthropogenic sources 7% and natural sources 7%. Annually 23% of domestically emitted NH3 and 36% for NOx are exported outside the terrestrial land of China. We find that atmospheric nitrogen deposition is about half of the nitrogen input from fertilizer application (29.6 Tg N a−1), and is much higher than that from natural biological fixation (7.3 Tg N a−1) over China. A comparison of nitrogen deposition with critical load estimates for eutrophication indicates that about 15% of the land over China experiences critical load exceedances, demonstrating the necessity of nitrogen emission controls to avoid potential negative ecological effects.

Assessing the Impact of Sulfur Atmospheric Deposition on Terrestrial Ecosystems Close to an Industrial Corridor in the Southeast of Mexico

The main objective of this research work was to diagnose the vulnerability of terrestrial ecosystems to S deposition in Atasta region in Campeche State, Mexico, comprising two simultaneous sampling programs in both, soil and atmospheric deposition on an annual basis during three climatic periods: dry, rainy and cold fronts seasons. From the estimation of soil properties estimation (pH, texture, mineralogy, cationic exchange capacity, and basis saturation %), critical loads and sensitivity classes were assigned to sampled soils based according to the empirical methodology proposed by UNECE. During the dry season, 10 sites fell into sensitivity class 2 (moderately sensitive) and 3 (sensitive). On the other hand, during the rainy season, 8 sites showed a sensitivity class 1 (highly sensitive) and 2 sites presented a sensitivity class 2 (moderately sensitive); whereas along cold fronts season, 12 sites fell into sensitivity class 1 that corresponds to highly sensitive. Sensitivity classes showed a seasonal trend, with a higher sensitivity during rainy and cold fronts seasons; this agrees with the kind of sources influencing on the study area as a result of the prevailing meteorology during these climatic periods. Likewise, S concentration in atmospheric deposition was determined by turbidimetric method, and S deposition fluxes were estimated from surface area of the funnel opening of the sampling device and the sampling period. S deposition fluxes ranged from 0.29 and 14.06 kg S ha-1·yr-1; with a mean value of 8.57 kg S ha-1·yr-1. From the comparison between the current deposition rates and proposed critical loads, exceedances percentages were obtained (from 1.65% to 62.8%) and mapped to identify critical zones of S deposition in the studied area. It was established the important role which mangrove vegetation plays in the attenuation of the potential ecological effects on terrestrial ecosystems of the study area associated to atmospheric deposition.

Critical levels and loads and the regulation of industrial emissions in northwest British Columbia, Canada

Northwest British Columbia, Canada, a sparsely populated and largely pristine region, is targeted for rapid industrial growth owing to the modernization of an aluminum smelter and multiple proposed liquefied natural gas (LNG) facilities. Consequently, air quality in this region is expected to undergo considerable changes within the next decade. In concert, the increase in LNG capacity driven by gas production from shale resources across North America has prompted environmental concerns and highlighted the need for science-based management decisions regarding the permitting of air emissions. In this study, an effects-based approach widely-used to support transboundary emissions policy negotiations was used to assess industrial air emissions in the Kitimat and Prince Rupert airsheds under permitted and future potential industrial emissions. Critical levels for vegetation of SO2 and NO2 and critical loads of acidity and nutrient nitrogen for terrestrial and aquatic ecosystems were estimated for both regions and compared with modelled concentration and deposition estimates to identify the potential extent and magnitude of ecosystem impacts. The critical level for SO2 was predicted to be exceeded in an area ranging from 81 to 251 km2 in the Kitimat airshed owing to emissions from an existing smelter, compared with <1 km2 in Prince Rupert under the lowest to highest emissions scenarios. In contrast, the NO2 critical level was not exceeded in Kitimat, and ranged from 4.5 to 6 km2 in Prince Rupert owing to proposed LNG related emissions. Predicted areal exceedance of the critical load of acidity for soil ranged from 1 to 28 km2 in Kitimat and 4–10 km2 in Prince Rupert, while the areal exceedance of empirical critical load for nutrient N was predicted to be greater in the Prince Rupert airshed (20–94 km2) than in the Kitimat airshed (1–31 km2). The number of lakes that exceeded the critical load of acidity did not vary greatly across emissions scenarios in the Kitimat (21–23 out of 80 sampled lakes) and Prince Rupert (0 out of 35 sampled lakes) airsheds. While critical loads have been widely used to underpin international emissions reductions of transboundary pollutants, it is clear that they can also play an important role in managing regional air emissions. In the current study, exceedance of critical levels and loads suggests that industrial emissions from the nascent LNG export sector may require careful regulation to avoid environmental impacts. Emissions management from LNG export facilities in other regions should consider critical levels and loads analyses to ensure industrial development is synergistic with ecosystem protection. While recognizing uncertainties in dispersion modelling, critical load estimates, and subsequent effects, the critical levels and loads approach is being used to inform regulatory decisions in British Columbia to prevent impacts that have been well documented in other regions.

硫黄・窒素沈着による森林生態系影響の全国評価 ―臨界負荷量を用いた推定―

硫黄・窒素沈着による森林生態系影響の全国評価 ―臨界負荷量を用いた推定―

On the methods of critical load estimation of spherical circle axially symmetrical shells

A relaxation method is applied to estimate and predict a critical set of parameters responsible for stability loss (buckling) of spherical circle axially symmetric shells. The buckling phenomenon under static loading was investigated by solving the Cauchy problem for a set of ordinary differential equations and the Hausdorff metrics was applied while quantifying the data obtained within the novel approach.