Critical Load Estimates Research Articles

Effects of Creep on the Strength of Eccentrically-Loaded Slender Reinforced Concrete Columns

Creep and shrinkage effects in concrete structures increase deformations over time but do not normally affect the strength of the structure in any appreciable way. However, for a concrete structure which is subject to second order effects, the loads experienced by the structure are dependent on its deformed shape and therefore the capacity of the structure to withstand the applied loads is dependent on the way it deforms over time. A slender reinforced concrete column is such a structure. This paper presents a first-principles method of analysing the time-dependent behaviour of slender concrete columns subjected to sustained eccentric loads and compares theoretical estimates of critical loads (at which the strength of the critical cross-section is exceeded by creep-induced internal actions) to the allowances made for the design of slender concrete columns by the Australian Standard for Concrete Structures AS3600-2009. In particular, the effects of the concrete compressive strength and the reinforcement ratio are investigated in terms of their influence on the creep-induced reduction of strength of slender columns. The method is based on the principle of superposition and makes use of the age-adjusted effective modulus method to predict the time-dependent behaviour of columns.

Shear buckling coefficient: proposal for tapered steel plates

This paper presents a new proposal for estimation of critical load for non-prismatic, thin plates simply supported on four edges subjected to shear. The research included wide parametric studies using more than 500 samples. The parameters taken into account were the web thickness, the panel aspect ratio and the inclination angle. The influence of each was analysed separately and then some simplifications were made in order to find coherent expressions to describe the behaviour of the studied panels. The numerical results were then used to validate the solution proposed in EN 1993-1-5. As a result of this comparison, it is concluded that new design formulations are needed for tapered plates with a considerable slope. Based on previous research by the authors concerning four various geometrical typologies of tapered panels, four expressions for the shear buckling coefficient kφ are proposed.

Influence of Root Rotation on Delamination Fracture Toughness of Composites

Large deviations have been observed while analysing composite double cantilever beam (DCB) specimens assuming each cracked half as a simple cantilever beam. This paper examines the effect of rotational spring stiffness(K)on the critical fracture energy(GIC)considering nonzero slope at the crack-tip of the DCB specimen by modelling each cracked half as the spring-hinged cantilever beam. The critical load estimates of DCB specimens fromGICare found to be in good agreement with in-house and existing test results of different composite material systems.

Regional scale gradients of climate and nitrogen deposition drive variation in ectomycorrhizal fungal communities associated with native Scots pine

Ectomycorrhizal fungi commonly associate with the roots of forest trees where they enhance nutrient and water uptake, promote seedling establishment and have an important role in forest nutrient cycling. Predicting the response of ectomycorrhizal fungi to environmental change is an important step to maintaining forest productivity in the future. These predictions are currently limited by an incomplete understanding of the relative significance of environmental drivers in determining the community composition of ectomycorrhizal (ECM) fungi at large spatial scales. To identify patterns of community composition in ECM fungi along regional scale gradients of climate and nitrogen deposition in Scotland, fungal communities were analysed from 15 seminatural Scots pine (Pinus sylvestris L.) forests. Fungal taxa were identified by sequencing of the ITS rDNA region using fungal-specific primers. Nonmetric multidimensional scaling was used to assess the significance of 16 climatic, pollutant and edaphic variables on community composition. Vector fitting showed that there was a strong influence of rainfall and soil moisture on community composition at the species level, and a smaller impact of temperature on the abundance of ectomycorrhizal exploration types. Nitrogen deposition was also found to be important in determining community composition, but only when the forest experiencing the highest deposition (9.8kg Nha(-1) yr(-1) ) was included in the analysis. This finding supports previously published critical load estimates for ectomycorrhizal fungi of 5-10kg Nha(-1) yr(-1) . This work demonstrates that both climate and nitrogen deposition can drive gradients of fungal community composition at a regional scale.

Global stability-based design optimization of truss structures using multiple objectives

This paper discusses the effect of global stability on the optimal size and shape of truss structures taking into account of a nonlinear critical load, truss weight and serviceability at the same time. The nonlinear critical load is computed by arc-length method. In order to increase the accuracy of the estimation of critical load (ignoring material nonlinearity), an eigenvalue analysis is implemented into the arc-length method. Furthermore, a pure pareto-ranking based multi-objective optimization model is employed for the design optimization of the truss structure with multiple objectives. The computational performance of the optimization model is increased by implementing an island model into its evolutionary search mechanism. The proposed design optimization approach is applied for both size and shape optimization of real world trusses including 101, 224 and 444 bars and successful in generating feasible designations in a large and complex design space. It is observed that the computational performance of pareto-ranking based island model is better than the pure pareto-ranking based model. Therefore, pareto-ranking based island model is recommended to optimize the design of truss structure possessing geometric nonlinearity.

Critical load estimation in young swimming rats using hyperbolic and linear models

We analysed the viability of critical load (CL) and anaerobic swimming capacity (ASC) estimation by different mathematical models and the effects of varying the number/intensity of predictive trials on these parameters in young swimming rats. After familiarised to swimming, 9 male animals had time to exhaustion (TEX) accessed in efforts against 9, 11, 13 and 15% of their body mass (bm). CL and ASC were calculated by the hyperbolic load vs. TEX (Hyp) as well as linear load vs. 1/TEX (Lin1) and load·TEX vs. TEX (Lin2) models. Moreover, parameters derived from the 11 possible combinations of 2, 3 or 4 efforts using the Lin1 regression were compared. The Lin1 model resulted in a lower R2 compared to Lin2 and Hyp methods (0.968±0.010 vs. 0.995±0.004 and 0.988±0.013; P<0.05), but no significant differences were found between models regarding CL (7.8±1.2, 7.9±1.1 and 7.8±1.0% bm) or ASC (526±129, 521±104 and 534±117% bm?s). Except for the atypical CL (1.4 ± 4.2% bm) and ASC (1079 ± 383% bm⋅s) from trials against 13 and 15% bm, varying the number/intensity of predictive bouts had no significant effects on parameter estimates. The observed viability and robustness of CL and ASC estimation by different mathematical models in young swimming Wistar rats suggest the load-time relationship as an interesting tool to investigate the physiological mechanisms underlying exercise tolerance in laboratory rodents.

Relationship between critical load exceedances and empirical impact indicators at Integrated Monitoring sites across Europe

Critical loads for acidification and eutrophication and their exceedances were determined for a selection of ecosystem effects monitoring sites in the Integrated Monitoring programme (UNECE ICP IM). The level of protection of these sites with respect to acidifying and eutrophying deposition was estimated for 2000 and 2020. In 2020 more sites were protected from acidification (67%) than in 2000 (61%). However, due to the sensitivity of the sites, even the maximum technically feasible emission reductions scenario would not protect all sites from acidification. In 2000, around 20% of the IM sites were protected from eutrophication. In 2020, under reductions in accordance with current legislation, about one third of the sites would be protected, and at best, with the maximum technically feasible reductions, half of the sites would be protected from eutrophication. Data from intensively monitored sites, such as those in ICP IM, provide a connection between modelled critical thresholds and empirical observations, and thus an indication of the applicability of critical load estimates for natural ecosystems. Across the sites, there was good correlation between the exceedance of critical loads for acidification and key acidification parameters in runoff water, both with annual mean fluxes and concentrations. There was also evidence of a link between exceedances of critical loads of nutrient nitrogen and nitrogen leaching. The collected empirical data of the ICP IM thus allow testing and validation of key concepts used in the critical load calculations. This increases confidence in the European-scale critical loads mapping used in integrated assessment modelling to support emission reduction agreements.

Mapping critical loads of nitrogen deposition for aquatic ecosystems in the Rocky Mountains, USA

Spatially explicit estimates of critical loads of nitrogen (N) deposition (CLNdep) for nutrient enrichment in aquatic ecosystems were developed for the Rocky Mountains, USA, using a geostatistical approach. The lowest CLNdep estimates (<1.5 ± 1 kg N ha−1 yr−1) occurred in high-elevation basins with steep slopes, sparse vegetation, and abundance of exposed bedrock and talus. These areas often correspond with areas of high N deposition (>3 kg N ha−1 yr−1), resulting in CLNdep exceedances ≥1.5 ± 1 kg N ha−1 yr−1. CLNdep and CLNdep exceedances exhibit substantial spatial variability related to basin characteristics and are highly sensitive to the NO3− threshold at which ecological effects are thought to occur. Based on an NO3− threshold of 0.5 μmol L−1, N deposition exceeds CLNdep in 21 ± 8% of the study area; thus, broad areas of the Rocky Mountains may be impacted by excess N deposition, with greatest impacts at high elevations.

Ecological ranges for the pH and NO3 of syntaxa: a new basis for the estimation of critical loads for acid and nitrogen deposition

AbstractQuestion: Can the abiotic ranges of syntaxonomic units (associations) in terms of pH and nitrate concentration be estimated and then in principle be used to estimate critical loads for acid and nitrogen deposition?Location: Europe.Methods: Using splines, abiotic ranges of syntaxonomic units were estimated on the basis of measured soil pH and nitrate concentration and vegetation relevés. Owing to limited calibration data, this yielded responses for only a few syntaxa. In a second attempt, we used a 160 000‐relevé training set; the syntaxon of each relevé was known but not their soil pH values and soil nitrate concentrations, so for each relevé, the soil pH and nitrate concentration were estimated by inference from species composition. We again estimated abiotic ranges using the spline method, including the 5th and 95th percentiles as a proxy for the ecological range.Results: The second (indirect) method yielded ranges for soil pH and for nitrate concentration for many of the associations. The means and percentiles were corrected for regression to the mean.Conclusions: It is not yet possible to directly estimate ranges for syntaxa for pH and nitrate on a large scale from the data available. However, indirectly estimated soil pH and nitrate concentrations are sufficiently available to derive ranges for many associations. The lower (5th) percentile of the indirectly estimated pH ranges for associations may be used as the starting point for the estimation of critical loads for acid deposition. The 95th percentile should still be regarded as a rather uncertain estimate of the maximum nitrate concentration.

Inter-annual variations in water yield to lakes in northeastern Alberta: implications for estimating critical loads of acidity

Stable isotopes of water were applied to estimate water yield to fifty lakes in northeastern Alberta as part of an acid sensitivity study underway since 2002 in the Athabasca Oil Sands Region (AOSR). Herein, we apply site-specific water yields for each lake to calculate critical loads of acidity using water chemistry data and a steady-state water chemistry model. The main goal of this research was to improve site-specific critical load estimates and to understand the sensitivity to hydrologic variability across a Boreal Plains region under significant oil sands development pressure. Overall, catchment water yields were found to vary significantly over the seven year monitoring period, with distinct variations among lakes and between different regions, overprinted by inter-annual climate-driven shifts. Analysis of critical load estimates based on site-specific water yields suggests that caution must be applied to establish hydrologic conditions and define extremes at specific sites in order to protect more sensitive ecosystems. In general, lakes with low (high) water yield tended to be more (less) acid sensitive but were typically less (more) affected by interannual hydrological variations. While it has been customary to use long-term water yields to define a static critical load for lakes, we find that spatial and temporal variability in water yield may limit effectiveness of this type of assessment in areas of the Boreal Plain characterized by heterogeneous runoff and without a long-term lake-gauging network. Implications for predicting acidification risk are discussed for the AOSR.

Comparison among model estimates of critical loads of acidic deposition using different sources and scales of input data

The critical load (CL) of acidic atmospheric deposition represents the load of acidity deposited from the atmosphere to the earth’s surface at which harmful acidification effects on sensitive biological receptors are thought to occur. In this study, the CL for forest soils was estimated for 27 watersheds throughout the United States using a steady-state mass balance approach based on both national and site-specific data and using different approaches for estimating base cation weathering. Results suggested that the scale and source of input data can have large effects on the calculated CL and that the most important parameter in the steady-state model used to estimate CL is base cation weathering. These results suggest that the data and approach used to estimate weathering must be robust if the calculated CL is to be useful for its intended purpose.

Direct Estimation of Critical Load for Single-Layer Reticulated Domes with Semi-Rigid Joints

Numerical model of a bolt-ball joint system is established using software ANSYS and verified through experiments. Based on the bendingrotation curves of the bolt-ball joints obtained through numerical simulation, a finite element model of single-layer reticulated domes with bolt-ball joint system is established using nonlinear beam element with end spring elements in software ANSYS. The analyses of the domes are carried out with different parameters including bending stiffness, ratio of rise to span, rotation-stiffness, ball size, asymmetric load distribution, tube section, support condition and initial imperfection. Several key parameters having influence on the load carrying capacity of a semi-rigidly jointed single-layer reticulated dome are thus identified. Finally, formulas are established for direct estimation of critical loads of semi-rigidly jointed single-layer reticulated domes under symmetric and asymmetric loading conditions.

Surface water acidification and critical loads: exploring the F-factor

Abstract. As acid deposition decreases, uncertainties in methods for calculating critical loads become more important when judgements have to be made about whether or not further emission reductions are needed. An important aspect of one type of model that has been used to calculate surface water critical loads is the empirical F-factor which estimates the degree to which acid deposition is neutralised before it reaches a lake at any particular point in time relative to the pre-industrial, steady-state water chemistry conditions. In this paper we will examine how well the empirical F-functions are able to estimate pre-industrial lake chemistry as lake chemistry changes during different phases of acidification and recovery. To accomplish this, we use the dynamic, process-oriented biogeochemical model SAFE to generate a plausible time series of annual runoff chemistry for ca. 140 Swedish catchments between 1800 and 2100. These annual hydrochemistry data are then used to generate empirical F-factors that are compared to the "actual" F-factor seen in the SAFE data for each lake and year in the time series. The dynamics of the F-factor as catchments acidify, and then recover are not widely recognised. Our results suggest that the F-factor approach worked best during the acidification phase when soil processes buffer incoming acidity. However, the empirical functions for estimating F from contemporary lake chemistry are not well suited to the recovery phase when the F-factor turns negative due to recovery processes in the soil. This happens when acid deposition has depleted the soil store of BC, and then acid deposition declines, reducing the leaching of base cations to levels below those in the pre-industrial era. An estimate of critical load from water chemistry during recovery and empirical F functions would therefore result in critical loads that are too low. Therefore, the empirical estimates of the F-factor are a significant source of uncertainty in the estimate of surface water critical loads and related calculations for quantifying lake acidification status, especially now that acid deposition has declined across large areas of Europe and North America.

Critical Loads Changing with Time

ABSTRACT The critical load is the maximal rate of contaminant addition that, over time, will result in environmental concentrations that do not exceed the highest acceptable concentration (i.e., the critical limit). Computationally, critical loads depend solely on critical limits and the expected rates at which contaminants are lost from the environmental media of concern. Losses include processes such as flushing (water bodies) or leaching (soils), sequestration in sediment, volatilization, and crop removal. A significant challenge is that loss rates will vary with time, especially in response to processes such as climate change. How should regulators deal with these changes with time? This Perspective compares the implications of three options where conditions are: (1) fixed to represent the present, (2) variable with no trend over time, and (3) variable with systematic trends (monotonic and cyclical) over time, and a fourth option using stochastic (probabilistic) evaluation of all plausible future conditions. Soil concentrations over 250 years were computed for each option. As expected, conditions that vary systematically with time can drastically change estimates of environmental concentration, and hence critical loads. However, if it is assumed that regulators periodically revisit critical load estimates taking into account changing conditions, long-term objectives can be achieved. One approach to changing conditions is to stochastically create a family of possible time series of conditions and outcomes. In the example developed here, the range of outcomes from the stochastic treatment encompassed those of the various time-series calculations. The regulatory implications of these findings are discussed.

Estimates of critical acid loads and exceedances for forest soils across the conterminous United States

Concern regarding the impacts of continued nitrogen and sulfur deposition on ecosystem health has prompted the development of critical acid load assessments for forest soils. A critical acid load is a quantitative estimate of exposure to one or more pollutants at or above which harmful acidification-related effects on sensitive elements of the environment occur. A pollutant load in excess of a critical acid load is termed exceedance. This study combined a simple mass balance equation with national-scale databases to estimate critical acid load and exceedance for forest soils at a 1-km 2 spatial resolution across the conterminous US. This study estimated that about 15% of US forest soils are in exceedance of their critical acid load by more than 250 eq ha −1 yr −1, including much of New England and West Virginia. Very few areas of exceedance were predicted in the western US.

A comparison of weathering rates for acid-sensitive catchments in Nova Scotia, Canada and their impact on critical load calculations

Critical loads are strongly dependent on the rate of release of base cations from the soil matrix. This study compares five commonly used methods for estimating weathering rates at five acid-sensitive catchments across Nova Scotia, Canada. Three of the methods (Zr Depletion, Clay Content, and the PROFILE model) are based on soil profiles and consider only the rooting zone, whereas the two remaining methods (the soil acidification model MAGIC and catchment Mass Balance Deficit) are catchment-based, and account for contributions from all soils within a catchment. Each weathering estimate method resulted in similar values among the five catchments, indicating similar sensitivity to acidic deposition among the study areas. Base cation weathering estimates were very low using the three soil profile-based methods, with rates varying from 3 to 13 mmol c m − 2 a − 1 . In contrast, catchment-based methods predicted base cation weathering rates an order of magnitude higher (60 to 155 mmol c m − 2 a − 1 ), possibly due to spatial heterogeneity of the soil deposits, and contributions from deeper soil (till). Critical load (sulphur and nitrogen) estimates using the profile-based weathering rates indicate that critical loads for forest soils are currently exceeded at all catchments by 23 to 61 mmol c m − 2 a − 1 . Predicted future reductions in acidic deposition should reduce the magnitude of critical load exceedance, but will not result in the catchments reaching a non-exceeded state.

Estimating Nutrients and Chlorophyll a Relationships in Finnish Lakes

We model the response of chlorophyll a-a surrogate for the phytoplankton community volume-to variations in lake total phosphorus (TP) and total nitrogen (TN) concentrations. The model is fitted to a large cross-sectional data set from the Finnish Lake monitoring network. The objective is to support the Finnish Government in identifying management actions to achieve compliance of the chlorophyll a concentration standard with a given confidence level and to provide tools for the estimation of critical (target) loads for nutrients in monitored lakes. We develop a Bayesian hierarchical linear model which combines advantages of both the currently preferred non-hierarchical lake-type-specific linear model and lake-specific linear model fitted separately using data from a single lake. The hierarchical model is less biased at lake-level compared to the lake type model. In contrast to the lake model, it predicts the lake specific chlorophyll a response to nutrients outside the lake specific observational range. The hierarchical model is used to calculate probabilities of chlorophyll a concentration exceeding the standard under different nitrogen and phosphorus concentration combinations. These probabilities can be used to estimate acceptable nitrogen-phosphorus concentration combinations by a lake manager. We discuss how our study can be useful in implementing the European Water Framework Directive.

On lower-bound estimates of critical loads for cylindrical shells

The paper proposes a new approach to estimate the lower bounds of critical loads for circular cylindrical shells. These bounds are compared with the ordinary lower bound of critical load under which a shell with initial deflections loses stability. The lower bound produced by the approach is higher than the ordinary bound and can be used in design

Determination and Mapping Critical Loads of Acidity and Exceedances for Upland Forest Soils in Eastern Canada

Critical loads of acidity were estimated for upland forests in Eastern Canada using the steady-state Simple Mass Balance (SMB) Model. A consistent methodology was applied to the entire region, although critical loads were estimated separately for the Atlantic provinces (New Brunswick, Nova Scotia, Prince Edward Island and Newfoundland), Quebec and Ontario using different data sources. In this project, critical load estimates and steady-state exceedance values did not include the effect of forest fire and forest harvesting, which could have a considerable impact on critical loads in Eastern Canada. The observed soil pH – base saturation relationship for forest soils indicated that the constants used into the calculation of alkalinity leaching should be set to 10 (M/M) for the molar Bc/Al ratio in soil leachate and 109 (mol L−1)2 for the gibbsite dissolution constant. The area-weighted median critical load for each province varied between 519 (Quebec) and 2063 eq ha−1 y−1 (Prince Edward Island), with a median critical load value for Eastern Canada of 559 eq ha−1 y−1. It is estimated that approximately 52% of the mapped area is exceeded in terms of acidity according to the 1994–1998 average total (wet + dry) atmospheric deposition. Greatest exceedances occurred in Ontario and Quebec and in the south of Nova Scotia, due to low critical loads and high loads of acid deposition.

Simulation of Critical Loads for Nitrogen for Terrestrial Plant Communities in The Netherlands

This paper describes a new method to derive nitrogen critical loads for vegetation, and its application to The Netherlands. An ‘inverted’ form of the soil chemical model SMART2 was used to estimate atmospheric nitrogen deposition at the critical conditions for 139 terrestrial vegetation types (associations) occurring in northwestern Europe, using an iterative search procedure. The critical conditions are the lower end of the pH range, and the upper end of the nitrogen availability range for each vegetation type. The critical load is assumed to be the nitrogen deposition that results in the critical conditions. The critical load values were subjected to a sensitivity and uncertainty analysis. Sensitivity analysis showed that the estimated critical N load mainly depends on the vegetation type and to a lesser extent on the soil type and the critical N availability. Of these variables N availability, which was estimated from Ellenberg’s indicator scale, contributes most to the uncertainty. The critical load averaged over all vegetation types and soil types is estimated to be 23 ± 7 kg N ha−1y−1. This is a rather reliable value because its uncertainty is small and it is in agreement with empirical estimates of critical loads. Critical loads per vegetation type are less reliable because they are not correlated to empirical values, although the ranges of simulated and empirical values usually overlap. At the site level, uncertainty becomes very large and it is not possible to determine critical loads with any practical significance. The uncertainties can only be reduced if more data become available on the abiotic response per species under field conditions, at least to nitrogen availability and soil pH.