Concept Of Safety Factor Research Articles

General partial safety factor theory for the assessment of the reliability of nonlinear structural systems

The paper develops a novel and general theory for characterizing the nonlinearity of structural systems and for applying partial safety factors to these systems. The theory establishes a key relationship between the partial safety factor concept and the reliability theory of nonlinear structural systems, using the degree of homogeneity as a measure of nonlinearity at the design point. This measure allows for an efficient mathematical decoupling of the reliability index into nonlinearity-invariant partial reliability indexes. This formulation enables the identification of critical safety situations in extreme cases of nonlinearities in complex nonlinear structural systems. The theory leads to two main outcomes based on the asymptotic behavior of the reliability index. First, the reliability index of any nonlinear structural system is always bounded between an upper and lower bound, which can be determined using the concept of nonlinearity-invariant partial reliability indexes. Second, nonlinearity-invariant critical partial safety factors ensure that the reliability index is greater than the target reliability index. The proposed theory provides a simple and easy-to-implement method for assessing the safety of nonlinear structural systems, which can be used in conjunction with existing codes and standards. The theory can be applied to a wide range of nonlinear systems in engineering practice, including structural and geotechnical problems. It is designed primarily to provide code writers with the necessary procedure for calibrating partial safety factors for nonlinear structural systems and to identify the over-safe or under-safe cases.

Non-linear structural models and the partial safety factor concept

Most modern structural design codes are based on the partial safety factor concept. The partial safety factors are calibrated on linear limit states. Structural design codes such as the Eurocode provide simplified rules on the application of partial safety factors to non-linear limit states. This paper investigates these rules and their effect on the structural reliability for various non-linear limit states. Moreover, we motivate adaptations of the current design rules. We focus on non-linear structural response functions, i.e., the non-linear relation between actions and their effects. In order to characterize the non-linearity of a structural response function, we introduce a new measure of non-linearity. We conduct a detailed parametric study and investigate two example structures. Our results show that for the case of a single dominant action, current design rules lead to sufficiently safe or only marginally unsafe structures. However, they can lead to a strong over-design.

Triggering Rainfall of Large-Scale Landslides in Taiwan: Statistical Analysis of Satellite Imagery for Early Warning Systems

Typhoon Morakot had a serious impact on Taiwan, especially the uncommon type of landslide called large-scale landslide (LSL), not many in number but serious in effect, the origin of which the study induced. To establish a specific relationship between LSL and triggering rainfall for future applications of LSL early warning predictions, relevant cases from satellite imagery, along with field investigation data, major event reports, and seismic data from 2004 to 2016, were collected. All collected cases are distributed around the mountainous area in Taiwan, and a total of 107 cases which were mainly distributed in the southern part of the mountainous area were finally selected, including 28 occurrence-time-known cases and 79 occurrence-time-unknown cases. In addition, 149 potential areas identified by the Soil and Water Conservation Bureau (SWCB) were used for improving bounding estimates. Based on the concept of safety factor, two dimensionless quantities, rainfall/landslide depth (R/D) and friction angle/slope (ϕ/θ), were analyzed by linear regression. In addition, D was assumed to be nonlinearly dependent on R, θ, and ϕ, and the parameter uncertainties were evaluated by the resampling with bootstrap method. Based on the currently obtained data, there were 8% Type-I errors in the results of the linear regression analysis, and 1% Type-II errors in the results of the nonlinear regression analysis. Through the comparison of statistical indicators, the results of nonlinear regression analysis have a better correlation trend. Based on the needs of early warning operations, more conservative indicators can reduce the risks faced by management operations. Therefore, according to the results of this study, the lower boundary values from nonlinear analysis could be used as the LSL early warning management settings. Incorporated with real-time rainfall forecasts, the variation of statistical indicators will provide the trend information dynamically, and will help to increase the response time for relevant evacuation operations, that will be welcome for the further extended applications to guide the evacuation operations of early warning systems.

Reliability-based design of fiber reinforced concrete slabs-on-ground in flexure as per ACI 360

Modern design codes apply the Load and Resistance Factor Design (LRFD) format to account for all uncertainties involved, primarily manufacturing, fabrication, and modeling errors. In this format, load effects are scaled-up by load factors while a resistance factor scales down the resistance. In this way, the LRFD design format ensures that all designs meet, consistently, a certain safety level. To determine the most appropriate factors, a reliability-based procedure is required, in which a target reliability index is selected, which corresponds to an acceptable probability of failure. Unlike most of the American Concrete Institute (ACI) design codes, which adopted the LRFD design format, the current ACI 360R for slabs-on-ground design is based on the concept of safety factors. The present work aims at calibrating the resistance factor,ϕ, for the flexural design of fiber reinforced concrete slabs-on-ground. A total of 56 laboratory tests gathered from previous studies were analyzed to determine the statistical parameters of the resistance model. Then a series of reliability analyses were conducted to calibrate the resistance factor. In the calibration process, dead and live loads with and without impact were considered in the load combinations. This study suggests that for a flexural design of fiber reinforced concrete slabs-on-ground subjected to dead and live (with or without impact) loads, to meet the target reliability index, a resistance factor ϕ = 0.8 is recommended. An example is presented to showcase the application of LRFD for the design of FRC slabs-on-ground.

Safety factors as a 'design' principle of animal form and function: an historical perspective.

For well over 150 years, factors of safety (also known as safety factors) have been a fundamental engineering concept that expresses how much stronger a system is compared with the intended load. The pioneering work of Robert McNeill Alexander in the early 1980s applied this engineering concept to biomechanics. Over the next decade, evidence from comparative biomechanics supported the idea that safety factors are a fundamental principle of animal form and function. In terms of physiology, Jared Diamond related the maximal capacity of a physiological process to normal functional demands and incorporated evolutionary thinking into the concept of safety factors. It was proposed that evolutionary reasoning is required to understand the magnitudes of biological reserve capacities, an idea called 'quantitative evolutionary design'. However, the general idea of safety factors as related to organismal form and function is much older. In 1906, Samuel James Meltzer, a physiologist and physician, presented the 5th Harvey Lecture to the New York Academy of Medicine; a lecture entitled 'The Factors of Safety in Animal Structure and Animal Economy', which was later published in Science in 1907. The 1907 paper is rarely cited and has never been cited within comparative biomechanics or comparative physiology. The purpose of this Commentary is to highlight Meltzer's historical contribution to the concept of safety factors as a general principle of organismal 'design'.

New insights on the cardiac safety factor: Unraveling the relationship between conduction velocity and robustness of propagation

Cardiac conduction disturbances are linked with arrhythmia development. The concept of safety factor (SF) has been derived to describe the robustness of conduction, but the usefulness of this metric has been constrained by several limitations. For example, due to the difficulty of measuring the necessary input variables, SF calculations have only been applied to synthetic data. Moreover, quantitative validation of SF is lacking; specifically, the practical meaning of particular SF values is unclear, aside from the fact that propagation failure (i.e., conduction block) is characterized by SF < 1. This study aims to resolve these limitations for our previously published SF formulation and explore its relationship to relevant electrophysiological properties of cardiac tissue. First, HL-1 cardiomyocyte monolayers were grown on multi-electrode arrays and the robustness of propagation was estimated using extracellular potential recordings. SF values reconstructed purely from experimental data were largely between 1 and 5 (up to 89.1% of sites characterized). This range is consistent with values derived from synthetic data, proving that the formulation is sound and its applicability is not limited to analysis of computational models. Second, for simulations conducted in 1-, 2-, and 3-dimensional tissue blocks, we calculated true SF values at locations surrounding the site of current injection for sub- and supra-threshold stimuli and found that they differed from values estimated by our SF formulation by <10%. Finally, we examined SF dynamics under conditions relevant to arrhythmia development in order to provide physiological insight. Our analysis shows that reduced conduction velocity (Θ) caused by impaired intrinsic cell-scale excitability (e.g., due to sodium current a loss-of-function mutation) is associated with less robust conduction (i.e., lower SF); however, intriguingly, Θ variability resulting from modulation of tissue scale conductivity has no effect on SF. These findings are supported by analytic derivation of the relevant relationships from first principles. We conclude that our SF formulation, which can be applied to both experimental and synthetic data, produces values that vary linearly with the excess charge needed for propagation. SF calculations can provide insights helpful in understanding the initiation and perpetuation of cardiac arrhythmia.

Probabilistic failure analysis of infinite slopes under random rainfall processes and spatially variable soil

ABSTRACTRainfall-induced landslides occur during or immediately after rainfall events in which the pore water pressure builds up, leading to shallow slope failure. Thereby, low permeability layers result in high gradients in pore water pressure. The spatial variability of the soil permeability influences the probability such low permeability layers, and hence the probability of slope failure. In this paper, we investigate the influence of the vertical variability of soil permeability on the slope reliability, accounting for the randomness of rainfall processes. We model the saturated hydraulic conductivity of the soil with a one-dimensional random field. The random rainfall events are characterised by their duration and intensity and are modelled through self-similar random processes. The transient infiltration process is represented by Richards equation, which is evaluated numerically. The reliability analysis of the infinite slope is based on the factor of safety concept for evaluating slope stability. To cope with the large number of random variables arising from the discretization of the random field and the rainfall process, we evaluate the slope reliability through Subset Simulation, which is an adaptive Monte Carlo method known to be especially efficient for reliability analysis of such high-dimensional problems. Numerical investigations show higher probability of slope failure with increased spatial variability of the saturated hydraulic conductivity and with more uniform rainfall patterns.

Long-Term In-Service Monitoring and Performance Assessment of the Main Cables of Long-Span Suspension Bridges.

Despite the recent developments in structural health monitoring, there remain great challenges for accurately, conveniently, and economically assessing the in-service performance of the main cables for long-span suspension bridges. A long-term structural health monitoring technique is developed to measure the tension force with a conventional sensing technology and further provide the in-service performance assessment strategy of the main cable. The monitoring system adopts conventional vibrating strings transducers to monitor the tension forces of separate cable strands of the main cable in the anchor span. The performance evaluation of the main cable is conducted based on the collected health monitoring data: (1) the measured strand forces are used to derive the overall tension force of a main cable, which is further translated into load bearing capacity assessment using the concept of safety factor; and (2) the proposed technique can also evaluate the uniformity of tension forces from different cable strands. The assessment of uniformity of strand forces of a main cable offers critical information in terms of potential risks of partial damage and performance deterioration of the main cable. The results suggest the proposed low-cost monitoring system is an option to provide approximate estimation of tension forces of main cables for suspension bridges. With the long-term monitoring data, the proposed monitoring-based evaluation methods can further provide critical information to assess the safety and serviceability performance of main cables.

Assessment of rock slope stability by probabilistic-based Slope Stability Probability Classification method along highway cut slopes in Adilcevaz-Bitlis (Turkey)

Rock slope stability is of great concern along highway routes as stability problems on cut slopes may cause fatal events as well as loss of property. In rock slope engineering, stability evaluations are commonly performed by means of analytical or numerical analyses, principally considering the factor of safety concept. As a matter of fact, the probabilistic assessment of slope stability is progressively getting popularity due to difficulties in assigning the most appropriate values to design parameters in analytical or numerical methods. Additionally, the effect of heterogeneities in rock masses and discontinuities on the analysis results is minimized through the probabilistic concept. In this study, slope stability of high and steep sedimentary rock cut slopes along a state highway in Adilcevaz-Bitlis (Turkey) was evaluated on the basis of probabilistic approach using the Slope Stability Probability Classification (SSPC) system. The probabilistic assessment indicates major slope stability problems because of discontinuity controlled and discontinuity orientation independent mass movements. Almost all studied cut slopes suffer from orientation-independent stability problems with very low stability probabilities. Additionally, the probability of planar and toppling failures is significantly high with respect to the SSPC system. The stability problems along the investigated rock slopes were also verified by field reconnaissance. Remedial measures such as slope re-design and reinforcement at the studied locations should be taken to prevent hazardous events along the highway. On the other hand, the probabilistic approach may be a useful tool during rock slope engineering to overcome numerous uncertainties when probabilistic and analytic results are compared.

Advances on the Failure Analysis of the Dam-Foundation Interface of Concrete Dams.

Failure analysis of the dam-foundation interface in concrete dams is characterized by complexity, uncertainties on models and parameters, and a strong non-linear softening behavior. In practice, these uncertainties are dealt with a well-structured mixture of experience, best practices and prudent, conservative design approaches based on the safety factor concept. Yet, a sound, deep knowledge of some aspects of this failure mode remain unveiled, as they have been offset in practical applications by the use of this conservative approach. In this paper we show a strategy to analyse this failure mode under a reliability-based approach. The proposed methodology of analysis integrates epistemic uncertainty on spatial variability of strength parameters and data from dam monitoring. The purpose is to produce meaningful and useful information regarding the probability of occurrence of this failure mode that can be incorporated in risk-informed dam safety reviews. In addition, relationships between probability of failure and factors of safety are obtained. This research is supported by a more than a decade of intensive professional practice on real world cases and its final purpose is to bring some clarity, guidance and to contribute to the improvement of current knowledge and best practices on such an important dam safety concern.

Variability characterisation of input parameters in pavement performance evaluation

Due to significant variability associated with the input parameters of pavement life and traffic repetitions, the performance evaluation in pavement design process becomes very uncertain. Uncertainty in performance evaluation can be handled using probabilistic design method. To calculate probability or reliability, it needs distributions and the parameters of distribution of the performance parameters, that is, pavement life and traffic repetitions. This paper attempts to establish these distributions and their goodness of fit based on statistical evidence. The uncertainty levels of traffic, pavement life and the pavement damage parameters are studied for the possible ranges of variations in different input parameters. Different possible combinations of distribution are considered, and it is observed that irrespective of the type of distribution of input parameters, the distributions of traffic, pavement life and damage parameters follow a lognormal distribution, with a wide range of coefficient of variation (COV). Sensitivity of COV parameters is also studied for reliability analysis in asphalt pavements. Finally, accounting the distributions and COVs as well, a factor of safety concept has been introduced towards a reliability-based deterministic design approach. Mechanistic–empirical (M–E) design method and, the fatigue and rutting failures are considered in the present work.

Safety examination of existing concrete structures using the global resistance safety factor concept

Current design procedures for structural concrete elements are based on member level (or local) safety checks, in the sense that the safety condition is evaluated at each cross-section individually. In the examination of existing structures, the exploitation of the redundancy of the structural system and its redistribution capacity may prove necessary to fulfil the safety requirements, demanding for a system level (or global) safety evaluation. This can be achieved using nonlinear finite element analysis (NLFEA) procedures and requires a safety format different than that based on partial safety factors.In this work, a simple safety format tailored for NLFEA of existing structures is described. It is shown how to define a global resistance safety factor based on a simple semi-probabilistic approach in line with the recommendations of the new Swiss standards for existing structures [1,2] that can capture the sensitiveness of the structural system resistance, R, to the random variation of the input variables. Besides enabling the use of updated information regarding the material properties, the proposed procedure allows performing reliability differentiation based on risk analysis, being therefore suitable for the safety examination of existing bridges.The definition of the semi-probabilistic global resistance safety factor is based on the assumption of a log-normal probability density function for the resistance R and on an estimate of its coefficient of variation, vR. The existing proposals for estimating vR are reviewed and compared. For statically determined structures with a single dominant failure mode (axial compression, bending or shear) the examination values of R computed with global resistance safety factors are shown to compare well with those obtained with partial safety factors. The reliability of the examination values of R is also evaluated through a comparison with the Monte Carlo simulation procedure and it is shown that the global resistance safety factor method is sufficiently accurate. Finally, a case-study is presented illustrating the application of the proposed procedure in the structural safety examination of an existing prestressed concrete bridge.

COLLAPSE PRESSURE ESTIMATES AND THE APPLICATION OF A PARTIAL SAFETY FACTOR TO CYLINDERS SUBJECTED TO EXTERNAL PRESSURE

The present paper investigates the collapse pressure of cylinders with intermediate thickness subjected to external pressure based on detailed elastic-plastic finite element (FE) analyses. The effect of the initial ovality of the tube on the collapse pressure was explicitly considered in the FE analyses. Based on the present FE results, the analytical yield locus, considering the interaction between the plastic collapse and local instability due to initial ovality, was also proposed. The collapse pressure values based on the proposed yield locus agree well with the present FE results; thus, the validity of the proposed yield locus for the thickness range of interest was verified. Moreover, the partial safety factor concept based on the structural reliability theory was also applied to the proposed collapse pressure estimation model, and, thus, the priority of importance of respective parameter constituting for the collapse of cylinders under external pressure was estimated in this study. From the application of the partial safety factor concept, the yield strength was concluded to be the most sensitive, and the initial ovality of tube was not so effective in the proposed collapse pressure estimation model. The present deterministic and probabilistic results are expected to be utilized in the design and maintenance of cylinders subjected to external pressure with initial ovality, such as the once-through type steam generator.

Buckling analysis of structural steel frames with inelastic effects according to codes

Steel building frames are often analyzed for stability in an elastic way, while most of their columns behave inelastically at the buckling stage. Most column design provisions allow for inelastic behavior, but overall inelastic stability analysis is rarely performed. In this study the analysis philosophy is centered on the overall frame stability and its true safety factor. As many columns show inelastic behavior at the buckling stage, the proposed procedure takes due consideration of this fact. Once the overall buckling factor for the frame is obtained, individual column effective length factors, and their true slenderness ratios are computed, and used in the design relationships. This procedure circumvents the use of design nomographs and numerous formulas proposed in the past to alleviate their shortcomings. The procedure proposed based on the overall safety factor concept is an iterative one. It starts with a stability analysis and gradually modifies the structural properties to take account of inelasticity and eventually converges to the final buckling factor and mode shape. Any type of lateral restraint can be exactly modeled and taken into consideration without the need for approximate simplifying assumptions. The design philosophy proposed herein is that all columns must have their design parameters as related to buckling capacity must be derived from a single buckling analysis valid for the whole structure, and not considered separately and isolated from the rest of the structure as is currently practiced. Examples are worked out to illustrate the procedure and the results are compared to those of others.

Power System Reliability Evaluation Using Safety Factor Concept And Simpson's 1/3rd Rule

This paper describes a methodology based on Gaussian distribution approach for generating capacity reliability evaluation of a power system. The presented methodology has developed using continuous probability distribution function. The failure probability evaluation of generating system accounts the load models as load duration curve and is based on maximum average generation capacity. The probability of load exceeding the generating capacity has also been considered in LOLP evaluation. The described methodology in this paper is based on safety factor concept and peak load considerations. The test results using proposed methodology and various discussions have been presented for various generating capacity and load data available at Vijay Wada super thermal power plant, A. P.; India. Obtained results from extensive testing of the proposed method at different generating capacity and load demand considerations of Indian power system confirm the validity of the developed approach.

Power system components modelling and reliability evaluation of generation capacity

This paper describes a methodology based on safety factor concept and peak load considerations for a reliability evaluation of a generation system. This paper also refers to major research papers presented for the evaluation of reliability of power systems, reliability indices and modelling of power system components. Load models are considered as a straight line and a stepped load duration curve is used for reliability evaluation of system using Simpson's 1/3rd rule. The probability of load exceeding the generating capacity has also been considered in Loss of Load Probability (LOLP) evaluation.

Probabilistic approach for biorhythmic analysis to prevent aviation accidents

This paper presents a new methodology, based on the probabilistic approach, for biorhythmic analysis to prevent aviation accidents. The methodology has been developed using the Gaussian distribution technique for reliability evaluation of the aviation system, keeping in mind the biorhythmic effects of the pilot. The normal distributed data of the US Air Force were tested and analysed based on the performance ability of pilot and the peak demand of the performance. The accident zone is that area of operation during which the performance demand exceeds the performance ability of the aircraft pilot. Failure probabilities, considering peak performance demand and the pilot's ability, have been evaluated using the Gaussian distribution approach. The safety factor concept has also been presented in this paper for biorhythmic analysis to prevent aviation accidents. The stepped incident-duration curve has been utilised to evaluate the pilot's reliability on the aviation system using Simpson's 1/3rd rule.

Welding of Thermoplastic Roofing Membranes Subjected to Different Conditioning Procedures

Abstract The use of thermoplastic roofing membranes has grown dramatically over the past years. This has occurred for a number of reasons including the proven track record of some products, the move to light colored “cool” materials, and the variety of systems available. A key benefit of thermoplastic membranes is the ability to hot air weld their seams, creating a permanent seal. As these single-ply membranes are installed in a one-ply configuration, a properly executed seam is critical to their long-term performance. Welding properties of membranes from five different manufacturers of thermoplastics: two polyvinyl chloride (PVC), two thermoplastic olefins (TPO), and one KEE (ketone ethylene ester) were studied. All materials were welded at twelve different combinations of welding temperature and speed. Each of these “welding windows” was completed with material as received, after 4 days immersed in water and after 30 days of exposure to severe soiling. Finished welds were assessed by peel testing in a tensile test apparatus. Differences in welding properties of specific materials and the generic types of products were evaluated, including sensitivity to changes in weld parameters, the effectiveness of manufacturer recommended cleaning/seam preparation, as well as the impact of the conditioning processes on weld quality. Integrating a previous study by others, a weld safety factor concept was developed which is a useful metric for assessing weld quality. This work demonstrated the need for clear, product specific welding guidelines for both new materials and for roof membranes exposed to the elements so as to ensure a proper weld.

Four Alternative Definitions of the Fuzzy Safety Factor

The concept of safety factor is nearly universally applied in structural engineering. There are presently several approaches for probabilistic interpretation of the safety factors in the literature. Herein we generalize the above approaches to derive four possible definitions of safety factor that are based on fuzzy sets: (1) the central fuzzy safety factor is defined as the ratio of the centroid abscissas of the membership functions, respectively, of the capacity and the demand of the structure; (2) the characteristic value of fuzzy safety factor as the lower bound of the α cut of the fuzzy safety factor for a specified level of the membership function; (3) the mean value of fuzzy safety factor as the centroid abscissa of the fuzzy capacity-to-demand ratio; and (4) the fuzzy multiplicative safety factor is defined as the abscissa of the centroid of the capacity multiplying to the abscissa of the centroid of the inverse of the demand. Fundamental problem of the strength of materials, namely, tension of an...

Fuzzy sets based interpretation of the safety factor

Safety factor is a universally utilized concept in several branches of engineering. On one hand, most engineers, as it were, neglect uncertainty, but on the other hand, the allowable stress level was introduced long time ago as a ratio of the yield stress to the so-called safety factor to provide the region for the safe utilization of the structure. Thus the uncertainty is introduced into practice by the “back door”. This observation led to a considerable literature dedicated to the probabilistic interpretation of the safety factor. The present paper deals with the novel aspect of elucidation of the concept of safety factor through the theory of fuzzy sets, apparently for the first time in the literature. The aim of the paper is to present the safety factor that is uniformly employed by engineers, but in the new light. The safety factor in the fuzzy setting is introduced. The ideas are illustrated on two strength of material problems; simple examples are chosen so as to allow for clearer illustration of ideas.