Traditional Safety Factor Research Articles

Evaluation of the casing strength reliability in deep gas well by taking into account the cement quality and strength uncertainty: Method, analysis and application

Casing damage is one of the most challenging engineering issues in deep gas wells, leading to significant economic losses and severe incidents such as gas leaks or high annular pressure. According to field data analysis, in addition to traditional factors like stress, temperature, or corrosion, cement sheath quality also impacts casing damage. Hence, this paper establishes a three-dimensional finite element model for casing-cement sheath -formation considering cement sheath quality. It discusses the impact of different cement sheath defects (such as void and eccentricity) on casing stress distribution under the influence of in-situ stresses, high-pressure fluids, and annular pressure. The analysis reveals that under adverse conditions, poor cement sheath quality exacerbates stress on the casing, increasing the risk of casing failure, with the degree of impact being cement void angle > cement eccentricity > cement void thickness. Based on this, a nonlinear fitting of changes in casing equivalent stress is conducted to establish a model for calculating casing external loads under cement void or eccentricity conditions. Considering the dual uncertainty of casing external load and strength parameters, a casing reliability evaluation method is established based on the external load calculation model and stress-strength interference theory. The reliability of casing strength is assessed and analyzed using a practical well in an oil field as an example. The results indicate that compared to traditional safety factor methods, the reliability evaluation method established in this paper can more intuitively and accurately display variations in casing reliability, offering a scientific basis for optimized design solutions. Optimizing cement sheath performance (such as reduced cement elastic modulus and Poisson's ratio) and enhancing cementing quality (by preventing cement voids and eccentricity) effectively reduce the risk of casing failure.

Direct method-based probabilistic shakedown analysis for the structure under multiple uncertain design conditions

Maintaining shakedown during the design stage is crucial for the engineering components under cyclic loading conditions. Due to the multiplicity of uncertainty existing in the actual operating parameters, probabilistic shakedown analysis is more conducive to dealing with risk management for critical infrastructures, compared with the traditional experience-based safety factors which mainly rely on deterministic evaluations and lack statistical information for decision-making. Aimed at reasonably considering the redundancy in structural integrity assessment against cyclic load conditions, a novel direct method-based probabilistic shakedown analysis is proposed under the new probabilistic Linear Matching Method framework (pLMM). The risk of losing the shakedown state is predicted by the physics-based estimation model, where the efficient iteration is employed to derive the reliability index. In the benchmark, the probabilistic shakedown boundary is constructed, with the additional influence of the uncertain cyclic loading pattern on the reliability fully reflected. This pLMM shakedown analysis facilitates the progress from over-reliance on the conservative safety factor towards precise risk management.

A Review of Research and Practice on the Theory and Technology of Reservoir Dam Risk Assessment

A current trend is to implement dam risk management. Dam risk analysis is the premise of dam risk management. Methods such as PRA, FMEA/FMECA, FTA, ETA, and group dam risk analysis have been proposed in studies at home and abroad. In practice, it is found that dam breaks or accidents occur even though the dam risk calculated by the existing methods meets the acceptable risk standard, and that many occurred accidents are at variance with dam risk analysis. This indicates that the existing methods have systematic defects, and the dam risk calculated based on such methods is only a part of the actual risk. This paper reviews the dam risk analysis theory and technical research and practice, discusses and analyzes the applicability and existing defects of the dam risk analysis theory, and proposes the future development direction of the dam risk analysis theory. It is concluded that the current dam risk assessment theories are tantamount to the traditional safety factor method coupled with probability analysis. The correlation among influencing factors of dam system risk, as well as the uncertainties of the said factors are not fully considered. Difficulties and opportunities coexist in China to link the existing dam safety standard system with the dam risk management system. The next step is to use system theory to carry out theoretical research on dam operation risk assessment, strengthen the connection between dam risk theory and management status, and formulate risk prevention regulations and technical standards.

A review of emerging strategies for incorporating climate change considerations into infrastructure planning, design, and decision making

ABSTRACT Climate change is affecting infrastructure in complex and uncertain ways. Traditional load factors, safety factors, and design standards appear misaligned with current and anticipated future conditions. Thus, adapting infrastructure for a changing climate will likely necessitate balancing trade-offs between new and old design paradigms. This literature review summarizes advances in the implementation and research of resilient infrastructure within the context of climate change. We identified three categories of adaptation strategies: (1) assessments and frameworks to incorporate climate data and risks into infrastructure design and planning, (2) modelling of decision making under uncertainty and policy analysis, and (3) examples of best practices, case studies, and workarounds to enhance resilience. This work highlights advances in infrastructure decision making under uncertainty and ways to instill resilience into infrastructure systems. It is expected to help form a knowledge basis for transitioning to infrastructure planning, design, and implementation that is congruous with a changing world.

Sliding stability analyses of a rock slope using deterministic, semi-probabilistic and probabilistic methods

Stability analyses of geotechnical structures in rock are traditionally performed using deterministic methods. In Europe, Eurocode7, introduced in the beginning of the 21st century, adopts limit state design and semi-probabilistic methods, using partial factors for the design of geotechnical structures. Meanwhile, reliability-based design, using probabilistic methods, is becoming more common in practical cases. The paper considers an intentionally simple case study—the analysis of a slope in a rock mass with one discontinuity, considered in a discrete way, forming a rock block to be stabilised by anchors—to compare the results obtained with the different methods. The objective is to calculate the force applied by the anchors so that the ultimate limit states of sliding of the rock block is verified. Deterministic-based design optimization considering both the traditional global safety factor approach and the partial factor approach following the Eurocode 7 are first applied. A reliability-based design optimization procedure—which takes geometrical and mechanical properties of the discontinuities as random variables—is then used, and the results are compared to the former ones. A discussion is presented concerning the consistency of the obtained results.

Safety and reliability evaluation of casing in ultra-deep well based on uncertainty analysis of extrusion load

The extrusion load on casing in ultra-deep well is uncertain, which limits the application of safety factor method. Therefore, the evaluation method of collapsing safety and reliability on casing during drilling in ultra-deep wells is put forward. Based on the extrusion load model in ultra-deep well considering the diversity of strength parameters of casing and the integrity of formation-cement sheath-casing system, the uncertainty distribution functions of collapse strength and extrusion load on casing are derived by introducing probability and statistics theory. Then, the theory of "stress-strength interference" is applied to obtain the reliability R, confidence interval and reliability-safety factor nR of casing. Taking multiple ultra-deep wells in the Kuqa block of the Tarim Oilfield as an example, the collapse safety and reliability analysis on casing is carried out. Several conclusions are made based on the oilfield statistics. The traditional safety factor is greater than the reliability-safety factor. The surface casing and the production casing are both safer than the technical casing. More accurate original data can narrow the confidence interval width of nR and reduce the collapse risk of technical casing. The change in reliability is consistent with the change of the reliability-safety factor. For technical casing, when R is greater than 0.50 and 0.92, nR is greater than 1.0 and 1.1 respectively. For production casing, when R is greater than 0.98, nR is greater than 1.1. For each type of casing, affected by the uncertainty of the extrusion load on casing, when the extrusion load exceeds a certain value (but this value is less than the casing strength), the reliability begins to decrease. The larger the standard deviation of extrusion load is, the more obvious the influence on reliability change will be. Compared with the traditional design safety factor, the change of the anti-collapse safety degree of the casing can be more intuitively displayed by the reliability, which could provide an important supplement for the selection of traditional design safety factor during drilling operations.

Slope Reliability Analysis Considering Variability of Shear Strength Parameters

The traditional safety factor method cannot consider the uncertainty in the slope system, and the reliability theory based on probability and statistics can more objectively evaluate the degree of influence on the slope, which has become a trend of slope stability evaluation. In this paper, the spatial variability of soil strength parameters cohesion c, internal friction angle φ is considered to build a stochastic variable model, the Monte Carlo method is adopted to study the effect of reliability index β for two parameters. The results shows that, the soil parameters c, have a significant impact on the reliability index β, however, φ is more sensitive in the calculation process which have a greater impact on the calculation of the safety factor and reliability index. The steeper slope has less reliability index. For high variability of the steep slope, a reliable indicator of φ variability is no longer sensitive. In actual engineering, the correlation of soil parameters c and is often not considered, so the reliable index calculated in this case is smaller than the actual one.

Advantages of second-order work as a rational safety factor and stability analysis of a reinforced rock slope

Landslides can be considered as a static–dynamic transition with the sudden release of kinetic energy. The sharp vanishing of the second-order work is also linked to this phenomenon. In this study, the relation between the second-order work and the kinetic energy is reviewed, and five advantages of the normalized global second-order work (D2Wn) as a factor of safety (FOS) are proposed and discussed, comparing this FOS with the one based on the strength reduction method. The D2Wn is considered in the explicit algorithm of the finite difference method, and its mesh-independence is numerically checked by a series of triaxial compression tests. By simulating the excavations of a reinforced rock slope, the stability analyses are performed using the D2Wn and the traditional FOS. The D2Wn is proven completely independent of the convergence criterion and more sensitive to the global failure. Finally, a recently developed energy-absorbing cable is considered for supporting the studied rock slope. Its supporting effect is compared with that of traditional cables.

Deterministic and Probabilistic Approaches in the Analysis of the Bearing Capacity of a Bridge Foundation on Undrained Clay Soil

Abstract This study aims at evaluating deterministic and probabilistic approaches for an analysis of the bearing capacity of a highway bridge foundation on undrained clay soil. The analysis of a rectangular concrete footing was presented for the ultimate strength limit state of the bearing resistance according to the formulation in ES EN 1991:2015 and ERA-Bridge Design Manual, which are the Ethiopian design codes for foundation structures. In the deterministic analysis, the traditional total safety factor method recommended by the ES EN 1991:2015, ERA and AASHTO LRFD method was implemented. It was assumed that design variables such as the soil parameters and loads would follow normal and lognormal distribution functions. With regard to the probabilistic methods, NESSUS-9.8 software, a statistical computer program, was used for the analysis. Comparisons were made between the results obtained from the traditional deterministic method and the reliability-based design approach. The evaluation asserts that the probabilistic approach is a better tool than the deterministic one for assessing the safety and reliability of geotechnical structures. The probabilistic design method rationally accounts for uncertainties more than the conventional deterministic method does. Thus, the author recommends that the National Design Codes of Ethiopia need to be revised and calibrated based on a reliability design format.

Role of Reliability Analysis in Structural Design

Modern structures require more critical and complex designs; the need for accurate and efficient approaches to assess uncertainties in loads, geometry, material properties, manufacturing processes involved and also the operational environment, has increased significantly. Reliability assessment techniques help to develop the initial guidance for robust designs. In this context, the classical methods such as theory of probability, statistical methods and reliability analysis methods are often used by structural engineers. Some of the methods which have been developed in the later stages include Monte Carlo Sampling, Latin Hyper Cube Sampling, First and Second Order Reliability Methods, Stochastic Finite Element Method and Stochastic Optimization. In addition, in those structural problems where randomness is relatively small, a deterministic model is usually used rather than a Stochastic Model. However, when the level of uncertainty is high, Stochastic approaches are necessary for system analysis and design. Number of probabilistic analysis tools have been developed to qualify uncertainties, but the most complex systems are still designed with simplified rules and schemes, such as factor of safety based designs. However, these traditional design processes do not directly account for the random nature of the most input parameters. Factor of safety is used to maintain some degree of safety in the structural design. Generally, the factor of safety is understood to be the ratio of the expected strength of response to the expected load. In practice, both the strength and load are variables, the values of which are scattered about their respective mean values. When the scatter of the variables is considered, the factor of safety could potentially be less than unity and the traditional factor of safety based design would fail. More likely is that the factor of safety is too conservative, which leads to an over expensive design.

Comparison of the reliability-based and safety factor methods for structural design

Abstract Reliability-based design optimization theory has been widely acknowledged as an advanced and advantageous methodology for complex structural system design. Comparatively, the traditional safety factor design method has fallen out of favor with designers since it is simply just a comprehensive expression of all the uncertainties existing in a practical engineering structure, which has been verified to be unreasonable. Moreover, there is no description of the method for searching for the optimal design. In this paper, a comparison of the two approaches is performed for the optimization results and process. It is demonstrated that the weight of the designed structure by the reliability-based optimization is not heavier than that by the safety factor design method under the same reliability requirements. The time efficiency, error estimates and sensitivity analysis are also compared to discuss the advantages and disadvantages of the two approaches. Eventually, the advancement of the reliability-based design optimization is illustrated with optimization designs of a two-bar truss and one practical supersonic wing.

The Exploration of Superiority about the Non-probability Reliability-Based Design Optimization Compared to the Safety Factor Method

Non-probability reliability-based design optimization (NRBDO) theory has been widely acknowledged as an advanced and advantageous methodology for complex structural system design, especially in practical engineering of aerospace. Conversely, the traditional safety factor (SF) design method faded out of the horizon of the designer since it considers only the mean value of design variable without the effect of dispersion properties, which has been verified to be not reasonable. In previous studies, only the physical interpretation that NRBDO method is superior compared to the SF method was given. In this paper, we make attempts to seek a mathematical explanation through design domain in which NRBDO method and SF method search for the optimal design solution, which presents strong evidences why NRBDO theory is more advanced and reasonable method from the aspects of mathematical proof. Eventually, the advancement of the NRBDO and the weakness of the SF method are illustrated with three numerical cases.

Reliability-based design of spread footings on fibre-reinforced clay

ABSTRACTThe potential use of fibres in a number of geotechnical engineering applications is gaining more interest in the geotechnical community. A select application consists of the improvement of soft grounds to mitigate their problematic shear strength characteristics. Extensive experimental work has been reported on the response/behaviour of fibre-reinforced clay (FRC) and was recently complemented by several strength prediction models. The effectiveness of these models has not been thoroughly evaluated yet. The objectives of this study are to (1) quantify the model uncertainty of a newly developed FRC model that is aimed exclusively at predicting the “undrained” shear strength of FRCs, (2) combine the model uncertainty with other conventional sources of uncertainty to assess the reliability levels that are inherent in the ultimate limit state design of spread footings that rest on a top FRC layer underlain by weaker natural soft clay, and (3) recommend factors of safety that would ensure a target reliability level for these footings. Results indicate that the traditional safety factor of 3 should be used with caution as it may not be sufficient to yield the desired level of reliability, particularly for smaller footings, lower applied stresses, larger scales of fluctuation, and larger target reliability indices.

Dynamic Reliability-Based Robust Optimization Design for the Hoist Drum Web Plate

Considering the traditional safety factor method of reliability design can’t well reflect the uncertainty of loads, and error is obvious by using the tension of the wire rope represents the stress state of the hoist drum web plate. Established stress model of the dangerous section of the hoist drum web plate. Deduced reliability index and reliability by using stress & strength interference theory and perturbation method. Sensitivity analysis and robust optimal design was performed on this basis. The results show that the strain on the hoist drum web plate has a great influence on reliability of itself, and the reliability robust optimization design information can be obtained by using strain on web plate and reliability as optimization objectives. These not only provide the theoretical basis for the safety maintenance and design of the hoist, but also have the practical application value for reliable and efficient delivery of hoist.

Technical note: Design flood under hydrological uncertainty

Abstract. Planning and verification of hydraulic infrastructures require a design estimate of hydrologic variables, usually provided by frequency analysis, and neglecting hydrologic uncertainty. However, when hydrologic uncertainty is accounted for, the design flood value for a specific return period is no longer a unique value, but is represented by a distribution of values. As a consequence, the design flood is no longer univocally defined, making the design process undetermined. The Uncertainty Compliant Design Flood Estimation (UNCODE) procedure is a novel approach that, starting from a range of possible design flood estimates obtained in uncertain conditions, converges to a single design value. This is obtained through a cost–benefit criterion with additional constraints that is numerically solved in a simulation framework. This paper contributes to promoting a practical use of the UNCODE procedure without resorting to numerical computation. A modified procedure is proposed by using a correction coefficient that modifies the standard (i.e., uncertainty-free) design value on the basis of sample length and return period only. The procedure is robust and parsimonious, as it does not require additional parameters with respect to the traditional uncertainty-free analysis. Simple equations to compute the correction term are provided for a number of probability distributions commonly used to represent the flood frequency curve. The UNCODE procedure, when coupled with this simple correction factor, provides a robust way to manage the hydrologic uncertainty and to go beyond the use of traditional safety factors. With all the other parameters being equal, an increase in the sample length reduces the correction factor, and thus the construction costs, while still keeping the same safety level.

Numerical modelling to identify key factors controlling interface behaviour of geosynthetic lining systems

Geosynthetics have been extensively used in landfills as a lining system to prevent leachate infiltration into groundwater. In piggy-back landfill expansion (PBLE), consisting of building a new landfill over an existing one, a lining system is implemented between the old and new waste. In this context, interface failure (stability) and deformation (integrity) of the lining system should be considered for the design. Such stability and integrity mainly depend on the PBLE geometry and the mechanical properties of the geosynthetics. Comprehensive numerical modelling simulations were performed to show how these factors influence the shear stresses, shear displacements, translational stability and the axial strains/forces within the various geosynthetics. The numerical modelling was conducted using the finite difference code FLAC 2D, focusing on a typical PBLE and considering geosynthetic interface strain softening, the nonlinear stiffness of geosynthetics, and the differentiation between the compressive and tensile behaviours of geosynthetics. The simulations showed that the lateral length of the PBLE, the type of geomembrane (textured or smooth) and the level of the leachate table in new waste are the factors that most influenced the mechanical behaviour of the lining system and its stability. Finally, a parameter called the stability ratio was proposed as a complement to the traditional factor of safety, to analyse the progressive slippage along the geosynthetic interfaces. The numerical results indicated that interface failure concurrently begins at the rightmost part of the lower flat area of the PBLE and near the corner of the inner slope before spreading out to the left as backfilling progresses.

Design of Geostructural Systems

AbstractThis paper begins with an extensive review of the literature covering the development of design rules for geostructural systems, beginning with traditional global safety factors and developing through partial factors for loads and resistances, and then considering the use of mobilization factors to limit soil strains. The paper then aims to distinguish two possible functions for geotechnical factors: to compensate for the uncertainty regarding soil strength, and to limit soil deformations that could compromise the associated structure before the soil strength can be fully mobilized, whatever it is. At present, design procedures generally conflate and confuse ultimate limit state (ULS) checks and serviceability limit state (SLS) deformation checks. Furthermore, most geotechnical engineers wrongly associate ULS with soil failure rather than with structural failure. The paper addresses this fundamental confusion by advocating mobilizable strength design (MSD), which is based on assumed soil-structure...

A METHOD FOR LINKING SAFETY FACTOR TO THE TARGET PROBABILITY OF FAILURE IN FIRE SAFETY ENGINEERING

Ensuring occupants’ safety in building fires is one of the most important aspects for fire safety engineering. Many uncertainties are inevitably introduced when estimating the occupant safety level, due to the high complexity of fire dynamics and the human behaviour in fires. Safety factor methods are traditionally employed to deal with such uncertainties. This kind of methods is easy to apply but leaves fire safety engineers unsure of the margin by which the design has failed. A method of linking safety factor and probability of failure in fire safety engineering is proposed in this study. An event tree is constructed to analyse potential fire scenarios that arise from the failure of fire protection systems. Considering uncertainties related to fire dynamics and evacuation, the traditional deterministic safety factor is considered as a random variable. Because there is no target probability of failure accepted by the whole fire safety engineering community, the concept of expected risk to life (ERL) is integrated to determine the target probability of failure. This method employs a Monte Carlo Simulation using Latin Hypercube Sampling (LHS) to calculate the required safety factor. A practical case study is conducted using the method proposed in this study.

Reliability Based Design Optimization Modeling Future Redesign With Different Epistemic Uncertainty Treatments

Design under uncertainty needs to account for aleatory uncertainty, such as variability in material properties, and epistemic uncertainty including errors due to imperfect analysis tools. While there is a consensus that aleatory uncertainty be described by probability distributions, for epistemic uncertainty there is a tendency to be more conservative by taking worst case scenarios or 95th percentiles. This conservativeness may result in substantial performance penalties. Epistemic uncertainty, however, is usually reduced by additional knowledge typically provided by tests. Then, redesign may take place if tests show that the design is not acceptable. This paper proposes a reliability based design optimization (RBDO) method that takes into account the effects of future tests possibly followed by redesign. We consider each realization of epistemic uncertainty to correspond to a different design outcome. Then, the future scenario, i.e., test and redesign, of each possible design outcome is simulated. For an integrated thermal protection system (ITPS) design, we show that the proposed method reduces the mass penalty associated with a 95th percentile of the epistemic uncertainty from 2.7% to 1.2% compared to standard RBDO, which does not account for the future. We also show that the proposed approach allows trading off mass against development costs as measured by probability of needing redesign. Finally, we demonstrate that the tradeoff can be achieved even with the traditional safety factor based design.

Partial safety factor system for Tetrapod armor layer depending on shape parameter of extreme wave height distribution

During the last decade, partial safety factor systems have been adopted in the design standards of coastal structures, which are based on probabilistic theories but have a format similar to the traditional safety factor system. Tetrapod is one of the widely used breakwater armor units in the world. The previous partial safety factor system was developed based on limited wave and structure data in several locations. In this paper, a partial safety factor system for Tetrapod armor units is developed by performing reliability analysis and optimal code calibration for 116 breakwater cross-sections and wave conditions in 31 harbors in Korea. The partial safety factors associated with different ranges of the shape parameter of the Weibull extreme wave height distribution for different target probabilities of failure are proposed. For other types of extreme distributions, the skewness of the distribution should be calculated and the partial safety factors of the Weibull distribution of the same skewness could be used (the skewness of the Weibull distribution changes with the shape parameter). The developed system is applied to existing breakwaters to examine its applicability.