Reliability-based Safety Factor Research Articles

Probabilistic analysis of near-field blast loads considering fireball surface instabilities and stochastic detonator location

High speed video analysis of near-field explosive detonations displays distinct stages of emergent hydrodynamic instabilities in the fireball/shock-air interface. Typically, beyond 10 charge radii, the instabilities experienced large growths giving rise to more chaotic behaviour of the interface and thus an increasing uncertainty in surface velocity. These surface instabilities are suggested as the primary cause of blast parameter variability in the near-field. However, as a deterministic tool, numerical simulation of the detonation process and subsequent blast wave propagation is not able to replicate the stochastic nature of fireball surface instabilities and hence near-field blast parameter variability. Therefore, it is necessary to develop new methods to simulate and characterise the stochastic features of the fireball/shock-air interface. This paper proposes an algorithm to generate an explosive charge element with random shape in finite element model in order to simulate irregularities in the fireball/shock-air interface, and therefore produce variabilities comparable to those from direct observation. The effect of chaotic fireball/shock-air interface on near-field loading is explored through a large number of numerical simulations in order to investigate the statistical distribution of parameters including peak overpressure and impulse. Subsequently, the effect of stochastic detonator location is explored in a similar manner. A computational procedure based on the Monte Carlo Method is proposed to establish a probabilistic model of near-field blast loads, termed PSL-Blast. The reliability of design blast loads calculated using the UFC 3-340-02 design manual is then estimated using PSL-Blast, which suggests that reliability decreases with decreasing scaled distance. Finally, reliability-based safety factors of blast loads are calculated based on different blast settings.

Calibration of reliability-based safety factors for sand boiling in excavations

This study calibrated the required factors of safety of five analysis methods for sand boiling using reliability theory. The factors of safety computed by the five analysis methods were compared with the results of a series of sand boiling model tests. The comparison shows that rigorous methods (Terzaghi’s and Harza’s methods) were more accurate in predicting the factors of safety compared to the simplified methods (Harr’s, simplified Terzaghi’s, and simplified Harza’s methods). The statistics of the model factor for each method, defined as the actual factor of safety divided by the computed one, was calibrated by the model test results. These statistics were then used to establish the relationship between the target probability of failure and the required factor of safety by reliability theory. Verification using a full-scale sand boiling case history shows that the required factor of safety calibrated by the reliability theory was more reasonable than the required factors of safety in references and design codes.

A reliability-based assessment of live bed scour at bridge piers

ABSTRACT Bridge pier scour is an important issue for safety evaluation of bridges. The existing scour depth prediction equations for bridge piers are mostly deterministic in nature, which do not incorporate the uncertainties due to scour parameters, selection of model and limited information about data. To incorporate these uncertainties, a reliability-based assessment of bridge pier scour is required. An attempt has been made herein to develop a reliability-based scour depth prediction model for live bed scour at bridge piers. An object-oriented constrained optimization technique of the first-order reliability method has been used for the reliability analysis. The influence of uncertainties, type of probability distribution and correlation among the basic input parameters on the failure probability have been studied in detail. To achieve the desired safety level in the design of pier foundation for the live bed scour, the reliability-based safety factor is proposed. A sensitivity analysis has also been carried out to obtain the effect of the individual random variables on the reliability of pier scour.

Reliability Analysis of Local Scour at Bridge Pier in Clay-Sand Mixed Sediments

Bridge pier scouring is an important issue for safety evaluation of bridges. The existing equations for bridge pier scour prediction are mostly deterministic in nature, which do not incorporate the uncertainties in various parameters of scouring. A methodology for reliability analysis of bridge pier against scour in cohesive sediments incorporating the uncertainties of the model and input parameters are presented herein using efficient spreadsheet algorithm for first order reliability method (FORM). The influence of uncertainties, the nature of probability distribution and correlation of basic input parameters on failure probability and reliability index has been studied and described briefly herein. A sensitivity analysis was also carried out to obtain the effect of the individual random variables on the reliability of pier scour. To achieve the desired safety level in the design of pier foundation, the reliability-based safety factor is proposed.

Reliability-based safety factor for metallic strip flexible pipe subjected to external pressure

Reliability-based safety factors for metallic strip flexible pipes(MSFP) subjected to external pressure are calibrated in this paper. The partial safety factors of such pipes are obtained by introducing a target reliability index and using a combination of Monte-Carlo simulation and FORM. The relationship between the safety factors and the coefficient of variation for key basic variables as well as the impact of different distribution types for both the resistance and load effect parameters on the calibrated results are investigated. Recommended design safety factor for MSFP is given similar to the widely used design safety factor for conventional metallic pipes. The calibration process presented in this paper is relatively easy to understand and to carry out. This also applies to cases with multiple components and even requiring complex iterations in relation to the mechanical model. The results obtained here can provide some guidance in connection with manufacturing procedures at the initial design stage of the MSFP.

Probabilistic Failure Prediction of High Strength Steel Rocket Motor Cases

In traditional deterministic analysis, uncertainties are either ignored or accounted by applying conservative assumptions. In those cases, only the mean values or nominal values are used in the analysis. Currently, the operating pressure of high strength steel rocket motor cases is predicted by arbitrarily assumed safety factor based on experience. This leads to over weight of motor cases and cost. Hence a methodology is required to predict the operating pressure more accurately by considering optimal safety factor. This paper presents the probabilistic failure assessment methodology to predict the safety factor for the specified reliability using various failure pressure prediction equations. In this study, the scatter in the yield strength, ultimate strength, and thickness of the structure is considered. Monte–Carlo simulation method is used to perform the probabilistic failure assessment. A suitable failure pressure prediction equation is identified among thirteen equations using stress–strength interference theory based on the statistical measure of the predicted and literature test failure pressure. The reliability-based safety factor is computed for the specified reliability with the use of identified failure pressure prediction equation. The safe operating pressure of steel rocket motor cases is computed for the specified reliability levels.

A Study on the Holding Capacity Safety Factors for Torpedo Anchors

The use of powerful numerical tools based on the finite‐element method has been improving the prediction of the holding capacity of fixed anchors employed by the offshore oil industry. One of the main achievements of these tools is the reduction of the uncertainty related to the holding capacity calculation of these anchors. Therefore, it is also possible to reduce the values of the associated design safety factors, which have been calibrated relying on models with higher uncertainty, without impairing the original level of structural safety. This paper presents a study on the calibration of reliability‐based safety factors for the design of torpedo anchors considering the statistical model uncertainty evaluated using results from experimental tests and their correspondent finite‐element‐based numerical predictions. Both working stress design (WSD) and load and resistance factors design (LRFD) design methodologies are investigated. Considering the WSD design methodology, the single safety is considerably lower than the value typically employed in the design of torpedo anchors. Moreover, a LRFD design code format for torpedo anchors is more appropriate since it leads to designs having less‐scattered safety levels around the target value.

Reliability analysis of scour downstream of a ski-jump bucket

The available equations for scour prediction downstream of a ski-jump bucket are mostly deterministic in nature and do not consider uncertainties of various scouring parameters adequately. A reliability-based assessment of scour in such situations is of paramount importance in examining the relationship between safety factor and reliability, which are considered to be key parameters for decisions in foundation design. This paper presents a methodology for the reliability assessment of scour downstream of a ski-jump bucket using the first-order reliability method (FORM). To study the influence of various random variables on the reliability against scouring, a sensitivity analysis is carried out. To achieve a desirable safety level in the design of a foundation, reliability-based safety factors are also proposed. The influence of correlation among the random variables on the reliability is also studied.

A reliability-based assessment of bridge pier scour in non-uniform sediments

The available scour equations for bridge pier are mostly deterministic in nature, which do not consider uncertainties of various scouring parameters adequately. A reliability-based assessment of bridge pier scour depth is of paramount importance in examining the relationship between safety factor and reliability, which are considered to be key parameters for decision-making in bridge foundation design. A methodology for the reliability assessment of bridge pier scour in non-uniform sediments are presented using the First Order Reliability Method (FORM). To study the influence of various random variables on the pier reliability against the scouring, a sensitivity analysis was carried out. To achieve a desirable safety level in the design of pier foundation, reliability-based safety factors are also proposed. The influence of the correlation among the random variables on the pier reliability was also assessed.

Reliability-based design model applied to mechanistic empirical pavement design

Most state highway agencies are being encouraged to change their pavement design procedures from the empirical-based procedure such as the AASHTO to mechanistic-empirical (M-E). Several issues need to be resolved before implementing M-E pavement design procedure in practice. One of the issues is that the design procedure should provide a consistent pavement performance level considering inherent variability associated with design input parameters and systematic bias of the design procedure itself. For a complete M-E pavement design procedure, the effects of input variability and model bias on predicted pavement performance must be quantified and considered. Some of the key principles for applying the reliability concept to M-E pavement design are presented in this paper. In particular, the selection of an appropriate reliability assessment technique and careful characterization of design input variability were considered because of their central role in calculating the reliability of pavement performance and determining the reliability-based safety factor of the pavement design procedure. In this paper, a reliability analysis model for evaluating uncertainties of existing M-E flexible pavement design procedures and a reliability-based pavement design approach using Load and Resistance Factor Design (LRFD) format are addressed.

A reliability-based safety factor for aircraft composite structures

Abstract The safety factor is widely used in aircraft design. Theoretically, design by using structural system reliability is much more reasonable than that based on the safety factor. However, because of the lack of the statistical data from the strength of materials used and the applied loads, design concepts based on the safety factor will still dominate for a period. The present safety factor for metallic aircraft structures is generally 1.5, but no final conclusions have yet been reached for the safety factor for composite structures. Several methods for determining the safety factor for composite structures are discussed in the paper. A technique based on structural system reliability is presented. This safety factor is influenced not only by the scatter of strength and exceptionally large loads but also the failure modes of the composite laminates. The paper also discusses the safety factor which provides the same reliability for composite structures as the 1.5 safety factor for the metallic structures. The value of the safety factor for aircraft structural design when using composite laminates is recommended.