Towards a New Limit State Function for Determining the Failure Pressure of a Pipeline Containing Mechanical Damage

Author(s):  
Chas Jandu ◽  
Bob Francini ◽  
Mike Taylor ◽  
Andrew Francis

Mechanical damage is generally considered to be damage that occurs to a pipeline when mechanical excavation, drilling, or boring equipment impinges on a buried pipeline creating scrapes, abrasions, gouges, punctures, and/or dents in the pipeline. Above ground pipelines may also be damaged in a similar manner from impacts by vehicles or projectiles or by willful acts of vandalism. In some cases, immediate failure will occur resulting in potentially catastrophic consequences. It is thus important to understand the conditions that would lead to such a failure in order to ensure that design parameters are selected such that immediate failures occur very rarely. In cases where the damage does not create an immediate failure or the release of gas, the concern generally is that a delayed failure will occur because the integrity of the pipeline has been significantly compromised. In such cases, the possibility is that repeated pressure fluctuations, small increases in pressure, or time-dependent creep will erode whatever margin of safety remains and a failure will ensue. Particularly unsettling are the cases in which damage of this nature is encountered through some form of inspection where the source of the damage and its time of creation are unknown. In such cases, the operator of the pipeline will generally not know what margin of safety remains. There are a number of models in existence that may be used to predict both instantaneous and delayed failures due to mechanical damage and indeed these have been used quite extensively as the basis of repair criteria and for determining safe pipeline operating conditions. Nonetheless, there are significant elements of uncertainty associated with these models and for this reason an adequate reserve factor needs to be incorporated or recourse must be made to probabilistic approaches that address such uncertainty. However, since pipelines are getting older and in some cases are being operated at higher pressures than they were previously, there is a requirement to obtain a better understanding of the significance of mechanical damage. In view of this Pipelines Research Council International (PRCI) and other research bodies, such as European Pipelines Research Group (EPRG), are taking a keen interest in this topic. To this end, PRCI have commissioned an extensive research program to investigate all key aspects of both instantaneous and delayed failures. Kiefner and Associates Incorporated (KAI) and Andrew Francis and Associated Ltd (AFAA) were commissioned to investigate the conditions that cause instantaneous failures. The purpose of this paper is to describe the approach that was adopted and the formulation of the new model that emerged from study. This model is being validated through testing which is currently ongoing.

2018 ◽  
Vol 140 (4) ◽  
Author(s):  
Hamoon Azizsoltani ◽  
Achintya Haldar

A novel reliability evaluation procedure of lead-free solders used in electronic packaging (EP) subjected to thermomechanical loading is proposed. A solder ball is represented by finite elements (FEs). Major sources of nonlinearities are incorporated as realistically as practicable. Uncertainties in all design variables are quantified using available information. The thermomechanical loading is represented by five design parameters and uncertainties associated with them are incorporated. Since the performance or limit state function (LSF) of such complicated problem is implicit in nature, it is approximately generated explicitly in the failure region with the help of a completely improved response surface method (RSM)-based approach and the universal Kriging method (KM). The response surface (RS) is generated by conducting as few deterministic nonlinear finite element analyses as possible by integrating several advanced factorial mathematical concepts producing compounding beneficial effect. The accuracy, efficiency, and application potential of the procedure are established with the help of Monte Carlo simulation (MCS) and the results from laboratory investigation reported in the literature. The study conclusively verified the proposed method. Similar studies can be conducted to fill the knowledge gap for cases where the available analytical and experimental studies are limited or extend the information to cases where reliability information is unavailable. The study showcased how reliability information can be extracted with the help of multiple deterministic analyses. The authors believe that they proposed an alternative to the classical MCS technique.


2015 ◽  
Vol 61 (3) ◽  
pp. 133-147 ◽  
Author(s):  
A. Dudzik ◽  
U. Radoń

AbstractThe study deals with stability and dynamic problems in bar structures using a probabilistic approach. Structural design parameters are defined as deterministic values and also as random variables, which are not correlated. The criterion of structural failure is expressed by the condition of non-exceeding the admissible load multiplier and condition of non-exceeding the admissible vertical displacement. The Hasofer-Lind index was used as a reliability measure. The primary research tool is the FORM method. In order to verify the correctness of the calculations Monte Carlo and Importance Sampling methods were used. The sensitivity of the reliability index to the random variables was defined. The limit state function is not an explicit function of random variables. This dependence was determined using a numerical procedure, e.g. the finite element methods. The paper aims to present the communication between the STAND reliability analysis program and the KRATA and MES3D external FE programs.


2011 ◽  
Vol 147 ◽  
pp. 197-202 ◽  
Author(s):  
Jiang Zhou ◽  
Jing Cao ◽  
Yu He ◽  
Jie Song

Lacking of explicit limit state function (LSF) will result large quantities of computational efforts for a FEAM based structural reliability analysis. An improved response surface (RS) method is proposed to analyze the failure probability of foundation pit through combining uniform design (UD) and non-parametric regression (NPR). Deferent levels of design parameters are first delicately selected according to UD and then FEAM is used to analysis corresponding pit response parameters including maximum lateral displacement of wall, settlement of ground, safety factor of overall stability, safety factors of against overturning, heave and piping. The RS relationship is then established through NPR based on inputs and responses. At last, a direct Mont Carlo Simulation is carried out to obtain the probability density function of response parameters.


Author(s):  
Andrew Francis ◽  
Chas Jandu ◽  
Marcus McCallum

Our Client was commissioned to construct an onshore high pressure gas pipeline. The pipeline was to be about 50km in length, 1066mm diameter, 15.88mm nominal wall thickness and constructed from X65 material. During the route selection phase it was discovered that it would be very difficult to avoid passing the pipeline through a locally highly populated area. In view of this it was naturally decided that the pipeline should be constructed from heavy wall sectioned pipe to mitigate the threat of failure due to causes including mechanical damage and corrosion. However, there was still a concern that the residual risk, even when the above mitigating measure had been taken, would still be unacceptably high. In view of this Andrew Francis & Associates Ltd (AFAA) were commissioned to assess the remaining risk levels using a quantified risk assessment technique in accordance with the UK pipeline design code, IGE/TD/1 Edition 4, which provides for the use of such techniques. The technique used by AFAA involved detailed Structural Reliability Analysis (SRA) combined with an assessment of the consequences of failure. AFAA began the study by identifying the possible failure modes and these included mechanical damage, external corrosion, fatigue crack growth and AC induced corrosion. However, discussions were held between AFAA and the Client and after giving due consideration to the benefits of modern construction standards, and the use of Fusion Bonded Epoxy (FBE) coating, it was agreed that the only significant threat to integrity was mechanical damage. AFAA used SRA to determine the likelihood of failure due to mechanical damage based on a state-of-art-limit state function taking account of key areas of uncertainty including variations in defect dimensions and material properties. A consequence model was used to determine the possible effects on the local population if a rupture of the pipeline was to occur. The consequence model was used to determine the amount of thermal dose that personnel, in the vicinity of the release, might receive, taking account of the transient nature of the gas flow. The mitigating effects of nearby buildings that would afford shelter from the effects of the thermal radiation levels were naturally taken into account. The results were expressed in terms of an F/N curve and assessed against the risk criteria contained in IGE//TD/1. It was concluded from the analysis that the proposed design did not pose an unacceptable level of risk and moreover that part of the proposed heavy wall section was unnecessary. However, in the interests of conservatism our customer proceeded with the original design. This paper describes the modelling technique used by AFAA and clearly presents the results and conclusions of the analysis.


Author(s):  
Singiresu S. Rao ◽  
Yang Zhou

Abstract The performance of a mechanical or structural system can be improved through a proper selection of its design parameters such as the geometric dimensions, external actions (loads) and material characteristics. The computation of the reliability of a system, in general, requires a knowledge of the probability distributions of the parameters of the system. It is known that for most practical systems, the exact probability distributions of the parameters are not known. However, the first few moments of the parameters of the system may be readily available in many cases from experimental data. The determination of the reliability and the sensitivity of reliability to variations or fluctuations in the parameters of the system starts with the establishment of a suitable limit state equation. This work presents a reliability analysis approach for mechanical and structural systems using the fourth order moment function for approximating the first four moments of the limit state function. By combining the fourth-order moment function with the probabilistic perturbation method, numerical methods are developed for finding the reliability and sensitivity of reliability of the system. An automobile brake and a power screw are considered for demonstrating the methodology and effectiveness of the proposed computational approach. The results of the automobile brake are compared with those given by the Monte Carlo method.


2014 ◽  
Vol 41 (10) ◽  
pp. 845-855 ◽  
Author(s):  
Sungho Mun

Reliability assessment has been used to evaluate the performance of pavement structures. However, probabilistic inversion analysis of pavement structure design has not yet been tested to determine the design parameters of the pavement performance function, given a specified reliability index. In this study, a limit state function numerical calculation and the inversion technique of the Nelder–Mead simplex algorithm were used to determine the design parameters for the pavement performance function. The method of moments was used to develop the forward limit state function, which was then compared to Monte Carlo simulations; the comparison indicated good agreement between the two methods. Additionally, several cases were studied to determine the design parameters of the pavement performance function for the reliability index specified in this study. The case studies indicated that the structure number significantly affected the pavement performance function.


2011 ◽  
Vol 255-260 ◽  
pp. 3421-3425
Author(s):  
Shi Bin Ma ◽  
Kai Wang ◽  
Yang Feng Wu ◽  
Lian Yu Wei ◽  
Ming Wei Zhang

The design of asphalt pavements in china is currently based on the multilayered elastic method, which is analytical in nature and yields stresses, strains, and deflections in the pavement system for a particular loading condition and pavement geometry, which are compared with established failure criteria to determine the performance of the given pavement. This design approaches is deterministic. In this paper, typical asphalt pavement structure reliability analysis was performed in which factors that affect pavement reliability regarded as input random , pavement surface deflection, layers of bottom stress and limit state function regarded as output variables , by reliability tool infinite element analysis, base on Monte Carlo’s Latin hypercube sampling method.At last the paper pertinently offered decision basis for improve the reliability of pavement structure and important reference values for drafting and selecting of asphalt pavement design parameters through calculating the reliability of pavement structure, sensitivity analysis of the design parameters is made.


Author(s):  
Seyede Vahide Hashemi ◽  
Mahmoud Miri ◽  
Mohsen Rashki ◽  
Sadegh Etedali

This paper aims to carry out sensitivity analyses to study how the effect of each design variable on the performance of self-centering buckling restrained brace (SC-BRB) and the corresponding buckling restrained brace (BRB) without shape memory alloy (SMA) rods. Furthermore, the reliability analyses of BRB and SC-BRB are performed in this study. Considering the high computational cost of the simulation methods, three Meta-models including the Kriging, radial basis function (RBF), and polynomial response surface (PRSM) are utilized to construct the surrogate models. For this aim, the nonlinear dynamic analyses are conducted on both BRB and SC-BRB by using OpenSees software. The results showed that the SMA area, SMA length ratio, and BRB core area have the most effect on the failure probability of SC-BRB. It is concluded that Kriging-based Monte Carlo Simulation (MCS) gives the best performance to estimate the limit state function (LSF) of BRB and SC-BRB in the reliability analysis procedures. Considering the effects of changing the maximum cyclic loading on the failure probability computation and comparison of the failure probability for different LSFs, it is also found that the reliability indices of SC-BRB were always higher than the corresponding reliability indices determined for BRB which confirms the performance superiority of SC-BRB than BRB.


2012 ◽  
Vol 532-533 ◽  
pp. 408-411
Author(s):  
Wei Tao Zhao ◽  
Yi Yang ◽  
Tian Jun Yu

The response surface method was proposed as a collection of statistical and mathematical techniques that are useful for modeling and analyzing a system which is influenced by several input variables. This method gives an explicit approximation of the implicit limit state function of the structure through a number of deterministic structural analyses. However, the position of the experimental points is very important to improve the accuracy of the evaluation of failure probability. In the paper, the experimental points are obtained by using Givens transformation in such way these experimental points nearly close to limit state function. A Numerical example is presented to demonstrate the improved accuracy and computational efficiency of the proposed method compared to the classical response surface method. As seen from the result of the example, the proposed method leads to a better approximation of the limit state function over a large region of the design space, and the number of experimental points using the proposed method is less than that of classical response surface method.


Sensors ◽  
2021 ◽  
Vol 21 (2) ◽  
pp. 536
Author(s):  
Kenneth A. Goldberg ◽  
Antoine Wojdyla ◽  
Diane Bryant

New, high-coherent-flux X-ray beamlines at synchrotron and free-electron laser light sources rely on wavefront sensors to achieve and maintain optimal alignment under dynamic operating conditions. This includes feedback to adaptive X-ray optics. We describe the design and modeling of a new class of binary-amplitude reflective gratings for shearing interferometry and Hartmann wavefront sensing. Compact arrays of deeply etched gratings illuminated at glancing incidence can withstand higher power densities than transmission membranes and can be designed to operate across a broad range of photon energies with a fixed grating-to-detector distance. Coherent wave-propagation is used to study the energy bandwidth of individual elements in an array and to set the design parameters. We observe that shearing operates well over a ±10% bandwidth, while Hartmann can be extended to ±30% or more, in our configuration. We apply this methodology to the design of a wavefront sensor for a soft X-ray beamline operating from 230 eV to 1400 eV and model shearing and Hartmann tests in the presence of varying wavefront aberration types and magnitudes.


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