A Distribution for Instantaneous Failures

A new one-parameter distribution is proposed in this paper. The new distribution allows for the occurrence of instantaneous failures (inliers) that are natural in many areas. Closed-form expressions are obtained for the moments, mean, variance, a coefficient of variation, skewness, kurtosis, and mean residual life. The relationship between the new distribution with the exponential and Lindley distributions is presented. The new distribution can be viewed as a combination of a reparametrized version of the Zakerzadeh and Dolati distribution with a particular case of the gamma model and the occurrence of zero value. The parameter estimation is discussed under the method of moments and the maximum likelihood estimation. A simulation study is performed to verify the efficiency of both estimation methods by computing the bias, mean squared errors, and coverage probabilities. The superiority of the proposed distribution and some of its concurrent distributions are tested by analyzing four real lifetime datasets.

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

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.

Weibull Model Allowing Nearly Instantaneous Failures

A generalized Weibull model that allows instantaneous or early failures is modified so that the model can be expressed as a mixture of the uniform distribution and the Weibull distribution. Properties of the resulting distribution are derived; in particular, the probability density function, survival function, and the hazard rate function are obtained. Some selected plots of these functions are also presented. An R script was written to fit the model parameters. An application of the modified model is illustrated.

Failure of Compressible/Dilatant Geomaterials

The paper presents a general constitutive equation for geomaterials allowing to describe dilatancy and/or compressibility during transient and stationary creep. The constitutive equation also describes the instantaneous response of the geomaterial, work-hardening during transient creep, instantaneous failure and creep failure. The damage produced by dilatancy is used to formulate a criterion for creep failure. Thus ultimate failure may be involved in various ways, depending on the initial and boundary conditions and certainly on the constitutive equation. Typical mining engineering examples are given. First is discussed the creep closure of a deep vertical cylindrical cavern, various possible instantaneous failures, creep failure, and spreading of damage by dilatancy into the rock mass. Second example discusses the instantaneous failure and creep failure around a horizontal tunnel, and the location where damage by dilatancy is more pronounced. The third example presents the case of a rectangular-like shaped cavern.