Transcript of ABNT NBR Introdução . v. Prefácio. NBR , Projeto e execução de fundações, ABNT, NBR , Estacas – Provas de carga estática, ABNT, NAYLOR, D. J., Finite Elements and. ABNT NBR – ABNT NBR Design and construction of foundations. Publication date: ; Original language.
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The study of pile foundation reliability and safety is based on the analysis of the probabilistic moments, average and coefficient of variation that are associated with the resistant surface. This surface imposes the condition that there is a wbnt population represented by the isolated elements of the foundation. The resistance values and the analyzed foundations that were solicited were abt on data published in the technical literature in which the resistance variable was measured from load tests.
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The number of tests in situ concludes, specifically that, for the diversity of the analyzed foundations, the order statistic can be a sufficiently useful tool to estimate the failure probability of pile foundations in cases in which the number of load tests are smaller. Pile foundation, which is the object of study, is the resistant surface that it is formed by the areas at ahnt pile bases [ 12 ].
The definition of a resistant surface is linked to a global analysis, which considers the structural and geotechnical variabilities [ 3 ] as well as the influence of the environment and human activity on the pile foundation see 6212. Ultimately, the problem may be condensed as part of the study of two random variables: Solicitation can be defined by the effect of actions on structural members [ 4 ], for example internal efforts, stress, strain, the structure as a whole, bending, rotation, etc.
In the case of pile foundations, besides the structural element, there is a continuous medium represented abt the soil massive. In each point of the abbnt a solicitation represented by a state of stress arises, which can be defined by the strain tensor.
The random environmental and functional actions that generate the solicitation variable may be classified according to their origin accidental, sysmic, geotechnical, etc. These are variable throughout the service life of structure. Usually, the weakest link in the pile-soil system is abht soil. In Brazil, the verification of structural strength and geotechnical resistance are normalized by [ 5 ] and [ 6 ]. In pile foundations, the resistance of each single foundation element pile and surrounding soil is not usually known because the design is based on soil strength that comes from standard penetration test procedure, and its verification is based on the load test of a few piles.
Thus, abnr probability of failure is based on resistance data before and after the execution of the qbnt. In this paper, the order statistic [ 910 ] is a tool that will be used to estimate the probability of failure of helical pipes.
This tool proposes estimates of the average and standard deviation for a set of abnnt data; therefore, it could be interesting to use it in pile foundations where the sample number is small: The failure probability is obtained from the relation between the solicitation S and the resistance R. The failure probability, defined by eq.
R and S are independent variables. Modified from [ 12 ]. At point A in Fig. The black area in Fig. The larger the area under this curve, the higher the pfthat is, the lower the reliability of the pile foundation. These measure the distance from the failure condition in terms of standard deviations. When MS is less or equal to zero, the failure occurs see Fig.
From the average and standard deviation of continuous random variables R and Sthe average and standard deviation of MS is determined. It is known that the estimator is a linear operator and that the variance follows the next expression [ 13 ], where X is any random variable. This is shown in eq. The deduction of this relation is shown below [ 1 ].
The Reliability Index is also found in [ 1415 ], as shown in eq. A knowledge of the two first probabilistic moments of the margin of safety and abmt of safety functions is not enough to define the probability density function. It is also necessary to know the shape of the performance function distribution. In practice, it is usual to adopt the hypothesis of normal or lognormal distributions.
The use of a simulation method is another way to estimate the failure probability. One of the methods most commonly used for this purpose is the Monte Carlo simulation, which consists of repeating deterministic solutions. The result is a set of values generated in accordance with their respective probability distributions, which are presumably known. This group of values is similar to a set of information derived from experimental observations. It is possible to statistically treat the generated deterministic values using all statistical inference methods.
Essentially, the Monte Carlo method 612 a random sampling technique, and as in any other sampling process, there is always some error involved. In pile foundations in which the population is finite, it has qbnt verified in practice that the statistical sample, obtained from standard penetration test procedure and dynamic and static load tests, accurately represents the finite population parameters [ 17 ] see Qbnt. Thus, the average and standard deviation of the sample can be taken as the average and standard deviation of the finite population.
In foundations engineering, the sampling plan is basically comprised of the n size of the sample. This is the main factor responsible for the accuracy of the bant between sample and population Fig. This is due to the fact that the sampling design does not meet the defined criteria because of the unknown soil variability.
Contemplating that the sample size can reduce the variability of soil mass is a mistake as this is an intrinsic characteristic of the geological and geotechnical environment.
In practice, we work with a single sample and, therefore, we have only single estimates calculated for this sample. From the sample we can make inferences about the population values through the sampling distribution that are associated with no addiction criteria where the estimator has an expectancy equal to the population value.
We can also make inferences using asymptotic normality when for certain sizes of samples the average sampling distribution is close to the normal distribution: The order statistic is based on ordering the elements of a set and using the extreme values: The main justification for the use of this tool is based on the fact that the number of tests using either the in situ test or load test will generally be small [ 10 ].
It is observed that when the number of the sample is small, the use of the order statistic seems to be consistent. In pile foundation, it is quite unusual that the sample size is equal to the population xbnt.
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If avnt happens, it is for a particular reason such as being orchestrated in academic research. Thus, the foundations dealt with here will aim to use the proposition [ 1 ] and the order statistic [ 1017 ].
We analyzed the results of 13 pile foundations located in several Brazilian states, published by [ 18 ].
The similar feature of the pile foundations is the structural element that, in this case, is a abbt helical pile molded in situ. Therefore, the variability of the strength of the pile foundation is predominantly derived from the geological-geotechnical formation where each building was built. The R and S variables related to resistant surfaces of the pile foundations are shown in Table 2.
It must be 61122 that the resistance is determined from a static load compression test, and the number n corresponds to the amount of load tests for each pile foundation that was analyzed. The table below also includes the global safety factor FSwhich shows abnf the only outcome of case 4 does not meet the recommendation by [ 6 ]: The results obtained with this proposition are compatible with the values found in the literature: Note the accuracy of the results obtained with the simplification [ 1 ] and the Monte Carlo simulation.
When dealing with the quantification of reliability, expressed in terms of failure probability, it is necessary to take into account the size N of the analyzed population. It can be observed that the value N obtained in Table 3 wbnt specific to no conditioning and independence between the resistance and solicitation variables, that is, factors as a group effect are not taken into consideration.
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Using the order statistic based on the maximum and minimum resistance, reliability analysis of the pile foundations is indicated in Table 4. Observing the global safety factors in Tables 2 and 4, we can see that there has been no significant change because the average values of resistance and solicitation inferred by order statistic approached the proposition [ 1 ]. However, analyzing Tables 3 2nd column and 4 11th columnwe can see agreement on the values of reliability index expressed by the order statistic and the proposal [ 1 ].
Therefore, generally, it is concluded that the order statistic is a promising tool to estimate the finite population parameters. Note that in many countries, it remains common to verify the safety of foundations using global safety factors. However, it is important to include an estimation of the failure probability in this verification and still ensure that the amount of tests carried out for this end is sufficient to produce a reliable estimate.
This work presented the implementation of the order statistic to evaluate the variability of the resistance and solicitation values on continuous helical type pile foundations. Therefore, it has estimated the probability of failure of such structures. From the above analysis, we can highlight the following points:. In practice, the population size of a pile foundation is much larger than the number of samples, either in the design stage in situ testsor in the execution of the pile foundation stage load test.
Facing the proposition [ 1 ], the order statistic seems to be a promising tool to estimate the population parameters for the resistance of isolated foundation elements. Jounal of Geotechnical and Geoenvironmental Engineering, 4pp. Proceedings of Uncertainty in the Geologic Environment: Geotechnical Special Publication, 58, Basis of Structural Design.
European Committee for Standardization. Projeto de Estruturas de Concreto – Procedimento. Journal of Geotechnical Engineering, 2pp. Canadian Geotechnical Journal, 32 1pp. Harper e Row, P. EdScrew piles – Installation and design in stiff clay. Proceedings of the Symposium on Screw Piles.
Transactions of ASCE, 1pp. H-S and Tang, W. Decision, Risk and Reliability. Structural Safety, 19 3pp. This is an open-access article distributed under the terms of the Creative Commons Attribution License. Services on Demand Article.
English pdf Article in xml format Article references How to cite this article Automatic translation Send this article by e-mail. Articles Use of the abnh statistics when predicting pile foundation failure probability. Abstract The study of pile foundation reliability and safety is based on the analysis of the probabilistic moments, average and coefficient of variation that are associated with the resistant surface.
Introduction Pile foundation, which is the object of study, is the resistant surface that it is formed by the areas at the pile bases [ 1abmt ].
Relation between the safety factor and reliability index The failure probability is obtained from the relation between the solicitation S and the resistance R.