تجزیه و تحلیل حساسیت از قابلیت اطمینان شمع بارگذاری شده عمودی

The purpose of this paper is to examine the influence of geotechnical uncertainties on the reliability of vertically loaded pile foundations and the use of this information in decision-making support, especially when gathering the information necessary for reliability analyses. Two case studies of single pile foundations were selected, and each uncertainty source was investigated to identify which are the most important and influential in the evaluation of vertical pile resistance under axial loading. Reliability sensitivity analyses were conducted using FORM (the first-order reliability method) and MCS (Monte Carlo simulations). The characterisation of uncertainties is not an easy task in geotechnical engineering. The aim of the analyses described in this paper is to optimise resources and investments in the investigation of the variables in pile reliability. The physical uncertainties of actions, the inherent variability of soil and model error were assessed by experimental in situ standard penetration tests (SPT) or from information available in the literature. For the cases studied, the sensitivity analysis results show that, in spite of the high variability of the soils involved, model error also plays a very important role in geotechnical pile reliability and was considerably more important than soil variability in both case studies. From a comparison of the two reliability methods (FORM and MCS), it was concluded that FORM is applicable in simple cases and as a first approach because it is an approximate method and sometimes does not have the capability to incorporate every detail of the problem, namely a specific probability density function or more specific limit conditions.

Pile foundations are often used for important structures, and thus, reliability evaluation is an important aspect of the design of such structures. Unlike the approach to reliability evaluation used in structural engineering, the traditional procedure used in geotechnical design addresses uncertainties through high global or partial safety factors, mostly based on past experience. This approach to addressing uncertainties does not provide a rational basis for understanding their influence on design. For this reason, and because of regulation codes (JCSS, 2001, CEN, 2002a, Watabe et al., 2009 and Honjo et al., 2010), and social concerns (such as sustainability), geotechnical engineers need to improve their ability to deal with uncertainties and probabilities to help with decision-making. Reliability methods have become increasingly important as decision support tools in civil engineering and in geotechnical applications, especially over the past two decades (Einstein, 2001, Honjo et al., 2002, Paikowsky, 2004, Honjo et al., 2005, Yang, 2006, Cherubini and Vessia, 2007, Fenton and Griffiths, 2007, Phoon, 2008, Juang et al., 2009, Honjo et al., 2010b, Huang et al., 2010 and Wang, 2011). Reliability analyses are conducted for the purpose of determining the probability of reaching a behavioural limit and involve introducing estimates of geometric, material and actions variability into the design process. The main benefit of reliability analysis is that it provides quantitative information about the parameters that most significantly influence the behaviour under study. This makes risk control, the determination of the potential causes of adverse effects on the structure, possible. The design of pile foundations still involves many limitations and uncertainties, particularly when there is not enough investment in soil characterisation and pile load tests. In addition to the uncertainties associated with soil characterisation (pile design based on insufficient data and using theoretical approaches that do not characterise the model error well), physical, statistical, spatial and human uncertainties exist. However, because it is technically and economically impossible to produce designs of pile foundations in the most unfavourable of cases, it is the engineer's goal to minimise the risk and limit it to an acceptable level in the most economical manner possible. First developed for other areas of engineering design, reliability theory needs to be adapted to the needs and objectives of geotechnical engineering. This requires consideration of spatial correlations and attention to the influence that the number of samples analysed has on the quantification of the standard deviations and means of geotechnical parameters. Although the extent to which this can be accomplished depends on the engineer's knowledge and the project's budget for investigation, geotechnical engineering definitely benefits from the consideration of reliability in design (Christian, 2004 and Najjar and Gilbert, 2009). The primary purpose of this paper is to demonstrate the application of reliability methods to two distinct case studies of vertical single pile foundations under axial loading. This paper also presents a simple and practical approach to performing reliability-based design (RBD) in geotechnical problems and obtaining valuable information from it. For that purpose, sensitivity analyses were conducted to study the influence of each uncertainty type. In addition, two well-known RBD methods, the first-order reliability method (FORM) and Monte Carlo simulations (MCS) were applied to the case studies for comparison. Another purpose of this paper is to demonstrate the advantages of employing RBD in the decision-making process for pile foundation design. The decision-making related to the economic and research investments required for gathering the information necessary to characterise the uncertainties associated with important random variables, in both pile design and its reliability, is facilitated by this type of balanced reliability analysis. Therefore, this work makes a significant contribution to the application of RBD to pile design. This type of approach is important not only for decision-making but also for identifying the direction in which geotechnical design research should proceed (Honjo, 2011).

This paper describes the application of reliability-based methodologies and sensitivity analyses applied to two distinct case studies of vertically loaded single piles (a bored pile and a steel pipe pile). This work is intended to contribute to preventing the loss of intuitive understanding when applying these tools to design problems, which is an important issue in geotechnical engineering. This work is also intended as an aid to pile design decision-makers in assessing the uncertainties associated with the random variables that most influence both the probability of failure and pile behaviour. Characterisation of uncertainty in geotechnical problems is a difficult task, and the values recommended in the literature often cannot be applied to a particular case under study due to high soil variability. Considering the physical uncertainties of actions, the inherent soil variability characterised through SPT results and the bearing capacity (resistance) model error for the reliability studies presented, the following summary statements can be made: - The application of two reliability methods (FORM and MCS), repeated for different pile lengths and different combinations of the uncertainties, reveals that FORM was only successfully applied to case study 1 (the bored pile). This suggests that FORM can be used as a first approach to reliability analysis. However, for more complex analyses, such as those conducted for case study 2 (a steel pipe pile), MCS should be used for the assessment of the probability of failure. - The reliability indexes obtained for the actual pile lengths were β=1.88 (case study 1, 6 m) and β=3.2 (case study 2, 43.5 m). While the reliability index in case study 2 satisfied the standard recommendations, the reliability index in case study 1 did not. This can be explained by the fact that case study 1 is an experimental field case study in which failure is obviously of minor consequence. The results of the sensitivity analyses for both case studies, using both FORM and MCS, confirm that not considering spatial correlation is conservative but technically incorrect. In addition, the results of these two case studies show that soil uncertainties were not as important as was expected. However, model uncertainties contributed greatly to the probability of failure for both cases studied. Meanwhile, the contribution of toe and side uncertainties depends greatly on the type of pile and the ratio between these two resistances.