Error Evaluation and Suitability Assessment of Common Reliability Methods in the Case of Shallow Foundations

Abstract

A geotechnical structure’s reliability index calculated using identical input parameters and assumptions can significantly vary as a function of the used method. The different approaches to solving the reliability problem could result in an error which depends on many factors. The most important error sources are the complexity of the performance function, the number of random variables, their mutual correlations, and marginal statistical distributions. A review of relevant literature in the field of reliability in geotechnical engineering revealed a lack of information on the errors of individual reliability methods for geotechnical problems and general criteria for assessing their suitability concerning the error size. The paper defines the reliability method error and proposes criteria for assessing the suitability of reliability methods in geotechnical engineering. Based on the proposed criteria, the suitability of common reliability methods was evaluated in the example of a shallow foundation, analysed according to Eurocode 7, DA 3, such that Ed=Rd. It is shown that due to the mathematically complex expression of the reliability integral, methods that are easier to use result in a larger error and are not suitable for a reliability analysis of shallow foundations. Sophisticated methods are more accurate but require specific knowledge and resources that are not often used in daily engineering practice.

Reliability of Municipal Solid Waste Landfills within the Eurocode Framework

“…The coefficients of variation for soil strength parameters according to [31] range from 0.1 to 0.5% for cohesion, and for the friction angle, they range from 0.05 to 0.2% [20,29]. For MSW, these values are significantly higher, as shown in Table 4.…”

“…where X m is the mean value of the property and COV X is the coefficient of variation in the property. In structural reliability analyses, variables with a larger coefficient of variation exert a greater impact on the outcomes, whereas variables with a smaller coefficient of variation have a lesser impact [2,29]. Consistent with this principle, in the reliability analyses conducted within this study, both the friction angle and cohesion are treated as random variables, and the MSW unit weight is considered a constant.…”

The Role of Geotechnical Monitoring at Design of Foundation Structures and their Verification – Part 2

“…When assessing important structures of significant construction types, attention should be paid to the determination of the reliability index through an appropriate method of the statistical probability of failure. It is worth noting that this design principle has already been implemented in the USA and is called Load and Resistance Factor Design (LRFD), which allows a more accurate reliability assessment than the currently valid principles in EC7 [20,25,26]. Reliability based methods are subject of current development in geotechnics, concerning previously described spread foundations, foundations on improved soil [27], and deep foundations [28][29][30][31], but also slopes [32], and soil retaining structures [33][34][35].…”

Modified, Reliability-Based Robust Geotechnical Design Method, in Accordance with Eurocode 7

“…The inverse Nataf transformation, which is a part of IPEM, is required only at the estimating points, and can be done simply, e.g., by using the built-in function of Microsoft Excel, or the Python program language used with the "SciPy" package. Since the accuracy of the calculations of β is highly dependent on the method used [19], the accuracy of IPEM for ULS and SLS of shallow foundation was examined. The Monte Carlo method was chosen as the control method, and the results are given in Tables 3 and 4.…”