Reducing Statistical Uncertainty in Elastic Settlement Analysis of Shallow Foundations Relying on Targeted Field Investigation: A Random Field Approach

Abstract

The present paper deals with the practical problem of reducing statistical uncertainty in elastic settlement analysis of shallow foundations by relying on targeted field investigation with the aim of an optimal design. In a targeted field investigation, the optimal number and location of sampling points are known a priori. As samples are taken from the material field (i.e., the ground), which simultaneously is a stress field (stresses caused by the footing), the coexistence of these two fields allows for some points in the ground to better characterize the serviceability state of structure. These points are identified herein through an extensive parametric analysis of the factors controlling the magnitude of settlement; the number of different cases considered was 3318. This is done in an advanced probabilistic framework using the Random Finite Element Method (RFEM) properly considering sampling of soil property values. In this respect, the open source RSETL2D program, which combines elastic finite element analysis with the theory of random fields, has been modified as to include the function of sampling of soil property values from the generated random fields and return the failure probability of footing against excessive settlement. Two sampling strategies are examined: (a) sampling from a single point and (b) sampling a domain (the latter refers to e.g., continuous cone penetration test data). As is shown in this work, by adopting the proper sampling strategy (defined by the number and location of sampling points), the statistical error can be significantly reduced. The error is quantified by the difference in the probability of failure comparing different sampling scenarios. Finally, from the present analysis, it is inferred that the benefit from a targeted field investigation is much greater as compared to the benefit from the use of characteristic values in a limit state design framework.

The Effect of Targeted Field Investigation on the Reliability of Earth-Retaining Structures in Passive State: A Random Field Approach

“…While Eurocode 7 uses characteristic values (cautious estimate of the mean of a set of values) so as to take account of the inherent variability of the soil, the various North America codes [4,[30][31][32] use mean values for soil properties. The following statistical equation using 95% confidence level is often adopted in practice for the calculation of the characteristic value [6,13,29,33]:…”

“…Yang et al [9,10] and Li et al [11] studied the importance of soil property sampling location in slope stability analysis. Jaksa et al [12] and Christodoulou and Pantelidis [13], on the other hand, studied the importance of soil property sampling location in footing's settlement analysis. Griffiths et al [14] studied the effect of sampling on the reliability of earth pressure analysis in the passive state based on the Random Finite Element Method (RFEM).…”

The Effect of Targeted Field Investigation on the Reliability of Axially Loaded Piles: A Random Field Approach

“…Soil heterogeneity is an important component in designing geotechnical engineering structures, where the proper soil parameter values need to be determined directly in the laboratory based on undisturbed samples or indirectly based on in-situ tests (usually continuous probing tests such as, the Cone Penetration Test (CPT) or the Standard Penetration Test (SPT)). Recent studies have shown that that the reliability of geotechnical engineering structures is greatly affected by the location and the number of sampling points [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. This sampling-related uncertainty is commonly known as statistical uncertainty.…”

An Analytical Random Field Solution for the Reliability of Axially Loaded Piles in the Ultimate Limit State Considering the Effect of Soil Sampling

“…While reliability of geotechnical engineering structures is a long-standing problem and a topic of research of major importance, only recently has the research interest focused on statistical uncertainty, i.e., on the effect of targeted field investigation on the reliability of structures. These studies [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] aim at finding the sampling location that minimizes statistical error; this location is called "optimal sampling location". In one of their previous works, the authors [6] studied numerically the effect of targeted field investigation on the reliability of axially loaded piles, aiming at an optimal Serviceability Limit State and Ultimate Limit State design (SLS and ULS, respectively; terms used in Eurocode 7 [21]).…”