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

Abstract

This work deals with the effect of targeted field investigation on the reliability of axially loaded piles, aiming at an optimal serviceability and ultimate limit state design. This is done in a Random Finite Element Method (RFEM) framework properly considering sampling in the analysis; the RFEM method combines finite element analysis with the random field theory. In this respect, the freely available program called RPILE1D has been modified by the authors as to consider sampling of both soil and pile properties. In each RFEM realization, failure is considered to have occurred when the calculated shaft resistance of pile considering spatially uniform properties (average of sampled values from the soil and pile random fields) is greater than the respective “actual” one considering spatially random properties for both soil and pile. The necessary numerical demonstration of the proposed methodology is done by considering two sampling strategies: a) sampling from a single point and b) sampling from a domain, both along the pile, whilst the various parameters governing the statistical uncertainty of the problem are examined; 5383 different cases were considered in total. As shown, a targeted field investigation may minimize or even eliminate the statistical error inserted in the design. The error is quantified by the difference in the probability of failure comparing different sampling scenarios. Another main finding is that the optimal horizontal sampling location occurs where the pile is going to be constructed. In addition, it is shown that the benefit of a targeted field investigation is much greater than the benefit gained using characteristic soil property values.

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

“…In this section, the Random Finite Element Method (RFEM) is employed in order the optimal sampling depth to be investigated and to the results to be set against the respective ones of Equations (22) and (27). The freely available RFEM program RPILE1D [32] (http://www.engmath.dal.ca/rfem) has been extended by the authors [6] to allow for the consideration of sampling in the analysis. The RPILE1D program is described in detail in [32], so only a brief description is given here.…”

“…The ULS state (which is examined in the present paper) is defined by the sum of the ultimate strength (U s ) over all the springs. The modified RPILE1D program [6] returns the probability of failure based on soil stiffness and ultimate strength values sampled from various depths of the respective 1D random fields along the pile. More specifically, the probability of failure is defined by the fraction of the realizations resulted in failure over the total number of realizations.…”

“…Allowing for a direct comparison between the RFEM method and the respective analytical work of this paper, the RPILE1D program presented by Christodoulou et al [6] was further modified as to (i) consider normal distributions (in addition to the log-normal ones already considered by the original program) and (ii) distinguish sampling cohesion values of soil from sampling internal friction values of soil, since both contribute to the ultimate soil resistance as described by Equation (1). Both modifications have been made so that the program to be consistent with the sampling procedure of the analytical model discussed in the previous sections.…”

“…Specifically, u top was equal to 10 kN/m, while u bottom was equal to 170, 20, 10.625 kN/m for Λ = 1/16, 1 and 16, respectively, although any top and bottom ratio of values that produces the same Λ gives the same probability of failure. It is also noted that the analysis by Christodoulou et al [6] corresponds to the case of Λ = ∞. Finally, for producing smooth numerical curves, the number of realizations was set to 250,000.…”

“…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]).…”