Axial service limit state analysis of drilled shafts using probabilistic approach

Abstract

Abstract. Drilled shafts are, typically, designed by considering the axial ultimate limit state. In this design methodology, the axial displacement requirements are verified once the design is completed. As an alternative, drilled shafts may be designed by considering the axial service limit state. Service limit state foundation design is more efficient when done using the load and resistance factor design (LRFD) approach. Furthermore, reliability may be rationally incorporated into the design process that utilizes the LRFD method. In this paper, we develop probabilistic approaches for axial service limit state analysis of drilled shafts. The variability of shaft-soil interface properties is modeled by lognormal probability distribution functions. The probability distributions are combined with a closed-form analytical relationship of axial loaddisplacement curves for drilled shafts. The closed-form analytical relationship is derived based upon the ''t-z'' approach. This analytical relationship is used with the Monte Carlo simulation method to obtain probabilistic load-displacement curves, which are analyzed to develop methods for determining the probability of drilled shaft failure at the service limit state. The developed method may be utilized to obtain resistance factors that can be applied to LRFD based service limit state design.Key words. drilled shaft, failure probability, load-displacement relation, serviceability.Notation: D: drilled shaft diameter, mm; dP/du: drilled shaft initial stiffness, kN/m; E s : soil elastic modulus, kN/m 2 ; K: shear modulus of shaft-soil interface, kN/m 2 ; K c : axial stiffness of debond zone, MN; K m : drilled shaft axial stiffness, MN; K t : drilled shaft tip soil stiffness, kN/m; L b : shaft interaction zone length, m; L d : shaft noninteraction length, m; P: drilled shaft load, kN; P t : drilled shaft tip resistance force, kN; P u : drilled shaft ultimate pullout capacity, kN; q: shear force per unit length, kN/m; q o : yield strength of shaft-soil interface, kN/m; u: displacement, mm; u o : interface displacement at yield, mm; u t : tip displacement, mm; " u: deformation at top of drilled shaft, mm; U: non-dimensional displacement; " u: non-dimensional displacement at top of interaction zone; x: location along the drilled shaft length; a: normalizing factor, cm; j: non-dimensional factor; k: scaling factor; l s : tip soil Poisson's ratio; s u : ultimate shear strength of shaft-soil interface, kN/m 2 ; n: nondimensional length; n o : location of transition point.

Reliability analysis of drilled shaft behavior using finite difference method and Monte Carlo simulation

“…Classic hyperbolic load-displacement curves can be observed, characterized by an initial tangent modulus that decreases with an increase in load, a pseudo yield point where the shaft-soil interface yields completely, and a point of ultimate failure where the tip of the drilled shaft fails by plunging. Similar results are obtained for a total stress analysis and are only dependent on the mean of the shaft-soil interface properties chosen in each analysis such as those shown in Misra and Roberts (2006).…”

“…Consequently, a probabilistic load-displacement relationship can be obtained, resulting in an improved technique for design of drilled shafts at the service limit state. This paper extends the previous work by Misra and Roberts (2006) to develop an approach for reliability analysis of drilled shafts by combining the finite difference technique for analyzing nonlinear load-displacement behavior with Monte Carlo simulation method. As a result, probabilistic relationships are obtained for drilled shaft design assuming both total (undrained) and effective (drained) stress parameters.…”

“…The upper 0.3-1.5 m of the shaft-soil interface, called the non-interacting zone length, L d , is considered to have negligible shear resistance due to ground disturbance, fill placement and construction technique utilized. Based upon the ''t-z'' methodology, we have previously presented the mathematical model that describes the load-displacement behavior of drilled shaft foundations accounting for shaft-soil interaction (Misra and Roberts 2006;Misra and Chen 2004). Here we state the governing equation, given in Eq.…”

“…Since the load-displacement relationship for the drilled shaft are highly nonlinear and have to be obtained using a numerical technique, probabilistic relations cannot be calculated using closed form relations, such as the first-order second moment (FOSM) method (Misra and Roberts 2006). Consequently, the Monte Carlo simulation method is utilized to obtain the probabilistic load-displacement solutions for the drilled shaft.…”

“…The required number of Monte Carlo trials is based upon achieving a particular level of reliability (Harr 1996;Baecher and Christian 2003). For the results reported in this paper, Monte Carlo simulations with 5000 trials were conducted as described in Misra and Roberts (2006). These simulations were performed using a computer program written utilizing Mathcad (2002) software for both total stress analysis and effective stress analysis.…”