Haijian Fan

Performance-Based Reliability Analysis of Laterally Loaded Drilled Shafts

AbstractAnalysis of laterally loaded piles or drilled shafts is a complex soil–structure interaction problem for which the p–y method has been widely accepted as a computational tool for predicting the load-displacement behavior. This paper presents a sampling-based method that can be applied to reliability analysis of the load-deflection behavior for laterally loaded piles. Various sources of uncertainties arising from soil properties, analysis model, and p–y criteria can be taken into account in the proposed method. In particular, soil properties needed as input for determining site-specific p–y curves were modeled as random fields. To statistically characterize the random field of a soil parameter, the field mean, the field variance, and the correlation structure are required. The performance of a pile under lateral loading is evaluated using a different set of random samples in each realization. The probability of failure, in which failure is defined as the event of not meeting the prescribed performa...

Probabilistic Framework for Strength Limit and Service Limit Checks of Drilled Shafts Considering Soil Spatial Variability

This paper presents a performance-based, probabilistic framework for design of a drilled shaft under axial and lateral loading that can consider spatial variability of soil properties at a project site. The performance criteria of a drilled shaft are stated in relation to the limiting tolerable deformations for strength limit and service limit, respectively. The computational algorithm for calculating the deformation of a drilled shaft is based on the commonly adopted load transfer method and the p-y method. “Geotechnical failure” is defined as an event in which the specified performance criteria are not met. Three failure modes are considered: axial movement, lateral deflection, and angular distortion. The spatial variability of soil properties is considered by using random field modeling techniques in which correlation length is introduced to account for site variability in addition to mean and variance. The method of fitting a sample autocorrelation function to a prescribed correlation function by using the method of ordinary least squares is introduced for determining site-specific correlation length for soil parameters. Geostatistical principles known as kriging are employed to estimate unknown parameters at unsampled locations from neighboring sampled locations. A numerical example is given to illustrate the application of the proposed methodologies. The example demonstrates that correlation length is an important statistical descriptor for characterizing site variability. Performance-based design provides unified consideration for both strength limit and service limit. Finally, the overall probability of failure for a drilled shaft when all three failure modes are considered is greater than the failure probability for any individual failure mode.

Reliability-Based Design of Laterally Loaded Piles Considering Soil Spatial Variability

The p-y method has been commonly used for analysis of laterally loaded piles. Recently, a sampling-based approach for reliability analysis of laterally loaded piles has been developed by the authors. With the performance criteria defined for the laterally loaded piles, the probability of non-satisfactory performance can be conveniently computed. However, at any project site, soil properties used as input in the computation, such as strength parameters and stiffness values, generally exhibit spatial variations. There is a need to take into account of this spatial variation in the reliability analysis. In this paper, the Monte Carlo simulation technique developed for reliability analysis of laterally loaded piles is briefly described first. Next, a statistical tool for taking into consideration of spatial variability of pertinent soil properties in the developed reliability analysis is presented. A design example is given to illustrate the influences of spatial variability of soil properties on the computed outcome. Specifically, the correlation length of the soil properties at the site can exert significant influences on the computed results. It is recommended that spatial correlation of soil properties should be considered in order to accurately perform reliability analysis and design of piles under lateral loads.

Application of Monte Carlo Simulation to Laterally Loaded Piles

This paper presents a robust Monte Carlo Simulation method that can be applied to the analysis of the load-deflection behavior for laterally loaded piles considering various sources of uncertainties arising from soil properties, analytical model, and p-y criteria. In particular, soil properties needed as input for determining site specific p-y curves could be modeled as random fields. In the simulation process, a large number of random samples are generated as input, and uncertainties arising from inputs and model errors are considered. Performance criteria on the basis of service limit state (i.e., allowable deflection at working loads) and strength limit state (i.e., capacity defined at the specified limiting deflection) can be evaluated for each random sample. The probability of failure, in which failure is defined as not meeting performance criteria, is calculated by the number of failures divided by the number of random samples. A design example is presented at the end of paper to demonstrate practical applications of the developed Monte Carlo simulation method.

Efficient Reliability Evaluation of Axially Loaded Piles in Spatially Varying Soils Using Importance Sampling

In reliability analysis, the crude Monte Carlo method is known to be computationally demanding. To improve computational efficiency, this paper presents an importance sampling-based algorithm that can be applied to conduct efficient reliability evaluation for axially loaded piles. The spatial variability of soil properties along the pile length is considered by random field modeling, in which a mean, a variance, and a correlation length are used to statistically characterize a random field. In each realization, the random fields are used as inputs to the well-established load transfer method to evaluate the load-displacement behavior of an axially loaded pile. Failure is defined as the event where the vertical movement at the pile top exceeds the allowable displacement. By sampling more heavily from the region of interest and then scaling the indicator function back by a ratio of probability densities, a faster rate of convergence can be achieved in the proposed algorithm. An example is given to demonstrate the accuracy and the efficiency of the proposed method. It is shown that the estimate based on the proposed method is unbiased. Furthermore, the size of samples can be greatly reduced in the developed method.

Performance-Based Reliability Design for Deep Foundations Using Monte Carlo Statistical Methods (DFI Student Paper Competition 2012)

Abstract Deep foundation designs for service limit state are still deterministic in the current AASHTO LRFD Specifications. To address this deficiency, a performance-based reliability design methodology is developed using the Monte Carlo statistical techniques. In the proposed methodology, the design criteria are defined in terms of the allowable displacement. The spatial variability of soil parameters is considered in the proposed methodology by modeling soil parameters as random fields. Failure is defined as the event that the induced displacement exceeds the limiting displacement. The probability of failure by Monte Carlo approach is the ratio of the number of unsatisfactory performance events to the sample size. Three numerical examples are given to illustrate the application of the proposed methodology for laterally loaded and axially loaded drilled shafts, respectively. The spatial variability and correlation of soil properties were shown to exert significant influences on the foundation design.