Prediction of the measured response of a scaled soil-pile-superstructure system

The validity of the Winkler foundation model is investigated by predicting the experimentally measured displacement transfer functions and strain spectra of a single pile embedded in a sandbox and supporting a single-degree-of-freedom superstructure. The foundation-superstructure system is a scale model and was subjected to shake table excitations. The distributed springs and dashpots of the Winkler foundation model are frequency dependent and the calibrated model predicts satisfactorily the displacement transfer function at different depths for both fixed- and free-tip pile conditions. On the other hand, the pile-axial-strains are substantially underestimated when expressed in terms of the second derivative of the computed elastic line of the pile. It is shown that a much more dependable prediction is achieved when pile-axial-strains are expressed in terms of the inertial forces acting along the pile-superstructure system.     

Evaluating accuracy for two empirical methods in predicting settlement of drilled shafts

Several theoretical, empirical and semi-empirical methods are available in the literature to predict settlement of drilled shafts in sandy soils. In the Arabian Gulf countries, specifically in the United Arab Emirates, equations and procedure from the rest of the world are being used in analysis and design of drilled shafts without proper validation. It is the aim of this study to assess the applicability and evaluate the accuracy of two well known, and commonly used methods for pile prediction in the United Arab Emirates (UAE), namely Vesic (1977) and Poulos (1979), via comparison with data from field pile load tests conducted on shafts drilled in the region. Some of these tests were conducted for the purpose of this study, while others were made available through the courtesy of International Piling Contractors who are active in the region (e.g. Bauer International and Swiss Borings). Pile load test data were analyzed to back-calculate the model parameters related to settlement under different loading stages. Geological data and soil properties were obtained from studies conducted at the relevant sites. An effort is made to correlate soil properties with the prediction models. Statistical analysis is conducted to assess the accuracy of the results obtained from the two methods at different stages of loading via those obtained from pile load tests. Moreover, a detailed parametric study is conducted to assess the effect of the related parameters on the predicted pile settlement and the estimated settlement at different stages of loading. The study concluded with a recommendation of the most appropriate models and procedures to be followed for predicting the settlement of drilled shafts in the UAE, together with useful charts and correlation relations. Results showed that settlement values predicted by Vesic (1977) and Poulos (1979) overestimates the true values. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Effect of Concrete Deformation on Displacement of an Axially Loaded Drilled Shaft

This article presents the settlement of drilled shafts resulting from their structural deformations. Although drilled shafts are widely used as foundations for settlement-sensitive structures such as bridges and high-rise buildings, the structural deformations of drilled shafts are not typically taken into account in the design process. However, if unexpected structural deformations of drilled shafts cause additional settlement to the foundation, the serviceability of the superstructure can be jeopardized. Unfortunately, very few research efforts have been made to quantify the structural deformation of drilled shafts; this needs to be addressed to accurately predict the settlement of drilled shafts. In this study, we investigate the effect of structural deformation on displacement of axially loaded drilled shafts. Finite element analyses were performed to quantify the structural deformation of drilled shafts. The analysis results indicated that the structural deformation of drilled shafts could be quite significant for long drilled shafts. The main factors that affected the structural deformation of drilled shafts were found to be pile length, the material properties of drilled shafts, and the relative humidity of surrounding soil. An approximate equation is proposed to estimate the long-term deformation of drilled shafts.     

Reliability analysis of drilled shaft behavior using finite difference method and <Emphasis Type="Italic">Monte Carlo</Emphasis> simulation

Load displacement analysis of drilled shafts can be accomplished by utilizing the “t-z” method, which models soil resistance along the length and tip of the drilled shaft as a series of springs. For non-linear soil springs, the governing differential equation that describes the soil-structure interaction may be discretized into a set of algebraic equations based upon finite difference methods. This system of algebraic equations may be solved to determine the load–displacement behavior of the drilled shaft when subjected to compression or pullout. By combining the finite difference method with Monte Carlo simulation techniques, a probabilistic load–displacement analysis can be conducted. The probabilistic analysis is advantageous compared to standard factor of safety design because uncertainties with the shaft–soil interface and tip properties can be independently quantified. This paper presents a reliability analysis of drilled shaft behavior by combining the finite difference technique for analyzing non-linear load–displacement behavior with Monte Carlo simulation method. As a result we develop probabilistic relationships for drilled shaft design for both total stress (undrained) and effective stress (drained) parameters. The results are presented in the form of factor of safety or resistance factors suitable for serviceability design of drilled shafts.     

Limiting equilibrium method for slope/drilled shaft system

The use of drilled shafts to stabilize an unstable slope has been a widely accepted practice. There are two basic design and analysis issues involved: one is to determine the global factor of safety of the drilled shafts stabilized slope and the other one is to determine the design earth thrust on the drilled shafts for structural design of the shafts. In this paper, a limiting equilibrium method of slices based solution for calculating global factor of safety (FS) of a slope with the presence of a row of drilled shafts is developed. The arching mechanisms due to the presence of the drilled shafts on slope were taken into account by a load transfer factor. The method for calculating the net force applied to the drilled shaft from the soil mass was also developed. The interrelationships among the drilled shaft location on the slope, the load transfer factor, and the global FS of the slope/shaft system were derived utilizing the developed numerical closed‐form solution. An illustrative example is presented to elucidate the use of the solution in optimizing the location of the drilled shafts on slope to achieve the desired global factor of safety of the slope/shaft system. Copyright © 2009 John Wiley & Sons, Ltd.     

Numerical analysis on post-grouted drilled shafts: A case study at the Brazo River Bridge,TX

This paper investigates the effects of post-grouting on the behavior of drilled shafts using a case study carried out at the Brazo River, Texas. Commercial finite element software, PLAXIS, was used to quantify the improvement of the tip resistance and side shear resistance of post-grouted drilled shafts (PGDS). The input material parameters of PLAXIS were initially estimated using CPT sounding results, and then the parameters were updated by calibrating the numerical results against full-scale STATNAMIC load test results. Based on the numerical analysis, the authors concluded that (1) the increase in total resistance of PGDS resulted from soil improvement at the shaft tip, (2) the apparent increase in side shear resistance resulted from side shear reversal that occurred during post-grouting, and (3) the apparent increase in the tip resistance of PGDS may be caused by stress relief of the grout. In addition, two approaches to estimate the resistance of PGDS were compared against numerical results. In this case study, the Axial Capacity Multiplier (ACM) approach over-predicted the total resistance whereas the Tip Capacity Multiplier (TCM) approach reasonably predicted the increase in total resistance.     

Importance sampling based algorithm for efficient reliability analysis of axially loaded piles

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. The local averaging subdivision technique is employed to generate random fields. 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 importance sampling algorithm while maintaining the same accuracy as in the crude Monte Carlo method. Two examples are given to demonstrate the accuracy and the efficiency of the proposed method. It is shown that the estimate based on the proposed importance sampling method is unbiased. Furthermore, the size of samples can be greatly reduced in the developed method.     

End Bearing Capacity of Drilled Shafts in Sand: A Numerical Approach

In this paper, a modeling procedure is carried out to numerically analyze the end bearing capacity of drilled shafts in sand. The Mohr–Coulomb elastic plastic constitutive law with stress dependent elastic parameters is used for all numerical analyses performed in this study. The numerical results are compared with the available experimental equations. It is seen that numerical results are in good agreement with experimental equations. The variation of the end bearing capacity of drilled shafts versus embedment depth is also studied. Numerical results show that with increase in pile embedment depth, the end bearing capacity increases. However, the rate of increase becomes smaller as the pile embedment depth increases. Also, numerical analyses show that, for equal settlement, the end bearing decreases with increase in the pile diameter. Finally, a sensitivity analysis is performed to obtain the separate effect of each sand parameter on the end bearing capacity of drilled shafts, and the parameters that are most influential are identified.     

On behavior of load transfer for drilled shafts embedded in weak rocks

This study deals with the formulation of an analytical solution for load transfer in drilled shaft and its application. The emphasis is on quantifying the mobilization of side resistances, which are closely related to shear behaviors of the concrete-rock interface. In this modelling, the side resistance is idealized by using elasticity-brittleness-plasticity, and a simple slip-line field is built to identify the critical shear displacement. The closed-form solution of load transfer is obtained by using the proposed shear model. Comparison between predictions and field observations is also made to validate performance of the proposed method.     

Vulnerability of floating tunnel shafts for increasing earthquake loading

Fragility curves constitute the cornerstone in seismic risk evaluations and performance-based earthquake engineering. They describe the probability of a structure to experience a certain damage level for a given earthquake intensity measure, providing a relationship between seismic hazard and vulnerability. In this paper a numerical approach is applied to derive fragility curves for tunnel shafts built in clays, a component that is found in several critical infrastructure such as urban metro networks, airport facilities or water and waste water projects. The seismic response of a representative tunnel shaft is assessed using tridimensional finite difference non-linear analyses carried out with the program FLAC^3D, under increasing levels of seismic intensity. A hysteretic model is used to simulate the soil non-linear behavior during the seismic event. The effect of soil conditions and ground motion characteristics on the soil-structure system response is accounted for in the analyses. The damage is defined based on the exceedance of the concrete wall shaft capacity due to the developed seismic forces. The fragility curves are estimated in terms of peak ground acceleration at a rock or stiff soil outcrop, based on the evolution of damage with increasing earthquake intensity. The proposed fragility models allows the characterization of the seismic risk of a representative tunnel shaft typology and soil conditions considering the associated uncertainties, and partially fill the gap of data required in performing a risk analysis assessment of tunnels shafts.