Reliability analysis of piles constructed on slopes under laterally loading

Response surface method is used to study the reliability analysis of laterally loaded piles in sloping ground. A development load-displacement （p-y） curve for laterally loaded pile response in sloping ground is used to model the pile-soil system, both the pile head displacement and the maximum bending moment of the piles are used as the performance criteria in this study. The reliability analysis method of the laterally loaded pile in sloping ground under the pile head displacement and the maximum bending moment failure modes is proposed, which is in good agreement with the Monte Carlo method. The influences on the probability index of failure by a number of parameters are discussed. It is shown that the variability of pile head displacement increases with the increase in the coefficients of variation of ultimate bearing capacity factor （Npu）, secant elastic modulus at 50%（E50） and level load （H）. A negative correlation between Npu and non-dimensional factor （λ） leads to less spread out probability density function （PDF） of the pile head displacement;in contrast, a positive correlation between Npu andλgives a great variation in the PDF of pile head displacement. As for bearing capacity factor on ground surface （Npo） and λ, both negative and positive correlations between them give a great variation in the PDF of pile head displacement, and a negative correlation will obviously increase the variability of the response.

Stereo particle image velocimetry measurement of 3D soil deformation around laterally loaded pile in sand

A developed stereo particle image velocimetry(stereo-PIV) system was proposed to measure three-dimensional(3D) soil deformation around a laterally loaded pile in sand.The stereo-PIV technique extended 2D measurement to 3D based on a binocular vision model,where two cameras with a well geometrical setting were utilized to image the same object simultaneously.This system utilized two open software packages and some simple programs in MATLAB,which can easily be adjusted to meet user needs at a low cost.The failure planes form an angle with the horizontal line,which are measured at 27°-29°,approximately three-fourths of the frictional angle of soil.The edge of the strain wedge formed in front of the pile is an arc,which is slightly different from the straight line reported in the literature.The active and passive influence zones are about twice and six times of the diameter of the pile,respectively.The test demonstrates the good performance and feasibility of this stereo-PIV system for more advanced geotechnical testing.

Ultimate Lateral Capacity of Rigid Pile in c–φ Soil

To date no analytical solution of the pile ultimate lateral capacity for the general c–φ soil has been obtained. In the present study, a new dimensionless embedded ratio was proposed and the analytical solutions of ultimate lateral capacity and rotation center of rigid pile in c–φ soils were obtained. The results showed that both the dimensionless ultimate lateral capacity and dimensionless rotation center were the univariate functions of the embedded ratio. Also,the ultimate lateral capacity in the c–φ soil was the combination of the ultimate lateral capacity（f;） in the clay, and the ultimate lateral capacity（f;） in the sand. Therefore, the Broms chart for clay, solution for clay（φ=0） put forward by Poulos and Davis, solution for sand（c=0） obtained by Petrasovits and Awad, and Kondner’s ultimate bending moment were all proven to be the special cases of the general solution in the present study. A comparison of the field and laboratory tests in 93 cases showed that the average ratios of the theoretical values to the experimental value ranged from 0.85 to 1.15. Also, the theoretical values displayed a good agreement with the test values.

Numerical Analysis of Laterally Loaded Long Piles in Cohesionless Soil

The capability of piles to withstand horizontal loads is a major design issue.The current research work aims to investigate numerically the responses of laterally loaded piles at working load employing the concept of a beam-on-Winkler-foundation model.The governing differential equation for a laterally loaded pile on elastic subgrade is derived.Based on LegendreGalerkin method and Runge-Kutta formulas of order four and five,the flexural equation of long piles embedded in homogeneous sandy soils with modulus of subgrade reaction linearly variable with depth is solved for both free-and fixed-headed piles.Mathematica,as one of the world’s leading computational software,was employed for the implementation of solutions.The proposed numerical techniques provide the responses for the entire pile length under the applied lateral load.The utilized numerical approaches are validated against experimental and analytical results of previously published works showing a more accurate estimation of the response of laterally loaded piles.Therefore,the proposed approaches can maintain both mathematical simplicity and comparable accuracy with the experimental results.

Stability Analysis of Piles Subjected to Lateral Load in Static and Seismic Conditions

It is disclosed a method for the stability analysis of foundation piles and piers subjected to lateral loading, both static and seismic conditions. The stability analysis for stratified soil is based upon the models of foundation soil-structure interaction and the Rankine＇s theory of earth passive pressure. In addition, its application is simpler and it can be solved using a spreadsheet. The procedure described in this work can be used in homogeneous soils as in stratified soils, considers the horizontal drag forces exerted by the soil mass against the foundation during an earthquake, can be used easily in the four pile and piers boundary cases, and considers the pore pressure generated in a fine saturated soil during an earthquake or during a rapid application of the horizontal load. The solution of two examples are shown, one in static condition and one in seismic condition, detailing the procedure step by step.

Nonlinear dynamic characteristics of piles embedded in rock

The nonlinear dynamic characteristics of a pile embedded in a rock were investigated. Suppose that both the materials of the pile and the soil around the pile obey nonlinear elastic and linear viscoelastic constitutive relations. The nonlinear partial differential equation governing the dynamic characteristics of the pile was first derived. The Galerkin method was used to simplify the equation and to obtain a nonlinear ordinary differential equation. The methods in nonlinear dynamics were employed to solve the simplified dynamical system, and the time-path curves, phase-trajectory diagrams, power spectrum, Poincare sections and bifurcation and chaos diagrams of the motion of the pile were obtained. The effects of parameters on the dynamic characteristics of the system were also considered in detail.

An analytical p-y curve method based on compressive soil pressure model in sand soil

With the high-quality development of urban buildings,higher requirements are come up with for lateral bearing capacity of laterally loaded piles.Consequently,a more accurate analysis to predict the lateral response of the pile within an allowable displacement is an important issue.However,the current p-y curve methods cannot fully take into account the pile-soil interaction,which will lead to a large calculation difference.In this paper,a new analytical p-y curve is established and a finite difference method for determining the lateral response of pile is proposed,which can consider the separation effect of pile-soil interface and the coefficient of circumferential friction resistance.In particular,an analytical expression is developed to determine the compressive soil pressure by dividing the compressive soil pressure into two parts:initial compressive soil pressure and increment of compressive soil pressure.In addition,the relationship between compressive soil pressure and horizontal displacement of the pile is established based on the reasonable assumption.The correctness of the proposed method is verified through four examples.Based on the verified method,a parametric analysis is also conducted to investigate the influences of factors on lateral response of the pile,including internal friction angle,pile length and elastic modulus of pile.

Application of Back Analysis on Laterally Loaded Single Pile

In views of the limitations of the existing methods for calculating the pile foundation capacity, a back analysis approach of the m-value is introduced. In order to consider the sensitivity of pile behavior to the m-value,the relationships between the applied horizontal loads at pile head and the corresponding m-value along with the pile stiffness changes are studied. Based on statistics data from the extensive in-situ tests, the back analysis results suggest an exponential expression for the m-value in various soil conditions and horizontal displacements at pile head. This method is capable of providing an accurate m-value in calculating the pile responses under lateral loads.