P-Y Model Of Dynamic Pile-soil Interaction In Liquefying Ground

Liquefaction is one of the main reasons of earthquake-induced damage to the pile-supported bridge. The study on dynamic pile-soil-structure interaction is the key to solve this problem in liquefying ground. Dynamic p-y curve method provides an effective way to investigate dynamic pile-soil interaction, and a technical approach to develop a base-displacement seismic design method for bridge pile foundation in liquefying ground. The most important step before application in analyzing dynamic pile-soil interaction is to determine the reasonable p-y curves of liquefying sand. However, the previous studies concern more about how to develop dynamic p-y curves for liquefying sand based on static p-y curve, which seems lack of experimental support and theoretical basis for seismic design. In fact, notwithstanding that the sand isn't fully liquefied, the properties of sand have changed a lot as a result of the increase of pore pressure. At present, the following two questions need to be systematically researched: one is how to determine dynamic p-y properties of liquefying ground quantificationally, the other is how to consider the effect of pore pressure ratio on p-y curve for analyzing of pile-soil interaction in liquefying ground.In view of the above-mentioned factors, the establishing procedure of p-y curves is proposed and three-dimensional finite element method (3D FEM) to investigate dynamic pile-soil interaction in liquefying ground based on shaking table tests. On the other side, the main factors affecting p-y curves are also studied and a modified method is proposed for the backbone curve of dynamic p-y curves, based on which it provided the modified model for pre-liquefaction and post-liquefaction and developed the modified dynamic pile-soil interaction model in liquefying ground. The main content and understandings obtained are as follows:Firstly, a series of large-scale shaking table tests for dynamic pile-soil-bridge structure interaction in liquefying ground were conducted successfully corresponding to liquefying ground covered with clay layer at surface and adopting reinforced concrete single pile-pier under sine waves with different amplitudes and frequencies. The same test had been conducted twice at the interval of 24 hours to obtain different conditions of relative density of sand. The sand was of medium-dense sand in the first test while it was dense sand in the second test. Based on the tests, the mechanism and the law of dynamic pile-soil interaction in liquefying ground are studied in the accumulation process of pore pressure in medium-dense sand and dense sand, this paper concluded the dynamic behavior of sand and pile foundation-supported bridge structure under two different ground conditions of medium-dense and dense sand, and specially analyzed the remarkable effect of different relative density sand on the dynamic behavior of pile foundation and bridge structure. Meanwhile, the tests provided the necessary test data for developing p-y curves of dynamic pile-soil interaction in liquefying ground in view of the accumulation process of pore pressure.Secondly, the method of developing p-y curves of dynamic pile-soil interaction in liquefying ground was proposed and verified according to beam theory from the results of shaking table tests. A series of dynamic p-y curves of medium-dense and dense sand were obtained under sine waves with different amplitudes and frequencies. Based on the above results, this study comprehensively concluded the basic features of p-y curves in pre-liquefied and post-liquefied state and preliminarily analyzed the effects of pore pressure, dynamic load frequency and sand relative density on dynamic p-y curves, a concave-up form of p-y curve for the medium-dense sand in post-liquefied state was discovered, the detailed physical meanings of liquefaction were explained, subsequently, the effects of p-y curves form of liquefying sand on dynamic pile-soil interaction were discussed.Thirdly, three finite element analysis models about dynamic coupling effect of saturated sand were summarized. Some governing equations of u-p formulation, and numerical method of time and spatial discrete were anew derived, and the basic equations group of 3D effective stress dynamic system were obtained. Based on OpenSees finite element numerical simulation platform, aiming at the finished shaking table tests, and adopting finite element manifestation of u-p formulation governing equation, a 3D finite element model and its solution approach was developed to investigate dynamic pile-soil interaction by introducing plastic multi-yield surface constitutive model which can take dynamic properties and shear dilatation of saturated sand and clay under cyclic loading into consideration. The pile linked with soil by rigid connector element, which could consider volume effect in the model, was simulated by beam-column element according to the theory of Euler-Bernoulli beam. The correctness of finite element model and calculation method was verified, according to the comparative analysis between numerical simulation and shaking table tests, including dynamic response of pile and bridge structure, dynamic characteristics especially pore pressure of liquefying ground, the effects of liquefaction on dynamic response of pile and free ground and the dilatation effect of medium-dense sand, which can effectively simulate pile-soil interaction in liquefying ground with different relative density.Fourthly, a series of numerical simulation from 3D finite element analysis method were conducted under a series of sine waves to investigate dynamic pile-soils-bridge structure interaction and the effects of pore pressure ratio, pile diameter, relative density of sand on dynamic p-y curves in liquefying ground, obtaining some dynamic p-y curves under sine waves with different amplitudes and frequency of 1Hz. An impact factor formulation of pile diameter was established based on different pore pressure ratios relative to the response of 0.2m pile diameter from three-dimensional finite element method. A series of p-y curves corresponding to different pore pressure ratios were obtained by dividing pore pressure ratio time histories into several segments, and a modified method of backbone curves of dynamic p-y curves taking pore pressure ratio as a control factor was proposed by adopting the establishing approach for backbone curves of stress-strain curve.Fifthly, an empirical formulation of initial stiffness of backbone curves cluster for dynamic p-y curves was provided under different pore pressure ratios. In light of the above-mentioned research, according to the backbone curve cluster of dynamic p-ycurves taking pore pressure ratio as the controlling variable, a simplified p-y curve model reflecting the form transformation of p-y curves between pre-liquefaction and post-liquefaction state was established piece-wisely, then the concrete expression of model and the evaluation technique of the parameters were presented. Besides, by considering the need of engineering design, the ultimate resistance of saturated sand under cyclic loading from API was selected as the ultimate resistance of simplified model.Finally, it's concluded that employing radiation damping in series rather than gap element in the macroelement will be better for dynamic pile-soil interaction via analyzing theory and mechanical components of macroelement. As for the above-mentioned conclusions, the macroelement of dynamic pile-soil interaction in liquefying ground was established by combining spring element, damping element and plasticity element reasonably, and by providing the calculation parameters and formulations. Herein, one thing to be noted was that the macroelement combines the new p-y model of medium-dense sand which well considered of the effects of liquefaction on soil springs in dynamic pile-soil interaction analysis. Through adopting the new-built macroelement, a simplified analysis method was investigated and established based on nonlinear Winkler foundation beam theory aiming at shaking table test, which considered the effect of lumped soil mass, inertial force from superstructure and radiation damping on dynamic response of the system. Finite element method was adopted to carry out numerical analysis and the reliability of the simplified model was verified by comparison between results from shaking table tests and calculations. Subsequently, the procedure of analyzing dynamic pile-soil interaction in liquefying ground was provided. A dynamic analysis of free liquefying ground was implemented based on the nonlinear finite element program which coupled fluid and solid for saturated sand in u-p formulation adopting multi-yield surface plastic constitutive model, the displacement and pore pressure ratio time histories obtained from numerical calculation were taken as the boundaries of the model. Finally, the effects of pile diameter, initial stiffness ratio between pile and soil and superstructure mass on dynamic pile-soil interaction was conducted by employing the proposed modified model, and some important understandings were obtained which aimed at providing significant reference for seismic design of bridge pile foundation.