Modeling Lateral Soil-Pile Response Based on Soil-Pile Interaction

Although most designers prefer the p-y curve method as compared to elastic continuum or finite-element analysis of laterally loaded pile behavior, the profession has reached a state where it is time that closer scrutiny be given to the traditional “Matlock-Reese” p-y curves used in the analysis. The traditional p-y curves were derived from a number of well-instrumented field tests that reflect a limited set of conditions. To consider these p-y curves as unique is questionable. As important as such curves have been to advancing the practice from elastic to nonlinear beam on elastic foundation analysis, such calibrated∕verified p-y curves reflect the specific field test conditions (particularly the pile properties) encountered. As presented in this paper, there are additional influences such as pile bending stiffness, pile cross-sectional shape, pile-head fixity, and pile-head embedment that have an effect on the resulting p-y curves. It is argued that strain wedge (SW) model formulation can be used to characterize such effects. SW model analysis predicts the response of laterally loaded piles and has shown very good agreement with actual field tests in sand, clay, and layered soils. The advantage of the SW model is that it is capable of taking into account the effect of changes in soil and pile properties on the resulting p-y curves.     

Seismic Soil-Pile-Structure Interaction Experiments and Analyses

A dynamic beam on a nonlinear Winkler foundation (or “dynamic p-y”) analysis method for analyzing seismic soil-pile-structure interaction was evaluated against the results of a series of dynamic centrifuge model tests. The centrifuge tests included two different single-pile-supported structures subjected to nine different earthquake events with peak accelerations ranging from 0.02 to 0.7g. The soil profile consisted of soft clay overlying dense sand. Site response and dynamic p-y analyses are described. Input parameters were selected based on existing engineering practices. Reasonably good agreement was obtained between calculated and recorded responses for both structural models in all earthquake events. Sensitivity of the results to dynamic p-y model parameters and site response calculations are evaluated. These results provide experimental support for the use of dynamic p-y analysis methods in seismic soil-pile-structure interaction problems.     

Undrained Lateral Pile Response in Sloping Ground

Three-dimensional finite element analyses were performed to study the behavior of piles in sloping ground under undrained lateral loading conditions. Piles of different diameter and length in sloping cohesive soils of different undrained shear strength and several ground slopes were considered. Based on the results of the finite element analyses, analytical formulations are derived for the ultimate load per unit length and the initial stiffness of hyperbolic p-y curves. New p-y criteria for static loading of piles in clay are proposed, which take into account the inclination of the slope and the adhesion of the pile-slope interface. These curves are used through a commercial subgrade reaction computer code to parametrically analyze the effect of slope inclination and pile adhesion on lateral displacements and bending moments. To validate the proposed p-y curves, a number of well documented lateral load tests are analyzed. Remarkable agreement is obtained between predicted and measured responses for a wide range of soil undrained shear strength and pile diameter, length, and stiffness.     

Strain Wedge Model Capability of Analyzing Behavior of Laterally Loaded Isolated Piles, Drilled Shafts, and Pile Groups

This paper demonstrates the application of the strain wedge (SW) model to assess the response of laterally loaded isolated long piles, drilled shafts, and pile groups in layered soil (sand and/or clay) and rock deposits. The basic goal of this paper is to illustrate the capabilities of the SW model versus other procedures and approaches. The SW model has been validated and verified through several comparison studies with model- and full-scale lateral load tests. Several factors and features related to the problem of a laterally loaded isolated pile and pile group are covered by the SW model. For example, the nonlinear behavior of both soil and pile material, the soil-pile interaction (i.e., the assessment of the p-y curves rather than the adoption of empirical ones), the potential of soil to liquefy, the interference among neighboring piles in a pile group, and the pile cap contribution are considered in SW model analysis. The SW model analyzes the response of laterally loaded piles based on pile properties (pile stiffness, cross-sectional shape, pile-head conditions, etc.) as well as soil properties. The SW model has the capability of assessing the response of a laterally loaded pile group in layered soil based on more realistic assumptions of pile interference as compared to techniques and procedures currently employed or proposed.     

Lateral Response Evaluation of Single Piles Using Inclinometer Data

In an effort to develop an efficient method for interpretation of lateral pile load test results via measured inclinometer data only, an analytical model is proposed based on energy conservation of a pile-soil system. A Fourier series function is used to represent deflection behavior of the pile-soil system. In order to obtain shear, moment, and soil reaction along the pile shaft, convergence of the series after differentiation is guaranteed by applying the Cesaro sum technique. The concrete cracking effect is also incorporated into the pile model to account for yielding of the pile itself. Three full-scale pile load cases are then used to verify the feasibility of the developed methodology as well as make comparison to other methods.     

p-y Criterion for Rock Mass

Drilled shafts socketed in rock mass have been used frequently as a foundation system to support both vertical and lateral loads. Traditionally, the lateral interaction between the drilled shaft and the surrounding rock medium has been characterized by means of nonlinear p-y curves; however, there is a lack of well verified p-y criterion for rock mass. In this paper, a hyperbolic p-y criterion is developed based on both theoretical derivations and numerical (finite element) parametric analysis results. The methods for determining pertinent rock parameters needed for constructing the proposed p-y curves are presented in the paper. Two full-scale lateral load tests on large diameter, fully instrumented drilled shafts socketed in rock conducted by the writers, together with additional four load test results reported by Gabr et al. were used to validate the applicability of the proposed hyperbolic p-y curves for rock mass. The comparisons between the computed shaft responses (both deflections and bending moments) and the actual measured responses are considered acceptable.     

Simplified Approach for the Seismic Response of a Pile Foundation

Pseudostatic approaches for the seismic analysis of pile foundations are attractive for practicing engineers because they are simple when compared to difficult and more complex dynamic analyses. To evaluate the internal response of piles subjected to earthquake loading, a simplified approach based on the “p-y” subgrade reaction method has been developed. The method involves two main steps: first, a site response analysis is carried out to obtain the free-field ground displacements along the pile. Next, a static load analysis is carried out for the pile, subjected to the computed free-field ground displacements and the static loading at the pile head. A pseudostatic push over analysis is adopted to simulate the behavior of piles subjected to both lateral soil movements and static loadings at the pile head. The single pile or the pile group interact with the surrounding soil by means of hyperbolic p-y curves. The solution derived first for the single pile, was extended to the case of a pile group by empirical multipliers, which account for reduced resistance and stiffness due to pile-soil-pile interaction. Numerical results obtained by the proposed simplified approach were compared with experimental and numerical results reported in literature. It has been shown that this procedure can be used successfully for determining the response of a pile foundation to “inertial” loading caused by the lateral forces imposed on the superstructure and “kinematic” loading caused by the ground movements developed during an earthquake.     

Lateral Load Capacity of Drilled Shafts in Jointed Rock

Large vertical (axial) and lateral loads often act on the heads of drilled shafts in jointed rock. In current design practice, the p-y curve method used in design of laterally loaded drilled shafts in soil is often also used for shafts in jointed rock. The p-y curve method treats the soil as a continuum, which is not appropriate in jointed rock, particularly when failure occurs due to sliding on joints. A new discontinuum model was developed to determine the lateral load capacity of drilled shafts or piers in a jointed rock mass with two and three joint sets. It consists two parts: a kinematic and a kinetic analysis. In the kinematic analysis, Goodman and Shi’s block theory is expanded to analyze the removability of a combination of blocks laterally loaded by a pier. Based on the expanded theory, a method was developed to select removable combinations of blocks using easily constructed two-dimensional diagrams. In the kinetic analysis, each kinematically selected removable combination of blocks is examined with the limit equilibrium approach to determine the ultimate lateral load capacity. Although the procedure is similar to slope stability analysis, it is more complicated with the addition of a lateral force and the vertical load exerted by the pier. Simple analytical relations were developed to solve for the ultimate lateral load capacity.     

Employment of the P-Multiplier in Pile-Group Analysis

This paper discusses the variation of the P-multiplier (Pm) used with the p-y curve to assess the response of a pile group under lateral loads, which is a crucial topic for the design of bridge pile foundations. Pm is influenced by the site geotechnical conditions (i.e., soil profile, type and properties), pile front and side spacings, and pile-group deflection. The presented study shows the needs to incorporate these factors with the recommended sets of Pm to avoid any compromise or uncertainty when Pm is treated as a single (unique) value based only on pile spacings. The current study addresses these influential elements using the strain wedge (SW) model technique, suggested Pm values, and data collected from full-scale pile-group load tests. The experimental results show that Pm is not unique and must be assessed based on the site geotechnical conditions along with the pile-row front and side spacings. Because the employed Pm values must be a function of these influential factors, additional full- and model-scale load tests with different pile spacings and soil types might be required. The paper also emphasizes that using other techniques, such as the SW model, in addition to the P-multiplier could increase the confidence in the predicted pile-group lateral response.     

Theoretical p-y Curves for Laterally Loaded Single Piles in Undrained Clay Using Bezier Curves

An alternative method was introduced for predicting the nonlinear p-y curves for monotonic unidirectional laterally loaded single piles in uniform undrained clay. On the basis of numerical studies, closed-form solutions were developed for locating the start of yield (ye); the ultimate yield point (yu); and the initial stiffness, Ki of the p-y curve. The nonlinear section of the curve between the start of the yield and the ultimate yield point was represented by Bezier polynomials (also known as de Casteljau’s algorithm). Using these relationships, a direct method of constructing the p-y curves was presented considering either tension failure or no tension failure of soils. For a typical pile configuration, the resulting load-deflection response was observed to compare favorably with the predictions from FLAC analysis and Matlock.     

Nonlinear Analysis of Torsionally Loaded Piles in a Two-Layer Soil Profile

This paper presents a method for predicting the nonlinear response of torsionally loaded piles in a two-layer soil profile, such as a clay or sand layer underlain by rock. The shear modulus of the upper soil is assumed to vary linearly with depth and the shear modulus of the lower soil is assumed to vary linearly with depth and then stay constant below the pile tip. The method uses the variational principle to derive the governing differential equations of a pile in a two-layer continuum and the elastic response of the pile is then determined by solving the derived differential equations. To consider the effect of soil yielding on the behavior of piles, the soil is assumed to behave linearly elastically at small strain levels and yield when the shear stress on the pile-soil interface exceeds the corresponding maximum shear resistance. To determine the maximum pile-soil interface shear resistance, methods that are available in the literature can be used. The proposed method is verified by comparing its results with existing elastic solutions and published small-scale model pile test results. Finally, the proposed method is used to analyze two full-scale field test piles and the predictions are in reasonable agreement with the measurements.     

Case History Evaluation of Laterally Loaded Piles

This paper examines seven case histories of load tests on piles or drilled shafts under lateral load. Since the current design software to estimate lateral load resistance of deep foundations requires p-y curves. The first approach used was correlative whereby soil parameters determined from in situ tests [standard penetration test (SPT) and cone penetration test (CPT)] were used as input values for standard p-y curves. In the second approach p-y curves were calculated directly from the stress deformation data measured in dilatometer (DMT) and cone pressuremeter tests. The correlative evaluation revealed that, on the average, predictions based upon the SPT were conservative for all loading levels, and using parameters from the CPT best predicted field behavior. Typically, predictions were conservative, except at the maximum load. Since traditionally SPT and CPT correlation-based p-y curves are for “sands” or “clays,” this study suggests that silts, silty sands, and clayey sands should use cohesive p-y curves. For the directly calculated curves, DMT derived p-y curves predict well at low lateral loads, but at higher load levels the predictions become unconservative. p-y curves derived from pressuremeter tests predicted well for both “sands” and “clays” where pore pressures are not anticipated.     

Applicability of Conventional p-y Relations to the Analysis of Piles in Laterally Spreading Soil

This paper presents a kinematic analysis of a single pile embedded in a laterally spreading layered soil profile and discusses the relevancy of conventional analysis models to this load case. The research encompasses the creation of three-dimensional (3D) finite-element (FE) models using the OpenSees FE analysis platform. These models consider a single pile embedded in a layered soil continuum. Three reinforced concrete pile designs are considered. The piles are modeled using beam-column elements and fiber-section models. The soil continuum is modeled using brick elements and a Drucker-Prager constitutive model. The soil-pile interface is modeled using beam-solid contact elements. The FE models are used to evaluate the response of the soil-pile system to lateral spreading and two alternative lateral load cases. Through the computation of force density-displacement (p-y) curves representative of the soil response, the FE analysis (FEA) results are used to evaluate the adequacy of conventional p-y curve relationships in modeling lateral spreading. It is determined that traditional p-y curves are unsuitable for use in analyses where large pile deformations occur at depth.     

Observed Seismic Lateral Resistance of Liquefying Sand

This paper presents results from a study of the dynamic response of pile foundations in liquefying sand during seismic loading. The study included a series of dynamic centrifuge tests of pile-supported structures and the back-calculation of time histories for the lateral resistance p and relative displacement y between a pile and the free-field soil. Details of the centrifuge experiments and the procedures used to back-calculate p and y time histories are described. The back-calculated p-y time histories provide a concise representation of the experimental results and can be compared to the equivalent p-y behavior predicted by soil-pile interaction analysis methods. The observed p-y behavior provides insight into the mechanisms of soil-pile interaction in liquefying sand, showing characteristics that are consistent with the undrained cyclic loading behavior of saturated sand, including the effects of relative density, cyclic degradation, pore-pressure generation, prior displacement (strain) history, and phase transformation behavior.     

Shaft Capacity of Open-Ended Piles in Sand

This paper presents the results from an experimental investigation designed to examine the effect of soil-core development and cyclic loading on the shaft resistance developed by open-ended piles in sand. An instrumented open-ended model pile was installed either by driving or jacking into an artificially-created loose sand deposit in Blessington, Ireland. The tests provided continuous measurements of the soil-core development and the radial effective stresses during installation and subsequent load tests. The equalized radial effective stresses developed at the pile-soil interface were seen to be dependent on the degree of soil displacement (plugging) experienced during installation, the distance from the pile toe, and the number of load cycles experienced by a soil element adjacent to the pile shaft. A new design method for estimating the shaft capacity of piles in sand is proposed and compared with measurements made on prototype field-scale piles.     

Nonlinear Finite-Element Modeling of Batter Piles under Lateral Load

In this paper, a finite-element model is developed in which the nonlinear soil behavior is represented by a hyperbolic relation for static load condition and modified hyperbolic relation, which includes both degradation and gap for a cyclic load condition. Although batter piles are subjected to lateral load, the soil resistance is also governed by axial load, which is incorporated by considering the P-Δ moment and geometric stiffness matrix. By adopting the developed numerical model, static and cyclic load analyses are performed adopting an incremental-iterative procedure where the pile is idealized as beam elements and the soil as elastoplastic spring elements. The proposed numerical model is validated with published laboratory and field pile test results under both static and cyclic load conditions. This paper highlights the importance of the degradation factor and its influence on the soil resistance-displacement (p-y) curve, number of cycles of loading, and cyclic load response.     

1880热轧带钢工程加热炉区深基坑围护及土体位移有限元分析

软土地基深基坑开挖过程中,由于降水质量、基坑围护不同,或者土方开挖工况选择不当,常会引起土体位移,对管桩产生较大的土压力,出现基坑滑坡、桩身偏斜等质量事故,特别是大面积群桩整体位移,对工程本身将造成较大的经济损失和工期延误.采用桩土共同建模,桩土单元之间位移协调的有限元方法,将桩土单元集成总体刚度矩阵整体分析,对宝钢1880热轧带钢工程加热炉深基坑开挖过程进行研究,对比计算了基坑开挖对土体侧移和土体应力分布的影响,对施工工况的设计具有参考作用.     

Photocoagulation and fluid-gas exchange to treat persistent macular holes after prior vitrectomy. A pilot study

A method is introduced to calculate wedge factors for an enhanced dynamic wedge (EDW). An analytic formula has been derived that allows the determination of wedge factors at the center of symmetric and asymmetric photon fields. The formalism is an extension of the "MU fraction approximation," which holds that the dynamic wedge factor is equal to the fraction of MU delivered to the point of calculation. Extensive data are presented, comparing measured enhanced dynamic wedge factors with the current method and the MU fraction model for both symmetric and asymmetric fields. For both 6 and 18 MV photons, the current method demonstrates improved results: Agreement to within 1% is obtained in all symmetric fields and within 2% for all asymmetric fields compared with discrepancies of up to 4% obtained with the MU fraction model.     

Physical Modeling of Lateral Clay-Pipe Interaction

This paper presents results from physical model testing of lateral clay-pipe interaction. The main reason for this research was the accident in Rio de Janeiro in January 2000 when more than 1×106?l of crude oil was spilled into Guanabara Bay due to thermal buckling of a pipeline. A set of centrifuge tests was performed for a model pipeline at shallow burial depths in order to assess the lateral resistance of the soft clay from the incident site. In addition, a set of 1-g model tests was also performed to observe the failure mechanism in more detail. These tests permitted the development of an analytical model, based on geotechnical and geometrical parameters, able to evaluate the soil resistance when subjected to lateral pipe movements for shallow burial depths. The centrifuge data are then compared with the proposed analytical model and with literature data, revealing good agreement in both cases.     

Volumetric Deformation of Natural Clays

A theoretical framework to describe the behavior of natural clay is proposed in a new four-dimensional space, consisting of the current stress state, stress history, the current voids ratio, and a measure of the current soil structure. A key assumption of the proposed framework is that both the hardening and the destructuring of natural clay are dependent on plastic volumetric deformation. Two different assumptions about how this destructuring occurs are proposed, based on which two versions of a complete constitutive model have been formulated. The behavior of reconstituted soil can also be simulated by the proposed model as a special case where the structure of soil has no effect on soil deformation. Characteristics of the proposed model are demonstrated through systematic simulations of the influence of soil structure on clay behavior. The simulated behavior of natural clay is compared qualitatively with widely available experimental data. It is seen that the proposed model successfully represents the main features of natural clays with various soil structures.