Wedge Failure Analysis of Soil Resistance on Laterally Loaded Piles in Clay

A fundamental study of pile-soil systems subjected to lateral loads in clay soil was conducted by using experimental tests and a lateral load-transfer approach. The emphasis was on an improved wedge failure model developed by considering three-dimensional combination forces and a new hyperbolic p-y criterion. A framework for determining the p-y curve on the basis of both theoretical analysis and experimental load test results is proposed. The proposed p-y method is shown to be capable of predicting the behavior of a large-diameter pile under lateral loading. The proposed p-y curves with an improved wedge model are more appropriate and realistic for representing a pile-soil interaction for laterally loaded piles in clay than the existing p-y method.     

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.     

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.     

Slope Stability Analysis with Nonlinear Failure Criterion

A linear failure criterion is widely used in slope stability analyses. However, the strength envelope of almost all geomaterials has the nature of nonlinearity. This paper computes rigorous upper bounds on slope stability factors under the condition of plane strain with a nonlinear yield criterion by employing the upper bound theorem of plasticity. A stability factor (or a limit load) computed using a linear Mohr-Coulomb (MC) failure criterion which circumscribes the actual nonlinear failure criterion is an upper bound value of the actual stability factor (or limit load). In this paper, an improved method using a “generalized tangential” technique to approximate a nonlinear failure criterion is proposed to estimate the stability factor of a slope on the basis of the upper bound theorem of plasticity. Using the “generalized tangential” technique, the curve of the nonlinear failure criterion is simplified as a set of straight lines according to the linear MC failure criterion. The straight line is tangential to the curve of the nonlinear failure criterion. The set of straight lines of the linear MC failure criterion is employed to formulate the slope stability problem as a classical optimization problem. The objective function formulated in this way is minimized with respect to the location of sliding body center and the location of tangency point. Two typical slope stability problems (a homogeneous soil slope with two slope angles and a vertical cut slope with a tension crack) are analyzed using the proposed method. For the soil slope with two slope angles, the computed results are compared with published solutions by others. The comparison shows that the proposed method gives reasonable and consistent values of the stability factor of the slope. For the vertical cut slope with a tension crack, a statically admissible stress field is constructed for the slope. The stress field does not violate the nonlinear failure criterion. Lower bound solutions are obtained by satisfying stress equilibrium conditions. The upper bound solutions obtained from the proposed method are equal to the lower bound solutions for the vertical cut slope. The agreement further supports the validation of the proposed approach. The influences of the strength parameters in the nonlinear criterion on the stability of slopes are also studied and discussed in this paper.     

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.     

Load Transfer Curves along Bored Piles Considering Modulus Degradation

The load-transfer (or t-z) curve, which reflects the interaction between a pile and the surrounding soil, is important for evaluating the load-settlement response of a pile subjected to an axial load using the load-transfer method. Preferably, the nonlinear stress-strain behavior of the soil should be incorporated into the t-z curve. This paper presents a practical approach for the estimation of t-z curves along bored piles by considering the nonlinear elastic properties and modulus degradation characteristics of the soil. A method for evaluating the modulus degradation curve from the results of a pressuremeter test is proposed. The results of load tests on one instrumented bored pile in Piedmont residual soil in Atlanta and another in the residual soil of the Jurong Formation in Singapore provide verification of the validity of the proposed approach.     

Determining the Shapes of Yield Curves for Unsaturated Soils by Modified State Surface Approach

Attention is increasingly paid to the elastoplastic behavior of unsaturated soils. In the development of an elastoplastic framework for unsaturated soils, it is necessary to determine the initial shape of the yield curve and its evolution with yielding. Accordingly, correct determination of shapes of yield curves is of significant importance. Existing methods rely on use of a series of specimens with “identical” stress history to determine the initial shape of yield curve. Preparation of such specimens requires thoughtful preparation, careful instrumentation, and lengthy equilibrium time, which makes identical specimens very difficult to obtain. As a result, the yield curve obtained through the existing methods could be misleading. Hence, this paper presents a simple method to correctly and rapidly determine the shapes of the yield curves and their evolution during yielding even if the soil specimens do no have identical stress histories. In this new method, a modified state surface approach, recently proposed to model the elastoplastic behavior of unsaturated soils under isotropic conditions, was applied. It overcomes the limitations in the existing methods, and allows correct and rapid determination of the elastic and plastic hardening surfaces, and then shapes of yield curves without additional laboratory work. An example was used to demonstrate the application of the proposed method. The comparison between the proposed method and other methods was discussed from which the capability and effectiveness of the proposed method were evaluated.     

Experimental Load–Transfer Curves of Laterally Loaded Piles in Nak-Dong River Sand

This paper describes the results of a model testing of the piles embedded in Nak-Dong River sand, located in south Korea, under monotonic lateral loadings. A number of features were studied, including the lateral resistance of piles, the effect of the installation method, and the pile head restraint condition. The study has led to recommendations of the load–transfer curves (p–y curves) for laterally loaded piles. Modification factors were developed to allow for both a different pile installation method and different pile head restraint conditions by comparison to existing model load tests. The proposed p–y curves were compared to the existing curves and were evaluated with the experimental data. The ultimate lateral soil resistance and subgrade modulus were investigated and discussed. It is revealed that the proposed p–y curves show significant differences in shapes and magnitudes when compared with existing p–y curve models. The accuracy of the proposed p–y curve model, considering the effect of installation method and pile head restraint condition, is very reasonable as shown by comparing measured and predicted lateral behavior of the pile.     

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.     

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.     

The yielding, plastic flow, and fracture behavior of ultra-high molecular weight polyethylene used in total joint replacements

The yielding, plastic flow, and fracture behavior of UHMWPE plays an important role in wear and failure mechanisms of total joint replacement components. The primary objective of this study was to compare the yielding, plastic flow, and fracture behavior of two implantable grades of UHMWPE (GUR 1120 vs 4150 HP). The first part of this work explored the hypothesis that up to the polymer yield point, the monotonic loading behavior of UHMWPE displays similar true stress strain behavior in tension and compression. Uniaxial tension and compression tests were conducted to compare the equivalent true stress vs strain response of UHMWPE up to 0.12 true strain. During monotonic loading, the equivalent true stress strain behavior was similar in tension and compression up to the yield point. However, investigation of the unloading behavior and permanent plastic deformations showed that classical deviatoric rate independent plasticity theory may dramatically overpredict the permanent strains in UHMWPE. A secondary goal of this study was to determine the ultimate true stress and strain for UHMWPE and to characterize the fracture surfaces after failure. Using a fracture mechanics approach, the critical flaw sizes were used in combination with the true ultimate stresses to predict the fracture toughness of the two resins. A custom video-based strain measurement system was developed and validated to characterize the true stress-strain behavior up to failure and to verify the accuracy of the incompressibility assumption in calculating the true stress-strains up to failure. In a detailed uncertainty analysis, theoretical expressions were derived for the relative uncertainty in digital video-based estimates of nominal strain, true strain, homogeneous stress, and true stress. Although the yielding behavior of the two UHMWPE resins was similar, the hardening and plastic flow behavior clearly discriminated between the GUR 1120 and 4150 HP. A statistically significant difference between the fracture toughness of the two resins was also evident. The long-term goal of this research is to provide detailed true stress strain data for UHMWPE under uniaxial tension and compression for future numerical simulations and comparison with more complex multiaxial loading conditions.     

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.     

Yielding behavior of prestrained interstitial-free steel and 70/30 brass

The yielding behavior of interstitial-free (IF) steel and 70/30 brass prestrained in plane strain tension and subsequently strained in uniaxial tension has been investigated experimentally. Upon reloading in uniaxial tension, brass exhibited a negative transient (decrease in flow stress) and steel exhibited a positive transient (increase in flow stress). When the yield stress is defined by the offset method, the positive transient is difficult to model using conventional yield theories as elastic deformation is thought to occur outside the original yield or loading surface. In this work, the yield point was defined using the axial strainvs transverse strain curve as measured with biaxial resistance strain gages. The curve has an initially linear elastic portion; the slope then gradually changes until the linear plastic slope is reached. The intersection of the elastic and plastic slopes is defined as the yield point. Using this alternate definition, the yielding behavior of the prestrained metals was investigated. The yield stress for both prestrained brass and steel was found to be lower than the expected monotonic stress. Compared to previous research based on a traditional definition of yield point, this result is unexpected in prestrained steel and shows that yielding does occur inside the loading surface. The positive transient may, therefore, be modeled using conventional yield theories provided that the yield surface is defined using this alternate technique.     

HTRB600级高强钢筋高温下的力学性能

为研究600 MPa级高强钢筋高温下的力学性能,对HTRB600级热处理高强钢筋进行高温下的拉伸试验,分别测得其在20,200,300,400,500,600,700及800℃高温下的弹性模量、比例极限、屈服强度、极限强度及应力-应变曲线.试验结果表明:HTRB600级高强钢筋高温下屈服强度、极限强度、比例极限与弹性模量均随着温度的升高而显著降低.500℃时其高温下的弹性模量、比例极限、屈服强度与极限强度降低为不足常温下的50%,800℃时已不足常温下的10%.高温下HTRB600级高强钢筋应力-应变曲线随温度的升高逐渐趋于圆滑,当温度达到200℃时,屈服台阶就已消失.600 MPa级钢筋高温下屈服强度和极限强度的降低程度明显大于其他钢筋500 MPa以下强度的钢筋.最后提出了适用于HTRB600级高强钢筋的高温下应力-应变曲线简化计算模型.      

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.     

Response of Laterally Loaded Large-Diameter Bored Pile Groups

This paper presents results of full-scale lateral load tests of one single pile and three pile groups in Hong Kong. The test piles, which are embedded in superficial deposits and decomposed rocks, are 1.5 m in diameter and approximately 30 m long. The large-diameter bored pile groups consist of one two-pile group at 6 D (D = pile diameter) spacing and one two-pile and one three-pile group at 3 D spacing. This paper aims to investigate the nonlinear response of laterally loaded large-diameter bored pile groups and to study design parameters for large-diameter bored piles associated with the p-y method using a 3 D finite-element program, FLPIER. Predictions using soil parameters based on published correlations and back-analysis of the single-pile load test are compared. It is found that a simple hyperbolic representation of load-deflection curves provides an objective means to determine ultimate lateral load capacity, which is comparable with the calculated values based on Broms' theory. Lateral deflections of bored pile groups predicted using the values of the constant of horizontal subgrade reaction, suggested by Elson and obtained from back-analysis of the single pile load test, are generally in good agreement with the measurements, especially at low loads.     

板形检测辊挠度变化对冷轧带钢原始波形信号的影响

 综合考虑板形检测辊自重及其所受带钢张力的影响,利用正弦波和样条曲线虚拟各通道的零点偏差,基于截点法建立了针对检测辊挠度动态变化的原始波形零点补偿模型。对于检测辊自重造成的离线零点偏差,对其进行虚拟正弦截点补偿;对于动态大张力造成的在线零点偏差,利用样条曲线实时拟合零点偏差。从实测曲线中减去零点偏差拟合曲线,即可获得更稳定的径向压力值或板形值,应用过程中还可以采用递推平滑法使其更可靠地反映在线带钢的实际板形状况。实测数据表明,各通道的原始波形AD零点偏差从补偿前的600左右下降到补偿后的50以内,径向压力零点偏差从130N左右下降到10N以内。因此,该零点补偿方法对于提高板形检测精度和板形控制精度具有重要的意义。     

Statistical Analysis of Fragility Curves

This paper presents a statistical analysis of structural fragility curves. Both empirical and analytical fragility curves are considered. The empirical fragility curves are developed utilizing bridge damage data obtained from the 1995 Hyogo-ken Nanbu (Kobe) earthquake. The analytical fragility curves are constructed on the basis of the nonlinear dynamic analysis. Two-parameter lognormal distribution functions are used to represent the fragility curves with the parameters estimated by the maximum likelihood method. This paper also presents methods of testing the goodness of fit of the fragility curves and estimating the confidence intervals of the two parameters (median and log-standard deviation) of the distribution. An analytical interpretation of randomness and uncertainty associated with the median is provided.     

Electrical Conductivity Breakthrough Curves

The factors affecting the applicability of electrical conductivity (EC) breakthrough curves as an indicator of chemical equilibrium between effluent and influent solutions in compatibility tests are illustrated. The shapes of EC breakthrough curves are shown to be a function of the flow rate, the solute retardation factor, the species of cation and anion in the permeant liquid, and the cation initially occupying the exchange complex of the clay. Measured data show that the magnitude of the EC in the soil due to the existence of soluble salts relative to the EC of the influent solution (permeant liquid) affects significantly the observed shapes of the EC breakthrough curves. Comparison between theoretically predicted and measured EC breakthrough curves varies from good to excellent, depending on the initial conditions for the test. The results indicate that chemical equilibrium can not be attained before complete EC breakthrough is attained, regardless of the shape of the EC breakthrough curve. Thus, EC breakthrough curves offer a potentially simple, practical, and inexpensive method for determining chemical equilibrium in laboratory compatibility tests involving permeation with electrolyte solutions.     

Effects of Edge-Stiffening Elements and Diaphragms on Bridge Resistance and Load Distribution

This research investigates the effects of barriers, sidewalks, and diaphragms (secondary elements) on bridge structure ultimate capacity and load distribution. Simple-span, two-lane highway girder bridges with composite steel and prestressed concrete girders are considered. The finite-element method is used for structural analysis. For the elastic range, typical secondary elements can reduce girder distribution factors (GDF) between 10 and 40%, depending on stiffness and bridge geometry. For the inelastic response, steel is modeled using von Mises yield criterion and isotropic (work) hardening. Concrete is modeled with a softening curve in compression with the ability to crack in tension. At ultimate capacity, typical secondary elements can reduce GDF an additional 5 to 20%, and bridge system ultimate capacity can be increased from 1.1 to 2.2 times that of the base bridge without secondary elements, depending on bridge geometry and secondary-element dimensions.