Seismic Behavior of Soil-Pile-Structure Interaction in Liquefiable Soils: Parametric Study

Nonlinearity of the soil medium plays a very important role on the seismic behavior of soil-pile-structure interaction. The problem of soil-pile-structure interaction is further complicated when the piles are embedded in liquefiable soil medium. A finite-element code was developed in MATLAB to model three-dimensional soil-pile-structure systems. Frequency dependent Kelvin elements (spring and dashpots) were used to model the radiation boundary conditions. A work-hardening plastic cap model was used for constitutive modeling of the soil medium. The pore pressure generation for liquefaction was incorporated by a two-parameter volume change model reported in the literature. In this paper, a 2×2 pile group in liquefiable soil is considered and a parametric study is conducted to investigate its seismic behavior. The effects of loading intensity and stiffness of the soil on the seismic behaviour of the soil-pile system are investigated, considering nonlinearity and liquefaction of the soil medium for a wide range of frequencies of harmonic excitations. The inertial interaction attributable to a structure is analyzed for a system consisting of a four-storied portal frame on the pile group-soil subsystem. The responses of the structure are investigated for harmonic excitation and transient excitations. The importance of consideration of nonlinearity and liquefaction of the soil medium for analysis and design of a pile-supported structure is highlighted. Results from an analysis considering a practical soil-pile problem are presented to demonstrate the applicability of the developed algorithm for a practical problem.     

Dynamic and Seismic Analysis of Foundations based on Free Field B-Spline Characteristic Response Histories

A direct time domain formulation for the analysis of unbounded media and foundations is developed that treats dynamic excitations and ground motion in a uniform manner. The method uses the boundary element method with higher order B-Spline fundamental solutions to compute the characteristic responses of the surface of the elastodynamic domain. Subsequently, time histories of the system response to general excitations are computed by a mere superposition scheme that accommodates in a uniform manner arbitrary time histories of external loads and/or ground motion. The characteristic responses are computed in the form of time dependent flexibility matrices of the medium that are sparse due to the finite duration of the B-Spline excitation signal and the characteristics of the wave propagation. The duration of the B-Spline impulse response is limited to only a few time steps. Consequently, significant savings in computing time and storage requirements are achieved. Furthermore, the characteristic responses do not depend on the type or wave form of the actual external excitations and the presence of rigid foundations. This is a significant advantage when the response of a system to excitations of long duration is to be computed. In addition, the proposed approach significantly reduces the size of the problems under consideration and yet fully considers the effects of the free field. The significance of nonrelaxed boundary conditions and correct representation of the free field is established. The method is demonstrated and validated through applications pertaining to the analysis of foundations and inclusions subjected to transient loads and seismic excitations.     

Failure Mechanisms of Pile Foundations in Liquefiable Soil: Parametric Study

This paper presents the response of piles in liquefiable soil under seismic loads. The effects of soil, pile, and earthquake parameters on the two potential pile failure mechanisms, bending and buckling, are examined. The analysis is conducted using a two-dimensional plain strain finite difference program considering a nonlinear constitutive model for soil liquefaction, strength reduction, and pile-soil interaction. The depths of liquefaction, maximum lateral displacement, and maximum pile bending moment are obtained for concrete and steel piles for different soil relative densities, pile diameters, earthquake predominant frequencies, and peak accelerations. The potential failure mechanisms of piles identified from the parametric analysis are discussed.     

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.     

Dynamic Behavior of Steel Deck Tension-Tied Arch Bridges to Seismic Excitation

The dynamic responses of steel deck, tension-tied, arch bridges subjected to earthquake excitations were investigated. The 620 ft (189 m) Birmingham Bridge, located in Pittsburgh, was selected as an analytical model for the study. The bridge has a single deck tension-tied arch span and is supported by two bridge piers, which in turn are supported by the pile foundations. Due to the complex configuration of the deck system, two analytical models were considered to represent the bridge deck system. Using the normal mode method, seismic responses were calculated for two bridge models and the results were compared with each other. Three orthogonal records of the El Centro 1940 earthquake were used as input for the seismic response analysis. The modal contributions were also checked in order to obtain a reasonable representation of the response and to minimize computational cost. Displacements and stresses at the panel points of the bridge are calculated and presented in graphical form.     

Effect of Nonlinear Soil Behavior on Inelastic Seismic Response of a Structure

The characteristics of the earthquake motions at the base of a structure are affected by the properties of the underlying soil through the soil amplification and soil–structure interaction phenomena. In this paper the effect of nonlinear soil behavior on the elastic and inelastic response spectra of the motions that would be recorded at the free surface of a soft soil deposit or at the base of each structure is investigated. The analyses are conducted for a soil layer by itself and for a complete soil structure system using a finite element discretization of the soil in cylindrical coordinates and an approximate linear iterative procedure to simulate nonlinear behavior. Studies are conducted for structures, with a constant base and variable height modeled as equivalent linear or nonlinear single degree of freedom systems and an input motion at the base of the soil deposit representative of rock outcrop motions. Both mat and pile foundations are considered. The results illustrate clearly the importance of the nonlinear soil behavior.     

Dynamic Ratcheting in Elastoplastic Single-Degree-of-Freedom Systems

In dynamic analysis, hysteretic damping often provides a reasonable model of the inelastic behavior of a structure. Nonlinearity presented by hysteretic damping, however, introduces the possibility of developing complicated motions not expected in linear dynamics. In this study, motions of a single-degree-of-freedom system with hysteretic damping under dual-frequency sinusoidal excitations are investigated through numerical simulation. Hysteretic damping behavior is represented by three different plasticity models: the elasto-perfectly-plastic model; the linear kinematic hardening model; and the two-surface model. Under certain conditions, the resultant motions from the elasto-perfectly-plastic model and the two-surface model exhibit a continual increment of plastic deformation in successive cycles. Parametric study shows that this dynamic ratcheting develops when applied frequencies are commensurable (i.e., related to each other with integer ratio), and the product of terms comprising the ratio is an even number. In the Poincaré section, motion from commensurable frequencies shows limit cycle behavior, whereas the boundedness of motion for incommensurable frequencies is depicted by having quasi-periodicity. On the other hand, the response of the linear kinematic hardening model is qualitatively different and, in particular, dynamic ratcheting does not develop, irrespective of the frequency commensurability. These findings suggest that model selection may have unanticipated consequences for the analysis and design of structural systems subjected to severe dynamic loadings, such as major earthquakes.     

Nonlinear Interaction of Soil–Pile in Horizontal Vibration

This paper presents a new model for analyzing a nonlinear soil–pile interaction subject to horizontal shaking of a vertical circular pile embedded in a soil layer of finite thickness. The pile rests on bedrock with either a pinned or a clamped support. The soil mass is assumed composing of a “semi-nonlinear” inner soil zone around the pile and a linear viscoelastic soil zone outside the inner zone. When the inner soil behaves linearly, the present solutions are identical to those obtained by Nogami and Novak in 1977. Numerical results show that soil resistance of less slender piles developed against the vibration is larger than that of more slender piles. Soil resistance depends more strongly on the size of the nonlinear inner zone when the pile is vibrating at a frequency higher than the natural frequency of the soil. Soil nonlinearity, in general, results in a smaller damping and stiffness of the soil–pile system, except at high frequency. At higher vibration frequency, the situation can be very complicated. The exact value of the dynamic stiffness of the soil–pile system depends on elastic shear wave speed, soil nonlinearity, vibration frequency, slenderness ratio of the pile, magnitude of vibration, and tip conditions of the pile. Generally speaking, the dynamic stiffness is smaller than the static stiffness. The normalized dynamic stiffness for pile with a pinned tip is, in general, larger than that with a clamped tip, while the reverse is true for the damping.     

Reduction Factor for the Unloading Point Method at Clay Soil Sites

Full-scale testing can be an integral component of quality control/quality assurance for projects involving construction of deep foundations. Rapid load tests are being used in the deep foundation industry as a method for assessing the axial static behavior of deep foundations. Since rapid load tests involve dynamics, inertial and damping forces must be considered in analyzing measured pile response to estimate the static pile response. The unloading point method (UPM) is typically used for this purpose. Generally considered a consequence of load rate effects in clays, results from the UPM must be further modified by a reduction factor to obtain a reasonable estimate of the static pile response. A reduction factor of 0.65 applied to the UPM for clay soil sites has been recommended by others. However, a review and analysis of readily available literature reporting static and rapid pile load test results at sites predominantly consisting of clay soils indicate that an average reduction factor of 0.47 is more appropriate. Rapid load testing should be used judiciously. When using the UPM to estimate static pile capacity from rapid load tests in clay, static load tests should be performed to validate the reduction factor used to interpret rapid load tests.     

Seismic Site Response for Near-Fault Forward Directivity Ground Motions

Forward directivity effects in the near-fault region produce pulse-type motions that differ significantly from ordinary ground motions that occur at greater distances from the causative fault. Current code site factors are based on empirical observations and analyses involving less intense nonpulse ordinary ground motions. Nonlinear site response analyses with bidirectional shaking are performed using representative site profiles to quantify seismic site response effects for intense near-fault motions resulting from forward directivity. Input rock motions are represented with simplified velocity pulses that characterize the amplitude and period of forward directivity motions. Results indicate that site response affects both the amplitude and period of forward directivity pulses, and hence, local site conditions should be considered when evaluating seismic designs in the near-fault region. Stiff soil sites tend to amplify the peak ground velocity and increase the period of pulse-type motions, particularly, when the period of the rock motion coincides with the degraded period of the site. Amplification is limited at soft soil sites by the dynamic strength of the weak soil, so attenuation occurs for intense input motions. This nonlinearity is not reflected in the site factors in current building codes. Guidance is provided for estimating the amplitude and pulse period for velocity pulses at soil sites.     

Liquefaction-Induced Settlement of Pile Groups in Liquefiable and Laterally Spreading Soils

The results of a series of dynamic centrifuge tests on model pile groups in (level) liquefied and laterally spreading soil profiles are presented. The piles are axially loaded at typical working loads, which has enabled liquefaction-induced settlements of the foundations to be studied. The development of excess pore pressures within the bearing layer (dense sand) was found to lead to a reduction in pile capacity and potentially damagingly large coseismic settlements. As the excess pore pressure increased, these settlements were observed to exceed postshaking downdrag-induced settlements, which occur due to the reconsolidation of liquefied sand around the pile shaft. In resisting settlement, the pile cap was found to play an important role by compensating for the capacity lost by the piles. This was shown to be achieved by the development of dilative excess pore pressures beneath the pile cap within the underlying loose liquefied sand which provide increasing bearing capacity with settlement. The centrifuge test data show good qualitative and quantitative agreement with the limited amount of model and full-scale data currently available in the literature. The implications of settlement for the design of piled foundations to serviceability conditions in both level and sloping ground are discussed, with settlement becoming an increasingly important consideration for laterally stiffer piles. Finally, empirical relationships have been derived from the test data to relate suitable static safety factors to given increases in excess pore pressure in the bearing layer within a performance-based design framework (i.e., based on limiting displacements).     

Investigation of Foundation Vibrations Resting on a Layered Soil System

This paper presents an investigation of the dynamic response of foundations resting on a layered soil underlain by a rigid layer. Model block vibration test results are used for the investigation. For the analysis, two different methods, namely, the equivalent spring-mass-dashpot model and the cone model, are used. A simple method to estimate the equivalent stiffness of the foundations resting on any multilayered soil system is presented. Obtaining stiffness from the proposed method and using different values of the damping factor ranging between 1.5 and 10.0%, the dynamic response of a foundation resting on a layered soil system is computed. One-dimensional wave propagation in an elastic cone for the analysis of foundations resting on the elastic homogeneous half-space or layered soil is also used to compute dynamic responses of the foundations resting on different layered soil. Finally, results obtained from two analytical methods are compared with the test results. It has been observed from the comparison that the results obtained by the equivalent spring-mass-dashpot model with a damping factor of 1.5% matched well with the experimental results for all cases. Results obtained by the cone model match well with experimental results for the cases where the top layer is softer than the bottom layer.     

不同桩体材料复合地基承载及变形性状对比试验研究

通过室内模型试验,实测得到碎石桩、夯实水泥土桩和CFG桩复合地基桩土荷载分担比、桩土应力比和桩间土深层变形,并对三类不同桩体材料复合地基的承载及变形性状进行了对比分析.认为碎石桩复合地基和夯实水泥土桩复合地基均存在有效桩长或有效复合土层厚度;碎石桩桩长超过有效桩长,对提高复合地基承载力和压缩模量、减小变形效果不明显,除一些特别情况如为处理可液化地基外,设计桩长可适当超过有效桩长,但不宜过长;夯实水泥土桩复合地基的有效桩长与桩身强度相关性显著,应以桩身强度控制进行夯实水泥土桩桩体设计,使按桩身强度确定的单桩承载力大于或等于由桩周土及桩端土的抗力所提供的单桩承载力;CFG桩复合地基桩身强度高,桩体自身压缩性小,可全桩长发挥侧阻作用,当桩端落在好的持力层时,能很好地发挥端阻,提高承载力,减小变形,设计时应优先选择好的桩端持力层进行设计.      

Role of Linear Elasticity in Pile Group Analysis and Load Test Interpretation

This paper compares linear-elastic and nonlinear pile group analysis methods through settlement analyses of hypothetical scenarios and real case studies, and elaborates on the implications for interpretation of pile load test data. Comparisons between linear-elastic and nonlinear methods justify the proposition that pile-to-pile interaction is dominated by linear elasticity, characterized by the small-strain soil stiffness. As the size of a pile group increases, nonlinearity in individual pile behavior becomes overwhelmed by the interaction effects. In such cases, similar estimates will be achieved by both linear and nonlinear methods if the soil modulus is derived from the initial tangent, rather than some secant stiffness, assessed from the load test data. The study clarifies the capabilities and limitations of linear elasticity in pile group analysis and provides guidance on pile test interpretation for analysis of pile group response.     

Effect of Soil Permeability on Centrifuge Modeling of Pile Response to Lateral Spreading

This paper presents experimental results and analysis of six model centrifuge experiments conducted on the 150?g-ton Rensselaer Polytechnic Institute centrifuge to investigate the effect of soil permeability on the response of end-bearing single piles and pile groups subjected to lateral spreading. The models were tested in a laminar box and simulate a mild infinite slope with a liquefiable sand layer on top of a nonliquefiable layer. Three fine sand models consisting of a single pile, a 3×1 pile group, and a 2×2 pile group were tested, first using water as pore fluid, and then repeated using a viscous pore fluid, hence simulating two sands of different permeability in the field. The results were dramatically different, with the three tests simulating a low permeability soil developing 3–6 times larger pile head displacements and bending moments at the end of shaking. Deformation observations of colored sand strips, as well as measurements of sustained negative excess pore pressures near the foundations in the “viscous fluid” experiments, indicated that an approximately inverted conical zone of nonliquefied soil had formed in these tests at shallow depths around the foundation, which forced the liquefied soil in the free field to apply its lateral pressure against a much larger effective foundation area. Additional p-y and limit equilibrium back-analyses support the hypothesis that the greatly increased foundation bending response observed when the soil is less pervious is due to the formation of such inverted conical volume of nonliquefied sand. This study provides evidence of the importance of soil permeability on pile foundations response during lateral spreading for cases when the liquefied deposit reaches the ground surface, and suggests that bending response may be greater in silty sands than in clean sands in the field. Moreover, the observations in this study may serve as basis for realistic practical engineering methods to evaluate pile foundations subjected to lateral spreading and pressure of liquefied soil.     

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.     

非均质土中海上风电单桩基础动力响应特性

采用有限元分析软件ABAQUS建立了非均质土中海上风电单桩基础数值计算模型,将桩基础受到的波浪、洋流及风荷载等效成双向对称循环荷载,对水平循环荷载作用下桩身水平位移、桩身剪力、桩身弯矩和桩侧土抗力进行了研究,并对不同循环次数下桩身水平位移进行了对比分析。研究表明,桩身水平位移随时间变化逐渐累积,随着循环次数的增加,泥面处桩身最大位移发生的时间点滞后;桩身剪力出现负值;桩身弯矩最大值发生在浅层土体;桩身外壁土抗力曲线随时间的变化在埋深约2/3处出现分界点,分界点上下范围内土抗力变化规律正好相反,在淤泥土和粉砂土分界面处增加显著;不同时间点桩身内壁沿埋深承担的荷载基本不变。      

Three-Dimensional Analysis of Lateral Pile Response using Two-Dimensional Explicit Numerical Scheme

A procedure for exploiting a two-dimensional (2D) explicit, numerical computer code for the 3D formulation of dynamic lateral soil-pile interactions is considered. The procedure is applied to two models using simultaneous computation of a series of plane strain boundary value problems, each of which represents a horizontal layer of soil. The first model disregards the shear forces developed between the horizontal layers, and may be considered as a generalized Winkler model. The second model takes account of these forces by coupling the behavior of the horizontal layers. Several verification problems for a single pile and pile groups in a homogeneous soil layer modeled as a viscoelastic material were solved and compared to known solutions in order to assess the reliability of the models. Excellent agreement was observed between results of the present analyses and existing solutions.     

Dynamic Experiments and Analyses of a Pile-Group-Supported Structure

Experimental data on the seismic response of a pile-group-supported structure was obtained through dynamic centrifuge model tests, and then used to evaluate a dynamic beam on a nonlinear Winkler foundation (BNWF) analysis method. The centrifuge tests included a structure supported on a group of nine piles founded in soft clay overlying dense sand. This structure was subjected to nine earthquake events with peak accelerations ranging from 0.02 to 0.7g. The centrifuge tests and dynamic analysis methods are described. Good agreement was obtained between calculated and recorded structural responses, including superstructure acceleration and displacement, pile cap acceleration and displacement, pile bending moment and axial load, and pile cap rotation. Representative examples of recorded and calculated behavior for the structure and soil profile are presented. Sensitivity of the dynamic BNWF analyses to the numerical model parameters and site response calculations are evaluated. These results provide experimental support for the use of dynamic BNWF analysis methods in seismic soil-pile-structure interaction problems involving pile-group systems.