Intensity measures for the seismic response of pile foundations

In this study the efficacy of various ground motion intensity measures for the seismic response of pile foundations embedded in liquefiable and non-liquefiable soils is investigated. A soil-pile-structure model consisting of a two-layer soil deposit with a single pile and a single degree-of-freedom superstructure is used in a parametric study to determine the salient features of the seismic response of the soil-pile-structure system. A suite of ground motion records scaled to various levels of intensity are used to investigate the full range of pile behaviour, from elastic response to failure. Various intensity measures are used to inspect their efficiency in predicting the seismic demand on the pile foundation for a given level of ground motion intensity. It is found that velocity-based intensity measures are the most efficient in predicting the pile response, which is measured in terms of maximum curvature or pile-head displacement. In particular, velocity spectrum intensity (VSI), which represents the integral of the pseudo-velocity spectrum over a wide period range, is found to be the most efficient intensity measure in predicting the seismic demands on the pile foundation. VSI is also found to be a sufficient intensity measure with respect to earthquake magnitude, source-to-site distance, and epsilon, and has a good predictability, thus making it a prime candidate for use in seismic response analysis of pile foundations.     

A discrete model for response estimation of soil-structure systems with embedded foundations

The need for simplifi ed physical models representing frequency dependent soil impedances has been the motivation behind many researches throughout history. Generally, such models are generated to capture impedance functions in a wide range of excitation frequencies, which leads to relatively complex models. That is while there is just a limited range of frequencies that really in? uence the response of the structure. Here, a new methodology based on the response-matching concept is proposed, which can lead to the development of simpler discrete models. The idea is then used to upgrade an existing simple model of surface foundations to the case of embedded foundations. The applicability of the model in both frequency domain and time domain analyses of soil-structure systems with embedded foundations is discussed. Moreover, the accuracy of the results is compared with another existing discrete model for embedded foundations.     

Winkler model for dynamic response of composite caisson-piles foundations: Lateral response

As the first part of a sequence focusing on the dynamic response of composite caisson-piles foundations (CCPFs¹), this paper develops a simplified method for the lateral response of these foundations. A Winkler model for the lateral vibration of the CCPF is created by joining the two components, the caisson and the pile group, where the four-spring Winkler model is utilized for the caisson and axial–lateral coupled vibration equations are derived for the pile group. For determining the coefficients of the four-spring Winkler model for the caissons, embedded footing impedance is used and a modification on the rotational embedment factor is made for the sake of the geometrical difference between shallow footings and caissons. Comparisons against results from finite element simulations demonstrate the reliability of this modified four-spring Winkler model for caissons in both homogenous and layered soils. The proposed simplified method for the lateral vibration of CCPFs is verified also by 3D finite element modeling. Finally, through an example, the idea of adding piles beneath the caisson is proved to be of great significance to enhance the resistance of the foundation against lateral dynamic loads.     

Kinematic bending moments in pile foundations

In this paper the kinematic seismic interaction of single piles embedded in soil deposits is evaluated by focusing the attention on the bending moments induced by the transient motion. The analysis is performed by modeling the pile like an Euler–Bernoulli beam embedded in a layered Winkler-type medium. The excitation motion is obtained by means of a one-D propagation analysis. A comprehensive parametric analysis is carried out by varying the main parameters governing the dynamic response of piles like the soil properties, the bedrock location, the diameter and embedment in the bedrock of piles. On the basis of the parametric analysis, a new design formula for predicting the kinematic bending moments for both the cross-sections at the deposit–bedrock interface and at the pile head is proposed.     

Winkler model for lateral response of rigid caisson foundations in linear soil

A generalized spring multi-Winkler model is developed for the static and dynamic response of rigid caisson foundations of circular, square, or rectangular plan, embedded in a homogeneous elastic. The model, referred to as a four-spring Winkler model, uses four types of springs to model the interaction between soil and caisson: lateral translational springs distributed along the length of the caisson relating horizontal displacement at a particular depth to lateral soil resistance (resultant of normal and shear tractions on the caisson periphery); similarly distributed rotational springs relating rotation of the caisson to the moment increment developed by the vertical shear tractions on the caisson periphery; and concentrated translational and rotational springs relating, respectively, resultant horizontal shear force with displacement, and overturning moment with rotation, at the base of the caisson. For the dynamic problem each spring is accompanied by an associated dashpot in parallel. Utilising elastodynamic theoretical available in the literature results for rigid embedded foundations, closed-form expressions are derived for the various springs and dashpots of caissons with rectangular and circular plan shape. The response of a caisson to lateral static and dynamic loading at its top, and to kinematically-induced loading arising from vertical seismic shear wave propagation, is then studied parametrically. Comparisons with results from 3D finite element analysis and other available theoretical methods demonstrate the reliability of the model, the need for which arises from its easy extension to multi-layered and nonlinear inelastic soil. Such an extension is presented in the companion papers by the authors [Gerolymos N, Gazetas G. Development of Winkler model for lateral static and dynamic response of caisson foundations with soil and interface nonlinearities. Soil Dyn Earthq Eng. Submitted companion paper; Gerolymos N, Gazetas G. Static and dynamic response of massive caisson foundations with soil and interface nonlinearities—validation and results. Soil Dyn Earthq Eng. Submitted companion paper.].     

Simplified mechanical subgrade model for dynamic response analysis of shallow foundations

Baranov proposed an approach for the treatment of the subgrade in the dynamic response analysis of a rigid foundation which is partially embedded. The approach is based on a Winkler approximation together with wave equation solutions developed for simplified conditions. The paper extends and modifies Baranov's approach so as to be applicable to surface foundation problems, by introducing an internal coupling mechanism. Closed form expressions are presented for the steady state harmonic responses of a massless rigid footing and an elastic beam on the surface of the presented subgrade model. These expressions can accommodate the inhomogeneity of the subgrade in a straightforward manner. The model is found to perform well in reproducing the continuous subgrade medium behaviour. The dynamic responses of structures are often highly dependent on the subgrade modelling and therefore great caution is needed in modelling the subgrade.     

Dynamic nonlinear response of pile foundations under vertical vibration—Theory versus experiment

The influence of nonlinearity on the dynamic response of cast-in-situ reinforced concrete piles subjected to strong vertical excitation was studied. Forced vibration test of single piles (L/d=10, 15, 20) and 2×2 pile groups (s/d=2, 3, 4 for each L/d) were conducted in the field for two different embedded conditions of pile cap. From the measured nonlinear response curves, the effective pile–soil system mass, stiffness and damping were determined and the nonlinear response curves were back-calculated using the theory of nonlinear vibration. The test results were compared with the continuum approach of Novak with dynamic interaction factor approach using both linear and linear-equivalent numerical methods. Reasonable match between the measured and predicted response was found for linear-equivalent methods by introducing a weak boundary-zone around the pile to approximately account for the nonlinear behaviour of pile–soil system. The test data were used to establish the empirical relationship in order to estimate the extent of soil separation around the pile with soil under vertical vibration.     

A simple model for non-vanishing rotational hysteresis in haematite

The model, applicable to fine-grained haematite, assumes that the magnetization of a grain is constrained to lie in the basal plane, within which there is a single easy axis. Following Stoner and Wohlfarth (1948), torque curves and rotational hysteresis are calculated, for various field strengths, as a function of the orientations of the basal plane and easy axis. The results show that, for certain orientations, rotational hysteresis may be expected to persist to very high field strengths. Further, the dependence of rotational hysteresis on orientation implies that rotational hysteresis is anisotropic and thus, that, for a distribution of grains, the anisotropy of resultant rotational hysteresis will reflect the degree of preferred orientation. It may therefore serve as a rock fabric parameter. Calculated models of resultant rotational hysteresis for assumed preferred orientation distributions compare favourably with measurements on a sample of Cambrian purple slate from North Wales.     

地震区跨活动断层桥梁桩基动力时程响应分析

为了研究强震区桥梁跨活动断层时,桩基在地震中的动力响应,以海文大桥为工程背景,利用Midas GTS有限元软件建立其强震区桩-海床岩土体-断层耦合作用的数值模型,研究不同强度(0.20g～0.60g)的50年超越概率为10%的地震波(后文简称5010地震波)作用下,桥梁桩基加速度、位移、弯矩及剪力的动力时程响应特性。结果表明：上部大厚度松散土体对桩身加速度有放大及滤波作用,而基岩对桩身加速度几乎不产生作用;断层上、下盘桩基础的桩顶水平位移随输入地震动强度的增大而增大,但达到振幅的时刻一致;上、下盘桩基础桩顶竖向位移时程响应都在50 s以后产生永久沉降;桩身最大弯矩截面处时程响应均在40 s以后产生永久弯矩;应重点考虑上部覆盖层软硬土体界面和基岩界面的抗弯承载力设计,及桩顶和基岩面附近的抗剪承载力设计;上盘桩基础按桩身加速度、弯矩、桩顶水平位移等动参数控制设计,下盘桩基础按动剪应力控制设计。     

Modelling of raked pile foundations in liquefiable ground

Raked piles are believed to behave better than vertical piles in a laterally flowing liquefied ground. This paper aims at numerically simulating the response of raked pile foundations in liquefying ground through nonlinear finite element analysis. For this purpose, the OpenSees computer package was used. A range of sources have been adopted in the definition of model components whose validity is assessed against case studies presented in literature. Experimental and analytical data confirmed that the backbone force density–displacement (p–y) curve simulating lateral pile response is of acceptable credibility for both vertical and raked piles. A parametric investigation on fixed-head piles subject to lateral spreading concluded that piles exhibiting positive inclination impart lower moment demands at the head while those inclined negatively perform better at liquefaction boundaries (relative to vertical piles). Further studies reveal substantial axial demand imposed upon negatively inclined members due to the transfer of gravity and ground-induced lateral forces axially down the pile. Extra care must be taken in the design of such members in soils susceptible to lateral spreading such that compressive failure (i.e. pile buckling) is avoided.     

A novel hysteresis model in unsaturated soil

This study presents a novel hysteresis model based on van Genuchten's soil‐moisture relationships. The proposed model yields a series of closed‐form relationships in which two shape factors α and η are determined from the main drying and wetting curves. Experimental and literature‐cited data were used to assess model accuracy. The proposed model was also compared with the Scott and KP models. Analytical results indicate that the present model is simple, accurate and effective in constructing the series of wetting and drying scanning curves. Notably, the proposed model outperforms the Scott and KP models in terms of model accuracy. Moreover, the novel model eliminates the pumping effect and has perfect closure at scanning curve reversal points. Copyright © 2004 John Wiley & Sons, Ltd.     

Probabilistic pseudo-static analysis of pile foundations in liquefiable soils

This paper presents the development, implementation, and application of a probabilistic framework for the pseudo-static analysis of pile foundations in liquefied and lateral spreading soils. The framework allows for rigorous consideration and propagation of the large uncertainties regarding quantification of seismic loads and soil–pile interaction relationships, which exist in the pseudo-static method. Building upon previous relationships proposed by others, the key features of the presented framework are outlined. In particular, the uncertainty estimation of the induced lateral soil displacements; superstructure inertia loads; and stiffness and strength of the liquefied soils are discussed in detail. The results of applying the pseudo-static method to a case study bridge structure are compared to that obtained using a rigorous seismic effective stress analysis within a similar framework. It is illustrated that the consideration of uncertainties in the pseudo-static framework provides enhanced communication of the foundation's seismic performance to end-users, and that the pseudo-static method provides seismic performance prediction consistent with that obtained using advanced seismic effective-stress analyses.     

A lumped parameter model for time‐domain inertial soil‐structure interaction analysis of structures on pile foundations

The paper presents a lumped parameter model for the approximation of the frequency‐dependent dynamic stiffness of pile group foundations. The model can be implemented in commercial software to perform linear or nonlinear dynamic analyses of structures founded on piles taking into account the frequency‐dependent coupled roto‐translational, vertical, and torsional behaviour of the soil‐foundation system. Closed‐form formulas for estimating parameters of the model are proposed with reference to pile groups embedded in homogeneous soil deposits. These are calibrated with a nonlinear least square procedure, based on data provided by an extensive non‐dimensional parametric analysis performed with a model previously developed by the authors. Pile groups with square layout and different number of piles embedded in soft and stiff soils are considered. Formulas are overall well capable to reproduce parameters of the proposed lumped system that can be straightforwardly incorporated into inertial structural analyses to account for the dynamic behaviour of the soil‐foundation system. Some applications on typical bridge piers are finally presented to show examples of practical use of the proposed model. Results demonstrate the capability of the proposed lumped system as well as the formulas efficiency in approximating impedances of pile groups and the relevant effect on the response of the superstructure.     

Azimuthal variation in AVO response for fractured gas sands

Natural fractures in reservoirs play an important role in determining fluid flow during production, and hence the density and orientation of fractures is of great interest. In the presence of aligned vertical fractures, the reflection amplitude at finite offset varies with azimuth. The effect of natural fractures on the azimuthal AVO response from a gas-sandstone reservoir encased within shale is investigated. A simple expression for the difference in P-wave reflection coefficient from the top of the reservoir parallel and perpendicular to the strike of the fractures is obtained in terms of the normal and tangential compliances, Z_N and Z_T, of the fractures. This expression is valid for small anisotropy and material contrasts and is compared with the results of numerical modelling. For a given value of Z_T, the azimuthal variation in reflection coefficient at moderate offsets is found to increase with decreasing Z_N/Z_T. For gas-filled open fractures Z_N/Z_T ≈ 1, but a lower ratio of Z_N/Z_T may result from the presence of cement or clay within the fractures, or from the presence of a fluid with non-zero bulk modulus. For Z_N/Z_T = 1 and moderate offsets, the variation with offset of the reflection coefficient from the top of the fractured unit is dominated by the contrast in Poisson's ratio between the gas sand and the overlying shale, the effect of fractures only becoming noticeable as the critical angle for the unfractured sandstone is approached. However, for reflections from the base of the fractured unit, the variation in reflection amplitude with azimuth is much greater at conventional seismic offsets than for the reflection from the top. Azimuthal variations in the strength of the reflection from the top of the reservoir depend only on the variation in reflection coefficient, whereas the raypath is also a function of azimuth for reflections from the base of the fractured unit, leading to stronger, more visible, variations of AVO with azimuth. It follows that an azimuthal variation in AVO due to fractures in the overburden may be misinterpreted as due to the presence of aligned fractures in the reservoir.     

A response-based simplified model for vertical vibrations of embedded foundations

A simplified damped oscillator model is proposed to simulate unbounded soil for the vertical vibration analysis of rigid embedded foundations. Based on the dynamic responses of a foundation–soil system, an optimal equivalent model is determined as the best simplified model. Magnification responses of a foundation–soil system simulated by the optimal equivalent model are well consistent with those obtained by the half-space theory and by a widely used computer program even as embedment depth or vibrating mass increases. The optimal equivalent model utilizing only three parameters can result in responses as accurate as the existing models, which use more parameters. This proposed method uses much simpler procedure than optimization techniques used by most existing discrete models. This proposed method may also be easily and accurately applied to practical soil–structure interaction analysis.     

Dynamic behaviour of pile foundations in homogeneous and non-homogeneous media

A three-dimensional formulation based on Green's functions of cylindrical loads in layered semi-infinite media is employed to investigate the dynamic behaviour of piles in homogeneous and non-homogeneous half spaces. The pile-soil-pile interaction taking place in pile groups is incorporated in the model. The results presented in this paper include the dynamic stiffnesses and dampings of single piles as well as those of representative 2 × 2 and 4 × 4 square pile groups in the soil media considered in this study. In addition, the distribution of forces applied on the pile cap among the individual piles in a group is investigated.     

橡胶垫隔震装置的双向弹塑性恢复力模型

改进了铅芯叠层钢板橡胶垫隔震装置的Park模型，提出其双向弹塑性恢复力模型。建议的模型克服了Park模型不能从橡胶垫力学试验曲线上直观获取所需参数的缺点。采用本文建议模型的结构分析程序HBTA2．0可以方便地用于实际隔震结构的弹塑性动力分析，计算结果也更为合理。     

Complex-parameter kelvin model for elastic foundations

A new rigorous approach in modelling mechanical behaviour is developed. The dynamic response of a rigid disc resting on an elastic half-space is approximated by a macroscopic force-displacement relationship, where not only the coefficients but also the order of time derivatives are complex valued. It is shown that comlex-parameter constitutive models are not simply an elegant alternative in modelling mechanical behaviour, but are the outcome of rigorous non-linear regression analysis on complex-valued functions, like the dynamic stiffness of dissipative systems. Complex-parameter constitutive models are very attractive since a minimum number of parameters is required to obtain a satisfactory fit of the ‘exact’ response. A two-parameter generalized Kelvin model reproduces closely the ‘exact’ dynamic stiffness of the disc for all three vertical, horizontal and rocking modes studied herein. Frequency- and time-domain algorithms to solve complex-order differential equations are developed, validated and used to calculate the foundation–response under earthquake excitation. It is the excellent agreement of results and the economy in number of parameters that make complex-parameter models so attractive in constitutive modelling.     

A generalized least-squares model

Summary A interpolation method is given for the case in which a function consisting of a systematic and a random part is to be estimated from measurements affected by errors. This is a combined problem of parameter estimation, filtering and prediction, which has applications in different fields of geodesy and gravimetry. The solution of the problem is derived from a least-squares principle; it is formally very similar to a general case of least-squares adjustment. Address: Hardenbergstr. 34, 1 Berlin 12.     

The effects of liquefaction-induced lateral spreading on pile foundations

Observations of pile foundation performance during previous earthquakes have shown that pile failure has been caused by lateral ground movements resulting from soil liquefaction. The recognition that lateral ground movements may play a critical role in pile performance during an earthquake has important implications for design and risk assessment, and requires that analytical models be devised to evaluate these potential problems.In this paper, parametric studies were conducted to estimate the maximum bending moments induced in piles subjected to lateral ground displacement. The results are summarized in charts using dimensionless parameters.The analyses reveal that the existence of a nonliquefiable layer at the ground surface can affect significantly the maximum bending moment of the pile. When a relatively thick nonliquefiable layer exists above a liquefiable layer, neither the material nonlinearity of the soil nor loss of soil stiffness within the liquefiable layer significantly affect the maximum bending moment. When the thickness of the liquefiable soils is greater than about three times that of an overlying intact layer, soil stiffness in the liquefiable layer must be chosen carefully when evaluating the maximum bending moment.