Simplified approach for design of raft foundations against fault rupture. Part Ⅱ： soil-structure interaction

This is the second paper of two, which describe the results of an integrated research effort to develop a four-step simplified approach for design of raft foundations against dip-slip （normal and thrust） fault rupture. The first two steps dealing with fault rupture propagation in the free-field were presented in the companion paper. This paper develops an approximate analytical method to analyze soil-foundation-structure interaction （SFSI）, involving two additional phenomena： （i） fault rupture diversion （Step 3）; and （ii） modification of the vertical displacement profile （Step 4）. For the first phenomenon （Step 3）, an approximate energy-based approach is developed to estimate the diversion of a fault rupture due to presence of a raft foundation. The normalized critical load for complete diversion is shown to be a function of soil strength, coefficient of earth pressure at rest, bedrock depth, and the horizontal position of the foundation relative to the outcropping fault rupture. For the second phenomenon （Step 4）, a heuristic approach is proposed, which ＂scans＂ through possible equilibrium positions to detect the one that best satisfies force and moment equilibrium. Thus, we account for the strong geometric nonlinearities that govern this interaction, such as uplifting and second order （P-△） effects. Comparisons with centrifuge-validated finite element analyses demonstrate the efficacy of the method. Its simplicity makes possible its utilization for preliminary design.     

Kinematic interaction factors of deep foundations with inclined piles

The beneficial or detrimental role of battered piles on the dynamic response of piled foundations has not been yet fully elucidated. In order to shed more light on this aspect, kinematic interaction factors of deep foundations with inclined piles, are provided for single‐battered piles, as well as for 2 × 2 and 3 × 3 groups of piles subjected to vertically incident plane shear S waves. Piles are modelled as linear‐elastic Bernoulli beams, whereas soil is assumed to be a linear, isotropic, homogeneous viscoelastic half‐space. Different pile group configurations, pile‐soil stiffness ratios, and rake angles are considered. The relevance and main trends observed in the influence of the rake angle on the kinematic interaction factors of the analysed foundations are inferred from the presented results. An important dependence of the kinematic interaction factors on the rake angle is observed together with the existence of an inclination angle at which cap rotation and excitation become out of phase in the low‐to‐mid frequency range. The existence of a small batter angle that provides minimum cap rotation is also shown. Copyright © 2014 John Wiley & Sons, Ltd.     

Filtering action of embedded massive foundations: New analytical expressions and evidence from 2 instrumented buildings

This paper deals with the effect of the foundation mass on the filtering action exerted by embedded foundations. The system under examination comprises a rigid rectangular foundation embedded in a homogeneous isotropic viscoelastic half‐space under harmonic shear waves propagating vertically. The problem is addressed both theoretically and numerically by means of a hybrid approach, where the foundation mass is explicitly included in the kinematic interaction between the foundation and the surrounding soil, thus referring to a “quasi‐kinematic” interaction problem. Based on the results of an extensive parametric study, it is shown that the filtering problem depends essentially on three dimensionless parameters, i.e.: the dimensionless frequency of the input motion, the foundation width‐to‐embedment depth ratio, and the foundation‐to‐soil mass density ratio. In complements to the translational and rotational kinematic interaction factors that are commonly adopted to quantify the filtering effect of rigid massless foundations on the free‐field motion, an additional kinematic interaction factor is introduced, referring to the horizontal motion at the top of a rigid massive foundation. New analytical expressions for the above kinematic interaction factors are proposed and compared with foundation‐to‐free‐field transfer functions computed from available earthquake recordings on two instrumented buildings in LA (California) and Thessaloniki (Greece). Results indicate that the foundation mass can have a strong beneficial effect on the filtering action with increasing foundation‐to‐soil mass density and foundation width‐to‐embedment depth ratios.     

Parametric earthquake response of torsionally coupled buildings with foundation interaction

A study is made of the effect of soil-structure interaction on the coupled lateral and torsional responses of asymmetric buildings subjected to a series of historical free-field earthquake base motions. It sh shown that for particular classes of actual buildings the equivalent rigid-base responses are significantly increased for structures founded on medium-stiff soils, and hence the assumption of the major building codes that a conservative estimate of response is obtained by considering the structure to be fixed rigidly at its base is shown to be inconsistent with the presented dynamic results. It is shown that foundation interaction produces greatest amplification of torsional coupling effects for structures subjected to a particular class of European strong-motion earthquake records, identified by similarities in their spectral shape, for which the vibrational energy of the ground motion is distributed approximately uniformly over the range of frequencies which are of interest for real structures. It is recommended that provision be made in the torsional design procedures of building codes for the increase in the coupled torsional response due to soil-structure interaction as indicated in this study. Such provision should be based on the results of comprehensive parametric studies employing a wide selection of earthquake records and accounting for expected variations in localized soil conditions.     

结构-基础-土-河流相互作用地震反应分析

为了研究不同基础形式下河水对成层软土地基上建筑物地震反应的影响,构建了结构-基础-土-河水体系动力相互作用的非线性完全有限元计算模型,在考虑土体重力的前提下,对筏片基础、桩筏基础、箱形基础、桩箱基础相互作用体系进行了时域数值分析。计算结果表明,建筑物靠近河水时,筏基和箱基体系顶部位移发生了向河水一侧的偏移,而采用桩基和桩箱基础时其偏移度明显减小。同种基础形式下,建筑物距河水越远,其框架剪力峰值越大,而不同基础形式的同种工况,桩箱基础时柱剪力最大,筏片基础时最小。单纯筏基和箱基时,基础周围土体均大量进入塑性,上部结构仍保持弹性;而采用下部有桩基础的筏基或箱基时,地基土体只有很少量进入塑性,上部框架结构进入了塑性。     

Study of vibrating foundations considering soil-pile-structure interaction for practical applications

An investigation of soil-pile-structure interaction is carried out, based on a large reciprocating compressor installed on an elevated concrete foundation （table top structure）. A practical method is described for the dynamic analysis, and compared with a 3D finite element （FE） model. Two commercial software packages are used for dynamic analysis considering the soilpile-structure interaction （SPSI）. Stiffness and damping of the pile foundation are generated from a computer program, and then input into the FE model. To examine the SPSI thoroughly, three cases for the soil, piles and superstructure are considered and compared. In the first case, the interaction is fully taken into account, that is, both the superstructure and soil-pile system are flexible. In the second case, the superstructure is flexible but fixed to a rigid base, with no deformation in the base （no SSI）. In the third case, the dynamic soil-pile interaction is taken into account, but the table top structure is assumed to be rigid. From the comparison beteen the results of these three cases some conclusions are made, which could be helpful for engineering practice.     

土-结构相互作用效应对结构基底地震动影响的试验研究

利用土与结构动力相互作用振动台模型试验数据,通过各种试验工况下土层表面与基础表面加速度反应的比较,深入探讨了土与结构动力相互作用效应对高层建筑结构基底地震动的影响。从输入地震动频谱特性、输入地震动强度水平和上部结构动力特性3个方面详细分析了与SSI效应对高层建筑基底震动影响程度有关的一些因素。结果表明：SSI效应对高层建筑基底地震动的影响与输入地震波的动力特性有很大关系。在地震动的频谱成分方面,SSI效应对高层建筑基底地震动的影响主要体现为土层表面和基础表面在与输入地震动卓越频率相近处的频谱成分有较大差异;SSI效应对高层建筑基底地震动的影响程度随着输入加速度峰值水平的增加而减小;在某一特定地震波作用下,当上部结构的振动频率与地震地面运动的卓越频率相近时,SSI效应对高层建筑基底地震动的影响较为强烈。     

桩-土-结构相互作用对结构弹塑性变形特性的影响

在桩-土-结构弹塑性动力相互作用模型研究的基础上,设计了考虑场地类别、输入地震动等因素的基于相互作用模型的多层和高层钢筋混凝土框架结构算例,分析了桩-土-结构相互作用对结构弹塑性变形特性的影响,并与不考虑相互作用的结构底部固端模型的计算结果进行了对比。分析表明:相互作用对结构的弹塑性变形的影响不容忽视,考虑相互作用后梁柱塑性铰出现的程度降低;结构底部位移增加而顶部位移减小;薄弱层的层间位移可能增加而其余层的层间位移则减小。现行的结构弹塑性变形验算方法未考虑土-结构相互作用的做法的合理性值得进一步评判。     

Site effects and soil-structure interaction in the valley of Mexico

An engineering approach is proposed for representing both site effects and soil-structure interaction in extended alluvial valleys, by using the one-dimensional model of shear were propagation corrected empirically to account for lateral heterogeneities and generated surface waves. The peak structural response is expressed by means of spectral contours that are a function of the predominant period of the site and the fundamental period of the structure. Variations of the peak spectral ordinates with the prevailing site period can be deduced from these contours. A number of events of firm ground, representative of the most dangerous earthquakes expected in Mexico City, are assumed as design earthquakes. Making use of the resulting spectral contours, the provisions for site effects recommended in the Mexican seismic code are evaluated. Also, considering as control motion the 1985 Michoacan earthquake recorded at a representative firm site, spectral contours with soil-structure interaction are obtained which allow one to identify the significant interaction effects originating in the Valley of Mexico for medium- and long-period structures. The influence and relative importance of the critical parameters involved are examined within practical ranges of interest.     

Identification of soil–structure interaction effect in base-isolated bridges from earthquake records

Identification of system parameters with the help of records made on base-isolated bridge during earthquakes provides an excellent opportunity to study the performance of the various components of such bridge systems. Using a two-stage system identification methodology for non-classically damped systems, modal and structural parameters of four base-isolated bridges are reliably identified using acceleration data recorded during 18 earthquakes. Physical stiffness of reinforced concrete columns, dynamic properties of soil and foundation impedance are found by available theoretical models in conjunction with pertinent information from the recorded accelerographs. Soil–structure interaction (SSI) effect in these bridges is examined by comparing the identified and physical stiffness of the sub-structure components. It is found that SSI is relatively pronounced in bridges founded in weaker soils and is more strongly related to the ratio of pier flexural stiffness and horizontal foundation stiffness than soil shear modulus, G_s, alone. However, substantial reduction in G_s is observed for moderate seismic excitation and this effect should be taken into account while computing foundation impedance.     

考虑地基土液化影响的高层建筑地震反应分析

为了研究地基土液化对高层建筑地震反应的影响，本文简要介绍了分时段等效线性有效应力动力分析方法，且将其中的等效线性化方法改进为逐步迭代非线性方法，并利用ANSYS程序的参数化设计语言将这一分析方法并入ANSYS程序中，最后分析了考虑液化时桩基-高层建筑体系的地震反应。认为对于单层砂土-桩基-高层建筑体系来说，砂土的液化对上部结构地震反应有较大的影响；而对于本文采用的上海土-桩基-高层建筑体系来说，砂土层的液化未对上部结构的地震反应产生明显的影响。     

Rocking response of flexible circular foundations on layered media

The analysis of the response of a flexible circular foundation on layered media due to an arbitrarily distributed vertical loading is presented. The analysis is based on the ‘ring method’ approach, i.e. discretization of the foundation in a set of concentric rings. The arbitrarily distributed loading is expanded in the circumferential direction in a Fourier series. The influence coefficient matrix of soil for each element of the series is evaluated utilizing the stiffness matrix approach. The stiffness matrix of the foundation is obtained from the finite difference energy method approach. Numerical examples illustrate the influence of several soil-foundation parameters on the rocking response of a foundation. Results are presented in terms of displacement and soil reaction distributions and impedance functions point to significantly different responses of flexible and rigid foundations.     

土-结构相互作用地震反应分析软件及其二次开发

本文简要介绍了目前在土-结构相互作用分析中常用的有限元软件ANSYS7.0、FLAC和MSC.M arc,通过比较评价其各自优缺点和适用性后,根据高层建筑结构土-结构相互作用地震反应分析的特点,建议利用带有灵活接口的大型非线性有限元分析软件MSC.M arc作为其分析工具,并尝试对MSC.M arc进行二次开发,将多层土E-B本构关系模型作为子程序加入其中。     

场地土对地震波的放大效应

基于几次大地震现象的启迪，分析在盆地效应的作用下，墨西哥城具特殊工程地质性质的软土，放大地震波，增强地震烈度，加重地震灾害。指出强震区场地土条件对地震动特性的影响可导致地基土的卓越周期与建筑物的自振周期产生共振，这一效应使自振周期较长的工程结构在地震力的作用下破损并导致建筑物彻底毁坏。研究震区盆地效应是服务于工程抗震工作的重要方面。     

土-结构动力相互作用对结构控制的影响

本文研究了土-结构动力相互作用对采取不同控制措施的结构控制效果的影响。文中首先建立了主动调谐质量阻尼器(ATMD)、半主动磁流变阻尼器(MR)和被动多重调谐质量阻尼器(MTMD)等三种结构控制措施在时域中的控制算法和控制律，然后基于子结构法，采用间接边界元方法，通过傅里叶变换，推导了分别安装三种结构控制措施的受控结构在频域中的运动方程，数值仿真分析了某36层高层建筑的地震反应及其控制效果。结果表明，当采用ATMD或MTMD控制时，考虑土-结构动力相互作用后结构地震反应有所减小；当采用MR控制时，考虑土-结构动力相互作用后结构地震反应有很大程度的减小。由此看来，在设计软土地基上高层结构的结构控制措施时，不考虑土-结构动力相互作用对结构控制效果的影响是偏于安全的。     

Vertical earthquake response of megawatt‐sized wind turbine with soil‐structure interaction effects

The dynamic response of a wind turbine on monopile is studied under horizontal and vertical earthquake excitations. The analyses are carried out using the finite element program SAP2000. The finite element model of the structure is verified against the results of shake table tests, and the earthquake response of the soil model is verified against analytical solutions of the steady‐state response of homogeneous strata. The focus of the analyses in this paper is the vertical earthquake response of wind turbines including the soil‐structure interaction effects. The analyses are carried out for both a non‐homogeneous stratum and a deep soil using the three‐step method. In addition, a procedure is implemented which allows one to perform coupled soil‐structure interaction analyses by properly tuning the damping in the tower structure. The analyses show amplification of the ground surface acceleration to the top of the tower by a factor of two. These accelerations are capable of causing damage in the turbine and the tower structure, or malfunctioning of the turbine after the earthquake; therefore, vertical earthquake excitation is considered a potential critical loading in design of wind turbines even in low‐to‐moderate seismic areas. Copyright © 2015 John Wiley & Sons, Ltd.     

1-g Experimental investigation of bi-layer soil response and kinematic pile bending

The effect of soil inhomogeneity and material nonlinearity on kinematic soil–pile interaction and ensuing bending under the passage of vertically propagating seismic shear waves in layered soil, is investigated by means of 1-g shaking table tests and nonlinear numerical simulations. To this end, a suite of scale model tests on a group of five piles embedded in two-layers of sand in a laminar container at the shaking table facility in BLADE Laboratory at University of Bristol, are reported. Results from white noise and sine dwell tests were obtained and interpreted by means of one-dimensional lumped parameter models, suitable for inhomogeneous soil, encompassing material nonlinearity. A frequency range from 0.1 Hz to 100 Hz and 5 Hz to 35 Hz for white noise and sine dwell tests, respectively, and an input acceleration range from 0.015 g to 0.1 g, were employed. The paper elucidates that soil nonlinearity and inhomogeneity strongly affect both site response and kinematic pile bending, so that accurate nonlinear analyses are often necessary to predict the dynamic response of pile foundations.     

Variations in the dynamic response of structures founded on piles induced by obliquely incident SV waves

Although the seismic actions generally consist of a combination of waves, which propagates with an angle of incidence not necessarily vertical, the common practice when analyzing the dynamic behavior of pile groups is based on the assumption of vertically incident wave fields. The aim of this paper is to analyze how the angle of incidence of SV waves affects the dynamic response of pile foundations and piled structures. A three-dimensional boundary element-finite element coupling formulation is used to compute impedances and kinematic interaction factors corresponding to several configurations of vertical pile groups embedded in an isotropic homogeneous linear viscoelastic half-space. These results, which are provided in ready-to-use dimensionless graphs, are used to determine the effective dynamic properties of an equivalent single-degree-of-freedom oscillator that reproduces, within the range where the peak response occurs, the response of slender and nonslender superstructures through a procedure based on a substructuring model. Results are expressed in terms of effective flexible-base period and damping as well as maximum shear force at the base of the structure. The relevance and main trends observed in the influence of the wavefront angle of incidence on the dynamic behavior of the superstructure are inferred from the presented results. It is found that effective damping is significantly affected by the variations of the wave angle of incidence. Furthermore, it comes out that the vertical incidence is not always the worst-case scenario.     

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.