Stochastic dynamic stiffness of a surface footing for offshore wind turbines: Implementing a subset simulation method to estimate rare events

The purpose of this study, which concerns the stochastic dynamic stiffness of foundations for large offshore wind turbines, is to quantify uncertainties related to the first natural frequency of a turbine supported by a surface footing and to estimate the low event probabilities. Herein, a simple model of a wind turbine structure with equivalent coupled springs at the base is calibrated with the mean soil property values. A semianalytical solution, based on the Green׳s function for a layered half-space is utilized for estimation of foundation responses. Soil elastic modulus and layer depth are considered as random variables with lognormal distributions. The uncertainties are quantified, and the estimation of rare events of the first natural frequency is discussed through an advanced reliability approach based on subset simulation. This analysis represents a first step in the estimation of the safety with respect to the failure of a turbine in the fatigue limit state.     

Centrifuge modeling of load-deformation behavior of rocking shallow foundations

Shallow foundations supporting building structures might be loaded well into their nonlinear range during intense earthquake loading. The nonlinearity of the soil may act as an energy dissipation mechanism, potentially reducing shaking demands exerted on the building. This nonlinearity, however, may result in permanent deformations that also cause damage to the building. Five series of tests on a large centrifuge, including 40 models of shear wall footings, were performed to study the nonlinear load-deformation characteristics during cyclic and earthquake loading. Footing dimensions, depth of embedment, wall weight, initial static vertical factor of safety, soil density, and soil type (dry sand and saturated clay) were systematically varied. The moment capacity was not observed to degrade with cycling, but due to the deformed shape of the footing–soil interface and uplift associated with large rotations, stiffness degradation was observed. Permanent deformations beneath the footing continue to accumulate with the number of cycles of loading, though the rate of accumulation of settlement decreases as the footing embeds itself.     

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.     

弦支穹顶结构动力反应分析

以天津开发区商务中心大堂的弦支穹顶为研究对象,分析了弦支穹顶结构体系的自振特性,分别运用随机模拟风振分析方法和时间历程分析方法,对其进行了风振和地震反应分析,得到了结构在动力荷载作用下的响应时程,并对分析结果进行了频谱分析和统计分析。研究发现弦支穹顶结构的自振频率呈密集型分布,且振型复杂;结构的风振响应基本以受迫振动为主,没有出现明显的峰值共振现象;结构的地震响应在前几阶基频处出现了较为明显的峰值共振现象;从振动的幅值角度看,风荷载的动力作用效应相对于地震荷载要显著。     

含氯盐遗址土盐渍风蚀效应试验研究

盐渍风蚀是中国西北干旱区岩土体盐渍劣化加剧风蚀损耗的一种普遍破坏效应,导致遗址体底部盐渍区掏蚀凹进,严重威胁遗址整体稳定。基于室内试验,采用脱盐遗址土掺入不同含量NaCl后制成重塑样,模拟自然干湿循环条件养护并进行声波测试和风洞试验,就遗址土盐渍劣化和风蚀损耗效应做出初步分析。结果表明:含氯盐遗址土试样盐渍劣化和风蚀损耗过程中含盐量是内在因素,干湿循环起着外助力作用。     

Investigation of the dynamic response of rigid footings on tensionless Winkler foundation

The dynamic response of a rigid footing resting on an elastic tensionless Winkler foundation is examined. A parametric investigation, concerning the effect of the main parameters on the response, is performed for harmonic excitation. The parameters examined include the stiffness and the damping of the foundation, the excitation frequency and the superstructure characteristics and loads. The maximum rocking response, the minimum length of contact after uplift, the maximum stress developed at the soil and the factor of safety with respect to the bearing capacity of the soil are used to measure the effect of each dimensionless parameter. An example for earthquake excitation is also given for a plane frame. The results are compared to the ones of a simplified static approach based on the maximum values of the applied loads, similarly to the procedure that is usually applied in practice. The results show that the static approach can predict the response satisfactorily if resonance does not happen, if the stiffness of the foundation is not large compared to the stiffness of the superstructure and if the dynamic part of the axial force of the column is not large; in these cases, it may underestimate or overestimate the response significantly, depending on the sign of the dynamic axial force that is considered.     

Performance evaluation of a shallow foundation built on structured clays under seismic loading

Due to the increased need of storage, larger and higher structures are being built all over the world, thus requiring a more careful evaluation of the mechanical performance of their foundation deposits both in terms of bearing capacity and compressibility behaviour. The design of such structures and their serviceability and stability is largely governed by the effects of the dynamic loading conditions principally because of their significantly elevated risk in seismic prone zones. In this paper, numerical analyses using an advanced constitutive model, able to account for the initial soil structure and its progressive degradation, have been performed to investigate the seismic response of a silo foundation built on structured clays. The proposed analyses involve the use of a fully-coupled finite element approach. For the dynamic simulations, three different input motions have been selected form earthquake databases according to the seismic hazard study of the specific site. The results of the silo dynamic response are illustrated in terms of signal amplification, permanent excess pore water pressures, accumulated displacements and structure induced degradation during and after the seismic loading. The dynamic behaviour of the footing indicates that extreme earthquake events can induce large destructuration in natural clays, leading to ground settlements up to twice the observed ones under static loads, which need to be properly accounted for in the design. This suggests that there are significant advantages in using advanced models which recognise the existence of initial soil structure and its subsequent damage due to the applied dynamic loads.     

风荷载作用下的土-结构动力特性分析

结构的动力特性直接影响到动力荷载的作用效应。动力特性分析中,土体的影响不可忽视。与地震荷载不同,动风荷载自结构向土体传播,土体的惯性力可以忽略。无质量地基法可以满足针对风荷载的土-结构动力分析的要求。本文首先推导土-结构动力相互作用的运动方程,在此基础上,以剪力墙箱型基础结构为基本分析对象,确定有限地基域的范围,分析土-结构整体动力特性。认为：足够的基础埋深,可以有效控制建筑物的摆动;为控制建筑物的动力特性,可以采取措施适当使地基土增加一定的刚度;如何在上部结构的质量和刚度之间建立对应关系以控制土-结构系统的动力特性,有待进一步研究。     

Simplified discrete systems for dynamic analysis of structures on footings and piles

A simplified discrete system in the form of a simple oscillator is developed to simulate the dynamic behavior of a structure founded through footings or piles on compliant ground, under harmonic excitation. Exact analytical expressions for the fundamental natural period and the corresponding damping coefficients of the above system are derived, as function of geometry and the frequency-dependent foundation impedances. In an effort to quantify the coupling between swaying and rocking oscillations in embedded foundations such as piles, the reference system is translated from the footing–soil interface to the depth where the resultant soil reaction is applied, to ensure a diagonal impedance matrix. The resulting eccentricity is a measure of the coupling effect between the two oscillation modes. The amounts of radiation damping generated from a single pile and a surface footing are evaluated. In order to compare the damping of a structure on a surface footing and a pile, the notion of static and geometric equivalence is introduced. It is shown that a pile may generate significantly higher radiation damping than an equivalent footing, thus acting as an elementary protective system against seismic action.     

Dynamic response of tipping core buildings

When subjected to major earthquakes, core-stiffened buildings may begin to tip. That is, the overturning moment on the core's footing becomes so large that the footing breaks contact with the ground and begins to rock. A method is described for including the effects of tipping in the analysis of multistorey core-braced structures. Curves are presented which summarize the maximum response to both pulse and earthquake excitations; these data are elucidated via a typical design example. By comparison to fixed-base behaviour, tipping greatly reduces the base shear and moment. This makes possible a more economical design. However, attention must be devoted to avoiding potential soil-mechanics problems associated with the wobbling behaviour of the tipping core.     

Prediction of pile response to lateral spreading by 3-D soil–water coupled dynamic analysis: Shaking in the direction perpendicular to ground flow

The 1995 Kobe earthquake seriously damaged numerous buildings with pile foundations adjacent to quay walls. The seismic behavior of a pile group is affected by movement of quay walls, pile foundations, and liquefied backfill soil. For such cases, a three-dimensional (3-D) soil–water coupled dynamic analysis is a promising tool to predict overall behavior. We report predictions of large shake table test results to validate 3-D soil–water coupled dynamic analyses, and we discuss liquefaction-induced earth pressure on a pile group during the shaking in the direction perpendicular to ground flow. Numerical analyses predicted the peak displacement of footing and peak bending moment of the group pile. The earth pressure on the pile in the crustal layer is most important for the evaluation of the peak bending moment along the piles. In addition, the larger curvatures in the bending moment distribution along the piles at the water side in the liquefied ground were measured and predicted.     

An experimental study on the rocking response of bridge piers with spread footing foundations

Some spread footing foundations from real retrofitting practices in Taiwan were extended to be uneconomically large due to the restriction of foundation uplift regulated in the design code. Although rocking mode of spread footings induced from foundation uplift is not favorable in current design code, recent studies have shown that the rocking of a spread footing may have a beneficial effect on the dynamic performance of piers by reducing the earthquake forces that can be transmitted to the pier base. This implies that the plastic deformation that occurs at the pier's plastic zone can be decreased and as a result the ductility demand of piers can possibly be reduced. In order to gain a better understanding of the structural behavior related to rocking and to clarify that if the widening and strengthening of the foundations to limit the rocking mechanism of spread footing is necessary for the retrofitting work, a series of preliminary rocking experiments were performed. A total of three circular reinforced concrete columns with spread footing foundations were tested. Using pseudo‐dynamic tests and a cyclic loading test, these columns were subjected to different levels of earthquake accelerations, including a near field ground motion. The results of the tests and the rocking behavior of the footings are discussed in this paper. From the benchmark test, the difference between the response behavior of a rocking base and a fixed base foundation was highlighted. By comparing the experimental responses of the retrofitted column with the responses of the original one, the effect of the rocking mechanism on the ductility demand and strength demand of the columns was also identified. Copyright © 2010 John Wiley & Sons, Ltd.     

Earthquake damage potential and critical scour depth of bridges exposed to flood and seismic hazards under lateral seismic loads

Many bridges located in seismic hazard regions suffer from serious foundation exposure caused by riverbed scour. Loss of surrounding soil significantly reduces the lateral strength of pile foundations. When the scour depth exceeds a critical level, the strength of the foundation is insufficient to withstand the imposed seismic demand, which induces the potential for unacceptable damage to the piles during an earthquake. This paper presents an analytical approach to assess the earthquake damage potential of bridges with foundation exposure and identify the critical scour depth that causes the seismic performance of a bridge to differ from the original design. The approach employs the well-accepted response spectrum analysis method to determine the maximum seismic response of a bridge. The damage potential of a bridge is assessed by comparing the imposed seismic demand with the strengths of the column and the foundation. The versatility of the analytical approach is illustrated with a numerical example and verified by the nonlinear finite element analysis. The analytical approach is also demonstrated to successfully determine the critical scour depth. Results highlight that relatively shallow scour depths can cause foundation damage during an earthquake, even for bridges designed to provide satisfactory seismic performance.     

Earthquake response analysis of multistorey buildings including foundation interaction

An efficient method, based on the Ritz concept, for dynamic analysis of response of multistorey buildings including foundation interaction to earthquake ground motion is presented. The system considered is a shear building on a rigid circular disc footing attached to the surface of a linearly elastic halfspace. In this method, the structural displacements are transformed to normal modes of vibration of the building on a rigid foundation. The analysis procedure is developed and numerical results are presented to demonstrate that excellent results can be obtained by considering only the first few modes of vibration. As the number of unknowns are reduced by transforming to generalized co-ordinates, the method presented is much more efficient than direct methods.     

Vulnerability of floating tunnel shafts for increasing earthquake loading

Fragility curves constitute the cornerstone in seismic risk evaluations and performance-based earthquake engineering. They describe the probability of a structure to experience a certain damage level for a given earthquake intensity measure, providing a relationship between seismic hazard and vulnerability. In this paper a numerical approach is applied to derive fragility curves for tunnel shafts built in clays, a component that is found in several critical infrastructure such as urban metro networks, airport facilities or water and waste water projects. The seismic response of a representative tunnel shaft is assessed using tridimensional finite difference non-linear analyses carried out with the program FLAC^3D, under increasing levels of seismic intensity. A hysteretic model is used to simulate the soil non-linear behavior during the seismic event. The effect of soil conditions and ground motion characteristics on the soil-structure system response is accounted for in the analyses. The damage is defined based on the exceedance of the concrete wall shaft capacity due to the developed seismic forces. The fragility curves are estimated in terms of peak ground acceleration at a rock or stiff soil outcrop, based on the evolution of damage with increasing earthquake intensity. The proposed fragility models allows the characterization of the seismic risk of a representative tunnel shaft typology and soil conditions considering the associated uncertainties, and partially fill the gap of data required in performing a risk analysis assessment of tunnels shafts.     

A frequency‐dependent and intensity‐dependent macroelement for reduced order seismic analysis of soil‐structure interacting systems

The computational demand of the soil‐structure interaction analysis for the design and assessment of structures, as well as for the evaluation of their life‐cycle cost and risk exposure, has led the civil engineering community to the development of a variety of methods toward the model order reduction of the coupled soil‐structure dynamic system in earthquake regions. Different approaches have been proposed in the past as computationally efficient alternatives to the conventional finite element model simulation of the complete soil‐structure domain, such as the nonlinear lumped spring, the macroelement method, and the substructure partition method. Yet no approach was capable of capturing simultaneously the frequency‐dependent dynamic properties along with the nonlinear behavior of the condensed segment of the overall soil‐structure system under strong earthquake ground motion, thus generating an imbalance between the modeling refinement achieved for the soil and the structure. To this end, a dual frequency‐dependent and intensity‐dependent expansion of the lumped parameter modeling method is proposed in the current paper, materialized through a multiobjective algorithm, capable of closely approximating the behavior of the nonlinear dynamic system of the condensed segment. This is essentially the extension of an established methodology, also developed by the authors, in the inelastic domain. The efficiency of the proposed methodology is validated for the case of a bridge foundation system, wherein the seismic response is comparatively assessed for both the proposed method and the detailed finite element model. The above expansion is deemed a computationally efficient and reliable method for simultaneously considering the frequency and amplitude dependence of soil‐foundation systems in the framework of nonlinear seismic analysis of soil‐structure interaction systems.     

Dynamic soil–structure interaction effects on the seismic response of asymmetric buildings

An approach is formulated for the linear analysis of three-dimensional dynamic soil–structure interaction of asymmetric buildings in the time domain, in order to evaluate the seismic response behaviour of torsionally coupled buildings. The asymmetric building is idealized as a single-storey three-dimensional system resting on different soil conditions. The soil beneath the superstructure is modeled as linear elastic solid elements. The contact surface between foundation mat and solid elements of soil is discretised by linear plane interface elements with zero thickness. An interface element is further developed to function between the rigid foundation and soil. As an example, the response of soil–structure interaction of torsionally coupled system under two simultaneous lateral components of El Centro 1940 earthquake records has been evaluated and the effects of base flexibility on the response behaviour of the system are verified.     

A fundamental dual‐zone continuum theory for dynamic soil–structure interaction

A continuum theory for an improved characterization of dynamic soil–structure interaction in the framework of three‐dimensional elastodynamics is presented. Effective in demonstrating the importance of integrating free‐field and near‐field effects under general soil and foundation conditions, a compact two‐zone delineation of the soil medium is proposed as a quintessential mechanics perspective for this class of problems. Sufficient to deliver a practical resolution of some perennial analytical and experimental conflicts, a fundamental formulation commensurate to a gradated unification of the homogenization approach and any sole free‐field inhomogeneous representation is developed and implemented computationally. Specialized to the problem of a rigid circular footing on sand, a nominal set of dynamic contact stress distributions and related impedance functions by the dual‐zone theory is included for theoretical and engineering evaluation. Through its comparison with benchmark analytical solutions and relevant physical measurements, the usage of the underlying conceptual platform as an advanced yet practical foundation for general dynamic soil–structure interaction is illustrated. Copyright © 2010 John Wiley & Sons, Ltd.     

Dynamic equivalent soil characteristics identification using earthquake records

Techniques for soil property estimation can be categorized into two main groups, in-situ and laboratory methods. Previous investigations indicated that strong ground motions record provides a very useful tool to estimating the in-situ characteristics of soil. The main objective of the present work is to utilize the particle swarm optimization algorithm(PSOA) integrated with linear site response method to obtain the equivalent soil profile characteristics from the available surface and bedrock earthquake motion records. To demonstrate the numerical efficiency and the validity of this approach, the procedure is validated against an available case. Then this procedure is utilized to identify the soil properties profiles of the site by using strong ground motions data recorded during the Bam earthquake of December 26, 2003. The magnitude and PGA of Bam earthquake were MW 6.6 and 0.8 g respectively.