Transient response of single piles under horizontal excitations

The general time-domain boundary element in cylindrical co-ordinates developed for the study of wave propagation in a layered half-space is extended to the response analysis of single piles under horizontal transient excitations. The pile is treated as a beam, and therefore, only the bending stiffness has to be considered in the analysis. As required by the non-axisymmetric nature of the problem, the soil is modelled by boundary (cylindrical) elements with the vertical, radial and tangential displacements as well as their corresponding tractions as independent variables. The characteristic matrices for the two different types of element can be formed in the usual manner, and they are combined to form the equation of motion for the whole system by virtue of compatibility and equilibrium conditions along the pile-soil interface. The transient responses of a pile under Heaviside loads are found to converge to the static values. Parametric studies are carried out to reveal the influences of pile-soil stiffness ratio (E_p/E_s) and soil layering.     

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.     

Experimental investigation on seismic behavior of single piles in sandy soil

This paper describes a quasi-static test program featuring lateral cyclic loading on single piles in sandy soil. The tests were conducted on 18 aluminum model piles with different cross sections and lateral load eccentricity ratios, e/d, (e is the lateral load eccentricity and d is the diameter of pile) of 0, 4 and 8, embedded in sand with a relative density of 30% and 70%. The experimental results include lateral load-displacement hysteresis loops, skeleton curves and energy dissipation curves. Lateral cap...     

Nonlinear seismic response analysis of earth dams

The objective of this paper is to propose a general and efficient numerical procedure for analysing the dynamic response of geotechnical structures, which are considered as both nonlinear and two phase systems. In Section 2, the appropriate coupled dynamic field equations for the response of a two-phase soil system are briefly reviewed. The finite element spatial discretization of the field equations is described and time integration for the resulting nonlinear semi-discrete finite element equations is discussed. In Section 3, iterative techniques are examined for the solution of the global nonlinear system of finite element equations. A large amount of computational effort is expended in the iterative phase of the solution and so the iterative procedure used must be both reliable and efficient. The performance of three iterative procedure is examined: Newton Raphson, Modified Newton Raphson and Quasi-Newton methods, including BGFS and Broyden updates. Finally, in Section 4, the elasto-plastic earthquake response analysis of a two phase nonhomogeneous earth dam is presented. Extensive documentation exists¹ for the particular problem selected including recorded earthquake motions at the base and crest of the dam. The results of the numerical calculations are compared to the recorded response of the dam.     

Experimental investigation on seismic behavior of single piles in sandy soil

This paper describes a quasi-static test program featuring lateral cyclic loading on single piles in sandy soil. The tests were conducted on 18 aluminum model piles with different cross sections and lateral load eccentricity ratios, e/d, (e is the lateral load eccentricity and d is the diameter of pile) of 0, 4 and 8, embedded in sand with a relative density of 30% and 70%. The experimental results include lateral load-displacement hysteresis loops, skeleton curves and energy dissipation curves. Lateral capacity, ductility and energy dissipation capacity of single piles under seismic load were evaluated in detail. The lateral capacities and the energy dissipation capacity of piles in dense sand were much higher than in loose sand. When embedded in loose sand, the maximum lateral load and the maximum lateral displacement of piles increased as e/d increased. On the contrary, when embedded in dense sand, the maximum lateral load of piles decreased as e/d increased. Piles with a higher load eccentricity ratio experienced higher energy dissipation capacity than piles with e/d of 0 in both dense and loose sand. At a given level of displacement, piles with circular cross sections provided the best energy dissipation capacity in both loose and dense sand.     

Mechanics and performance of a tied-back wall under seismic loads

In this paper the stability of a tied-back wall subjected to seismic loads is analysed for a predetermined mode of failure (rotation about the top of the wall) and the analysis is compared with data from tests on this type of wall using the seismic simulator at the State University of New York at Buffalo. We carried out a pseudo-static analysis of the problem using the Mononobe-Okabe earth pressure coefficients, wherein the dynamic effects due to the seismic loading are converted into equivalent static loads. The acceleration ratio at which the wall fails by rotation about the top was obtained by considering the moments due to the various lateral earth pressure resultants and the inertial forces induced in the soil due to the seismic loading. We found that the presence of wall friction on the passive side significantly enhances the stability of the flexible retaining wall under seismic loads. Thus, flexible retaining walls supporting dry cohesionless soil can be very efficient during earthquakes. Under moderate earthquakes, an increase in the depth of embedment increases the dynamic factor of safety significantly. However, beyond a certain acceleration ratio for a soil with a particular value of ø, any increase in the depth of emdedment has no effect in impeding failure, irrespective of any change in the geometry of the system. Seismic design charts are presented to evaluate the stability of, and to design, flexible retaining walls embedded in dry cohesionless soils under seismic loading.     

Analysis of unanchored liquid storage tanks under lateral loads

Many liquid storage tanks consist of a steel cylindrical shell, which is welded to a base plate, but not fixed to the foundation. When such an unanchored tank is subjected to lateral loads due to earthquake induced hydrodynamic pressures in the liquid, the tank wall tends to uplift locally, pulling the base plate up with it. The contact problem of the partially uplifted base plate and its interaction with the the cylindrical shell is solved in this paper using the finite difference energy method, and a Fourier decomposition of the displacements in the circumferential direction. Non-linearities due to contact, finite displacements and yield of the steel are included in the analysis. However, the equations for the shell are linearized. This uncouples the equations for the Fourier displacement coefficients in the cylindrical shell, and enables the degrees of freedom for the shell to be eliminated by static condensation at very little computational cost. Comparing the analytical results to (for the most part existing) experimental results, produces good agreement in some cases and not so good in others. A number of effects that could give rise to such differences are discussed. In most cases they represent experimental conditions that are not known or modelled in the analysis. The analysis results are also compared to those from a simplified analysis in which the hold-down action of the base plate is modelled by means of nonlinear Winkler springs.     

Morison方程中动水阻力项对桥梁桩柱地震反应的影响

深水桥梁地震反应计算时,当采用Morison公式考虑水的作用时,增加了一个附加惯性项和一个附加阻尼项,其中附加阻尼项是非线性的。由于非线性附加阻尼项的存在,给采用反应谱方法求解桥梁的地震反应带来不便。讨论了非线性阻尼项对一般桥梁桩、墩结构地震反应的贡献,得到的结论是阻尼项的贡献很小,可以忽略。从而水中桥梁地震反应的计算就得到了很大的简化。     

Response of single piles and pipelines in liquefaction-induced lateral spreads using controlled blasting

Two full-scale experiments using controlled blasting were conducted in the Port of Tokachi on Hokkaido Island, Japan, to assess the behavior of piles and pipelines subjected to lateral spreading. Test specimens were extensively instrumented with strain gauges to measure the distribution of moment during lateral spreading. This allowed us to compute the loading condition, as well as to conduct damage and performance assessments on the piles and pipelines. This paper presents the test results and discussions on the response of single piles and pipelines observed from the full-scale experiments. Based on the test results, it can be concluded that using controlled blasting successfully liquefied the soil, and subsequently induced lateral spreading. The movements of the single pile, as well as the transverse pipelines, were approximately the same as the free field soil movement. Observed moment distribution of the single pile indicated that global translation of the liquefied soil layer provided insignificant force to the pile. In addition, the degree of fixity at the pile tip significantly affected the moment along the pile as well as the pile head displacement. The pile with a higher degree of fixity at the pile tip had smaller pile head displacement but larger maximum moment.     

竖向地震荷载下人字批顶结构石窟的稳定性分析

我国部分石窟的空间建造采用了人字批顶形式,体现了中国传统建筑形式与佛教石窟建造形式上的融合.选取莫高窟典型的人字批顶结构的254号石窟作为研究对象,建立了三维的石窟计算模型,考虑了竖向地震荷载作用,通过输入不同地震加速度时程,计算了4种模型情况下石窟岩体的拉应力分布情况.结果表明,石窟的人字批顶处易形成较大拉应力区,易遭受地震破坏;石窟中心塔柱可以有效地提高所在石窟岩体的抗震能力,但对下部窟体的上部岩体会产生应力集中,是窟体防护加固的重点部位.同时,对于洞窟密集而又分上下几层的石窟群,在抗震防护中应充分考虑竖向地震荷载的作用.     

地铁隧道地震反应非线性分析

本文对动力有限元法中的一系列问题进行了讨论,对土体动力本构模型和土-结构接触面模型的设定提出了建议．在此基础上以天津地铁1、2号线工程为实例,分别对水平地震作用下圆形盾构隧道的动位移、动应力与动应变以及地表位移等动力反应进行了非线性分析,得出了一些有益的规律和结论,从而为地铁隧道的抗震设计与研究提供参考和依据。     

Nonlinear analysis for dynamic lateral pile response

An analysis of pile lateral response to transient dynamic loading and to harmonic loading is presented allowing for nonlinear soil behavior, discontinuity conditions at the pile-soil interface and energy dissipation through different types of damping. Furthermore, the effect of neighbouring piles is taken into account for piles in a group. The validity of the approach was examined and a reasonable agreement with field tests and more rigorous solutions was found. Equivalent linear stiffness and damping parameters of single piles and interaction factors for approximate nonlinear analysis are presented.     

水平成层场地地震反应非线性分析

本文首先推导了李小军积分格式(中心差分与Newmark平均加速度法相结合)的增量形式,并据此离散动力平衡方程,同时,采用Pyke提出的土动力本构模型以及多次透射人工边界条件,提出了一种水平成层场地地震反应非线性分析的显式有限元方法,并据此编制了计算机程序。数值实验表明,这种方法能较好地模拟土层在强地震作用下的非线性特性。     

城市地下变电站非线性地震反应分析

为研究城市地下变电站结构及其内部电气设备的动力特性及地震反应规律,以西安市快速轨道交通二号线张家堡地下变电站为工程背景,依据黏弹性人工边界理论及有限单元法,建立考虑土体-结构-设备动力相互作用的三维有限元计算模型,首先通过半空间自由场模型验证了地震动输入方法的有效性,继而开展地下变电站系统的模态分析和动力时程分析,得到了该类结构的动力特性及地震响应规律。研究结果表明,结构上覆土体及电气设备在地震作用下产生的惯性力是结构构件应力增长的主要原因,8度罕遇地震作用下地下变电站内电气设备的加速度放大系数明显超出规范要求,需要采取相应保护措施。     

拱坝非线性地震反应分析

本文根据一致粘弹性模型的概念，引入应变率的影响，将混凝土静态William-Warnke三参数模型改造成一致粘塑性William-Warnke三参数本构模型，并用这个模型对某高拱坝进行了非线性地震响应分析，与线弹性模型和应变率无关的William-Warnke三参数模型的结果进行了比较，初步探讨了应变率对拱坝地震反应的影响。     

地震荷载作用下黄土地基震陷研究

在某大型企业的地震安全性评价工作中,采用随机地震荷载输入动三轴进行了黄土震陷试验,探讨了该场地黄土在不同动荷载作用下的震陷特性。并对该场地地基未来可能发生的震陷灾害进行了评价,为工程地基抗震处理提供了依据。     

边坡动力响应的非线性特征分析

以节理岩质边坡作为研究对象,采用离散单元法,分析了边坡在地震作用下的变形特征,根据边坡演化过程中所表现出的非线性特征,应用相空间重构理论证明边坡的演化过程是混沌序列,边坡动力失稳过程包含2次分岔,边坡失稳的本质是分岔.     

Dynamic stiffness and kinematic response of single piles in inhomogeneous soil

The effect of soil inhomogeneity on dynamic stiffness and kinematic response of single flexural elastic piles to vertically-propagating seismic SH waves is explored. A generalized parabolic function is employed to describe the variable shear wave propagation velocity in the inhomogeneous stratum. A layered soil with piece-wise homogeneous properties is introduced to approximate the continuous inhomogeneity in the realm of a Beam-on-Dynamic-Winkler-Foundation model. The problem is treated numerically by means of a layer transfer-matrix (Haskell–Thompson) formulation, and validated using available theoretical solutions and finite-element analyses. The role of salient model parameters such as pile-head fixity conditions, pile-to-soil stiffness ratio, surface-to-base shear wave velocity ratio and rate of inhomogeneity is elucidated. A new normalization scheme for inertial and kinematic response of such systems is presented based on an average Winkler wavenumber. With reference to long piles in moderately inhomogeneous soils, results indicate that: (a) kinematic pile response is essentially governed by a single dimensionless frequency parameter accounting for pile-to-soil stiffness ratio, pile slenderness and soil inhomogeneity and (b) definition of a characteristic pile wavelength allows an approximate estimation of pile elastodynamic response for preliminary design or analysis. Issues related to domain discretization and Winkler moduli are discussed.     

Modelling of shear keys in bridge structures under seismic loads

Shear keys are used in the bridge abutments and piers to provide transverse restraints for bridge superstructures. Owing to the relatively small dimensions compared to the main bridge components (girders, piers, abutments, piles), shear keys are normally regarded as secondary component of a bridge structure, and their influences on bridge seismic responses are normally neglected. In reality, shear keys are designed to restrain the lateral displacements of bridge girders, which will affect the transverse response of the bridge deck, thus influence the overall structural responses. To study the influences of shear keys on bridge responses to seismic ground excitations, this paper performs numerical simulations of the seismic responses of a two-span simply-supported bridge model without or with shear keys in the abutments and the central pier. A detailed 3D finite element (FE) model is developed by using the explicit FE code LS-DYNA. The bridge components including bridge girders, piers, abutments, bearings, shear keys and reinforcement bars are included in the model. The non-linear material behaviour including the strain rate effects of concrete and steel rebar are considered. The seismic responses of bridge structures without and with shear keys subjected to bi-axial spatially varying horizontal ground motions are calculated and compared. The failure mode and damage mechanism of shear keys are discussed in detail. Numerical results show that shear keys restrain transverse movements of bridge decks, which influence the torsional–lateral responses of the decks under bi-axial spatially varying ground excitations; neglecting shear keys in bridge response analysis may lead to inaccurate predictions of seismic responses of bridge structures.     

Vertical response of single piles: transient analysis by time-domain BEM

The transient dynamic response of single piles in a layered half-space under a time-dependent vertical force is analyzed by an FEM-BEM coupling approach. The pile is modeled by FEM and the layered half-space is modeled by a general cylindrical coordinates time-domain BEM. Only one-dimensional discretization is necessary on the boundaries of the three-dimensional layered half-space by virtue of the Fourier theory, while the pile shaft can be discretized as a one-dimensional elastic beam. The compatibility and equilibrium conditions between pile shaft and soil layers are employed to assemble respective equations into one. Fairly good agreement between two unknown solutions and the current approach is found. Parametric studies reveal the influences of several dimensionless factors, such as E_p/E_s, l/r₀, _p/_s and ν_s. The effect of soil layering and the support condition of the pile tip is also reported by numerical examples.