基于子结构法的成层场地中沉积河谷的散射分析

土层场地对地震动的影响明显,研究成层场地局部复杂地形的波动场特性,对于抗震设防具有重要意义。基于土-结构相互作用理论,含有局部复杂地形的成层场地,可分解成广义结构（即近场复杂地形及其周围土体）和具有规则开挖边界的成层无限地基（即远场）。远场的格林函数可通过精细积分求解频域-波数域内的对偶波动方程获得,利用傅里叶逆变换得到频域-空间域内的柔度矩阵。近场可采用比例边界有限元进行模拟,通过高性能连分式的传递边界求解动刚度。自由场波动可通过传递矩阵法求得,将动刚度和自由场波动位移代入控制方程即可得到散射场的动力响应。数值算例验证了方法的准确性,并利用提出的方法讨论含有软夹层场地局部复杂场地的波动场特性。     

透射边界-地基-风电结构地震响应与破坏模式

近海风力发电结构是由无限域地基、基础及上部结构组成的体系,有限域透射人工边界和地震动输入模式直接影响结构体系的动力响应。首先,建立透射人工边界-地基-基础-塔筒结构和固定边界-地基-基础-塔筒结构的有限元模型;然后,简要澄清了透射边界地震动输入之所以采用外力而不采取地震动物理量（加速度、速度和位移）的原因所在;最后,对给出的3种作用模式：（1）固定边界地震动输入,（2）只考虑外源输入波作用,（3）同时考虑外源输入波和内源振动的散射波作用,分别进行计算分析和比较。通过数值计算并结合理论分析,（1）澄清了对透射边界采用外力进行地震激励输入的方法的原因,这种输入方法合理可靠,符合实际情况;（2）在地震波等效荷载的生成中,针对圆形横截面地基提出了一种阻尼力、刚度力的便捷性生成方法,大大减小了工作量;（3）从自身振动特点及阻尼设置角度,解释了地震作用下采用透射边界比采用固定边界时风电结构响应减小的原因;（4）指出了地震作用下透射边界地基模型在结构动力响应与倒塌计算中内源振动反射的不容忽视性。     

一维问题的等效远置动力人工边界条件

在土-结构动力相互作用分析中,黏性人工边界条件和黏弹性人工边界条件虽具有计算效率和精度较高的优点,但施加边界单元的工作量较大;远置边界虽然具有处理技术简单、精度高等优点,但又存在计算成本高的问题。为克服黏性人工边界和黏弹性人工边界施加边界黏弹性单元工作量大、远置边界计算成本高的缺点,基于波的传播理论和波在介质交界面上的反射、透射原理,通过设置完全透射层并大大降低波在透射层的传播速度的方法,提出了一种等效远置动力人工边界条件并对其进行数值验证分析。研究结果表明,所提出的等效远置动力人工边界条件仅需通过合理选取透射层的参数,即可实现反射波向无限地基传播的模拟,具有精度和效率较好、不需施加边界单元工作量等优点,可应用到土-结构动力相互作用分析当中。     

褥垫层作用下复合地基抗震性能有限元分析

采用大型非线性有限元程序ADINA,针对复合地基-基础-上部结构典型算例,建立了计算模型,并进行了有限元动力时程分析。计算模型中,桩体、桩间土、垫层、基础采用简化的线弹性模型,分别定义材料类型;上部结构采用弯矩曲率梁算法进行计算;在边界设置黏性边界模拟无限域中的动力人工边界。通过数值计算研究了不同桩体刚度对自由场地加固区地表和非加固区地表位移峰值和加速度峰值和桩身所受到的弯矩及剪力的影响;研究了上部结构在不同垫层性质（不同刚度和不同厚度）作用下的动力反应,从而得出垫层的合理设置,为复合地基设计施工提供依据。     

基于SBFEM的层状地基埋置管道动力响应求解与分析

针对层状地基,采用改进的比例边界有限元算法(SBFEM)与有限元算法相结合,求解层状地基内刚性埋置管道动力响应问题。改进的比例边界有限元算法引入一个新的坐标变换关系,以一条相似轴代替传统SBFEM的相似中心,并利用加权余量方法得到层状地基动力刚度矩阵方程,最后与有限元法在远场和近场交界面进行耦合,由此求得层状地基埋置管道的动力响应。数值算例验证了算法的准确性,并利用该算法分析了层状地基的非均质特性、泊松比以及埋置深度对管道动力响应的影响,以期为工程实际提供必要的数值依据。结果表明:地基的非均质特性和泊松比对埋置管道的动力响应均有显著的影响;随着埋置深度的加大,管道在相同荷载作用下的动力响应均减小。     

动力分析中无限地基两种近似方法的应用研究

在结构-地基的动力相互作用分析所提出的众多方法中,无质量地基和黏性边界地基仍然是应用最为广泛的近似方法。针对当前结构-地基动力相互作用分析中地基模型处理中的一些问题,通过结构-地基动力相互作用分析公式的推导以及各变量物理意义的解释,详细阐明了当前考虑地基影响的动力分析中无质量地基和黏性边界地基的概念和应用范围,对当前部分研究中应用这两种地基中存在的问题进行了分析说明,为简化地基动力分析模型提供了思路。     

基于切比雪夫谱元模型的成层场地地震反应分析

将切比雪夫谱元模型应用于成层场地的一维波动分析,发展了一种具有高阶数值格式的场地地震反应时域分析方法。通过谱单元离散基岩和覆盖土体,建立各个单元的波动方程,并在基岩内设置透射人工边界,模拟底部无限域对内域波动的影响;利用切比雪夫正交多项式构造高阶单元位移模式,得到空间离散后的场地节点运动方程;利用中心差分原理,结合人工边界的数值格式,推导了一种稳定的时域积分数值方案。最后通过2个算例阐释了该方法在场地地震反应分析中的应用,并与传统方法进行了对比分析。数值试验表明,该方法具有高精度特性,在使用较少节点的条件下仍能得到较为可靠的计算结果,可显著地提高场地地震反应分析的计算效率。     

移动荷载下高铁路基段振动加速度频谱衰减特性

采用精细化和多尺度建模技术,建立了设计速度为350 km/h的双线高速铁路轨道-路基-地基非线性耦合系统的真三维动力分析模型,将地基土和路基填筑材料的非线性纳入分析模型中,采用三维黏弹性静-动力统一人工边界技术对地基无限域进行模拟,采用动接触算法模拟底座板底面和基床表层表面之间的相互作用,考虑移动荷载作用前路基-地基中客观的静应力状态对后续动力计算的影响,依托大规模并行计算技术和单元生死技术,模拟了地基的初始应力场生成、路基结构和轨道系统的施工过程,在此基础上模拟了与8辆编组的某型动车组轮对空间位置相对应的、作用于钢轨顶部的压力荷载的移动过程。基于分析结果,归纳了移动荷载作用下高速铁路轨道-路基-地基系统中振动加速度频谱的衰减特性。     

覆盖层上土石坝非线性动力响应分析的地震波动输入方法

较多已建和待建的土石坝直接修筑于覆盖层上,合理描述土石坝与覆盖层之间的动力相互作用对大坝抗震安全评价至关重要。基于等效荷载和人工边界的地震波动输入方法能较好地反映出结构-地基之间的相互作用并得到了广泛应用。等效荷载和人工边界参数在均质线弹性地基条件下易于获得,而对于覆盖层地基,土体动力非线性特性给求解带来很大困难。鉴于此,首先根据覆盖层侧向边界的位移模式,发展了能高效、精确地获取多向地震动垂直入射时均质或成层覆盖层自由场非线性动力响应的简化模型;结合能动态实时获取地基材料参数的非线性人工边界,发展了一套覆盖层上土石坝非线性动力响应分析的地震波动输入方法。算例表明,发展的地震波动输入方法可大大减小计算网格量,并能较好地反映覆盖层对地震动频谱特性的影响且具有较高的精度。     

土-结构-流体动力相互作用的实时耦联动力试验

针对振动台试验中无限地基难以模拟和数值分析中流-固耦合作用难以计算两个难题,将最近发展的实时耦联动力试验方法引入土-结构-流体动力相互作用问题的研究。以一个渡槽结构为例,其中渡槽-水体作为物理子结构,采用振动台进行物理试验,而无限地基作为数值子结构,采用集总参数模型进行数值模拟。两个子结构之间实时交换数据,联合评估整个耦合体系的动力响应。试验结果和有限元数值模拟结果吻合良好,表明该试验方法具有较高精度。对不同特性地基土进行的试验对比分析结果表明：对于软土地基,考虑土-结构相互作用(SSI)的结构反应幅值明显减小,周期延长;随着地基土变硬,SSI效应逐渐变弱,结构反应最终收敛至刚性地基解。     

Semi‐analytical far field model for three‐dimensional finite‐element analysis

A challenging computational problem arises when a discrete structure (e.g. foundation) interacts with an unbounded medium (e.g. deep soil deposit), particularly if general loading conditions and non‐linear material behaviour is assumed. In this paper, a novel method for dealing with such a problem is formulated by combining conventional three‐dimensional finite‐elements with the recently developed scaled boundary finite‐element method. The scaled boundary finite‐element method is a semi‐analytical technique based on finite‐elements that obtains a symmetric stiffness matrix with respect to degrees of freedom on a discretized boundary. The method is particularly well suited to modelling unbounded domains as analytical solutions are found in a radial co‐ordinate direction, but, unlike the boundary‐element method, no complex fundamental solution is required. A technique for coupling the stiffness matrix of bounded three‐dimensional finite‐element domain with the stiffness matrix of the unbounded scaled boundary finite‐element domain, which uses a Fourier series to model the variation of displacement in the circumferential direction of the cylindrical co‐ordinate system, is described. The accuracy and computational efficiency of the new formulation is demonstrated through the linear elastic analysis of rigid circular and square footings. Copyright © 2004 John Wiley & Sons, Ltd.     

A non‐linear coupled finite element–boundary element model for the prediction of vibrations due to vibratory and impact pile driving

This paper presents a non‐linear coupled finite element–boundary element approach for the prediction of free field vibrations due to vibratory and impact pile driving. Both the non‐linear constitutive behavior of the soil in the vicinity of the pile and the dynamic interaction between the pile and the soil are accounted for. A subdomain approach is used, defining a generalized structure consisting of the pile and a bounded region of soil around the pile, and an unbounded exterior linear soil domain. The soil around the pile may exhibit non‐linear constitutive behavior and is modelled with a time‐domain finite element method. The dynamic stiffness matrix of the exterior unbounded soil domain is calculated using a boundary element formulation in the frequency domain based on a limited number of modes defined on the interface between the generalized structure and the unbounded soil. The soil–structure interaction forces are evaluated as a convolution of the displacement history and the soil flexibility matrices, which are obtained by an inverse Fourier transformation from the frequency to the time domain. This results in a hybrid frequency–time domain formulation of the non‐linear dynamic soil–structure interaction problem, which is solved in the time domain using Newmark's time integration method; the interaction force time history is evaluated using the θ‐scheme in order to obtain stable solutions. The proposed hybrid formulation is validated for linear problems of vibratory and impact pile driving, showing very good agreement with the results obtained with a frequency‐domain solution. Linear predictions, however, overestimate the free field peak particle velocities as observed in reported field experiments during vibratory and impact pile driving at comparable levels of the transferred energy. This is mainly due to energy dissipation related to plastic deformations in the soil around the pile. Ground vibrations due to vibratory and impact pile driving are, therefore, also computed with a non‐linear model where the soil is modelled as an isotropic elastic, perfectly plastic solid, which yields according to the Drucker–Prager failure criterion. This results in lower predicted free field vibrations with respect to linear predictions, which are also in much better agreement with experimental results recorded during vibratory and impact pile driving. Copyright © 2008 John Wiley & Sons, Ltd.     

A high‐frequency open boundary for transient seepage analyses of semi‐infinite layers by extending the scaled boundary finite element method

A high‐frequency open boundary has been developed for the transient seepage analyses of semi‐infinite layers with a constant depth. The scaled boundary finite element equation of pore water pressure is formulated first in the frequency domain. With the eigenvalue problem, the equation can be decoupled into modal equations whose modal dynamic permeability equation can be determined. The continued fraction technique is adopted to formulate the continued fraction solution in the frequency domain. All constants in the solution are determined recursively at the high‐frequency limit. By introducing auxiliary variables and the continued fraction solution to the relationship between the prescribed seepage flow and the pore water pressure in the frequency domain, the open boundary condition is obtained. After transformed to the time domain, the open boundary condition is expressed as a system of fractional differential equations. No convolution integral is required. The accuracy of the analysis results increases with the increasing orders of continued fraction. Copyright © 2015 John Wiley & Sons, Ltd.     

Transient seepage analysis in zoned anisotropic soils based on the scaled boundary finite‐element method

The scaled boundary finite‐element method, a semi‐analytical computational scheme primarily developed for dynamic stiffness of unbounded domains, is applied to the analysis of unsteady seepage flow problems. This method is based on the finite‐element technology and gains the advantages of the boundary element method as well. Only boundary of the domain is discretized, no fundamental solution is required and singularity problems can be modeled rigorously. Anisotropic and non‐homogeneous materials satisfying similarity are modeled with no additional efforts. In this study, firstly, formulation of the method for the transient seepage flow problems is derived followed by its solution procedures. The accuracy, simplicity and applicability of the method are demonstrated via four numerical examples of transient seepage flow – three of them are available in the literature. Homogenous, non‐homogenous, isotropic and anisotropic material properties are considered to show the versatility of the technique. Excellent agreement with the finite‐element method is observed. The method out‐performs the finite‐element method in modeling singularity points. Copyright © 2014 John Wiley & Sons, Ltd.     

Semi‐analytical elastostatic analysis of unbounded two‐dimensional domains

Unbounded plane stress and plane strain domains subjected to static loading undergo infinite displacements, even when the zero displacement boundary condition at infinity is enforced. However, the stress and strain fields are well behaved, and are of practical interest. This causes significant difficulty when analysis is attempted using displacement‐based numerical methods, such as the finite‐element method. To circumvent this difficulty problems of this nature are often changed subtly before analysis to limit the displacements to finite values. Such a process is unsatisfactory, as it distorts the solution in some way, and may lead to a stiffness matrix that is nearly singular. In this paper, the semi‐analytical scaled boundary finite‐element method is extended to permit the analysis of such problems without requiring any modification of the problem itself. This is possible because the governing differential equations are solved analytically in the radial direction. The displacement solutions so obtained include an infinite component, but relative motion between any two points in the unbounded domain can be computed accurately. No small arbitrary constants are introduced, no arbitrary truncation of the domain is performed, and no ill‐conditioned matrices are inverted. Copyright © 2002 John Wiley & Sons, Ltd.     

On the use of infinite elements in the analysis of two-dimensional layered elastic systems via discretized integral equations

A boundary integral equation approach is presented for the two-dimensional plane strain analysis of horizontally layered elastic systems resting on a rough and rigid base. The validity of Somigliana identity for unbounded layers is discussed and an Infinite Boundary Element is proposed in order to take into account the lateral unboundedness of the physical problem in the discretized equations. This element is implemented in a computer code based on a successive stiffness solution procedure. A series of numerical tests concerning single- and multi-layered problems is illustrated, and the performance of the proposed solution method is compared with that of more traditional boundary element and finite element techniques.     

粘弹性成层介质中稳态波的有限元模拟

本文将离散的局部透射边界与集中质量有限元方法相结合,用于模拟粘弹性成层介质中的稳态波动。并以一个受集中线力作用的粘弹性土层的出平面稳态波动为例,将有限元模拟与解析方法的计算结果进行比较,验证此模拟方法的有效性,着重显示在频域中实现高阶透射的可能性。     

A new development of the scaled boundary finite element method for wave motion in layered half-space

The scaled boundary finite element method (SBFEM) developed by Wolf and Song has shown certain parallels to the finite element method (FEM) and boundary element method (BEM). Because of its semi-analytical nature, SBFEM is particularly suitable for the analysis of wave propagation in unbounded domains. This paper makes a certain modification of the standard SBFEM. A new idea of scaling surface instead of a scaling center is introduced to formulate the governing SBFE equations for the analysis of wave propagation in multilayered half-space, which leads to simplifying the modeling and saving considerably the computational effort. In addition, by employing the proposed approach, some problems encountered in engineering practice, which are difficult to deal with by the conventional SBFEM, for example, 3D foundation impedance on half-space with irregular geographical features, can be effectively solved. The proposed approach also helps to simplify the solution of shell structures. Numerical examples are provided to validate the accuracy and efficiency of the proposed approach.