Upper bound limit analysis of active earth pressure with different fracture surface and nonlinear yield criterion

Conventional calculations of static and seismic active earth pressures of soils on a retaining wall are formulated assuming the soils obeying a linear Mohr–Coulomb yield criterion. However, experimental evidences show that the strength envelopes of almost all geomaterials are nonlinear in nature over a wide range of normal stresses. In this paper, the strength envelope of the backfill behind a retaining wall is considered to follow a nonlinear yield criterion. A simple method is proposed for calculating the static and seismic active earth pressures acting against a retaining wall using a nonlinear yield criterion. This method is based on the upper bound theorem of limit analysis. Both translational and rotational fracture surfaces are employed in the formulation for calculating active earth pressures. Quasi-static representation of earthquake effects using a seismic coefficient concept is adopted for seismic active earth pressure calculations. Instead of using directly the actual nonlinear yield criterion, a linear Mohr–Coulomb yield criterion, which is tangential to the nonlinear yield criterion, is used to formulate the active earth pressure problem as a classical nonlinear programming problem. A nonlinear sequential quadratic programming algorithm is used to search for the maximum solution. In order to assess the validity of the proposed method, values of active earth pressures for different values of seismic coefficients and nonlinear parameters in the yield criterion are calculated and compared with solutions obtained using an extended Rankine’s active earth pressure theory. For the case of static active earth pressure, the upper bound solutions using the present method with a translational fracture surface are equal to the extended Rankine’s theoretical solutions and are slightly smaller than those obtained using the present method with a rotational fracture surface. For the case of seismic active earth pressure, numerical results obtained using the present method with a rotational fracture surface is very close to the extended Rankine’s theoretical solutions. A study is conducted to investigate the effects of the parameters in the nonlinear yield criterion on the active earth pressures.     

Propagation of surface (seismic) waves: Ordinary differential equations with strongly nonlinear damping

Second-order ordinary differential equations (ODEs) with strongly nonlinear damping (cubic nonlinearities) govern surface wave motions that entail nonlinear surface seismic motions. They apply to dynamic crack propagation and nonlinear oscillation problems in physics and nonlinear mechanics. It is shown that the nonlinear surface seismic wave equation (Rayleigh equation) admits several functional transformations and it is possible to reduce it to an equivalent first-order Abel ODE of the second kind in normal form. Based on a recently developed methodology concerning the construction of exact analytic solutions for the type of Abel equations under consideration, exact solutions are obtained for the nonlinear seismic wave (NLSW) equation for initial conditions of the physical problem. The method employed is general and can be applied to a large class of relevant ODEs in mathematical physics and nonlinear mechanics.     

结构非线性随机地震反应的概率密度演化方法

运用随机过程的正交展开方法,将地震动加速度过程展开为由少量独立随机变量所调制的确定性函数的线性组合形式.结合概率密度演化理论,建立了结构非线性随机地震反应分析的密度演化方法.以滞回结构非线性反应分析为例,考察了一个具有10个自由度的剪切型框架结构的随机地震反应分析问题.分析表明,结构非线性地震反应具有明显的随机涨落现象,且概率密度曲线与常见的正态等分布相差甚远.     

Seismic passive pressures of earth structures by nonlinear optimization

Conventional seismic passive pressures of earth structures are based on a linear failure criterion in earthquake zones. However, experimental evidence shows that the strength envelopes are nonlinear over a wide range of normal stresses. In this paper, the analytical expressions of seismic passive pressures acting on inclined rigid walls are derived with nonlinear failure criterion. Quasi-static representation of earthquake effects using a seismic coefficient is adopted for seismic estimations. Instead of using the nonlinear criterion, a linear failure criterion, which is tangential to the nonlinear criterion, is used to formulate the seismic passive pressure problems as nonlinear programming problems. Analytical results are presented and compared with the previously published solutions using numerical technique. The influences of the parameters in the nonlinear failure criterion on seismic pressures and failure mechanisms are discussed.     

Dynamic chain system with seismic damper: reduction of nonlinear model

The efficiency of model reduction via balancing for a multimass system with a nonlinear inertial link is demonstrated. As an example, a three-mass dynamic system with a seismic damper is examined. The constraints of the seismic damper are assumed to be ideal. The order of the system of differential equations is reduced by one. It is pointed out that the difference between the numerically analyzed dynamic processes in the original and reduced systems is minor, which makes it possible to use the method for justified simplification of nonlinear systems     

粘滞阻尼器减震结构非线性随机振动的时域显式降维迭代随机模拟法

粘滞阻尼器在大型复杂结构减震设计中应用广泛。由于粘滞阻尼器的非线性阻尼力特性,粘滞阻尼器减震结构非平稳随机地震反应分析是一个典型的局部非线性随机振动问题。利用减震结构动力响应时域显式表达式的降维列式优势,仅针对与粘滞阻尼器相关的局部自由度进行非线性迭代计算,提出了局部非线性随机振动问题的时域显式降维迭代随机模拟法,为设置粘滞阻尼器的大型复杂减震结构非线性地震反应分析提供一种高效的随机振动方法。以安装了四个纵桥向粘滞阻尼器的某主跨1200m悬索桥为工程实例,开展E2水准地震激励下的非线性随机振动分析。计算结果显示,设置阻尼器后,主梁的纵桥向位移得到明显控制,降幅达到80%,大桥的关键截面内力也有5%左右的降幅。     

桥梁滞变非线性随机地震响应分析

对于含有滞迟剪切型单元的复杂多自由度系统,采用Bouc—Wen微分方程模型描述非线性抗力构件的滞变特性。以虚拟激励法代替常规的Lyapunov方程法结合等效线性化技术对平稳随机激励下系统的动力响应进行求解,激励谱可为白谱或其他任意形式。不但计算效率高,而且不引入除等效线性化之外的附加误差。对不同周期单自由度体系以数值模拟法验证了算法精度。在此基础上,对一座四跨桥进行了线性／非线性分析对比,得到合理的结果。     

SEISMIC RANDOM VIBRATION ANALYSIS OF LOCALLY NONLINEAR STRUCTURES

A nonlinear seismic analysis method for complex frame structures subjected to stationary random ground excitations is proposed. The nonlinear elasto-plastic behaviors may take place only on a small part of the structure. The Bouc-Wen differential equation model is used to model the hysteretic characteristics of the nonlinear components. The Pseudo Excitation Method (PEM) is used in solving the linearized random differential equations to replace the solution of the less efficient Lyapunov equation. Numerical results of a real bridge show that .the method proposed is effective for practical engineering analysis.     

Estimation of stochastic nonlinear dynamic response of rock-fill dams with uncertain material parameters for non-stationary random seismic excitation

This research investigates the effect of uncertain material parameters on the stochastic, dynamic response of a rock-fill dam-foundation system subjected to non-stationary random excitation. The uncertain material parameter of particular interest is the shear modulus, developed from a lognormal distribution model. The stochastic seismic response model of the dam-foundation system, with uncertain material parameters and subjected to random loads is the result of a Monte Carlo simulation method. The nonlinear behavior model arises from an equivalent linear method, which considers the nonlinear variation of soil shear modulus and soil damping as a function of shear strain. Specification of the non-stationary stochastic process arises from a simulation method, which generates artificial earthquake accelerograms obtained from the product of a deterministic function of time and a stationary process. The artificial earthquake ground acceleration records reflect the characteristics of soft, medium and firm soil types. Comparison of the numerical results from these approaches provides stochasticity in earthquake seismic excitation and randomness in material parameter (shear modulus) cases. Further, the results indicate that both these cases generally influence the nonlinear dynamic response of rock-fill dams to a non-stationary seismic excitation.     

基于遗传算法的设计地震反应谱标定方法

基于自然进化原理的遗传算法是一种解决复杂非线性规划问题十分有前景的方法。对遗传算法中一些有代表性的算法作了简要分析和评价。介绍了用地面峰值加速度(PGA)、峰值速度(PGV)和峰值位移(PGD)三个参数标定设计地震反应谱的模型。针对此分段非线性函数规划问题,运用MATLAB编写遗传算法程序进行了计算。计算表明遗传算法在全局优化、非线性优化、多参数优化等方面表现出了传统算法无法比拟的优势。     

指数模量成层土非线性地震反应的半解析算法

运用文献[1]所建议的动态应力应变关系及其推广的Masing加卸载准则,考虑土体在地震等产生的不规则加载条件下的非线性滞回特征,将增量法与相应场地地震线性反应解析解[2]相结合,提出了该动力非线性方程的半解析时域算法,基于改进的一维剪切梁模型,对剪切模量是其深度的某一指数函数的成层非均质土层,建立了求解土体地震反应的非线性分析技术。针对文献[2]中的土层剖面,做了计算、分析和讨论。     

基于Volterra级数的核爆地震参数化非线性特征提取方法

地震时间序列的模型参数可以作为核爆地震信号识别的特征.现有基于ARMA( autoregressive moving average)模型参数的地震信号特征提取方法是一种线性方法,且只利用了信号的二阶统计信息,识别精度不高.为此,利用地震波的混沌特性,提出了一种核爆地震非线性特征提取方法:首先对地震波信号进行相空间重构...     

大跨度结构抗震分析方法及近期进展

对反应谱方法、随机振动方法和时间历程法应用于大跨度结构抗震分析时的特点作了分析和对比。研究表明,地震地面运动的空间变化效应(特别是行波效应)对大跨度结构的响应有相当大的影响。反应谱方法对多点激励地震分析显得相当困难,而随机振动方法则有明显的优越性。对于强震作用下的大跨度结构非线性地震响应,时间历程法在现阶段仍应是主要的分析方法。      

考虑双向地震动作用的非对称结构多维Pushover分析

目前的Pushover分析多集中于平面单向分析,考虑到非对称结构反应的多维性,在单向地震动作用振型Pushover分析研究基础上,提出了考虑双向地震动作用的结构多维Pushover分析程序。采用弹性振型分解的思路,将非线性结构反应近似为结构多振型弹塑性反应的叠加,进而将结构按振型等效为多个等效方程,将每一等效方程转化为以双向实际地震记录的组合为地震输入的等效单自由度体系。在此基础上给出了考虑双向地震作用的非对称结构多维Pushover分析程序,并阐述了该方法与传统Pushover分析方法的区别,最后通过算例将该方法结果与非线性时程分析结果进行比较,证明了该方法具有一定的准确性。     

单桩横向非线性运动地震响应简化分析

采用退化的Bouc-Wen模型和动力Winkler地基梁模型,建立了一个单桩横向非线性运动地震响应的简化分析模型,将自由场位移,作为沿桩轴均匀分布的非线性弹簧和频率相关的粘壶的支撑运动,利用运动响应因子的概念以及相应的计算方法,计算并讨论了地震运动过程中,单桩横向非线性运动地震响应问题。计算结果表明,对于单桩横向非线性运动地震响应问题的简化分析,所提出的模型在物理上是合理的。     

隔震结构的研究概况和主要问题

简要概括了国内外隔震技术的应用发展状况.系统总结、评述了隔震结构若干方向的研究进展,包括隔震结构的非线性地震反应分析和非线性动力学性态分析、可靠度分析、优化设计、系统识别、试验研究等内容.指出了隔震技术发展中需要解决的几个主要问题,例如新型隔震元件、隔震体系的开发,隔震结构的经济可行性分析,与隔震技术发展相适应的设计、施工规范等.最后在结束语中探讨了隔震设计与基于功能的设计、分灾设计等结构抗震设计思想的关系.      

圆形地下连续墙场地地震反应的简化计算方法

首先将水平地震荷载作用沿环向展开为傅立叶级数,利用沿圆周法向和切向两个方向的正交性,再将水平地震荷载转化为一致横向荷载组合,使三维求解问题转变为一系列旋转子午面上二维问题的叠加,进而提出圆形地下连续墙场地地震反应的简化计算方法。之后,采用等效线性化方法来考虑土体非线性性质,进一步将非线性地震反应问题转化为线性问题求解。...     

Targeted energy transfers in vibro-impact oscillators for seismic mitigation

In the field of seismic protection of structures, it is crucial to be able to diminish ‘as much as possible’ and dissipate ‘as fast as possible’ the load induced by seismic (vibration-shock) energy imparted to a structure by an earthquake. In this context, the concept of passive nonlinear energy pumping appears to be natural for application to seismic mitigation. Hence, the overall problem discussed in this paper can be formulated as follows: Design a set of nonlinear energy sinks (NESs) that are locally attached to a main structure, with the purpose of passively absorbing a significant part of the applied seismic energy, locally confining it and then dissipating it in the smallest possible time. Alternatively, the overall goal will be to demonstrate that it is feasible to passively divert the applied seismic energy from the main structure (to be protected) to a set of preferential nonlinear substructures (the set of NESs), where this energy is locally dissipated at a time scale fast enough to be of practical use for seismic mitigation. It is the aim of this work to show that the concept of nonlinear energy pumping is feasible for seismic mitigation. We consider a two degree-of-freedom (DOF) primary linear system (the structure to be protected) and study seismic-induced vibration control through the use of Vibro-Impact NESs (VI NESs). Also, we account for the possibility of attaching to the primary structure additional alternative NES configurations possessing essential but smooth nonlinearities (e.g., with no discontinuities). We study the performance of the NESs through a set of evaluation criteria. The damped nonlinear transitions that occur during the operation of the VI NESs are then studied by superimposing wavelet spectra of the nonlinear responses to appropriately defined frequency – energy plots (FEPs) of branches of periodic orbits of underlying Conservative systems.     

Approximate MPA-based method for performing incremental dynamic analysis

In performance based earthquake engineering, it is important to accurately predict the seismic demand and capacities of structures. One recent estimation method is incremental dynamic analysis (IDA), which requires a series of nonlinear response history analyses (RHA) of the structure under various ground motions, each scaled to multiple levels of intensity, selected to cover entire range of structural response from elasticity, to yield and finally global dynamic instability. The implementation of IDA requires intensive computation and detailed knowledge of the nonlinear RHA of structures. In response to the complexity of IDA, an approximate method based on modal pushover analysis (MPA-based IDA) was developed. In MPA-based IDA, seismic demands are computed using the nonlinear RHA of the equivalent SDF systems instead of using nonlinear RHA of MDF systems. The objective of this study is to develop a simpler MPA-based IDA procedure that can avoid nonlinear RHA of equivalent SDF systems. For this purpose, MPA-based IDA employs the empirical equation of the inelastic displacement ratio (C _R ), defined as the ratio of peak displacement of the inelastic SDF system to that of the corresponding elastic SDF system given the strength ratio R, and that of the collapse strength ratio (R _c), which is the ratio of collapse intensity to yield strength. The proposed procedure is verified by comparing the seismic demands and capacities of 6-, 9-, and 20-story steel moment frames as determined by the proposed method and exact IDA.     

基于弹塑性模型的群桩-土-结构动力非线性数值分析

提出一种群桩-土弹塑性模型,结合动力文克尔理论,推导出了与桩(筏)-土属性及SSI体系频率相关的各项弹簧-阻尼单元动力阻抗,建立了三维框架土-结构相互作用有限元简化分析模型。针对不同地震激励,在不同桩-土条件下对模型进行了动力非线性时程分析,结果表明,在某些地震动和土-基础条件下,上部结构非线性作用效应结果可能大于固基假定情形,且桩-土弹塑性模型对上部结构柔弱层位置产生影响。应用本文简化方法可以快速、较准确有效地进行复杂的上下部结构动力时程分析及抗震评估。