Comparative study of rock slope stability analysis methods for hydropower projects

This paper presents a comparative study of methods used for the analysis of the stability of rock slopes for hydropower projects. The comparison concerns the application of the limit equilibrium method, the block element method, and the finite element method on the stability analysis of two hydropower engineering projects in China. The study results show that the limit equilibrium method and the block element method give very close result, while the finite element method gives more conservative safety factor.     

边坡三维极限平衡法的通用形式

基于以下假定条件:(1) 稳定系数定义为材料的强度折减系数;(2) 土体为刚体,底滑面服从Mohr-Columb强度破坏准则;(3) 微条柱底部法向力dNz的作用点处于条柱底部中点;(4)滑面剪力与底滑面和xoz平面交线的夹角为θ。本文建立了边坡三维极限平衡法的通用形式,通过给定不同的限制条件,可分别得到三维普通条分法 、三维简化毕肖普法 、三维简化简布法 、三维Spencer法 等三维极限平衡的具体算法。     

边坡可靠性与经济风险性分析及其应用

本文在边坡渐进破坏可靠性分析的基本原理和计算方法基础上 ,分析了影响边坡渐进破坏的主要因素 ,对白云鄂博铁矿的主矿边坡进行了二维渐进破坏可靠性计算 ;然后围绕边坡方案的可靠性分析结果 ,把经济决策理论引入边坡的经济分析中 ,结合边坡工程具体特点对边坡进行了投资—效益风险性分析。     

粘质海底稳定性实例分析

本文对南海珠江口盆地大陆架区和东海浙江沿岸象山港的粘质海底进行了稳定性分析。通过实例分析判定了该地区不稳定性的原因, 并给出了稳定性估计的直观图。文中还指出了今后研究的方向。     

船台滑道下含软弱层岸坡的空间稳定分析

芜湖江东船厂新建船台滑道位于有较厚软弱土层的岸坡上。本文采用三维有限元和刚体极限平衡理论结合的方法分析岸坡稳定, 对不同潜在滑动面进行探索, 求解最小安全系数及相应滑动面位置。分析结果已在施工实践中得到证实。     

A reexamination of the friction circle method for the stability analysis of slopes

Summary The stability of earth slopes according to the friction circle method, as normally employed, is based on the condition of equilibrium of forces, and on the condition that at limit equilibrium the actuating and resisting forces are concurrent at one point. This particular condition, assumed in place of the general one of equilibrium of moments at the said stability limit, is not in accordance with the fundamental hypotheses of the kinematics of motion; it gives rise as well to the indetermination of the couple of values of the soil resistance parameters c (cohesion) and (friction) at limit equilibrium.Therefore the problem is taken up again and resolved on the basis of rational equilibrium conditions and assuming that at failure in any point along the sliding circle the maximal strength of the material is developed and therefore limit values of c and proper to failure of the particular soil are uniformly reached along the circle itself.On this basis the condition of equilibrium of forces determines one parameter of the distribution pattern of the normal components of stresses along the circle; the value of a second parameter of the said distribution, involved in the condition of equilibrium of moments, can be easily determined in an approximate way.It is therefore possible to determine easily and speedily the arm of the total actuating force which realizes the limit condition of the supposed sliding movement along the considered circle. The comparison of this arm with the real one of the aforesaid force indicates the degree of stability for any considered circle.The extension of the method to an embankment made up of two zones of different materials is also examined.First published in Italian in L'Energia Elettrica, No. 12, Vol. XLI, 1964.     

The dynamic response of a strain-softening beam

The dynamic response of a strain-softening beam subjected to a transverse impulsive on its tip is investigated. A softening moment-curvature relation is assumed for the beam and a closed form solution is obtained for a special kind of load, which shows that there exists a softening region in the beam and this region propagates along the beam. This result indicates that, except for the possible discrete softening points with rotation discontinuity caused by the deformation localization^[1], the existence of the softening region and its travelling along the beam are the essential features of the dynamic response of a strain-softening beam. The results also show that the failure of the beam should take place under a special load and the critical condition on which the dynamic failure occurs is given. The project supported by National Natural Science Foundation of China     

Fractional Birkhoffian method for equilibrium stability of dynamical systems

In this paper, we present a new method, i.e. fractional Birkhoffian method, for stability of equilibrium positions of dynamical systems, in terms of Riesz derivatives, and study its applications. For an actual dynamical system, the fractional Birkhoffian method of constructing a fractional dynamical model is given, and then the seven criterions for fractional Birkhoffian method of equilibrium stability are established. As applications, by using the fractional Birkhoffian method, we construct four kinds of actual fractional dynamical models, which include a fractional Duffing oscillator model, a fractional Whittaker model, a fractional Emden model and a fractional Hojman–Urrutia model, and we explore the equilibrium stability of these models respectively. This work provides a general method for studying the equilibrium stability of an actual fractional dynamical system that is related to science and engineering.     

大型反倾库岸岩体变形过程及破坏机制数值模拟

随着边坡地质结构、地层岩性和诱发因素的不同,反倾岩体的主控变形破坏模式都会发生改变。金沙江龙蟠边坡岩体主要为反倾向千板岩和砂岩互层状结构,坡脚河床深厚覆盖层构成了边坡的软弱支座。本文运用离散单元法模拟了大型反倾库岸岩体在漫长的地质历史时期中的变形演化过程,并基于反倾岩体变形的时效性观点,引入强度折减法分析边坡在不同阶段的剪切屈服区扩展情况及相应的稳定性状态。结论表明龙蟠边坡变形岩体是重力弯曲蠕变为主导的成因机制,并归纳提出了软基效应和互层效应共同作用下的大规模反倾岩体的累进性剪切破坏模式,俗称“龙蟠模式”。     

A slope modification method for shallow water equations

A slope modification method is proposed for non-oscillatory schemes based on the Lax-Friedrich solver. The modified scheme is proved to be total-variation-diminishing (TVD) and second-order accurate. Application of the scheme to the shallow water equations produces sharp profiles for shocks and achieves high accuracy in the smooth regions of the solution.     

Simplified lattice Boltzmann method for non-Newtonian power-law fluid flows

In this paper, we present a simplified lattice Boltzmann method for non-Newtonian power-law fluid flows. The new method adopts the predictor-corrector scheme and reconstructs solutions to the macroscopic equations recovered from the lattice Boltzmann equation through Chapman-Enskog expansion analysis. The truncated power-law model is incorporated into this method to locally adjust the physical viscosity and the associated relaxation parameter, which recovers the non-Newtonian behaviors. Compared with existing non-Newtonian lattice Boltzmann models, the proposed method directly evolves the macroscopic variables instead of the distribution functions, which eliminates the intrinsic drawbacks like high cost in virtual memory and inconvenient implementation of physical boundary conditions. The validity of the method is demonstrated by benchmark tests and comparisons with analytical solution or numerical results in the literature. Benchmark solutions to the three-dimensional lid-driven cavity flow of non-Newtonian power-law fluid are also provided for future reference.     

The stability of limit cycles in nonlinear systems

In this paper, a necessary condition is first presented for the existence of limit cycles in nonlinear systems, then four theorems are presented for the stability, instability, and semistabilities of limit cycles in second order nonlinear systems. Necessary and sufficient conditions are given in terms of the signs of first and second derivatives of a continuously differentiable positive function at the vicinity of the limit cycle. Two examples considering nonlinear systems with familiar limit cycles are presented to illustrate the theorems.     

Simplified method for simulation of ergodic spatially correlated seismic ground motion

A simplified method for the simulation of the ergodic spatially correlated seismic ground motion is proposed based on the commonly used original spectral representation method. To represent the correlation in the ground motion, the phase angles are given by explicit terms with a clear physical meaning. By these explicit terms, the computational efficiency can be improved by converting the decomposition of the complex cross-spectral matrix into the decomposition of the real incoherence coefficient matrix. Double-indexing frequencies are introduced to simulate the ergodic seismic ground motion, and the ergodic feature of the improved method is demonstrated theoretically. Subsequently, an explicit solution of the elements of the lower triangular matrix under the Cholesky decomposition is given. With this explicit solution, the improved method is simplified, and the computational efficiency can be improved greatly by avoiding the repetitive Cholesky decomposition of the cross-spectral matrix in each frequency step. Finally, a numerical example shows the good characteristic of the improved method.     

Global asymptotic stability for Hopfield-type neural networks with diffusion effects

The existence, uniqueness and global asymptotic stability for the equilibrium of Hopfield-type neural networks with diffusion effects are studied. When the activation functions are monotonously nondecreasing, differentiable, and the interconnected matrix is related to the Lyapunov diagonal stable matrix, the sufficient conditions guaranteeing the existence of the equilibrium of the system are obtained by applying the topological degree theory. By means of constructing the suitable average Lyapunov functions, the global asymptotic stability of the equilibrium of the system is also investigated. It is shown that the equilibrium (if it exists) is globally asymptotically stable and this implies that the equilibrium of the system is unique.     

Some general results on the stability and flow failure of rigid viscoplastic structures

The evolution of structures made of materials which obey a rigid viscoplastic constitutive law, conceived as a generalisation of the classical Bingham model, and submitted to several loading parameters, is examined here in connection with the limit analysis (or yield design) theorems. A minimum principle for the velocities is established, from which it is shown in particular that the structure remains motionless as far as the loading belongs to the domain of safe loadings, while flow failure is triggered as soon as it is loaded beyond its limit load. Such a property is illustrated on the example of a uniform layer of Bingham material flowing on an inclined plane, due to the combined action of gravity and surface shear loading, considered as two independent loading parameters.     

Analysis on stability of an autonomous dynamics system for sars epidemic

Introduction Severeacuterespiratorysyndrome(SARS)spreadsmostrapidlythroughthe23areasand countriesintheworldsincethefirstSARScasewasreportedinGuangdonginNovember,2002andreachedtheitsclimaxinApril May2003.Althoughtheperiodoftheepidemicwasover now,itwasnotclearaboutSARSorigin,themechanismoftransmission,andtheregularityof SARSemergingexceptthatSARSasanovelcoronaviruswasknown.ThestudiesofSARS weremadebyavarietyofwaysandinmanyfieldsinorderthatSARSwouldbewellknown andeffectivemeasuresofi…     

A perturbation-incremental method for strongly non-linear non-autonomous oscillators

A perturbation-incremental method is extended for the analysis of strongly non-linear non-autonomous oscillators of the form , where g(x) and are arbitrary non-linear functions of their arguments, and ε can take arbitrary values. Limit cycles of the oscillators can be calculated to any desired degree of accuracy and their stabilities are determined by the Floquet theory. Branch switching at period-doubling bifurcation along a frequency-response curve is made simple by the present method. Subsequent continuation of an emanating branch is also discussed.     

关于浮体的平衡与稳定性

本文讨论了浮体的平衡与稳定问题, 介绍了定倾中心的定义, 并结合一个具体的例子, 给出了浮体稳定性3种不同的判别方法, 最后, 根据能量方法说明了用定倾高度判定浮体稳定性的理论依据.     

带弹簧支撑超静定结构位移的简化计算方法

针对带有弹性支撑的超静定结构的位移计算问题, 对利用虚功原理得到的位移计算一般公式进行了进一步推导, 提出了该类结构位移的简化计算方法. 文中计算公式表达形式简洁, 且与一般刚性支撑超静定结构的位移计算方法一致. 通过与有限元分析结果的对比,证明了该公式的正确性.     

Diffusion stability of bubbles in a cluster

The diffusion stability of gas bubbles in one-fraction and two-fraction clusters subjected to an acoustic field is studied. For a one-fraction cluster, numerical values were obtained for the initial gas concentrations in the liquid at which the bubble tends to one of two equilibrium states because of diffusion processes between the bubble and the ambient liquid. It is found that a two-fraction cluster tends to become a one-fraction cluster. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 40–48, July–August, 2007.