考虑地震力方向的倾倒式危岩可靠度分析

侧向卸荷作用导致高陡边坡发育大量危岩体,危岩体在降雨、地震作用下易发生失稳破坏,判断其失稳的概率对危岩防治具有重要意义.该文以倾倒式危岩体为例,建立了考虑地震力作用方向下最危险方向的物理力学模型,利用函数极值理论建立了最危险地震力作用方向的表达式,结合可靠度理论建立了倾倒式危岩体可靠度指标、失稳概率表达式及判断标准.通过对重庆南川金佛山危岩体案例的分析表明:工况1的最危险地震力作用方向与水平方向的偏转角θ在5°范围内,工况2的最危险地震力作用方向与水平方向的偏转角θ在10°左右;危岩体最危险作用方向不是一个固定角,其值与危岩体形态、裂隙水作用力大小、岩腔深度等有关.当主控结构面裂隙长度较小时,最危险地震力作用方向与水平夹角很小,随主控结构面裂隙长度增大,最危险地震力作用方向与水平夹角显著增大;危岩体失稳概率随主控结构面裂隙长度增加而增大,工况2较工况1增大幅度更明显.该研究成果对危岩的防灾减灾具有重要意义.     

High-performance computer simulation of wave processes in geological media in seismic exploration

A class of problems arising in seismic exploration are investigated, namely, seismic signal propagation in multilayered geological rock and near-surface disturbance propagation in massive rock with heterogeneities, such as empty or filled fractures and cavities. Numerical solutions are obtained for wave propagation in such highly heterogeneous media, including those taking into account the plastic properties of the rock, which can be manifested near a seismic gap or a wellbore. All types of explosion-generated elastic and elastoplastic waves and waves reflected from fractures and the boundaries of the integration domain are analyzed. The identification of waves in seismograms recorded with near-surface receivers is addressed. The grid-characteristic method is used on triangular, parallelepipedal, and tetrahedral meshes with boundary conditions set on the rock-fracture interface and on free surfaces in explicit form. The numerical method proposed is suitable for the study of the interaction between seismic waves and heterogeneous inclusions, since it ensures the most correct design of computational algorithms on the boundaries of the integration domain and at media interfaces. A parallel software code implemented with the help of OpenMP and MPI was used to execute computations on parallelepipedal and tetrahedral grids.     

Vibrations of the surface of an elastic double-layered half-space with a periodic system of cracks

The two-dimensional problem of the normal incidence of a plane transverse wave from the far field on to the free surface of an elastic double-layered half-space, comprising a homogeneous layer attached to a semi-infinite base of a different elastic material, is considered. At the boundary between the two media there is a system of plane cracks, arranged periodically along the separation line, which models the fracture zone at the interface between dense solid rock and soft sedimentary rock. The effect of the fractures on the transmission of a transverse seismic wave generated by a deep-focus earthquake, and of the type of vibrations of the free surface of the ground that result, is studied. It is difficult to predict whether the seismic wave is strengthened or weakened by the fracture zone. The effect of the system of cracks on vibrations of the free surface largely depends on the physical and geometrical parameters and, primarily, on the vibration frequencies.     

基于Schwarz-Christoffel变换的圆形隧道围岩应力分布特征研究

隧道围岩应力还原到实际区域的变换方法被越来越多地应用到工程实践中,对复杂形状围岩体内的隧道围岩应力计算方法和隧道围岩稳定性的研究具有重要的实践指导意义.该文建立了不规则岩体中开挖圆形隧道的力学模型,运用复变函数理论,通过映射函数Schwarz-Christoffel变换,得到复平面单位圆到隧道所处多边形岩体的映射函数,在复变函数数域内分析了多边形岩体应力的求解步骤,运用弹性力学理论等推导了不规则岩体中圆形隧道的复变应力函数Φ(ξ)和φ(ξ)的表达式,并得出围岩体任一点应力分量σρ和σθ的解析通式.通过具体算例分析可知,岩体形状对圆形隧道的稳定性有较大的影响,隧道所处4种形状下的围岩体最大应力值分布规律为:顶底板的最大应力值从六边形、五边形、四边形、圆形围岩体依次减小,帮部的最大应力值从圆形、四边形、五边形、六边形围岩体依次减小.     

Global existence of solutions to a parabolic–elliptic chemotaxis system with critical degenerate diffusion

This paper is devoted to the analysis of nonnegative solutions for a degenerate parabolic–elliptic Patlak–Keller–Segel system with critical nonlinear diffusion in a bounded domain with homogeneous Neumann boundary conditions. Our aim is to prove the existence of a global weak solution under a smallness condition on the mass of the initial data, thereby completing previous results on finite blow-up for large masses. Under some higher regularity condition on solutions, the uniqueness of solutions is proved by using a classical duality technique.     

A decomposition scheme for acoustic obstacle scattering in a multilayered medium

We consider the acoustic wave scattering by an impenetrable obstacle embedded in a multilayered background medium, which is modelled by a linear system constituted by the Helmholtz equations with different wave numbers and the transmission conditions across the interfaces. The aim of this article is to construct an efficient computing scheme for the scattered waves for this complex scattering process, with a rigorous mathematical analysis. First, we construct a set of functions by a series of coupled transmission problems, which are proven to be well-defined. Then, the solution to our complex scattering in each layer is decomposed as the summation in terms of these functions, which are essentially the contributions from two interfaces enclosing this layer. These contributions physically correspond to the scattered fields for simple scattering problems, which do not involve the multiple scattering and are coupled via the boundary conditions. Finally, we propose an iteration scheme to compute the wave field in each layer decoupling the multiple scattering effects, with the advantage that only the solvers for the well-known transmission problems and an obstacle scattering problem in a homogeneous background medium are applied. The convergence property of this iteration scheme is proven.     

Ultra-low frequency passive vertical vibration isolation system

An ultra-low frequency passive vertical vibration isolator is constructed by mounting a couple of additional masses on the crank-arms of the torsion spring. The theoretical analysis and experimental results show that the system with additional masses can achieve better vertical vibration isolation and longer resonant period. Measured displacement response of the test mass under seismic excitation reaches 3 x 10^{-12 m/√ Hz} around 10 Hz, and the isolation ratio comes to about 60 dB attenuation at 6 Hz, which is about 30 dB lower than that of the system without additional masses.     

Numerical investigation of seismic attenuation in fluid-saturated fractured media: An extended view of the Skempton coefficient

The interpretation of data from seismic exploration gains from consideration of hydro-mechanical processes in particular when the waves propagate through fluid-filled fractured porous rocks. We specifically investigate attenuation processes in porous rock containing complex fracture networks with the main objective to identify effective hydro-mechanical material properties by computational homogenization. To this end, we generate stochastic fracture ensembles and approximate fractures as ellipses with low aspect ratio (1/100). In other words, the fractures constitute thin and long hydraulic conduits with high permeability. Full periodic boundary conditions are employed on the small scale. We observe a strongly heterogeneous pressure propagation in the fracture network and the surrounding rock. The properties of the macroscopic substitute model are derived by means of a volume averaging technique. We identify a dependence of effective properties on fluid saturation and amount of fractures. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Three-dimensional evolution of the boundary of a polluted area in a bounded piecewise homogeneous porous material

A mathematical model describing the three-dimensional evolution of a liquid-liquid interface in a piecewise homogeneous porous medium containing impermeable rock and a basin with a free liquid is constructed using the Leibenzon-Muskat model. As an example, the dispersion of pollutants from a point source is numerically simulated.     

屈服条件由应力张量的二次齐次函数与一次齐次函数之和来表达的极限分析定理

本文建立了由应力张量σ_ij的二次齐次函数与一次齐次函数的和来表达其屈服条件的刚理想塑性体的极限分析变分原理,它可用于岩土力学的极限分析问题,并把屈服条件为应力张量σ_ij 的二次齐次函数或一次齐次函数来表达的情况作为其特例.     

Optimum Tuned Mass Dampers for Structures at Rock and Soil Sites

In optimum design of tuned mass dampers (TMD), several factors are effective. One of the most important factors is the characteristics of the excitation. Earthquake excitations recorded at soil and rock sites show different characteristics in period and damping. In this paper, optimum TMD properties are separately searched for seismic structures at soil sites and rock sites. For each optimization, six different earthquake records were used. A design methodology was used by employing harmony search (HS). The approach was applied to a ten story structure with one second critical period. Although more damping ratio for TMD is needed for soil sites than rock sites, TMD is more effective for rock sites than soil sites. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Sharp estimates of the error of interpolation by bilinear splines for some classes of functions

On a two-point homogeneous space X, we consider the problem of describing the set of continuous functions having zero integrals over all spheres enclosing the given ball. We obtain the solution of this problem and its generalizations for an annular domain in X. By way of applications, we prove new uniqueness theorems for functions with zero spherical means.     

The smallest enclosing ball problem and the smallest intersecting ball problem: existence and uniqueness of solutions

In this paper we study the following problems and their further generalizations: given a finite number of nonempty closed subsets of a normed space, find a ball with the smallest radius that encloses all of the sets, and find a ball with the smallest radius that intersects all of the sets. These problems can be viewed as generalized versions of the smallest enclosing circle problem introduced in the nineteenth century by Sylvester which asks for the circle of smallest radius enclosing a given set of finite points in the plane. We will focus on sufficient conditions for the existence and uniqueness of an optimal solution for each problem, while the study of optimality conditions and numerical implementation will be addressed in our next projects.     

Analytic solutions for unsteady flows over a superhydrophobic surface

A class of unsteady analytic solutions for the evolution of viscous Newtonian fluids over a superhydrophobic surface is derived. The surface is represented by regular rectilinear riblets and the fluid is assumed to flow along the grooves’ direction. A mixed boundary condition is imposed on the surface, consisting in homogeneous Neumann conditions over the riblet voids and homogeneous Dirichlet conditions on the wall intervals. The transition between the above conditions is modelled through a Robin condition with non-constant smooth coefficients in a completely general manner. A global solution is derived and relevant examples, that can be fruitfully adopted as benchmark solutions for testing numerical solvers, are discussed.     

Bifurcation of limit cycles for a class of cubic polynomial system having a nilpotent singular point

In this paper, center conditions and bifurcations of limit cycles for a class of cubic polynomial system in which the origin is a nilpotent singular point are studied. A recursive formula is derived to compute quasi-Lyapunov constant. Using the computer algebra system Mathematica, the first seven quasi-Lyapunov constants of the system are deduced. At the same time, the conditions for the origin to be a center and 7-order fine focus are derived respectively. A cubic polynomial system that bifurcates seven limit cycles enclosing the origin (node) is constructed.     

Non-linear seismic response of concrete gravity dams to near-fault ground motions including dam-water-sediment-foundation interaction

This study focuses on non-linear seismic response of a concrete gravity dam subjected to near-fault and far-fault ground motions including dam-water-sediment-foundation rock interaction. The elasto-plastic behavior of the dam concrete is idealized using Drucker–Prager yield criterion based on associated flow rule assumption. Water in the reservoir is represented by 9-noded isoparametric quadrilateral fluid finite elements while the dam, the foundation rock and the sediment layer are modeled by using 8-noded isoparametric quadrilateral solid finite elements. The program NONSAP modified for elasto-plastic analysis of fluid-structure systems using the Lagrangian fluid finite element is employed in the response calculations. The fluid element includes the effects of surface waves and sloshing behavior of fluids. Non-linear seismic analyses of the selected concrete dam subjected to both near-fault and far-fault ground motions are performed. The results obtained from linear and non-linear analyses are compared with each other.     

Ultra-low frequency passive vertical vibration isolation system

An ultra-low frequency passive vertical vibration isolator is constructed by mounting a couple of additional masses on the crank-arms of the torsion spring. The theoretical analysis and experimental results show that the system with additional masses can achieve better vertical vibration isolation and longer resonant period. Measured displacement response of the test mass under seismic excitation reaches 3 x 10^{-12 m/√ Hz} around 10 Hz, and the isolation ratio comes to about 60 dB attenuation at 6 Hz, which is about 30 dB lower than that of the system without additional masses. Project supported by the National Natural Science Foundation of China (Grant Nos. 19425008, 49674246 and 59678032).     

Fast enclosure for all eigenvalues in generalized eigenvalue problems

A fast method for enclosing all eigenvalues in generalized eigenvalue problems Ax=λBx is proposed. Firstly a theorem for enclosing all eigenvalues, which is applicable even if A is not Hermitian and/or B is not Hermitian positive definite, is presented. Next a theorem for accelerating the enclosure is presented. The proposed method is established based on these theorems. Numerical examples show the performance and property of the proposed method. As an application of the proposed method, an efficient method for enclosing all eigenvalues in polynomial eigenvalue problems is also sketched.     

Fast verified computation for solutions of algebraic Riccati equations arising in transport theory

A fast algorithm for enclosing the solution of the nonsymmetric algebraic Riccati equation arising in transport theory is proposed. The equation has a special structure, which is taken into account to reduce the complexity. By exploiting the structure, the enclosing process involves only quadratic complexity under a reasonable assumption. The algorithm moreover verifies the uniqueness and minimal positiveness of the enclosed solution. Numerical results show the efficiency of the algorithm.