基于突变理论的改进极限平衡法边坡稳定分析

结合某工程边坡,通过考虑边坡在破坏时突然失稳的变化特征,结合突变理论,分析了该边坡在天然状态和保水状态下的各自稳定性,通过对比发现,在考虑滑坡的突变特征的前提下,对滑坡的稳定性计算更加真实可靠。

防屈曲钢板剪力墙稳定性研究

以新型抗侧力构件防屈曲耗能钢板剪力墙为研究对象,基于板的稳定性理论,考虑混凝土盖板抗弯刚度和抗弯承载力,分析整体和局部屈曲内嵌钢板弹塑性性能,推导出了防屈曲钢板剪力墙整体稳定临界荷载值和最小混凝土盖板厚度表达式.引入钢板非弹性阶段切线模量因数η,优化了防屈曲钢板剪力墙整体稳定临界荷载表达式,得到了非弹性阶段最小混凝土盖板厚度参考式.对板的微分方程推导得到了内嵌钢板屈曲半波数和半波式屈曲褶皱对混凝土盖板挤压力表达式,并进行有限元分析.得到四螺栓单元局部稳定要求螺栓间距方程式,给出了螺栓间距与混凝土盖板厚度之间的关系式和最大螺栓间距与混凝土盖板建议比值,其最大螺栓间距与混凝土盖板厚度比值l0/tc=90.

Consensus tracking protocol and formation control of multi-agent systems with switching topology

Consensus tracking control problems for single-integrator dynamics of multi-agent systems with switching topology are investigated. In order to design effective consensus tracking protocols for a more general class of networks, which are aimed at ensuring that the concerned states of agents converge to a constant or time-varying reference state, new consensus tracking protocols with a constant and time-varying reference state are proposed, respectively. Particularly, by contrast with spanning tree, an improved condition of switching interaction topology is presented. And then, convergence analysis of two consensus tracking protocols is provided by Lyapunov stability theory. Moreover, consensus tracking protocol with a time-varying reference state is extended to achieve the fbrmation control. By introducing formation structure set, each agent can gain its individual desired trajectory. Finally, several simulations are worked out to illustrate the effectiveness of theoretical results. The test results show that the states of agents can converge to a desired constant or time-varying reference state. In addition, by selecting appropriate structure set, agents can maintain the expected formation under random switching interaction topologies.

Stability analysis of shallow tunnels subjected to seepage with strength reduction theory

Based on strength reduction theory,the stability numbers of shallow tunnels were investigated within the framework of upper and lower bound theorems of limit analysis. Stability solutions taking into account of water seepage were presented and compared with those without considering seepage. The comparisons indicate that the maximum difference does not exceed 3.7%,which proves the present method credible. The results show that stability numbers of shallow tunnels considering seepage are much less than those without considering seepage,and that the difference of stability numbers between considering seepage and without considering seepage increase with increasing the depth ratio. The stability numbers decrease with increasing permeability coefficient and groundwater depth. Seepage has significant effects on the stability numbers of shallow tunnels.

Fluid–solid coupling analysis of rock pillar stability for concealed karst cave ahead of a roadway based on catastrophic theory

In order to study the mechanism of water inrush from a concealed, confined karst cave, we established a fluid–solid coupling model of water inrush from a concealed karst cave ahead of a roadway and a strength reduction method in a rock pillar for preventing water inrush based on catastrophic theory. Fluid–solid coupling effects and safety margins in a rock pillar were studied. Analysis shows that rock pillar instability, exerted by disturbance stress and seepage stress, is the process of rock pillar catastrophic destabilization induced by nonlinear extension of plastic zones in the rock pillar. Seepage flow emerges in the rock pillar for preventing water inrush, accompanied by mechanical instability of the rock pillar. Taking the accident of a confined karst cave water-inrush of Qiyi Mine as an example, by studying the safety factor of the rock pillar and the relationship between karst cave water pressure and thickness of the rock pillar,it is proposed that rock pillar thickness with a safety factor equal to 1.5 is regarded as the calculated safety thickness of the rock pillar, which should be equal to the sum of the blasthole depth, blasting disturbance depth and the calculated safety thickness of the rock pillar. The cause of the karst water inrush at Qiyi Mine is that the rock pillar was so small that it did not possess a safety margin. Combining fluid–solid coupling theory, catastrophic theory and strength reduction method to study the nonlinear mechanical response of complicated rock engineering, new avenues for quantitative analysis of rock engineering stability evaluation should be forthcoming.

Study on Dynamic Response of the “Dualistic” Structure Rock Slope with Seismic Wave Theory

Currently, scant attention has been paid to the theoretical analysis on dynamic response mechanism of the ＂Dualistic＂ structure roek slope. The analysis presented here provides insight into the dynamic response of the ＂Dualistie＂ structure rock slope. By investigating the principle of energy distribution, it is shown that the effect of a joint plays a significant role in slope stability analysis. A dynamic reflection and transmission model （RTM） for the ＂Dualistic＂ structure rock slope and explicit dynamic equations are established to analyze the dynamic response of a slope, based on the theory of elastic mechanics and the principle of seismic wave propagation. The theoretical simulation solutions show that the dynamic response of the ＂Dualistic＂ structure rock slope （soft-hard） model is greater than that of the ＂Dualistic＂ strueture rock slope （hard-soft） model, especially in the slope crest. The magnifying effect of rigid foundation on the dynamic response is more obvious than that of soft foundation. With the amplitude increasing, the cracks could be found in the right slope （soft-hard） crest. The crest failure is firstly observed in the right slope （soft-hard） during the experimental process. The reliability of theoretical model is also investigated by experiment analysis. The conclusions derived in this paper could also be used in future evaluations of Multi-layer rock slopes.

THEORETICAL ANALYSIS OF THE STABILITY OF A DEEP ROADWAY

In this paper the thickness of a broken zone, a state parameter of roadway surrounding rock, is used as the index to evaluate the stabi1ity of surrounding rock of a deep roadway. The paper gives a theoretic formula for calculating the thickness of the broken zone. The author points out that not only the ultimate strength of rockmass but its residual strength and strain-softening level all have a great influence on the stability of surrounding rock of a deep roadway. The paper’s results show that to reinforce surrounding rock, raise its residual strength and lower its strain-softening level should be taken as a basic requirement for supports of a deep roadway. In addition, the research also indicates that it is impossible for roadway supports to change surrounding rock states of a deep roadway, so it is certain for them to work in a broken state. For this reason, a sufficient yieldable quantity is necessary for roadway supports used in deep mining.

Application of material strength reserve method to the stability analysis of earth dam of feilaixia multipurpose project

The material strength reserve method is practical in the study of the stability and failure mechanism of earth dam by analysing the development of failure zone of different shear strength parameters of the earth mass of the dam. The stability in the concrete dam and ensemble architecture has got general application while analysing. In combination with Feilaixia Multipurpose Project, application of this method to earth dam stability analysis was studied by plane Finite Element Method(FEM) for the first time. Through plane FEM, we can get the failure mechanism of earth dam and appraise to the security, for operating and managing put forward some reference suggestions.

Base stability analysis of braced deep excavation in undrained anisotropic clay with upper bound theory

It is imperative to evaluate factor of safety against basal heave failure in the design of braced deep excavation in soft clay.Based on previously published field monitoring data and finite element analyses of ground settlements of deep excavation in soft clay,an assumed plastic deformation mechanism proposed here gives upper bound solutions for base stability of braced deep excavations.The proposed kinematic mechanism is optimized by the mobile depth(profile wavelength).The method takes into account the influence of strength anisotropy under plane strain conditions,the embedment of the retaining wall,and the locations of the struts.The current method is validated by comparison with published numerical study of braced excavations in Boston blue clay and two other cases of excavation failure in Taipei.The results show that the upper bound solutions obtained from this presented method is more accurate as compared with the conventional methods for basal heave failure analyses.

Effects of delay in immunological response of HIV infection

In this paper, a human immunodeficiency virus （HIV） infection model with both the types of immune responses, the antibody and the killer cell immune responses has been introduced. The model has been made more logical by including two delays in the acti-vation of both the immune responses, along with the combination drug therapy. The inclusion of both the delayed immune responses provides a greater understanding of long-term dynamics of the disease. The dependence of the stability of the steady states of the model on the reproduction number R0 has been explored through stability theory. Moreover, the global stability analysis of the infection-free steady state and the infected steady state has been proved with respect to R0. The bifurcation analysis of the infected steady state with respect to both delays has been performed. Numerical simulations have been carried out to justify the results proved. This model is capable of explaining the long-term dynamics of HIV infection to a greater extent than that of the existing model as it captures some basic parameters involved in the system such as immunological delay and immune response. Similarly, the model also explains the basic understanding of the disease dynamics as a result of activation of the immune response toward the virus.

FURTHER RESEARCH OF A NEW KIND OF SERIES REPAIRABLE SYSTEM

This paper is devoted to studying the uniqueness and existence of the system dynamic solution by using C0-semigroup theory and discussing its exponential stability by analyzing the spectrul distribution of system operator and its quasi-compactness. Some primary reliability indices are discussed with the eigenfunction of system operator and the optimal vacation time to get the maximum system profit is analyzed at the end of paper.

Geometric approach to the stability analysis of the periodic solution in a semi-continuous dynamic system

Integrated pest management （IPM） is a long-term management strategy and has been proved to be more effective in pest control. To well-understand the mechanism and effect of the action of IPM, the geometric theory of the involved semi-continuous dynamic systems is becoming more and more important. In this work, a geometric approach is applied to analyze the stability of the positive order-one periodic solution in semi-continuous dynamic systems. A stability criterion to test the stability of the order-one periodic solution is established. As an application, a stage-structure model involved chemical control is presented to show the efficiency of the proposed method. The sufficient conditions to insure the existence of the periodic solution are provided. In addition, the number and the stability of the periodic solutions are discussed accordingly. The simulations are carried out to verify the results.

The Volterra-Lyapunov matrix theory for global stability analysis of a model of the HIV/AIDS

In this paper, we analyze a nonlinear mathematical model of the HIV/AIDS and screening of unaware infectives on the transmission dynamics of the disease in a homoge- neous population with constant immigration of susceptibles incorporating use of condom, screening of unaware infectives and treatment of the infected. We consider constant con- trols and thereafter by incorporating the theory of Volterra-Lyapunov stable matrices into the classical method of Lyapunov functions, we present an approach for global stability analysis of HIV/AIDS. The analysis and results presented in this paper make building blocks toward a comprehensive study and deeper understanding of the funda- mental mechanism in HIV/AIDS. A numerical study of the model is also carried out to investigate the analytical results.

Structures,stabilities,and IR and ^(13)C-NMR spectra of dihedral fullerenes:A density functional theory study

Dihedral fullerenes are thermodynamically stable molecules with Dnd or Dnh symmetry. Based on experimental findings, two series of dihedral fullerenes with five-fold （C5） and six-fold （C6） symmetry have been studied using density functional theory （DFT）. The DFT calculations showed that for both series the stabilities increased with increasing fullerene size. Structural analyses indicated that the stabilities are related to specific local geometries. In the case of the more abundant C5 series, the presence of approximately planar pentagons and hexagons on the top bowl favors their formation. That is to say, those fuller- enes with small dihedral angles within the polygons are readily formed, because planar hexagons lead to strengthened conjuga- tion which lowers average bonding energies （ABE） and increases thermodynamic stabilities. Non-planar hexagons at equatorial positions in tube-shaped fullerenes have an adverse effect on the conjugation and inhibit their formation. Calculations also demonstrated that fullerenes in the two series, including C50（D5h）, C60（O6h）, C80（O5d）, C96（D6d）, Cllo（D5h）, and Cl20（D5d）, have thermodynamically stable triplet structures with strong conjugation. The calculated IR and 13C NMR spectra of the fullerenes show some similarities and regular trends due to their homogenous structures. The electronic structures indicate that short dou- ble bonds in hexagons with high electron occupancies are readily attacked by electrophilic agents and can also be coordinated by transition metals. Mechanistic discussions suggested that C2 additions and C2 losses constitute reversible processes at high temperature and C2 additions in pentagonal fusions are crucial to the kinetics of the curvature of structures. C3 additions lead to the formation of large fullerenes of other types.

Stability analysis of n-species Lotka-Volterra almost periodic competition models with grazing rates and diffusions

In this pape, almost periodic solution of a n-species Lotka-Volterra competition system with grazing rates and diffusions is investigated. By using the method of upper and lower solutions anti Schauder fixed point theorem as well as Lyapunov stability theory, we give sufficient conditions under which the strictly positive space homogeneous almost perilodic solution of the system is globally asymptotically stable. Moreover, some numerical simulations are given to validate our theoretical analysis.

Stability Analysis for Car Following Model Based on Control Theory

Stability analysis is one of the key issues in car-following theory. The stability analysis with Lyapunov function for the two velocity difference car-following model(for short, TVDM) is conducted and the control method to suppress traffic congestion is introduced. Numerical simulations are given and results are consistent with the theoretical analysis.