Study On Self-Organized Criticality,Fractal And Theory Of Disasters

Based on the sand-pile model test,this article did deep research on the criterion of self-organized criticality(SOC)about granular system in civil engineering field.The relationship between the fabric characteristics and dynamic behavior of two typical disaster system,earthquake system and loose deposits system,was discussed based on the criterion of SOC.Finally,aiming at the earthquake disaster and slope gravitational disaster in highway and railway engineering,this article carries out the special research on the formative mechanism,the process of movement and forecast,prevention measures of disasters in the frame of idea of SOC.In details,the main jobs and conclusions of this dissertation are as follows.1.On the basis of previous sand-pile model test,a series of sand-pile model tests of different grain size distribution were carried out.Under the large-scale conditions,the avalanches of uniform sand and non-uniform sand,which grain size distribution curve were discontinuity,exhibited quasi-period distribution or normal distribution,however,the avalanches of non-uniform sand which grain size distribution curve were continuity presented the characteristics of self-organized criticality.2.The concept of information entropy was provided to describe the information contained by the power-law distribution of SOC system.The information entropy of avalanches was defined and analyzed in the sand-pile slopes evolvement for the first time.The information entropy gradually increases with the evolving of sand-pile,and reaches a maximum to stabilization in the critical state.The information entropy of avalanches indicates the disorder degree of systems and represents the complex of sand-pile systems evolvement,which is important to understand the potential action mechanism of complex system. Meanwhile,the information entropy of avalanches indicate also to obtain the critical state by changing the information entropy,the value of entropy show the distance between current state and critical state,and the value is more smaller to show more further critical state,but more greater to more nearer its,when information entropy reach the greatest value,it shows the sand-pile system attach the critical state.3.Correlation dimension was constructed by using the amount of sands under riddle,and the concrete calculating formula was deduced,therefore,we obtained dimensions of sand-pile with one-side and different grain size distribution,and gained the grain size distribution of sand-pile system bearing SOC present fractal distribution combined with sand-pile test,so we put forward the configuration of SOC system have fractal characteristics and the fractal configuration of system can be considered a hypothesis of SOC,and proved the hypothesis by means of cellular automata sand-pile model,which grains array in space have fractal characteristics.4.According as the laws of G-R,the earthquake activities were analyzed in the tectonic regions of the Chinese mainland,we found the earthquake activities in space and energies distribution show SOC as a whole.The fractal characteristics and trans-scale features of fractal structural of faults in Chinese mainland and tectonic regions were researched comprehensively with the macroscopic grid method in fractal theory.A fractal fracture mechanics simple model was established,the quantitative relationship between earthquake the activities value,b, the dimensions of faults,D and the dimensions of fault-face,d was presented, furthermore,the physical mechanism of the b and the positive correlation between the b and the D were discussed.From the theory and practice,these simple models proved the SOC phenomenon of earthquake have its origin in the process of dynamics of SOC and its fractal faults;made clear the consequence between the configuration fractal and earthquake activities.5.The dimensions law of grain size distribution of loose deposits along the national road 317 from Doujiangyan to Wenchuan(7-site in road section K74+775～K75+740)were studied,the results showed that the grain size distribution of loose deposits have fractal structure,and the dimensions increase with slope height,when the value of dimensions was littler,the more components of coarse grain to loose deposits on slope,but the value was greater,the more components of smaller grain,in a word,the value of dimensions varied from two to three.From the theory of particle flow,combined with the test results of large-scale relative density meter and direct shear apparatus,the relation between macroscopically mechanical character of the identical particles and the fractals distribution of grain size was discussed based on the data of experiments. Furthermore,we also deduced the relation between coefficients of stress,φ,and grains density of loose deposits and dimensions of grain size distribution.From these results,we found the fluidness of loose deposits was not flowing,when the value of dimension D of grains was little,during the landslip process,the effect of disturbances upon the systems of loose deposits on a slope strengthened the loose deposits fall,accordingly,it limited the increasing trend of systems sensitivity,and the intensities of disturbances does not always exceed the capability of self-stability,ultimately,the system of loose slope had the character of SOC.So we deduced the capability of a system of loose slope restriction against disturbances spreading was decided by the fractal character of system itself.6.This article analyzed a characteristic of Self-organized criticality of rock failure process.A method which use Self-organized extent parameterαto express stress transfer among units and stress concentration in local units was put forward. Based on the theory that the failure strength of rock units obey second power Weibull distribution,a mechanical model was established with renormalization group theory,and the critical probability of rock failure,pc,was derived.Results indicate that the failure of units is independent and stochastic,and the system evolves to a stable state when the failure probability of unit,p,is less than the critical failure probability pc.When p is higher than pc,the failure of units focus on the macroscopic-transfixion tension split plane,which is a dynamic attractor of Self-organized criticality.The critical failure probability pc and the unit capacity of bearing extemal load F is related to initial condition,pc as well as F/F₀,decrease with the increase of Self-organized extent parameterα,and furthermore,F/F₀＜1. The failure stress of units decreases due to stress transfer.7.We testified the disaster of landslips have the character of SOC using the space distribution of landslips in a region,and analysis on sequence of velocity and time to a single landslip evolvement process.Landslides generally occur on the main slide surface whose strength is the lowest among multitudinous discontinuities.Traditional stability analysis methods for slide surface are mostly a kind of deterministic analysis based on the limit equilibrium theory of rigid body or improved limit equilibrium theory.Actually, slide surface is a kind of extended dissipative dynamical complex systems which vary in the time and space dimension,it exchanges substance,energy and information with outside environment.The evolvement process of slide surface is a self-organized criticality phenomenon which is far away from the equilibrium state.SOC is the dynamical attractor in the course of slide surface running through. By using pattern dynamic model,the "domino-effect" mode and the "chain reaction" process of slide surface failure was analyzed in this paper.A sort of auto-amplifying interactional joining process among damage units was described with deterministic,irreversible,non-linear,non-local and non-characteristic scale dynamic regulation.Distribution functions ofφ(p)andξ(p)were introduced to depict the distribution of rupture attractable area in phase space.At length,the possible destruction patterns of slide surfaces with different damage ratio were also discussed.8.Finally,this article analyzed the predictability of SOC and the apocalypse of the theory of SOC to forecast and prevention of disasters.Under the frame of theory of SOC,The precursor monitoring data of the debris flow disaster was processed and analyzed with a method of improved rescaled range analysis(RSH algorithm).And,a time window which contains sequences history and longtime memory information was defined when calculating Hurst index H.The method can predict debris flow disaster.From the angle of dependable design,we built a model of dependable analysis of the system of safeguard to a loose slope,and the model was applied to practice engineering.