Safety thickness analysis of tunnel floor in karst region based on catastrophe theory

Based on the tunnel shape, span and depth, the previous elliptical plate model and clamped beam model were modified.The modified model was applied to different situations. For the elliptical plate model, the water effects were considered. For the clamped beam model, water and horizontal stress were considered. Corresponding potential functions and cusp catastrophe models of rock system were established based on the catastrophe theory. The expressions of critical safety thickness were derived with necessary and sufficient conditions. The method was applied to the practical engineering. Some parameters related to the stability were discussed. The results show that elastic modulus and thickness are advantageous to the floor stability, and that the load, span,horizontal stress and water are disadvantageous to the floor stability.

Catastrophe theory-based risk evaluation model for water and mud inrush and its application in karst tunnels

This paper presents a risk evaluation model of water and mud inrush for tunnel excavation in karst areas.The factors affecting the probabilities of water and mud inrush in karst tunnels are investigated to define the dangerousness of this geological disaster.The losses that are caused by water and mud inrush are taken into consideration to account for its harmfulness.Then a risk evaluation model based on the dangerousness-harmfulness evaluation indicator system is constructed,which is more convincing in comparison with the traditional methods.The catastrophe theory is used to evaluate the risk level of water and mud inrush and it has great advantage in handling problems involving discontinuous catastrophe processes.To validate the proposed approach,the Qiyueshan tunnel of Yichang-Wanzhou Railway is taken as an example in which four target segments are evaluated using the risk evaluation model.Finally,the evaluation results are compared with the excavation data,which shows that the risk levels predicted by the proposed approach are in good agreements with that observed in engineering.In conclusion,the catastrophe theory-based risk evaluation model is an efficient and effective approach for water and mud inrush in karst tunnels.

Application of Catastrophe Theory in 3D Seismic Data Interpretation of Coal Mine

In order to detect fault exactly and quickly, cusp catastrophe theory is used to interpret 3D coal seismic data in this paper. By establishing a cusp model, seismic signal is transformed into standard form of cusp catastrophe and catastrophe parameters, including time-domain catastrophe potential, time-domain catastrophe time, frequency-domain catastrophe potential and frequency- domain degree, are calculated. Catastrophe theory is used in 3D seismic structural interpretation in coal mine. The results show that the position of abnormality of the catastrophe parameter profile or curve is related to the location of fault, and the cusp catastrophe theory is effective to automatically pick up geology information and improve the interpretation precision in 3D seismic data.

Evaluation of the propensity for coal spontaneous combustion based on catastrophe theory

Generally, different prevention measures should be taken according to spontaneous combustion propensities. The current methods to evaluate the propensity of coal spontaneous combustion, such as chromatographic method of oxygen adsorption, oxidation kinetics method and activation energy method, are mostly affected by human factors. Their boundaries among different classes of propensities were all established by subjective judgments. A new evaluation method using catastrophe theory is introduced. This method can accurately depict the process of coal spontaneous combustion and the evaluation index, ＂catastrophe temperature＂, be obtained based on the model. In terms of catastrophe temperature, the spontaneous combustion propensity of different coals can be sequenced. Experimental data indicate that this method is appropriate to describe the spontaneous combustion process and to evaluate the propensity of coal svontaneous combustion.

The Study of Chamber Rockburst by the CUSP Model of Catastrophe Theory

By means of CUSP model of catastrophe theory. this paper has studied thephysics process of rockburst occured on circular chamber. The present paper has nolonly described the instability process of rockburst more deeply. but also got the crilicaldepth of plastic softening area of chamber that is valuable in the controlling engineering of rockburst. the chamber displacement jump and energy liberation have been derived. the influence of rock parameters on the rockburst has been discussed .

Catastrophe Theory Models for Stress-dependent Behaviour in a NiTi Shape Memory Alloy

The measurements by Huibin XU et al of the stress-dependence ot hysteresis in a NiTi shape memo ry alloy are modeled by catastrophe theory. The cusp catastrophe is used with the strain as the behaviour variable and the control parameters being functions of the stress and the temperature. A two constant model is found to be preferred to a four constant model.

Stability of interbed for salt cavern gas storage in solution mining considering cusp displacement catastrophe theory

Cusp displacement catastrophe theory can be introduced to propose a new method about instability failure of the interbed for gas storage cavern in bedded salt in solution mining.We can calculate initial fracture drawing pace of this interbed to obtain 2D and 3D gas storage shapes at this time.Moreover,Stability evaluation of strength reduction finite element method(FEM)based on this catastrophe theory can used to evaluate this interbed stability after initial fracture.A specific example is simulated to obtain the influence of the interbed depth,cavern internal pressure,and cavern building time on stability safety factor(SSF).The results indicate:the value of SSF will be lower with the increase of cavern building time in solution mining and the increase of interbed depth and also this value remains a rise with the increase of cavern internal pressure Especially,we can conclude that the second-fracture of the interbed may take place when this pressure is lower than 6 MPa or after 6 days later of the interbed after initial fracture.According to above analysis,some effective measures,namely elevating the tube up to the top of the interbed,or changing the circulation of in-and-out lines,can be introduced to avoid the negative effects when the secondfracture of the interbed may occur.

Development of a wheat aphid population dynamics model based on cusp catastrophe theory

Aphids are a major global wheat,pest that can cause considerable loss of yield.Modeling of aphid population dynamics is an integral part of management strategies to manage or control aphid populations.In this paper,first,a wheat aphid population dynamics model was developed based on a logistic model and theⅠlollingⅢfunctional response,which includes three factors:temperature,natural enemies and insecticide.Second,this model fitted with a cusp catastrophe model to describe how abrupt changes in the wheat aphid population were influenced by these factors,Finally,the system was validated with field data from 2016 to 2018.The bifurcation set of the cusp catastrophe model was deemod to be the quantified dynamic control threshold,so an outbreak of aphid's population can be explained according to the variation of control variables.In short,this aphid population model was successfully validated on survey data,which can be used to guide the prevention and control of aphids.

Modeling and simulation of voluntary employee turnover using catastrophe theory: A case study on a manufacturing enterprise in China

The Lewisian turning-point obviously increase the labor costs of Chinese manufacturing firms,it made the employee turnover to become the key problem that how to keep the enterprise human resource stability.Here,the conceptual catastrophe model of employee turnover is built from the new perspective of empirical study and catastrophe theory.In particular,we developed a parameter estimation method of the Cusp catastrophe model based on qualitative simulation and fuzzy math,and then to demonstrate the rationality and robustness of this method by a practical case on a manufacturing enterprise.In the end,a series of virtual experiments are carried out for the employee turnover in the period of China’s economic transformation.The main results are that,how to measure the warning,critical and mutation area of employee turnover;the real relationship between the complex economic environment and the demission of employees;the control policy from the macroscopic governmental measures and microscopic enterprise ways.

Catastrophe Theory and Semiophysics:With an Application to "Movie Physics"

In the humanities the applications of catastrophe theory and other models stemming from "dynamic systems theory",a field of applied mathematics based on topology and differential calculus,was the first theoretical innovation since the computer/mind-boom which began in the sixties and brought many research fields to public recognition and institutional success which exploited the metaphor of the computer as mind or artificial intelligence;cf.AI and the Chomsky paradigm.The rise of dynamic model designs began in the late sixties with the publications of Rene Thom,a Fields Medal winner in mathematics,and Christopher Zeeman,a renowned researcher in applied mathematics(mostly in biology and psychology/neurology).The French and English endeavor received much support after 1974-1977 culminating in a joint conference in Cerisy-la-Salle in 1982.The first sections review this development,the catastrophe controversy 1978-1980 and later developments mainly in the work of Rene Thom and his major followers(Petitot,Wildgen,& Brandt).Thorn's new impulse,his "semiophysics"(Thom,1988),and the research which followed are summarized and the notions of "saillance" — "pregnance"(perceptual salience and biological relevance) including its evolutionary aspects are sketched.A specific application to the concept of sign applying the hyper-cycles proposed by Eigen and Schuster(1979) is put forward.Eventually,a new application by the author called "movie physics" is described,which gives a hint to further evolutions of this new field of semiotic theorizing,mainly in the media.

Catastrophe stability analysis for shallow tunnels considering settlement

Limit analysis of the stability of geomechanical projects is one of the most difficult problems.This work investigates the influences of different parameters in NL failure strength on possible collapsing block shapes of single and twin shallow tunnels with considering the effects of surface settlement.Upper bound solutions derived by functional catastrophe theory are used for describing the distinct characteristics of falling blocks of different parts in twin tunnels.Furthermore the analytical solutions of minimum supporting pressures in shallow tunnels are obtained by the help of the variational principle.Lastly,the comparisons are made both in collapsed mechanism and stability factor with different methods.According to the numerical results in this work,the influences of different parameters on the size of collapsing block are presented in the tables and the limit supporting loads are illustrated in the form graphs that account for the surface settlement.

The Theory of Relativity on the Finsler Spacetime

According to some local properties of Lorentz transformation, Einstein stated: 'Vetheitiss greater than that of light have no possibility of existence.' He neglected to point out the applicable range of the special theory of relativity. In fact, it could only be applied to the subluminal-speeds. This paper shows that if ones think of the possibility of the existence of the superluminal-speeds and redescribe the special theory of relativity following Einstein's way, it could be supposed that the physical spacetime is a Finsler spacetime, characterized by the metric ds4=gijkldxidxidxkdxl. If so, a new spactime transformation could be found by invariant ds4 and the theory of relativity is discussed on this transformation it is possible that the Finsler spacetime F(x,y) may be endowed with a catastrophic nature. Based on the different properties between the ds2 and ds4, it is discussed that the flat spacetime will also have the catastrophic nature on the Finsler metric ds4. The spacetime transformations and the Physical quantities will suddenly change at the catastrophe set of the spacetime, the light cone. It will be supposed that only the dual velocity of the superluminal-speeds could be observed. If so, a particle with the superluminal-speed v> c could be regarded as its anti-particle with the dual velocity v1=c2/ v< c. On the other hand, it could be assumed that the horizon of the field of the general relativity is also a catastrophic set. If so, a particle with the superluminal-speeds could be projected near the horizon of these fields, and the particle will move on the sauce-like curves. It is very interesting that, in the Schwarzschild fields, the theoretical calculation for the sauce-like curves should be in agreement with tie data of the superluminal expansion of extragalactic radio sources observed year after year. (see Gao, 1992b).The ca- tastrophe of spacetime has some deep cosmological means. According to the some interested subjects in the Process of evolution of the universe the catastrophe nature of the Finsler spacetime and its cosmological impli= cations are discussed. It is shown that the nature of the universal evolution could be attributed to the geometric features of the Finsler spacetime. (see Cao, 1993)

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.

Damage failure of cemented backfill and its reasonable match with rock mass

In order to study the failure mechanism of backfill and the reasonable matches between backfill and rock mass, and to achieve the object of safe and efficient mining in metal mine, four types of backfills were tested under uniaxial compression loading, with cement?tailing ratios of 0.250:1, 0.125:1, 0.100:1 and 0.083:1, respectively. With the help of the stress?strain curves, the deformation and failure characteristics of different backfills with differing cement?tailing ratios were analyzed. Based on the experimental results, the damage constitutive equations of cemented backfills with four cement?tailing ratios were proposed on the basis of damage mechanics. Moreover, comparative analysis of constitutive model and experimental results were made to verify the reliability of the damage model. In addition, an energy model using catastrophe theory to obtain the instability criteria of system was established to study the interaction between backfill and rock mass, and then the system instability criterion was deduced. The results show that there are different damage characteristics for different backfills, backfills with lower cement?tailing ratio tend to have a lower damage value when stress reaches peak value, and damage more rapidly and more obviously in failure process after peak value of stress; the stiffness and elastic modulus of rock mass with lower strength are more likely to lead to system instability. The results of this work provide a scientific basis for the rational strength design of backfill mine.

Research on basic characteristics of complex system brittleness

The goal of this paper is to research one new characteristic of complex system. Brittleness, which is one new characteritic of complex system, is presented in this paper. The linguistic and qualitative descriptions of complex system are also given in this paper. Otherwise, the qualitative description of complex system is presented at first. On the basis of analyzing the existing brittleness problems, linguistic description and mathematic description of brittleness are given as well. Three kinds of phenomena to judge brittleness of complex system are also given, based on catastrophe theory. Basic characteristics of brittleness are given on the basis of its mathematic description. Two critical point sets are defined by using catastrophe theory. The definition of brittleness and its related theory can serve the control of complex system, and provide theoretical basis for the design and control of complex system.

Catastrophic mechanism of coal and gas outbursts and their prevention and control

Based on the engineering observations of coal and gas outbursts during mining processes and the experimental results,we built a thin plate mechanical model for layered and spalled coal bodies.We studied the mechanical mechanism of outbursts,due to instability,of thin plates of coal rocks under the action of in-plane load and normal load,by using the catastrophe theory.The total potential function is derived for the layered rock system,the cusp catastrophe model for the system is established,the bifurcation set that makes the system unstable is given,the process in which gradual change of action forces leads to catastrophic change of state is analyzed,and the effect of movement path of point(P,q) in the control space on the stability of rock plate is analyzed.The study results show that during the process of coal mining,the stability of the layered coal bodies depends not only on its physical properties and dimensions but also on the magnitudes and changing paths of the in-plane load and the normal load.When the gas in the coal bodies ahead of the mining face is pre-drained,the gas pressure can be reduced and the normal load q can be lowered.Consequently,disasters such as coal and gas outbursts can be effectively prevented.

Catastrophic model for stability analysis of high pile-column bridge pier

According to the engineering features of higher pile-column bridge pier in mountainous area, a clamped beam mechanical model was set up by synthetically analyzing the higher pile-column bridge pier buckling mechanism. Based on the catastrophe theory, the cusp catastrophe model of higher pile-column bridge pier was established by the determination of its potential fimction and bifurcation set equation, the necessary instability conditions of high pile-column bridge pier were deduced, and the determination method for column-buckling and lateral displacement of high pile-column bridge pier was derived. The comparison between the experimental and calculated results show that the calculated curves agree with testing curves and the method is reasonable and effective.

The status evaluation of the permafrost environment along the Chaida'er-Muli Railway in southern Qilian Mountains in northern Qinghai Province,China

Engineering construction has major influence on the permafrost environment.This paper analyzes the interaction between engineering construction and permafrost environment along the Chaidaer-Muli Railway(simply,CMR) based on the press-state-response(PSR) framework.The permafrost environmental system is divided into three subsystems,consisting of permafrost thermal stability,proneness to the freeze-thawing erosion and permafrost ecological fragility.Each subsystem considers its most important influencing factors.Catastrophe Progression Method(CPM) is applied to calculate the current environment condition along the railway.The result indicates that:(1) as far as the thermal stability is concerned,most sections along the CMR are mainly concentrated in rank Ⅲ(fair situation),and a few in Ⅱ(good situation) and Ⅳ(bad situation),respectively;(2) for the proneness tothe freeze-thawing erosion,the entire railway route falls largely in rank Ⅱ(good situation);(3) along the CMR,the ecological fragility of the permafrost environment is in rank Ⅱ(good situation),or slightly fragile;(4) overall,the permafrost environments along the CMR are in rank Ⅲ(fair situation) or Ⅱcondition(good situation).In general,the permafrost environment along the CMR is fair.It is mainly because a series of active measures of protecting permafrost were taken for stabilizing the CMR foundation soils.On the one hand,we should try our best to minimize the influences that engineering activities have exerted on ecology and environment,on the other hand,the positive measures have made improvements to prevent the permafrost environment from deterioration.

Effect of turbulent atmosphere on the on-axis average intensity of Pearcey–Gaussian beam

The propagation characteristics of the Pearcey–Gaussian（PG） beam in turbulent atmosphere are investigated in this paper.The Pearcey beam is a new kind of paraxial beam,based on the Pearcey function of catastrophe theory,which describes diffraction about a cusp caustic.By using the extended Huygens–Fresnel integral formula in the paraxial approximation and the Rytov theory,an analytical expression of axial intensity for the considered beam family is derived.Some numerical results for PG beam propagating in atmospheric turbulence are given by studying the influences of some factors,including incident beam parameters and turbulence strengths.

Research on the Model of Household Credit Risk Evaluation of Rural Microfinance

Since rural microfinance is a credit which grants loans without collateral and guarantees to farmers,it is considerably important to evaluate and control the household credit risk.Through establishing the evaluation index system and then using catastrophe progression theory,three common types of catastrophe system and the normalization formula,we get the comprehensive evaluation.Finally,we take the empirical test and the result shows that this method is simpler and more objective which can be used by the credit cooperatives to decide whether to authorize the loans.