井筒移动与形变的动态数据处理

从井筒形变的力学模型入手,推导了井筒发生突变时的临界压力,按照灰色系统思想,探讨了带有突变现象的灰色非线性模型来预计井筒形变的可行性。实例表明,在突变点火大地改善了拟合精度,它为解释各项工程破裂现象及其预计方法提供了一种有效的数学方法。

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.

Cusp Model for Risk Analysis

Aim To assess simultaneously various risk states of a system. Methods\ Using the catastrophe and fuzzy theory, the energy and uncertainty in a system are set as two control variables and the function of the system is used as the state variable for analysis. Results and Conclusion\ A risk analysis model named the cusp model is presented. Various states regarding the safety of the system such as the accident state, no accident state and miss state can be represented at will on the cusp model.

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.

Reasonable location parameters of pick and nozzle in combined cutting system

The drum shearer and high pressure water jet combined cutting system is an effective technology to cut hard coal-rock, but one problem of the technology is the choice of pick and nozzle location parameters. In order to solve the problem, the process and mechanism of combined cutting arc studied and mining seepage catastrophe theory is used to construct the mathematic and physical model of combined cutting hard coal-rock. Based on the model and detailed analysis of combined cutting mechanism, the single pick and nozzle combined cutting test-bed is built to test the main pick and nozzle location parameters of drum shearer and water jet combined cutting system. Test results show that the best vertical distance between the pick-tip and nozzle center point is the sum of cutting thickness and proper target distance in the Y axial direction; the best horizontal distance is the length between pick-tip point and coal-rock surface bursting crack point in the X axial direction. The best incident angle of water jet should be the same as the bursting crack line＇s angle in theory, but considering other important factors comprehensively, it is more reasonable when the incident angle of water jet is 90°.

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.

Research on traffic flow forecasting model based on cusp catastrophe theory

This paper intends to describe the relationship between traffic parameters by using cusp catastrophe theory and to deduce highway capacity and corresponding speed forecasting value through suitable transformation of catastrophe model. The five properties of a catastrophe system are outlined briefly, and then the data collected on freeways of Zhujiang River Delta, Guangdong province, China are examined to ascertain whether they exhibit qualitative properties and attributes of the catastrophe model. The forecasting value of speed and capacity for freeway segments are given based on the catastrophe model. Furthermore, speed-flow curve on freeway is drawn by plotting out congested and uncongested traffic flow and the capacity value for the same freeway segment is also obtained from speed-flow curve to test the feasibility of the application of cusp catastrophe theory in traffic flow analysis. The calculating results of catastrophe model coincide with those of traditional traffic flow models regressed from field observed data, which indicates that the deficiency of traditional analysis of relationship between speed, flow and occupancy in two-dimension can be compensated by analysis of the relationship among speed, flow and occupancy based on catastrophe model in three-dimension. Finally, the prospects and problems of its application in traffic flow research in China are discussed.

Catastrophe analysis of deep tunnel above water-filled caves

To explore the influence of karst cavity pressure on the failure mechanisms of rock layers above water-filled caves, novel blow-out and collapse mechanisms are put forward in this study. The proposed method uses the nonlinear optimization to obtain the failure profiles of surrounding layered rock with water-filled cave at the bottom of the tunnel. By referring to the functional catastrophe theory, stability analysis with different properties in different rock layers is implemented with considering the incorporation of seepage forces since the groundwater cannot be ignored in the catastrophe analysis of deep tunnel bottom. Also the parametric analysis is implemented to discuss the influences of different rock strength factors on the failure profiles. In order to offer a good guide of design for the excavation of deep tunnels above the water-filled caves, the proposed method is applied to design of the minimum effective height for rock layer. The results obtained by this work agree well with the existing published ones.

Application of cusp catastrophe theory to reliability analysis of slopes in open-pit mines

A method of slope reliability analysis was developed by imposing a state equation on the limit equilibrium theory, given the basis of a fixed safety factor technique. Among the many problems of reliability analysis, the most important problem is to find a performance function. We have created a new method of building a limit state equation for planar slip surfaces by applying the mathematical cusp catastrophe theory. This new technique overcomes the defects in the traditional rigid limit equilibrium theory and offers a new way for studying the reliability problem of planar slip surfaces. Consequently, we applied the technique to a case of an open-pit mine and compared our results with that of the traditional approach. From the results we conclude that both methods are essentially consistent, but the reliability index calculated by the traditional model is lower than that from the catastrophic model. The catastrophe model takes into consideration two possible situations of a slope being in the limit equilibrium condition, i.e., it may or may not slip. In the traditional method, however, a slope is definitely considered as slipping when it meets the condition of a limit equilibrium. We conclude that the catastrophe model has more actual and instructive importance compared to the traditional model.

Characteristics of Period—Doubling Bifurcation Cascades in Quasi—discontinuous Systems

Many systems can display a very short, rapid change stage (quasi-discontinuous region) inside a relatively very long and slow change process. A quantitative definition for the 'quasi-discontinuity' in these systems has been introduced. With the aid of a simplified model, some extraordinary Feigenbaum constants have been found inside the period-doubling cascades, the relationship between the values of the extraordinary Feigenbaum constants and the quasi-discontinuity of the system has also been reported. The phenomenon has been observed in Pikovsky circuit and Rose-Hindmash model.

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.

A CUSP CATASTROPHE, PRECURSORS PATTERN AND EVOLUTION PROCESS OF ROCKBUST OF COAL PILLAR UNDER A HARD ROCK SUBJECT TO ELASTIC SUPPORT

The rockburst of the poal pillar under a thick hard roof stratum is modelled as the instability failure problem of coal pillars under strata subject to elastic support. The instability mechanism of rockburst is studied by applying cusp catastrophic theory. The effects of the stiffness ratio of the system and loads imposed on the system on the rockburst are explicated.The factors affecting rockbursts are discussed. Based on them, the evolution process, the forewarning regularity arid forewarning sings of rockbursts are studied. It is indicated that the subsidence velocity of roof stratum, which increases quickly and tends to infinity, is the forewarning measurable signs of the rockbursts of coal pillar.

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.

STUDY ON MATHEMATICAL MODEL OF GAS EXPLOSION IN COAL MINE

Based on the principle of gas explosion in underground coal mine, mutation theory and mathematic method were adopted to establish" Mathematical model of coal mine gas explosion"and advanced some new concepts and ideas. The model can simply and precisely indicates underground air status and conforms to part of experimental data, provided a new method for research and experiment of explosion disaster theory.