Coal-rock structures in deep coal-bearing strata, due to their intricate mechanical properties, are the primary carriers of rock burst hazards. This study, incorporating singular point catastrophe theory, develops a mathematical model of the coal-rock to investigate the instability mechanisms and influencing factors of these structures. The results reveal the following: (1) By integrating the sharp corner mutation model, the mathematical formulation of the failure criterion for the coal-rock composite system was derived. (2) The failure process of the coal-rock composite structure is gradual. The strength of the coal significantly influences the peak instability strength of the composite structure, whereas the strength of the rock has a relatively minor impact on it. (3) As the proportion of rock thickness decreases, the number of fractures within the rock also diminishes, with these fractures primarily developing on the side of the rock adjacent to the coal-rock contact surface. The findings of this research can serve as valuable references for the prevention of rockbursts in the protection of coal pillars.

Abstract The rheological characteristics of debris flow are the basis of the analysis of debris flow initiation, migration and deposition process. In order to explore the rheological characteristics of debris flow mud, according to the shear characteristics of debris flow fluid in different stages, taking Nanyang expansive soil mud as experimental material and using mcr702 rheometer blade rotor system, rheological experiments (twice increasing shear and once decreasing shear) were carried out on mud with different solid volume concentrations. According to the experimental results, the effects of different experimental processes and solid volume concentration on mud rheological parameters are analyzed, and the following conclusions are obtained: In the process of increasing shear rate, when the shear rate is less than 0.002s-1, the first shear stress is lower than the second shear stress; However, the first shear stress is higher than the second shear stress if the shear rate exceeds 0.002s-1. When the shear rate is greater than 1.83s-1, the mud is in the stable flow stage, the shear stress has a power-law relationship with the shear rate, and its rheological parameters increase exponentially with the volume concentration of mud. In the process of decelerating shear, the shear stress decreases in power law with the decrease of shear rate, which is a group of parallel lines in the double logarithmic coordinate system. Its flow index is less affected by solid volume concentration. The static yield stress of mud (the peak shear stress of the first increasing speed) is much larger than the stable flow yield stress (the shear stress value corresponding to the critical shear rate of 1.83s-1), and the difference decreases with the decrease of the volume concentration of mud solids. The static yield stress and steady flow yield stress of mud increase exponentially with the volume concentration of solid.

The yield stress of mud is the basis for analyzing the flow and desilting of debris flow. Nanyang expansive soil mud was used as experimental materials, and the rheological curves of mud with different solid volume concentrations were obtained by using the stress scanning rheological experiment of Antonpa mcr702 rheometer. For Nanyang expansive soil slurry with different solid volume concentration, the change process of shear stress with shear rate is analyzed. According to the experimental results, the rheological process of Nanyang expansive soil slurry is divided into three stages: stress growth, stress attenuation and stress stability. The slurry concentration has obvious influence on the dynamic and static shear stress of mud.

The yield stress of mud is one key to analyze the initiation and deposition of debris flow. Taking Chengdu clay as the experimental material, slurries with different solid volume concentrations were prepared. Using the blade rotor system of mcr301 rheometer and the continuous shear experimental method, the dynamic change process of shear stress of slurries with different solid volume concentrations was obtained with the shear rate increasing and decreasing continuously. According to the experimental results, the static and dynamic yield stress of Chengdu clay slurry is determined, and the influence of solid volume concentration on the yield stress is analyzed. The following conclusions are obtained: Chengdu clay slurry is a non-Newtonian fluid with yield stress. In the process of accelerated shear, for Chengdu clay slurry with solid volume concentration exceeding 35%, the shear rate is in the range of 0.01–1 s −1 , and the shear stress increases rapidly to the maximum. When the shear rate exceeds 1 s −1 , the shear stress decreases rapidly and finally tends to be stable. The shear rate appears stress overshoot near 1s −1 . However, in the process of increasing shear rate, for Chengdu clay slurry with solid volume concentration of no more than 35%, the shear stress increases rapidly in the range of shear rate of 0.01–0.1 s −1 , and the shear rate exceeds 0.1 s −1 . The shear rate has little effect on the shear stress, and the stress overshoot disappears. In the process of deceleration shear, for all solid volume concentrations in the semi logarithmic coordinate system, the mud shear stress decreases steadily with the decrease of shear rate. The static and dynamic yield stress of slurry increases exponentially with particle concentration.

The determination of rheological model about the debris flow is the basis of the simulation of mud flow impact distance and sedimentary fan. By using a mcr301 rheometer, rheological experiments of Chengdu clay slurry with different solid volume concentrations were carried out and the effect of solid volume concentration on shear stress were analyzed. Then the rheological process of Chengdu clay slurry with different solid volume concentration was fitted on the basis of the power law model, the Bingham model and the H–B model. The conclusions are drawn as follows: Chengdu clay mud is a typical shear-thinning non-Newtonian body. The influence of solid concentration on the flow curve is different. When the solid volume concentration is not less than 34% and the shear rate is less than 1.0 s−1, the shear stress increases rapidly as the shear rate increases. Meanwhile, when the shear rate is greater than 1.0 s−1 the shear stress decreases with the increase in the shear rate. When the solid volume concentration is less than 31.6% and the shear rate is less than 1.0 s−1, the shear stress increases with the increase in the shear rate, while when the shear rate is more than 1.0 s−1, the shear stress is less affected by shear rate. In the range of low shear rate (less than 1.0 s−1), the increase amplitude of shear stress (slope of semi logarithmic coordinate flow curve) increases as the solid volume content increases. The flow curve of Chengdu clay mud can be reflected in the whole process by using the Herschel and Bulkley model. It is the best mathematical model to fit the rheological process of Chengdu clay mud. According to the above results, the effect of solid volume concentration on the yield stress of the H–B model is analyzed.

泥浆是泥石流动力学的重要研究对象.细小的黏性颗粒是黏性泥石流泥浆的基本组成部分,传统流变模型可以描述粘性泥石流中颗粒物质相互作用,然而各灾害点物质组成的差异性使得泥浆流变模型的应用各有不同,且当前研究缺少对不同模型应用的详细讨论.本研究利用MCR301流变仪,开展不同含水量成都粘土泥浆流变实验,分析成都粘土泥浆剪切应力随剪切速率变化过程、含水量对剪切应力的影响;对比分析幂律模型、宾汉模型和Herschel&Bulkley模型(H-B模型),拟合各含水量成都粘土泥浆的流变实验结果.得出如下结论:(1)随着含水量由50％增大到400％,成都粘土泥浆切应力迅速降低,由超过8000 Pa降低到5 Pa左右;当剪切速率约为0.2 s-1时,剪切应力随剪切速率增加而迅速增大,但当剪切速率大于0.2 s-1时,剪切应力随剪切速率增加而增长缓慢,成都粘土泥浆表现出典型的剪切稀化非牛顿体流体;(2)H-B模型能很好地反映各含水量成都粘土泥浆剪切应力与剪切速率的变化全过程(剪切稀化),是拟合成都粘土泥浆流变过程的最佳数学模型;(3)泥浆屈服应力(τHB)和流动指数(ηHB)随含水量的增加迅速减小.本文流变模型实验的开展和研究对深入认知和探索泥石流致灾全过程具有重要意义.

Mixed flow composed of coarse particle and mud is a common mountain disaster. Because of its typical granular material characteristics, fluid theory based on continuum hypothesis is difficult to describe discontinuous deformation. Therefore, the rotary shear and normal bonding experiments of clay mud are carried out by MCR301 to determine the mechanical parameters of the normal and the tangential direction of the mud (131% moisture content). According to the theory of granular material, with PFC3D as the platform, write the numerical viscosity slope model test programme, according to the mud test results, set the parameters of the numerical model, reproduction process and the discontinuous deformation phenomenon, and is verified by the same size physical model test. The results show that the PFC3D discrete element method based on granular material theory can well reproduce the movement process and discontinuous deformation phenomenon of the coarse particle mud mixing flow slope, and provide a new way for in-depth analysis of the complex landslide movement process.

探讨含水率对泥石流浆体力学特性影响是泥石流运移过程研究的基础性内容.以成都龙泉区黏土为实验材料,配制11种不同含水率的泥浆,利用安东帕MCR301流变仪,对不同含水率泥浆开展两循环旋转剪切实验(每循环剪切过程分为增速剪切(0-30 s-1)和减速剪切(30-0 s-1)两阶段),分析含水率对泥浆剪切过程、剪应力变化过程、剪切应力峰值及灵敏度的影响.实验结果表明:①初剪应力峰值和复剪应力峰值与含水率呈幂律关系.②由于剪切过程的差异性导致含水率对泥浆的剪应力与剪切速率的影响也具有差异性:当含水率低于100％时,第一、第二循环各阶段剪切过程中剪切应力变化过程完全不重合,且初剪应力峰值和复剪应力峰值随含水率增大迅速降低,灵敏度随含水率的增加迅速减小到1;当含水率高于100％时,第一、第二循环各阶段剪应力变化过程基本一致,含水率对应力峰值和泥浆灵敏度的影响可以忽略不计.③影响成都黏土泥浆剪切过程、剪切应力变化、剪应力峰值和灵敏度的含水率阈值是100％.本文对成都区黏土泥浆开展了动态剪切试验,探讨了含水率对泥浆特性的影响,可为其他区域黏土特性的研究提供参考,具有重要的研究意义!

Mud is the main component of viscous debris flow. The physical model experiments of viscous debris flow were carried out through the mixing mud with different density and fixed components of coarse particles. The width, longitudinal movement distance and motion velocity were recorded by video cameras during experiment. Through viscous debris flow physical model experiments, the influence of mud to transverse width, longitudinal movement distance and motion velocity was discussed. The physical model experiment results show that the motion forms change from inviscid particle flow to viscous debris flow and to the whole mass sliding with the increase of mud density; the width and the length along the slope decrease with mud density increasing; the movement process has classified phenomena about viscous debris flow composed by different mud densities: the velocity increases rapidly with time and the change gradient is steady when the density of mud is lower than 1.413g/cm3; the movement process can be divided into two stages when the density of mud is higher than 1.413g/cm3: the movement velocity is lower and the gradient change is small in the initial stage; but in the second stage, the movement velocity increases quickly, and the gradient is higher than the first stage, and with steady value.

[Objective] The aim of the study is to analyze the influence of mud on the moving ways,width and longitudinal distance and velocity of viscous debris flow on slope,and help to provide the references for disaster prevention.[Methods] The experimental model was built for viscous debris flow,and a series of model experiments were carried out through the device.The viscous debris flow composed of Chengdu clay mud and coarse particles.[Results] The adhesion force between the coarse particles increased,and the movement patterns changed from the inviscid debris flow to the viscous debris flow,and to the massive sliding with increasing mud density.The width and distance on slope decreased with increasing mud density.The migration process could be differentiated according to mud density.The velocity increases rapidly and the gradient is large when mud density was lower than 1.413 g/cm3.The migration process can be divided into two stages when mud density was higher than 1.413 g/cm3,the velocity increased slowly and the gradient changes little in the first stage but the velocity increased quickly,and the gradient changed quickly in the second stage.[Conclusion] The mud affects the movement pattern and the moving process of viscous debris flow.

The motion forms (deformation) of the sliding soil along the slope include inviscid particle flow, viscous particle flow, and mass sliding. The motion forms were mainly influenced by the mechanical properties of the viscous mud medium filling. The effect of the medium filling on the motion forms of the sliding soil is worth discussing. The sliding soil can be seen as the mixture which is composed of the medium filling and coarse particles. The Chengdu clay with different moisture contents were selected as the medium filling. Their mechanical parameters were experimentally measured for simulating the moving process of the sliding soil. Different motion forms of the sliding soil were numerical simulated based on PFC3D by changing the specific mechanical parameters. The mechanical parameters of the Chengdu clay are experimentally determined. The numerical results show that with the moisture content of the filling slurry medium in the range of >302%, 101%~182%, and <80%, the motion form of the sliding soil belongs to the inviscid particles flow (similar with the sliding sand), viscous particles flow (seen as the viscous flows); and mass sliding (seen as the block sliding along the slope surface), respectively.

Since viscous debris flow is comprised of coarse particles and viscous mud, its movement process exhibits discontinuous deformation. Thus the fluid theory, which is based on continuous medium assumption, is difficultly applied to describe the process. Considering the influence of viscous media, a numerical model for viscous debris movement is firstly compiled according to the theory of granular materials and the platform of PFC3D software. Then the model parameters are obtained from the experimental results of indoor tensile tests and rotary shear tests on the viscous mud, which is called Chengdu clay and its density is 1.413 g/cm(3). Moreovernumerical simulation of viscous debris movement is performed, which reproduces the movement process and the phenomenon of discontinuous deformation during the process. Meanwhile, the numerical simulations are verified by the experiment with the same size of the physical model. The results show that the PFC3D discrete element method, based on theory of granular materials, is applicable to simulate the movement process and present the phenomenon of discontinuous deformation during the movement process of viscous debris soil. This study provides a new way for further analyzing the viscous debris movement on slope under the impact of viscous media.

Simulating motion process of incompact landslip-collapse soil. Monitoring evolution process of average contact force and unbalance force when which are moving. Simulation results indicate that: Process of its motion manifest the macro space position changes, as well as, are the change process about contact stress, unbalance force within the inter particle and single particle movement mechanics etc. Average contact force reflects close degree between particles, fluctuation extent of microscopic parameter and levels of interaction between particles. Microscopic parameters of movement process can be used in the theoretic modeling analysis of complex movement of the incompact soil.

In this paper, we introduce orthogonal vector-valued wavelets with 3-scale. We propose a necessary and sufficient condition for the existence of orthogonal vector-valued wavelets by using paraunitary vector filter bank theory, we develop a new procedure for constructing a class of orthogonal compactly supported vector-valued wavelets. Characterization of vector-valued wavelet packets is investigated by virtue of time-frequency method and algebra theory. Moreover, it is shown how to construct various orthonormal bases of a vector-valued function space from these wavelet packets.

Wavelet analysis has been developing a popular mathematical branch for twenty years. In this paper the notion of orthogonal vector-valued two-dimensional wavelet packets, which is a generalization of uni-wavelet packets, is introduced. Their orthogonality properties are discussed by virtue of time-frequency analysis method, operator theory and matrix theory. Orthogonality formulas are established. Three orthonormal basis of L2(R2,Cu) is established from these orthogonal vector-valued wavelet packets.

The text expatiate on the course of modeling or adjusting of gray prediction.Making use of the date that the settlement of composite foundation.GM(1.1)model is established by Ggray Theory.The model can be used to simulate P～S curve of the settlement,also can be used to predict the unknown part of P～S curve of composite foundation of cement mixing pile,We also can use of the model to analyse the bearing capacity for composite foundation of cement mixing pile.