Fuli calculation

The occurrence of water inrush in coal seam floor means the sudden change of mine hydrogeological state, the release of stress field energy and the destruction of rock structure. It is a instability phenomenon, or a generalized non-equilibrium phase transition phenomenon. The key to correctly predict water inrush from coal seam floor is to understand the instability mechanism and reveal the evolution of groundwater and strata state and the process of instability from the perspective of nonlinear theory

as far as water inrush from coal seam floor is concerned, the most important defect is the existence of water filled fissures connected with aquifer groundwater. Due to the increase of stress or groundwater pressure, or both, the water filled fracture has a large expansion force. When the rock wall that prevents the expansion of water filled fracture becomes weak, the deformation of rock wall, crack growth and even collapse will lead to water inrush from the pit floor. Therefore, in the process of coal mining, although the rock structure is disturbed and the stress distribution is adjusted, the key to the water inrush from the coal floor is whether a part of the water resisting strata becomes weak. The so-called weakness can be the thinning of the effective aquifuge thickness or the singular concentration of stress. In a word, there are two necessary conditions for water inrush, one is the existence of water filled fractures, the other is the weakening of water filled fracture wall, which makes the fracture development communicate with the mining face under the action of stress. The above viewpoint seems obvious, but for a long time, there has been a tendency in the study of water inrush from coal floor, which often equates the defects of water resisting strata with cracks leading to material fracture, and determines the instability conditions. The essence of crack instability which leads to water inrush is different from that which leads to material fracture. For the cracked material, macroscopically, the material is uniform, complete and regular, while for the fractured coal seam floor water resisting strata, the instability is inced by inhomogeneity, incompleteness and irregularity. We should emphasize the difference between the two processes with different time scales. One is the process of defect development, which is a slow process and evolves graally in response to the disturbance of rock morphology. This development process does not lead to instability, that is, it does not lead to water inrush. The other is the sudden change process in which the defect rises sharply in the weak place and the rock stratum is damaged, which is a fast process, which is the instability process leading to water inrush. To fully understand the water inrush phenomenon, we need to have a clear understanding of both processes. The water inrush from coal floor has the characteristics of non-linear and non-equilibrium. The order parameter equation can be established by using domination principle, and the system can be described by order parameter. For the equation with multiple order parameters, we can describe it by potential function

5.2.2.1 establish physical model

water inrush from coal seam floor is transient in time and local in space. The study of water inrush mechanism is equivalent to the study of how the water resisting strata lose stability, and the prediction of water inrush means to determine the instability conditions as accurately as possible and to link them with measurable parameters. According to the previous analysis, we know that the existence of water filled fissures and weak fissures is the prerequisite for water inrush. On this basis, we give a simplified model of water inrush, which is called plug model for short (Fig. 5.2). In the model, the circular water column is used to simulate the water filled fracture, and the plug is used to simulate the local instability layer block. The interaction between the plug and other strata is simplified as spring interaction

Fig. 5.2 plug model schematic diagram

this seemingly oversimplified model is actually very helpful for the understanding of water inrush. A circular plug with thickness of H and cross-section radius of R is investigated. The bottom of the plug is under the action of groundwater with pressure of P. the deformation mainly occurs in the vertical direction of the plug. Although the plug is a part of the whole wall, the deformation of the rest of the wall is considered to be negligible. The deformation of the plug is described by the displacement of the center of mass of the plug, and the interaction between the plug and the rest of the wall is equivalent to the potential action. In this way, we have the equation describing the plug < sup > [70] < / sup >

coal mine floor water inrush

where: S = π R < sup > 2 < / sup > the cross-sectional area of the plug m < sup > 2 < / sup >; P is the groundwater pressure kg; M is the comprehensive mass of the plug, M = π r² H _{ρ< sub> ρ is the comprehensive density of rock, kg / M < sup > 3 < / sup >, and G is the referenced gravitational acceleration constant, M / s < sup > 2 < / sup >; The influence of token dissipation is related to the speed of motion< sub> μ is the dissipation coefficient; F < sub > JG < / sub > is equivalent to the lateral friction of the plug, and f structure is the internal stress caused by deformation. The shear stress acting on the unit area of the plug side is introced σ， Then f < sub > JG < / sub > can be expressed as:}

coal mine floor water inrush

here σ It is a function of the displacement of the mass center in the vertical direction of the plug, and its overall behavior is shown in Figure 5.3. In the small displacement region, σ It changes linearly, and continues to increase Z, σ It reaches the maximum at z = Z < sub > C < / sub >, and then reaches the maximum at z = Z < sub > C < / sub > σ It dropped rapidly to zero again. For the static behavior of the plug, equation (5.3) is simplified as the equilibrium equation:

coal mine floor water inrush

where Z < sub > EQ < / sub > is the equilibrium position of the plug, Ω It is the tangential stress on the side of the plug under the condition of stress balance, which can be expressed by the following formula:

coal mine floor water inrush

where: it is the vertical stress per unit volume of the plug; Unit: n; R is the radial length corresponding to the fracture, unit: M

Fig. 5.3 stress strain curve of plug Ω ≥ σ< Sub > C < / sub > instability

in order to discuss the dynamic behavior of the plug conveniently, the formula (5.3) is rewritten as:

water inrush from coal mine floor

the shear stress acting on the side of the plug σ The following simple form is selected: substituting the above formula into formula (5.7) and scaling the displacement coordinate Z with the critical equilibrium coordinate ZC, the Z in the equation (5.8) is measured in Z < sub > C < / sub >, corresponding to the small vibration frequency of the free plug. In equation (5.8), we introce a perturbation term fr (T) to describe other external disturbances in order to analyze the response behavior and resonance instability of the plug

coal mine floor water inrush

as the plug approaches the critical equilibrium position, i.e. Z < sub > EQ < / sub > → 1, the vibration frequency tends to zero. The phenomenon that the frequency of the vibration mode becomes smaller and zero at the critical point is called mode softening in the theory of phase transition. It means that the equivalent spring acting on the plug softens, which belongs to the general characteristics of phase transition

strata is closely related to the degree of local stress concentration. This conclusion tells us that we can use the response of the bottom or side of the aquiclude to analyze and determine the stress distribution, which has practical application value. Besides the water inrush mechanism of equilibrium instability, there is also resonance instability mechanism. That is to say, although Z < sub > EQ < / sub > < 1 is a stable equilibrium, when the equilibrium position is not far from the critical position, the softening frequency of vibration mode becomes lower, which may cause resonance instability in response to mining disturbance. Generally speaking, resonance instability occurs only near the critical point

we solved the equation (5.8) numerically to understand the global behavior of the plug model. Because (5.8) is a nonlinear equation, its solution shows complex behavior. Fortunately, we are not interested in the detailed behavior of the solution, we only care about the stability of the solution. The typical numerical results are shown in Fig. 5.4, and the periodic force fr = f < sub > e < / sub > COS is used in the calculation ω< Sub > 0 < / sub > t ω< Sub > 0 < / sub > = 100, stable equilibrium position Z < sub > EQ < / sub > = 0.9. The plug model is a phenomenological model. Although it is simple, it is not a mediocre model. The basic characteristics and mechanism of water inrush are reflected in the model

Fig. 5.4 results of plug model Ω ≥ σ< When sub > C < / sub >, water inrush will occur e to balance instability. Using this result to predict water inrush from coal floor, the main problem is how to give a correct explanation to the physical quantities in the model in a measurable sense. Related critical shear stress σ< Sub > C < / sub > is the Proctor coefficient. Proctor's coefficient is a coefficient in proctor's rock pressure theory, also known as firmness coefficient. It is generally expressed as one percent of the ultimate compressive strength of rock. According to Wannian mine water control results report, the compressive strength of sandstone is generally about 48mpa. For the macro detection of specific hydrogeological structure, the parameters that are easy to measure are aquifer groundwater pressure P and aquifuge thickness h, followed by the basic state of structure occurrence. It is known that the density of sandstone is generally about 2200-2600kg / M < sup > 3 < / sup >. In the section with water filled fracture, the thickness of aquiclude is H-H, and the groundwater pressure is changed to P-H < sub > p-h ρ sg Here h is the local height of the water level at the water inrush. Now it will be used to judge the physical quantity of instability Ω It is revised as:

water inrush from coal mine floor Ω To judge whether water inrush or not, the criterion formula:

coal mine floor water inrush

the specific application of this criterion also needs to determine the constants related to rock mechanical properties σ< Sub > C < / sub > and H and R related to fracture defect size. Generally speaking, h and R are related to rock structure, water pressure, coal mining and other factors, so it is very difficult to determine them. Using the existing water inrush data and phenomenological theory, we can determine R and H:

coal mine floor water inrush

the above judgment formula (5.11) was used to test 10 water inrush cases in Wannian mine (table 5.1), and satisfactory results were obtained. It is proved that the nonlinear theory is suitable for the prediction of water inrush from the pit floor, and it should be further studied and applied in the future

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