Method for predicting grouting filling amount of adjacent gangue in caving zone

Abstract

The invention relates to the technical field of caving zone adjacent-position gangue grouting, and discloses a caving zone adjacent-position gangue grouting filling amount prediction method which specifically comprises the following steps that 1, gangue slurry with the concentration of 70% is injected into a gap between a fractured rock mass and a basic roof through a grouting pipe end hole, slurry seepage in adjacent grouting is divided into early-stage low-pressure diffusion and later-stage pressure seepage, and gangue slurry shows remarkable non-Newtonian fluid mechanical properties in the flowing process. According to the method, based on the seepage mechanics theory, the influence of the slurry property and the percolation effect is considered, the caving zone adjacent position grouting seepage model is constructed, the grouting diffusion range, the grouting seepage slope angle and the grouting filling amount can be accurately calculated, and coordinated development of coal development and environmental protection is better facilitated. Meanwhile, in combination with caving zone adjacent position grouting three-dimensional numerical simulation analysis, the slurry seepage three-dimensional unsteady state diffusion process is described, the caving zone adjacent position grouting diffusion rule is revealed, and the prediction precision is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of gob-side adjacent gangue grouting, and particularly to a method for predicting the filling amount of gob-side adjacent gangue grouting. Background Art

[0002] Gangue is the main solid waste in coal mines. The discharge volume of coal mine gangue is large, the disposal and utilization rate are low, and the environmental safety problems are prominent. The gob gangue grouting filling technology is to break the gangue and make a slurry by adding water according to a certain particle size gradation, and then transport it to the broken space in the gob through equipment such as a filling pump and a conveying pipeline, so as to achieve the purpose of efficient gangue disposal.

[0003] The pumping pressure of the gob-side adjacent grouting filling technology is relatively low, and the slurry mainly diffuses by seepage. In geotechnical body grouting, the injected slurry is mainly chemical slurry or cement-based slurry, which is quite different from the gob grouting filling technology in terms of filling materials, and the injection object is different, and the research on the seepage mechanism of the slurry in the broken gangue in the gob is not involved. It should be particularly pointed out that due to the horizontal or inclined arrangement of the grouting pipe and the small grouting pressure in the gob-side adjacent grouting, the gob-side adjacent grouting mainly diffuses by seepage relying on its own gravity, while the geotechnical body grouting mainly relies on high-pressure grouting. The research on the seepage characteristics of the gob grouting slurry needs to consider both the structural effect of the broken gangue in the gob and the rheological characteristics of the slurry itself. In the research on gob grouting filling, it mainly focuses on the raw materials and mix ratios of the slurry, pipeline transportation performance, rheological characteristics and strength, etc., while there are relatively few research reports on the flow and accumulation laws of the slurry entering the broken gangue in the gob, and the theoretical research on the flow and accumulation laws of the slurry is relatively lacking. The existing research results have laid a good research foundation for calculating the diffusion range and slurry filling amount of gob grouting. Most of the existing gob slurry diffusion models are geometric models constructed based on the phenomenological theory for the final range or shape of grouting diffusion. Generally, it is considered that the slurry diffusion shape is a flat cylinder, a frustum of a cone, a collapsed triangular cone, an ellipse, etc. The slurry diffusion range is mainly determined based on experience or numerical simulation results. The gob grouting numerical simulation is generally based on two-dimensional modeling and cannot obtain the height of the slurry accumulation. The large stockpile, increasing amount and low utilization rate of mine solid waste restrict the coordinated development of coal development and environmental protection. Due to the complexity of the spatial structure evolution of the gob and the diffusion law of the gangue slurry, it is difficult to determine the gob grouting effect, which restricts the development of this technology.

[0004] In view of this, the present application proposes a method for predicting the filling amount of gob-side adjacent gangue grouting. Summary of the Invention

[0005] The main object of the present invention is to provide a prediction method for the grouting filling volume of adjacent gangue in the caving zone, which is used to solve the problems that the large stockpile, increasing increment and low utilization rate of mine solid waste restrict the coordinated development of coal mining and environmental protection. Due to the complexity of the spatial structure evolution of the caving zone and the diffusion law of gangue slurry, it is difficult to determine the grouting effect in the caving zone, which restricts the development of this technology.

[0006] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] The prediction method for the grouting filling volume of adjacent gangue in the caving zone specifically includes the following steps:

[0008] Step 1: Inject the 70% - concentration gangue slurry into the void between the fractured rock mass and the basic roof through the end hole of the grouting pipe. The gangue slurry shows significant non - Newtonian fluid mechanics properties during the flowing process. After the gangue slurry enters the caving zone through the pumping pipeline, the pressure - seepage diffusion process of adjacent - position grouting can be divided into 4 stages: low - pressure diffusion stage, longitudinal penetration stage, transverse seepage initiation stage and transverse continuous seepage stage;

[0009] In the low - pressure diffusion stage, the slurry at the outlet end of the pumping pipeline has a certain initial flow velocity. Affected by the self - weight of the slurry, a slurry coverage area with a certain radius will be formed near the grouting port, and its radius is:

[0010]

[0011] In the formula, Q r is the filling injection volume per unit time, m 3 / s; B r is the width of the void between the fractured rock mass and the basic roof in the caving zone, m; C r is the correction coefficient; V pl is the critical flow velocity to suspend solid particles, m / s;

[0012] Step 2: Through the analysis of the slurry rheological test, the yield stress of the 70% - concentration gangue slurry is obtained as 25 Pa, denoted as the slurry yield stress τ0;

[0013] Step 3: In the longitudinal penetration stage, the rheological behavior of the slurry seepage process converting gravitational potential energy into kinetic energy and deformation energy. Affected by the self - weight of the slurry, a slurry longitudinal penetration channel with a certain radius will be formed near the grouting port. Generally, the radius of the longitudinal channel takes the average value of the major - axis and minor - axis radii of the grouting diffusion range in the low - pressure diffusion stage as r;

[0014] Step 4: In the transverse seepage initiation stage, as the slurry injection volume increases, the slurry seepage behavior is mainly driven by the gravity difference formed by the height difference of the slurry surface, and at the same time is affected by the seepage resistance of the gangue in the caving zone. The slurry at the bottom of the caving zone gradually spreads transversely and develops into a truncated cone. The slurry diffusion range is d, and the seepage slope angle is θτ ;

[0015] Step 5. In the stage of lateral continuous seepage, as the injection volume of the slurry increases, the slurry undergoes lateral re-seepage phenomenon with the initial truncated cone accumulation body, and the lateral diffusion range of the slurry continues to increase. At this time, the diffusion range of the slurry is d', and the seepage slope is θ τ ';

[0016] Step 6. The seepage driving force of the adjacent grouting slurry in the caving zone is its self-weight, and the additional resistance is mainly the seepage resistance. Considering the influence of the porosity Ψ, the seepage path tortuosity factor F, the average particle diameter D m , the yield stress τ0 of the slurry, and the seepage straight-line distance L, the pressure change during the seepage process of the slurry can be obtained by the following formula:

[0017]

[0018] In the formula, ΔP is the pressure change amount during the seepage process of the slurry, Pa; D m is the average particle diameter, m; τ0 is the yield stress of the slurry, Pa, which can be obtained through rheological tests; L τ is the seepage straight-line distance, m; Ψ is the porosity; F is the seepage path tortuosity factor;

[0019] Step 7: The height of the undeformed cylinder is h0. The slurry within the height range of h1 is subjected to a stress greater than the yield stress τ0, and the slurry flows until the stress drops to the yield stress and stops. Among them, the slurry within the range of h0 is the non-yield body, and the slurry within the range of h1 is the yield body;

[0020] Step 8: In the slurry above the yield region, the vertical stress does not exceed the yield stress, and the slurry in this region remains stable and does not yield; during the yield flow process, it is assumed that the interface layer between the yield and non-yield materials is a horizontal surface, and the shear stress of this interface layer is equal to the yield stress of the slurry;

[0021] Therefore, the final height is composed of the non-yield region (h0) and the yield region (h1), and the height h0 can be determined by the following formula:

[0022]

[0023] In the formula, ρ is the density of the slurry, kg / m 3 ; g is the acceleration of gravity, N / kg;

[0024] Step 9: In the yield region, the height can be divided into micro-elements with a thickness of d z and a radius of r z , and at this time the shear stress of the slurry is τ z ; after its yield flow, it decreases to a thickness of d z1 and a radius of r z1, at this time, the yield stress of the slurry is τ z1 ; After yielding, the cross-sectional area of the slurry spreading around increases, causing the shear force of the slurry on any given plane to decrease to the yield stress, and the slurry stops flowing;

[0025] Therefore, the product of the stress and the cross-sectional area is proportional to the weight of the slurry above the plane, and the expression is:

[0026]

[0027] The height h1 of the slurry yield region can be obtained by integrating d z1 over the yield region, and the expression is as follows:

[0028]

[0029] Step 10: According to the conservation of slurry volume, the grouting diffusion range d in the lateral seepage stage:

[0030]

[0031] In the formula, r is the radius of the slurry low-pressure diffusion stage, m;

[0032] The seepage gradient of the slurry is tanθ τ , and the seepage gradient angle θ of the slurry in the lateral seepage stage τ :

[0033]

[0034] The filling volume of the slurry in the lateral seepage stage:

[0035]

[0036] Step 11: As the grouting volume increases, the slurry continuously seeps laterally, and the angle α between the side of the truncated cone and the vertical direction τ continually increases. When the grouting volume is V i , the shear stress of the slurry is τ zi = ρgV i / πd i 2 cosα τi ; When the lateral continuous seepage stage is completed, the shear force of the slurry on the side of the truncated cone is equal to the yield stress. Considering the change of seepage resistance during this seepage process and combining with Equation (2), the stress balance equation of the bottom-layer slurry is obtained as:

[0037]

[0038] In the formula, α τ is the angle between the side of the truncated cone and the vertical direction, °; l i is the length of the side of the truncated cone, where li = h1 / cosα τ , m; V' is the final filling volume of the slurry, m 3 ;

[0039] Final grouting diffusion range d':

[0040]

[0041] Final grouting seepage slope angle:

[0042]

[0043] The final grouting filling volume is:

[0044]

[0045] When the final grouting hole height is 6 m and other parameters remain unchanged, with the increase of the seepage slope angle, the filling volume decreases;

[0046] By combining equations (9), (10), (11) and (12), the grouting diffusion range, grouting seepage slope angle, and grouting filling volume can be predicted.

[0047] Furthermore, after the gangue slurry enters the caving zone through the pumping pipeline in step 1, it is first driven at low pressure and spreads in an elliptical shape. Then, affected by the gravity effect, it preferentially seeps vertically downward and then spreads freely in all directions. When it flows to the gangue retaining wall, the slurry gradually rises until the grouting stops, and finally a truncated cone-shaped filling body is formed.

[0048] Furthermore, in step 2, the yield stress of the 70% concentration gangue slurry is obtained by testing with a Viscotester iQ rheometer. The essence of the gangue slurry is a solid-liquid two-phase mixed fluid composed of fine-grained gangue particles and water.

[0049] Furthermore, in step 8, considering that the broken rock blocks in the caving zone are relatively large, the exponential empirical formula (F = 1 / Ψ 1-u ), u generally takes 2.1 - 2.2, to establish the relationship between the tortuosity factor F of the seepage path and the porosity Ψ. The smaller the porosity, the more complex the seepage path and the greater the seepage resistance. The average particle diameter D of the caving zone m takes 0.12 m.

[0050] Furthermore, in step 11, when the slurry diffuses into the lateral continuous seepage stage, the diffusion distance of the slurry should be no less than 8 m at this time. The truncated cone-shaped slurry undergoes flow deformation in the height h1 region. At this time, using the method of "horizontal segmentation layer" in the lateral seepage stage will result in a large error. Therefore, it is assumed that in this stage, the truncated cone takes the center of its lower base as the center, and laminar flow is formed by the continuous slip of the side surface. The upper base radius r remains unchanged during the lateral seepage process, and the shear stress on the inclined surface of the side surface of the slurry is the resultant force of the vertical stress and the horizontal stress.

[0051] Based on the seepage mechanics theory, considering the properties of the slurry and the influence of the filtration effect, the present invention constructs a gob-side grouting seepage model, which can accurately calculate the grouting diffusion range, the grouting seepage slope angle, and the grouting filling volume, and is more beneficial to the coordinated development of coal mining and environmental protection. At the same time, the present invention combines the three-dimensional numerical simulation analysis of gob-side grouting, depicts the three-dimensional unsteady diffusion process of slurry seepage, reveals the gob-side grouting diffusion law, and improves the prediction accuracy.

[0052] Parts not involved in this device are the same as or can be implemented using existing technologies. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 It is a prediction model diagram of the gob-side gangue grouting filling volume prediction method of the present invention.

[0054] Figure 2 It is a schematic diagram showing the change of the yield zone height with the final grouting hole height of the gob-side gangue grouting filling volume prediction method of the present invention.

[0055] Figure 3 It is a schematic diagram showing the change of the grouting volume with the seepage slope angle of the gob-side gangue grouting filling volume prediction method of the present invention.

[0056] Figure 4 It is a test diagram of the rheological properties of the slurry of the gob-side gangue grouting filling volume prediction method of the present invention.

[0057] Figure 5 It is a schematic diagram showing the change of the slurry density during the grouting seepage process of the gob-side gangue grouting filling volume prediction method of the present invention.

[0058] Figure 6 It is a diagram showing the evolution law of the slurry concentration of the gob-side gangue grouting filling volume prediction method of the present invention.

[0059] Figure 7 It is a schematic diagram of the three-dimensional unsteady diffusion process of the gob-side grouting slurry of the gob-side gangue grouting filling volume prediction method of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0060] To enable those skilled in the art to better understand the solution of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the scope of protection of the present invention.

[0061] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged under appropriate circumstances so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device that includes a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or are inherent to these processes, methods, products or devices.

[0062] An exemplary embodiment of the present disclosure provides a method for predicting the grouting filling amount of adjacent gangue in the caving zone, which specifically includes the following steps:

[0063] Step 1: Inject the gangue slurry with a concentration of 70% into the void between the fractured rock mass and the main roof through the end hole of the grouting pipe. The gangue slurry exhibits significant non-Newtonian fluid mechanics properties during the flowing process; after the gangue slurry enters the caving zone through the pumping pipeline, the pressurized seepage diffusion process of adjacent grouting can be divided into 4 stages: low-pressure diffusion stage, longitudinal penetration stage, transverse seepage initiation stage, and transverse continuous seepage stage;

[0064] First, the slurry is mainly in the low-pressure diffusion state, forming an elliptical grouting diffusion range near the grouting hole. Due to the low injection pressure of the slurry, its diffusion range is limited. Then, it is mainly in the pressurized seepage state. The seepage process of the slurry transforms the gravitational potential energy into kinetic energy and deformation energy rheological behavior, and finally reaches a static state after experiencing internal friction (viscosity) and external friction (the friction of the gangue in the caving zone on the expansion of the slurry);

[0065] Among them, after the gangue slurry enters the caving zone through the pumping pipeline, it is first driven by low pressure and spreads in an elliptical shape. Then, affected by the gravity effect, it preferentially seeps vertically downward, and then spreads freely in all directions. When it flows to the gangue retaining wall, the slurry gradually rises until the grouting stops, and finally forms a truncated cone-shaped filling body;

[0066] Such as Figure 1As shown in (a), the slurry at the outlet end of the pumping pipeline has a certain initial flow rate. Affected by the self-weight of the slurry, a slurry coverage area with a certain radius will be formed near the grouting port, and its radius is:

[0067]

[0068] In the formula, Q r is the filling injection volume per unit time, m 3 / s; B r is the gap width between the broken rock mass in the caving zone and the basic roof, m; C r is the correction coefficient; V pl is the critical flow rate to suspend solid particles, m / s;

[0069] Step 2: Through the rheological test analysis of the slurry, the yield stress of the 70% concentration gangue slurry is 25 Pa, denoted as the slurry yield stress τ0; the yield stress of the 70% concentration gangue slurry is measured by a Viscotester iQ rheometer. The essence of the gangue slurry is a solid-liquid two-phase mixed fluid composed of fine-grained gangue particles and water;

[0070] Step 3: In the longitudinal penetration stage, the rheological behavior of the slurry seepage process that converts gravitational potential energy into kinetic energy and deformation energy is affected by the self-weight of the slurry, and a slurry longitudinal penetration channel with a certain radius will be formed near the grouting port. The radius of the longitudinal channel is generally taken as the average value of the major axis and minor axis radii of the grouting diffusion range in the low-pressure diffusion stage, which is r, as Figure 1 the ideal cylindrical slurry flow body shown in (b);

[0071] Step 4: In the transverse seepage startup stage, as the slurry injection volume increases, the slurry seepage behavior is mainly driven by the gravity difference formed by the slurry liquid level height difference, and at the same time, it is affected by the seepage resistance of the gangue in the caving zone. The slurry at the bottom plate of the caving zone gradually spreads laterally and develops into a truncated cone, Figure 1 the slurry diffusion range in (c) is d, and the seepage slope angle is θ τ ; different from the self-flow slope, the seepage slope is defined here as the slope or slope angle formed by the slurry seepage and diffusion in the caving zone. The seepage slope can better describe the changes in the stacking height and diffusion range during the slurry diffusion process;

[0072] Step 5: In the transverse continuous seepage stage, as the slurry injection volume increases, the slurry undergoes transverse re-seepage phenomenon with the initial truncated cone accumulation body, and the slurry lateral diffusion range continues to increase. At this time, the slurry diffusion range is d', and the seepage slope is θ τ '; the slurry is affected by the low-speed creep effect during the continuous injection process, and the slurry stacking surface is relatively smooth. Since the grouting pressure is small and the upper surface of the truncated cone is not affected by external forces, its shape remains unchanged during the seepage process (i.e., the upper bottom radius r of the truncated cone remains unchanged), asFigure 1 as shown in (d);

[0073] Generally, the size of the caving zone is much larger than the seepage range of the slurry, so the injected medium has no boundary constraint conditions. As the slurry is continuously injected, when the shear stress of the slurry is less than the yield stress, the slurry will not deform and the single-hole grouting is completed;

[0074] The essence of the gangue slurry is a solid-liquid two-phase mixed fluid composed of fine-grained gangue particles and water. Assuming that the slurry does not segregate, dehydrate, or delaminate during the seepage process, it can be regarded as a homogeneous flow for research. Generally, the gangue slurry is considered a Bingham fluid. The slurry seeping in the caving zone is divided into countless horizontal layers, and the shear stress received by each layer of slurry depends on the resultant force of the gravity of the upper slurry and the seepage resistance;

[0075] Step 6: The seepage driving force of the adjacent grouting slurry in the caving zone is its own weight, and the additional resistance is mainly the seepage resistance. Considering the influence of the porosity Ψ, the seepage path tortuosity factor F, the average particle diameter D m , the yield stress τ0 of the slurry, and the seepage straight-line distance L, the pressure change during the slurry seepage process can be obtained by the following formula:

[0076]

[0077] In the formula, ΔP is the pressure change amount during the slurry seepage process, Pa; D m is the average particle diameter, m; τ0 is the yield stress of the slurry, Pa, which can be obtained through rheological tests; L τ is the seepage straight-line distance, m; Ψ is the porosity; F is the seepage path tortuosity factor;

[0078] Step 7: Considering that the size of the broken rock blocks in the caving zone is large, an exponential empirical formula (F = 1 / Ψ 1-u ) is adopted. Generally, u takes 2.1 - 2.2. The relationship between the seepage path tortuosity factor F and the porosity Ψ is established. The smaller the porosity, the more complex the seepage path and the greater the seepage resistance. The average particle diameter D of the caving zone m takes 0.12 m; through the analysis of the slurry rheological test, the yield stress of the 70% concentration gangue slurry is 25 Pa. When the yield stress of the slurry decreases, the seepage diffusion distance increases. The seepage straight-line distance corresponding to different seepage stages is different. For the longitudinal penetration stage of grouting, it is generally the sum of the short axis length of the low-pressure diffusion ellipsoid and the height of the final grouting hole. For the lateral diffusion stage, it is generally the lateral diffusion distance of the slurry. The farther the seepage straight-line distance L is, the greater the seepage resistance; the height of the undeformed cylinder is h0, and the slurry within the height h1 is subjected to a stress greater than the yield stress τ0, and the slurry flows until the stress drops to the yield stress and stops. Among them, the slurry within the range of h0 is the non-yield body, and the slurry within the range of h1 is the yield body;

[0079] Assume that the slurry behaves as an elastic solid. When pressure is applied in the normal direction, the maximum shear stress that can act on the slurry is equal to half of the pressure. In the slurry above the yield region, the vertical stress does not exceed the yield stress, and the slurry in this region remains stable and does not yield.

[0080] Step 8: In the slurry above the yield region, the vertical stress does not exceed the yield stress, and the slurry in this region remains stable and does not yield. During the yield flow, assume that the interface layer between the yielded and unyielded materials is a horizontal surface, and the shear stress at this interface layer is equal to the yield stress of the slurry.

[0081] Therefore, the final height consists of the unyielded region (h0) and the yield region (h1), and the height h0 can be determined by the following formula:

[0082]

[0083] where ρ is the density of the slurry, kg / m 3 ; g is the acceleration due to gravity, N / kg;

[0084] Step 9: In the yield region, the height can be divided into infinitesimal elements with a thickness of d z and a radius of r z At this time, the shear stress of the slurry is τ z ; after yield flow, it decreases to a thickness of d z1 and a radius of r z1 At this time, the yield stress of the slurry is τ z1 ; when the cross-sectional area of the slurry spreading around increases after yield, causing the shear force of the slurry on any given plane to decrease to the yield stress, the slurry stops flowing.

[0085] Therefore, the product of the stress and the cross-sectional area is proportional to the weight of the slurry above the plane, and the expression is:

[0086]

[0087] The height h1 of the yield region of the slurry can be obtained by integrating d z1 over the yield region, and the expression is as follows:

[0088]

[0089] From Figure 2 it can be seen that when other parameters remain unchanged and the final grouting hole height is changed, it is found that the height of the grouting yield region increases with the increase of the final grouting hole height. The higher the final grouting hole height, the greater the self-weight of the slurry.

[0090] Step 10: According to the conservation of slurry volume, the grouting diffusion range d in the lateral seepage stage:

[0091]

[0092] In the formula, r is the radius in the low-pressure diffusion stage of the slurry, m;

[0093] The seepage gradient of the slurry is tanθ τ , and the seepage gradient angle θ of the slurry in the transverse seepage stage τ :

[0094]

[0095] Slurry filling volume in the transverse seepage stage:

[0096]

[0097] When the slurry diffusion enters the transverse continuous seepage stage, the diffusion distance of the slurry should be no less than 8 m at this time. The conical slurry undergoes flow deformation in the height h1 area. At this time, using the "horizontal segmentation layer" method in the transverse seepage stage will produce a large error. Therefore, it is assumed that in this stage, the conical frustum takes the center of its lower bottom circle as the center, and the side surface continuously slips to form a laminar flow. The upper bottom radius r remains unchanged during the transverse seepage process. The shear stress on the inclined surface of the slurry side surface is the resultant force of the vertical stress and the horizontal stress;

[0098] Step 11: As the grouting volume increases, the slurry undergoes transverse continuous seepage, and the angle α between the side surface of the conical frustum and the vertical direction τ continually increases. When the grouting volume is V i , the shear stress of the slurry is τ zi = ρgV i / πd i 2 cosα τi ; When the transverse continuous seepage stage is completed, the shear force of the slurry on the side surface of the conical frustum is equal to the yield stress. Considering the change of seepage resistance during this seepage process and combining with Equation (2), the stress balance equation of the bottommost layer of slurry is obtained as:

[0099]

[0100] In the formula, α τ is the angle between the side surface of the conical frustum and the vertical direction, °; l i is the length of the side surface of the conical frustum, where l i = h1 / cosα τ , m; V' is the final filling volume of the slurry, m 3 ;

[0101] Final grouting diffusion range d':

[0102]

[0103] Final grouting seepage gradient angle:

[0104]

[0105] The final grouting filling volume is:

[0106]

[0107] When the final grouting hole height is 6m and other parameters remain unchanged, with the increase of the seepage slope angle, the filling volume decreases, as Figure 3 shown;

[0108] By combining equations (9), (10), (11) and (12), the grouting diffusion range, the grouting seepage slope angle, and the grouting filling volume can be predicted;

[0109] In the mathematical model of adjacent grouting seepage of the paste in the caving zone, the values of the paste seepage slope, the expansion range, and the filling volume are mainly affected by the grouting pressure, the grouting pipe angle, the paste rheological parameters, the paste flow velocity, the void ratio and tortuosity of the caved gangue;

[0110] For the seepage yield model with pressure in the caving zone, the tortuosity factor F and the average particle diameter D of the seepage path m are empirical parameters, and the seepage of the gangue paste in the caving zone is affected by both gravity and filtration effects. The filtration effect will cause changes in the paste rheological parameters and an increase in the seepage resistance. At the same time, the void distribution in the caving zone is not uniform, which will lead to certain deviations in the calculation results. However, this model comprehensively considers the paste properties, the caving zone structure, and their interaction, and derives the calculation formulas for the grouting diffusion range, the grouting seepage slope angle, and the grouting filling volume, laying a certain theoretical foundation for the development of the adjacent grouting technology in the caving zone.

[0111] Establishment of a three-dimensional grouting numerical model: Based on the volume of fluid (VOF) method for porous media, using the ANSYS-Fluent computational fluid dynamics (CFD) software, a three-dimensional grouting numerical model of the caving zone is established according to the actual geological conditions of the project to study the three-dimensional unsteady diffusion process of the paste in the caving zone.

[0112] To simplify the grouting process, this application ignores the influence of the suspension particles and the time-varying viscosity of the paste on the paste diffusion, as well as the influence of the fluid on the porous media. Based on the N-S equation to describe the basic mechanical laws of fluid motion, the VOF method is used to describe the paste diffusion to obtain the paste diffusion characteristics in real time. The VOF model can simulate two or more immiscible fluids by solving a set of momentum equations and track the volume fraction of each fluid throughout the region. The porous media model is established by adding a momentum source term to the standard momentum equation.

[0113] The slump and spread of the gangue paste with a mass concentration of 70% are measured by the slump test, and the average self-flow slope of the paste is calculated to be 3.8%. AsFigure 4 As shown, the curves of the yield stress and viscosity coefficient of the gangue slurry varying with the concentration were obtained by testing with a Viscotester iQ rheometer. As Figure 4 (a) shows, the viscosity coefficient of the slurry increases exponentially with the increase in concentration. As Figure 4 (b) shows, the yield stress of the slurry increases exponentially with the increase in concentration. The correlation coefficients R of the fitting curves of the yield stress and viscosity coefficient 2 are 0.972 and 0.973 respectively, showing a high degree of correlation. When the concentration is greater than 70%, the viscosity of the slurry shows a trend of rapid growth with the increase in concentration.

[0114] The three-dimensional grouting model of the caving zone simulates that the size of the caving zone is 100m×50m×10m, the porosity is set to be non-uniformly distributed, the porosity range is 0.01 - 0.28, the final hole position of the grouting pipe is located in the fractured rock mass, and the grouting parameters are shown in Table 5.4. The PISO algorithm is used for the solution method. The time step is set to 1s, and the grouting stage is calculated and solved as shown in Table 1 below.

[0115]

[0116] Table 1 Grouting parameters

[0117] When the final hole position of the grouting pipe is located in the fractured rock mass, the seepage process of the slurry is mainly manifested as low-pressure diffusion in the early stage - pressure seepage in the later stage. The numerical simulation results show that the grouting filling and diffusion process in the adjacent position of the caving zone has undergone 4 stages of changes, which is consistent with the foregoing theoretical analysis. Figure 5 For the change in the density of the slurry during the grouting seepage process, it can be found that the density of the slurry slightly increases at the grouting hole position and decreases with the increase in the diffusion distance.

[0118] As Figure 5 (a) shows, it is the low-pressure diffusion stage. The diffusion range of the slurry is approximately circular, and its radius is 4.2m. As Figure 5 (b) shows, with the increase in the grouting volume, affected by the gravity effect, the slurry preferentially flows downward, and the grouting diffusion range is elliptical, with the major axis being 6.5m and the minor axis being 4.2m. The diffusion radius of the slurry is greater than the height of the final grouting hole, and the slurry seeps to the bottom plate. Under the action of the grouting pressure, the slurry seeps upward, but the gravity will hinder the diffusion of the slurry, resulting in the diffusion distance of the slurry being smaller than the downward seepage distance, and the final effective grouting height is 8.5m.

[0119] As Figure 5 (c) shows, it is the longitudinal penetration stage. With the increase in the grouting volume, a longitudinal penetration channel of the slurry with a certain radius size is formed near the grouting port. Its diameter is affected by the diffusion range of the slurry in the low-pressure diffusion stage, generally being the minor axis length of the elliptical slurry diffusion range, that is, 4.2m.

[0120] As Figure 5 (d) shows, it is the initial stage of horizontal seepage. At the position 3.3 m away from the bottom plate, the shear stress of the slurry is greater than the yield stress of the slurry, and it gradually spreads horizontally. The diffusion shape of the slurry initially forms a truncated cone. The diffusion range of the slurry is 13.1 m, and the seepage slope is 70.2%.

[0121] As Figure 5 (e) shows, it is the stage of continuous horizontal seepage. As the injection volume of the slurry increases, the slurry undergoes continuous horizontal seepage with the initial truncated cone accumulation body. The horizontal diffusion range of the slurry continues to increase. At this time, the diffusion range of the slurry is 27.4 m, and the seepage slope is 17.3%.

[0122] As Figure 5 (f) shows, with the continuous injection of the slurry, the slurry overcomes the yield stress and seepage resistance and continues to spread. When the shear stress of the slurry is less than the yield stress, the slurry stops spreading. At this time, the diffusion range of the slurry is 38.6 m, and the seepage slope is 10.9%.

[0123] By comparing the grouting shapes during the whole process of grouting seepage, it can be found that the upper bottom surface of the truncated cone formed by grouting and the height of the yield area almost remain unchanged, which also verifies that the assumption in the aforementioned grouting seepage model that the radius of the upper bottom surface of the grouting truncated cone and the height of the yield area remain unchanged during the grouting seepage process is reasonable.

[0124] The results of the numerical simulation test show that the effective grouting height is 8.5 m, the short axis radius of grouting diffusion in the pressurized diffusion stage is 4.2 m, and other parameters are the same as those in Section 1.2. Substituting them into the grouting seepage mathematical model, the diffusion range of the slurry can be calculated to be 32.7 m. Compared with the theoretical calculation results of the test measurement results, the relative error of the long axis radius of the grouting diffusion range is 15.3%, which verifies the correctness of the grouting seepage model.

[0125] Figure 6 is the fitting curve of the slurry concentration distribution after grouting is completed. The test results show that the slurry concentration decreases exponentially with the increase of the grouting diffusion distance, and the fitting equation is y = -55 + 143e -0.02x , R 2 = 0.96.

[0126] Figure 7 is the three-dimensional unsteady diffusion process of the slurry for adjacent grouting, that is, the three-dimensional morphological changes composed of the diffusion range and the stacking height of the slurry at different times. Figure 7 (a) is the low-pressure diffusion stage. The main driving force for the slurry diffusion is the grouting pressure. At the edge of the grouting diffusion range, the pressure of the slurry changes little. Figure 7 (b) is the longitudinal penetration stage. Affected by self-weight, the pressure of the slurry increases from top to bottom. The pressure here is the resultant force of the self-weight of the slurry and the seepage resistance. Figure 7(c) is the horizontal seepage initiation stage. At the position 3.3 m away from the bottom plate, the slurry pressure is greater than the yield stress, resulting in horizontal seepage. Figure 7 (d) is the horizontal seepage continuation stage. With the increase in the grouting volume, the slurry undergoes continuous horizontal seepage, the seepage range expands, and the pressure at the grouting diffusion front is relatively high. The pressure on the surface of the three-dimensional grouting diffusion form is different from the internal pressure of the slurry, but the overall slurry pressure shows a gradually increasing pattern from top to bottom, which is consistent with the theoretical analysis. From the perspective of the three-dimensional grouting diffusion form, the slurry mainly evolves in the shape of a sphere - ellipsoid - truncated cone.

[0127] In summary: Based on the seepage mechanics theory, considering the properties of the slurry and the influence of the filtration effect, the present invention constructs a grouting seepage model for the adjacent position of the caving zone, which can accurately calculate the grouting diffusion range, the grouting seepage slope angle, and the grouting filling volume, and is more beneficial to the coordinated development of coal mining and environmental protection. At the same time, the present invention combines the three-dimensional numerical simulation analysis of the adjacent position grouting in the caving zone, depicts the three-dimensional unsteady diffusion process of the slurry seepage, reveals the grouting diffusion law in the adjacent position of the caving zone, and improves the prediction accuracy. The research results show that the grouting seepage presents an evolution law of a low-pressure diffusion stage, a longitudinal penetration stage, a horizontal seepage initiation stage, and a horizontal continuous seepage stage, and its shape changes from an ellipsoid and a cylinder to a truncated cone, revealing the diffusion mechanism of adjacent position grouting. The start and stop of the grouting diffusion in the caving zone are controlled by the yield stress. When the yield stress of the slurry is less than the shear stress, the slurry begins to diffuse. The porosity of the caving zone decreases, and the tortuosity of the seepage path increases, resulting in an increase in the seepage resistance and a decrease in the slurry diffusion distance. Combining the three-dimensional numerical simulation analysis of the adjacent position grouting in the caving zone, revealing the grouting diffusion law in the adjacent position of the caving zone, the low-pressure diffusion is in the shape of an ellipsoid, the longitudinal penetration is in the shape of a cylinder, the horizontal expansion is in the shape of a truncated cone, and the seepage slope continuously decreases and finally stabilizes.

[0128] The above shows and describes the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments. What is described in the above embodiments and the specification only illustrates the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed. The scope of protection claimed by the present invention is defined by the appended claims and their equivalents.

Claims

1. Prediction method for grouting filling quantity of adjacent gangue in caving zone, characterized in that: The specific steps include: Step 1: Inject 70% concentration of gangue slurry into the gap between the broken rock mass and the basic top through the adjacent grouting pipe. The gangue slurry exhibits significant non-Newtonian fluid mechanics properties during the flow process. After the gangue slurry enters the collapse zone through the pumping pipeline, the adjacent grouting pressurized seepage diffusion process can be divided into four stages: low-pressure diffusion stage, longitudinal penetration stage, lateral seepage start-up stage and lateral continuous seepage stage. In the low-pressure diffusion stage, the slurry at the outlet of the pumping pipeline has a certain initial flow rate, and under the influence of the slurry's own weight, a slurry coverage area with a certain radius will be formed near the grouting port, and its radius is: Where Q r is the filling injection volume per unit time, m 3 / s; B r is the void width between the broken rock mass in the caving zone and the basic roof, m; C r is the correction coefficient; V pl is the critical flow velocity to suspend solid particles, m / s; Step 2, obtaining the yield stress of the gangue slurry with a concentration of 70% by slurry rheology test, recorded as slurry yield stress τ0; Step 3: In the longitudinal penetration stage, the slurry seepage process converts the gravitational potential energy into kinetic energy and deformation energy. Under the influence of the slurry's own weight, a longitudinal slurry penetration channel with a certain radius will be formed near the grouting port. The radius of the longitudinal channel is generally taken as the average of the long axis and short axis radii of the grouting diffusion range in the low-pressure diffusion stage, which is r; Step 4. In the initial stage of horizontal seepage, as the grout injection volume increases, the grout seepage behavior is mainly driven by the gravity difference formed by the elevation difference of the grout surface, and is affected by the seepage resistance of the gangue in the caving zone at the same time. The grout at the bottom plate of the caving zone gradually spreads horizontally and develops into a truncated cone. The grout diffusion range is d, and the seepage slope angle is θ τ ; Step 5. In the stage of lateral continuous seepage, with the increase of the slurry injection volume, the slurry undergoes a lateral re-seepage phenomenon with the initial truncated cone accumulation body, and the lateral diffusion range of the slurry continues to increase. At this time, the diffusion range of the slurry is d', and the seepage slope is θ τ '; Step 6: The seepage driving force of the adjacent grouting slurry in the caving zone is its self-weight, and the additional resistance is mainly the seepage resistance. Considering the effects of the porosity Ψ, the seepage path tortuosity factor F, the average particle diameter D m , the yield stress τ0 of the slurry, and the seepage linear distance L, the pressure change during the slurry seepage process can be obtained by the following formula: where ΔP is the pressure change during the slurry seepage process, Pa; D m is the average particle diameter, m; τ0 is the yield stress of the slurry, Pa, which can be obtained through rheological tests; L τ is the straight seepage distance, m; Ψ is the porosity; F is the tortuosity factor of the seepage path; Step 7: The height of the undeformed cylinder is h0, the slurry within the height h1 range is subjected to a stress greater than the yield stress τ0, and the slurry flows until the stress is reduced to the yield stress and stops, wherein the slurry within the h0 range is an unyielded body, and the slurry within the h1 range is a yielded body; Step 8: In the slurry above the yield region, the vertical stress does not exceed the yield stress, and the slurry in this region remains stable without yielding; during the yield flow process, it is assumed that the interface layer between the yielded and unyielded materials is a horizontal surface, and the shear stress of the interface layer is equal to the slurry yield stress; Therefore, the final height consists of the unyielded area (h0) and the yielded area (h1). The height h0 can be determined by the following formula: where ρ is the density of the slurry, kg / m 3 ; g is the acceleration due to gravity, N / kg; Step 9: In the yield region, the height can be divided into micro-elements with a thickness of d z and a radius of r z , at which time the shear stress of the slurry is τ z ; after its yield flow, it decreases to a thickness of d z1 and a radius of r z1 , at which time the yield stress of the slurry is τ z1 ; when the cross-sectional area of the slurry diffusing around after yield increases, causing the shear force of the slurry on any given plane to decrease to the yield stress, the slurry stops flowing; Therefore, the product of stress and cross-sectional area is proportional to the weight of the paste above the plane and is expressed as: The height h1 of the paste yield zone can be obtained by integrating d z1 over the yield zone, and the expression is as follows: Step 10: According to the law of slurry volume conservation, the grouting diffusion range d in the lateral seepage stage is: Where r is the radius of the slurry at the low-pressure diffusion stage, m; The seepage gradient of the slurry is tanθ τ , and the seepage gradient angle θ of the slurry in the transverse seepage stage τ : Slurry filling volume in the lateral seepage stage: Step 11: As the grouting volume increases, the slurry continuously seeps laterally, and the angle α between the side of the truncated cone and the vertical direction τ constantly increases. When the grouting volume is V i , the shear stress of the slurry is τ zi = ρgV i / πd i 2 cosα τi ; when the lateral continuous seepage stage is completed, the shear force of the slurry on the side of the truncated cone is equal to the yield stress. Considering the change of seepage resistance during this seepage process and combining with Equation (2), the stress balance equation of the bottom-layer slurry is obtained as follows: where α τ is the angle between the side surface of the truncated cone and the vertical direction, °; l i is the length of the side surface of the truncated cone, where l i = h1 / cosα τ , m; V' is the final filling volume of the slurry, m 3 ; Final grouting diffusion range d': Final grouting seepage slope angle: The final grouting filling volume is: When the final grouting hole height is 6m, with other parameters unchanged, the filling volume decreases with the increase of the seepage slope angle; The combined equations (9), (10), (11) and (12) can predict the grouting diffusion range, grouting seepage slope angle, and grouting filling volume.

2. The prediction method of gob-side gangue grouting filling volume according to claim 1, characterized in that: After the gangue slurry described in step 1 enters the collapse zone through the pumping pipeline, it is first driven by low pressure and diffuses in an elliptical shape. Later, under the influence of gravity, it preferentially seeps vertically downward, and then expands and flows freely in all directions. When it flows to the gangue retaining wall, the slurry gradually rises until the grouting stops, and finally a truncated cone-shaped filling body is formed.

3. The prediction method of gob-side gangue grouting filling volume according to claim 1, characterized in that: In Step 2, the yield stress of the gangue slurry with a concentration of 70% was obtained by testing with a Viscotester iQ rheometer. The essence of the gangue slurry is a solid-liquid two-phase mixed fluid composed of fine-grained gangue particles and water. Through the analysis of the slurry rheological test, the yield stress of the gangue slurry with a concentration of 70% was found to be 25 Pa.

4. The prediction method for the grouting filling quantity of adjacent gangue in the caving zone according to claim 1, characterized in that: In Step 8, considering the relatively large size of the broken rock blocks in the caving zone, an exponential empirical formula (F = 1 / Ψ 1-u ) is adopted. Generally, u takes values from 2.1 to 2.2 to establish the relationship between the tortuosity factor F of the seepage path and the porosity Ψ. The smaller the porosity, the more complex the seepage path and the greater the seepage resistance. The average particle diameter D m of the caving zone is taken as 0.12 m.

5. The prediction method for the grouting filling amount of adjacent gangue in the caving zone according to claim 1, wherein: In Step 11, when the slurry diffusion enters the lateral continuous seepage stage, the slurry diffusion distance should be no less than 8 m at this time. The truncated conical slurry undergoes flow deformation in the height h1 region. At this time, using the "horizontal segmentation layer" method in the lateral seepage stage will result in a large error. Therefore, it is assumed that in this stage, the truncated cone takes the center of its lower bottom circle as the center, and laminar flow is formed by the continuous sliding of the side surface. The upper bottom radius r remains unchanged during the lateral seepage process, and the shear stress on the inclined surface of the slurry side surface is the resultant force of the vertical stress and the horizontal stress.

Images