A calculation method for injection rate and cumulative injection volume of slurry for dam toe plate curtain grouting

Abstract

A method for calculating the injection rate and cumulative injection volume of grouting slurry for a dam toe plate curtain grouting comprises the following steps: first, calculating the direction vector of the flow into the fissure from each side of a regular octagon, then calculating the flow rate into the fissure from each side of the regular octagon, then accumulating the flow rate into the fissure from each side to obtain the slurry flow rate injected into the fissure, then accumulating the flow rate injected into each fissure to obtain the slurry injection rate, and then using the integration principle based on the slurry injection rate calculated in the above steps to obtain the cumulative slurry injection volume. The algorithm of the present invention is reasonable, has a smaller computational load than traditional methods, improves calculation speed, and also improves calculation accuracy. It also has good adaptability to the three-dimensional random fracture network of the dam foundation rock mass, effectively avoiding the occurrence of excessive or insufficient grouting of the dam toe plate curtain grouting, and improving the construction quality of the dam.

Description

Technical Field

[0001] The invention relates to a method for calculating the injection rate and cumulative injection volume of grouting slurry, in particular to a method for calculating the injection rate and cumulative injection volume of dam toe plate curtain grouting slurry, and belongs to the technical field of dam construction. Background Art

[0002] Dam toe plate curtain grouting is a common method for preventing seepage in the upper reservoir of pumped-storage power stations. However, insufficient grouting and leakage during the grouting process are not uncommon. At the very least, this can lead to reservoir basin leakage, reducing the overall efficiency of the power station, and at worst, damage the stability of the dam and affect project safety. Grouting is a construction technology that involves disciplines such as fluid mechanics, engineering geology, hydrogeology, soil mechanics, rock mechanics, engineering mechanics, and exploration geophysics. Grouting construction is the process in which cement slurry, under the influence of construction conditions, undergoes physical and chemical reactions with fractured rock or gravel soil. Certain solidifying materials, such as cement, lime, or other chemicals, are injected into the foundation rock and soil within a certain range to fill cracks and pores in the rock and soil, prevent foundation leakage, and improve the integrity, strength, and stiffness of the rock and soil. Grouting is the combined effect of the grouting slurry and the grouting medium under the influence of the external construction environment.

[0003] Calculating the slurry injection rate and cumulative injection volume during the dam toe plate curtain grouting process is crucial and of great significance to engineering construction. Accurate calculations of these rates can effectively prevent over-grouting and under-grouting. Traditional methods for calculating these rates and volumes in existing technologies are computationally intensive. Limited by computer performance, the larger the model size, the slower the calculation speed, assuming a constant grid density. Furthermore, the complex and diverse fractures in the dam foundation rock mass undergoing grouting are subject to numerous factors influencing the slurry injection rate. For example, the slurry pressure decreases uniformly along the flow direction, and the dynamic viscosity of the slurry varies at various times. This results in traditional methods for calculating the slurry injection rate and cumulative injection volume being significantly different from actual conditions. These methods are not only slow but also inaccurate, hindering quality control of dam toe plate curtain grouting. An effective method for calculating the slurry injection rate and cumulative injection volume has long been lacking to address these technical issues. Summary of the Invention

[0004] The purpose of the present invention is to solve the problem that the existing deep underground dam foundation rock cracks cannot be directly observed, and the traditional method for calculating the slurry injection rate and the cumulative injection amount has a very large amount of calculation, not only slow in calculation speed, but also low in calculation accuracy, which easily leads to defects and shortcomings such as excessive grouting and insufficient grouting of the dam toe plate curtain. The present invention provides a reasonable algorithm, which has a smaller amount of calculation than the traditional method, improves the calculation speed, and also improves the calculation accuracy. It also has good adaptability to the three-dimensional random crack network of the dam foundation rock mass, effectively avoids the occurrence of excessive grouting and insufficient grouting of the dam toe plate curtain, and improves the construction quality of the dam.

[0005] To achieve the above-mentioned object, the technical solution of the present invention is: a method for calculating the injection rate and cumulative injection volume of slurry for curtain grouting of a dam toe plate, comprising the following steps:

[0006] A. First, calculate the direction vector flowing into the crack from each side of the regular octagon; taking the AB side as an example, obtain the coordinates of points A, B, and I, and calculate the coordinate vector and Pair Vector and Perform cross product to obtain the normal vector perpendicular to the crack surface and passing through point A Then for the vector and Perform a cross product and take the unit vector of the cross product result to obtain the direction vector flowing from AB into the crack

[0007] B. Then calculate the flow rate flowing into the crack from each side of the regular octagon; taking the AB side as an example, obtain the coordinates of points A and B, and calculate the length of the AB side l AB , get the single width flow vector at the center point of unit 1 to which the AB side belongs For single-width traffic and the direction vector of the AB edge flowing into the crack Perform dot product to obtain the single width flow rate from the AB side into the crack, and multiply the single width flow rate by the length of the AB side l AB Multiply them together to get the flow rate flowing into the crack from the AB side;

[0008] C. Then, using the Bingham grout flow equation for a single inclined fracture, the following derivation assumptions were made: ① The grout flows in a smooth fracture with a width of b; ② The upper, left, and right boundaries of the fracture are pressure-free (equal to atmospheric pressure), and the lower boundary is impermeable. An analytical formula for the fracture grouting rate was established and imported into the calculation. The flow rates flowing into the fracture from each side were accumulated to obtain the grout flow rate injected into the fracture.

[0009] D. Then the flow rate injected into each fracture is accumulated to obtain the slurry injection rate;

[0010] Through the above process, the calculation formula of slurry injection rate is obtained as follows:

[0011]

[0012] Where Q t is the grouting injection rate at time t; n represents the number of fracture surfaces intersecting with the grouting hole; m k is the number of sides of the polygonal cross section formed by the intersection of the kth fracture surface and the grouting hole; is the single width flow vector corresponding to the jth side of the kth polygonal section; is the unit normal vector corresponding to the jth side of the kth polygonal section; l AB is the length of the jth side of the kth polygonal section;

[0013] E. Based on the slurry injection rate calculated according to the above steps, the cumulative injection volume of the slurry can be obtained by using the integration principle.

[0014] Furthermore, the cumulative injection amount of the slurry in step E is as follows:

[0015]

[0016] Where V is the cumulative injection volume; T is the total grouting time; Q i , Q i-1 t i , t i-1 Slurry injection rate at the time.

[0017] Furthermore, the calculation formula for the crack roughness in step A is as follows:

[0018]

[0019] Among them: the relevant parameters are α = -0.58, β = -1.5.

[0020] The single fracture grouting flow rate formula in step C is as follows:

[0021]

[0022] Where r0 is the radius of the grouting hole, τ0, ν, and ρ are the initial shear strength, kinematic viscosity coefficient, and density of the slurry, respectively; β is the inclination angle of the crack; h0 and h1 are the grouting hole pressure head value and hydrostatic pressure head value, respectively.

[0023] The beneficial effects of the present invention are:

[0024] 1. The present invention adopts the vector method for calculation, and calculates the direction vector and flow rate flowing into the crack from each side of the regular octagon respectively, and accumulates the flow rate flowing into the crack from each side to obtain the slurry flow rate injected into the crack. Then, the flow rate injected into each crack is accumulated to obtain the slurry injection rate, and then the integral principle is used to obtain the cumulative injection amount of the slurry.

[0025] 2. This paper uses a numerical simulation method for the slurry diffusion process to establish a calculation model algorithm for slurry injection rate and cumulative injection volume. This algorithm analyzes the diffusion patterns of cement slurry during fracture grouting, revealing the diffusion behavior of cement slurry in complex fracture networks and its influencing factors. The computational model predicts grouting injection volume data in real time. Combined with actual unit project grouting construction, the monitoring data is compared with the simulated and predicted data. This data is used as a basis for feedback data to monitor, warn, and judge the grouting process.

[0026] 3. The algorithm of the present invention is reasonable, with less calculation amount than the traditional method, which improves the calculation speed and accuracy. It also has good adaptability to the three-dimensional random fracture network of the dam foundation rock mass, effectively avoiding the occurrence of excessive grouting and insufficient grouting of the dam toe plate curtain, and improving the construction quality of the dam. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 It is a schematic diagram of the intersection of the vertical grouting hole and the horizontal fracture surface of the present invention.

[0028] Figure 2 It is a schematic diagram of the orifice nodes and unit numbers of the vertical grouting holes of the present invention.

[0029] Figure 3 It is a three-dimensional diagram of the grid and boundary conditions of the parallel plate model of the present invention.

[0030] Figure 4 This is a diagram of the slurry pressure distribution in the cracks of the present invention.

[0031] Figure 5 This is a single-width flow distribution diagram of the slurry in the crack of the present invention.

[0032] Figure 6 This is a table showing the corresponding relationship between the slurry density and the slurry viscosity of the present invention.

[0033] Figure 7 It is a data table of the changing process of grouting pressure and slurry parameters of the present invention.

[0034] Figure 8 This is a parameter table of the change process of the crack roughness coefficient of the third grouting stage of the present invention.

[0035] Figure 9 This is a comparison table of numerical simulation results and monitoring results of the grouting injection rate of the grouting section of the present invention.

[0036] Figure 10 This is a comparison table of the numerical simulation results and monitoring results of the cumulative injection volume of the grouting section of the present invention. DETAILED DESCRIPTION

[0037] The present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments.

[0038] See also Figures 1 to 10 A method for calculating the injection rate and cumulative injection volume of dam toe plate curtain grouting slurry of the present invention comprises the following steps:

[0039] A. First, calculate the direction vector flowing into the crack from each side of the regular octagon; taking the AB side as an example, obtain the coordinates of points A, B, and I, and calculate the coordinate vector and Pair Vector and Perform cross product to obtain the normal vector perpendicular to the crack surface and passing through point A Then for the vector and Perform a cross product and take the unit vector of the cross product result to obtain the direction vector flowing from AB into the crack

[0040] B. Then calculate the flow rate flowing into the crack from each side of the regular octagon; taking the AB side as an example, obtain the coordinates of points A and B, and calculate the length of the AB side l AB , get the single width flow vector at the center point of unit 1 to which the AB side belongs For single-width traffic and the direction vector of the AB edge flowing into the crack Perform dot product to obtain the single width flow rate from the AB side into the crack, and multiply the single width flow rate by the length of the AB side l AB Multiply them together to get the flow rate flowing into the crack from the AB side;

[0041] C. Then, using the Bingham grout flow equation for a single inclined fracture, the following derivation assumptions were made: ① The grout flows in a smooth fracture with a width of b; ② The upper, left, and right boundaries of the fracture are pressure-free (equal to atmospheric pressure), and the lower boundary is impermeable. An analytical formula for the fracture grouting rate was established and imported into the calculation. The flow rates flowing into the fracture from each side were accumulated to obtain the grout flow rate injected into the fracture.

[0042] D. Then the flow rate injected into each fracture is accumulated to obtain the slurry injection rate;

[0043] Through the above process, the calculation formula of slurry injection rate is obtained as follows:

[0044]

[0045] Where Q t is the grouting injection rate at time t; n represents the number of fracture surfaces intersecting with the grouting hole; m k is the number of sides of the polygonal cross section formed by the intersection of the kth fracture surface and the grouting hole; is the single width flow vector corresponding to the jth side of the kth polygonal section; is the unit normal vector corresponding to the jth side of the kth polygonal section; l AB is the length of the jth side of the kth polygonal section;

[0046] E. Based on the slurry injection rate calculated according to the above steps, the cumulative injection volume of the slurry can be obtained by using the integration principle.

[0047] The cumulative injection amount of the slurry in step E is as follows:

[0048]

[0049] Where V is the cumulative injection volume; T is the total grouting time; Q i , Q i-1 t i , t i-1 Slurry injection rate at the time.

[0050] The calculation formula for the crack roughness in step A is as follows:

[0051]

[0052] Among them: the relevant parameters are α = -0.58, β = -1.5.

[0053] The single fracture grouting flow rate formula in step C is as follows:

[0054]

[0055] Where r0 is the radius of the grouting hole, τ0, ν, and ρ are the initial shear strength, kinematic viscosity coefficient, and density of the slurry, respectively; β is the inclination angle of the crack; h0 and h1 are the grouting hole pressure head value and hydrostatic pressure head value, respectively.

[0056] See also Figures 1 to 5 The present invention uses a vector method for calculation, which requires less computation than traditional methods and is highly adaptable to three-dimensional random fracture networks in dam foundation rock. By scientifically and skillfully utilizing computer technology and algorithms, the present invention not only increases calculation speed but also improves calculation accuracy. The specific steps and principles of the method are as follows:

[0057] First, calculate the direction vector flowing into the crack from each side of the regular octagon; taking the AB side as an example, obtain the coordinates of points A, B, and I, and calculate the coordinate vector and Pair Vector and Perform cross product to obtain the normal vector perpendicular to the crack surface and passing through point A Then for the vector and Perform a cross product and take the unit vector of the cross product result to obtain the direction vector flowing from AB into the crack

[0058] Then calculate the flow rate flowing into the crack from each side of the regular octagon; taking the AB side as an example, obtain the coordinates of points A and B, and calculate the length of the AB side l AB , get the single width flow vector at the center point of unit 1 to which the AB side belongs For single-width traffic and the direction vector of the AB edge flowing into the crack Perform dot product to obtain the single width flow rate from the AB side into the crack, and multiply the single width flow rate by the length of the AB side l AB Multiplying them together yields the flow rate flowing into the fracture from side AB. The flow rates flowing into each fracture are accumulated to yield the slurry flow rate injected into that fracture. The flow rates injected into each fracture are then accumulated to yield the slurry injection rate. Using the formula for the slurry injection rate, and then applying the integration principle based on the slurry injection rate calculated in the above steps, the cumulative slurry injection volume can be calculated.

[0059] In order to verify the effectiveness of the above calculation method, two plates with a length of 20m, a width of 20m, and a thickness of 2m were selected to form a parallel plate model. The crack width between the plates was 1mm, and the cracks were assumed to be smooth. The center of the crack was taken as the coordinate origin, and a pressure of 1MPa was applied to the left boundary of the model (x=-10), and a pressure of 0MPa was applied to the right boundary (x=10). The rest of the model boundaries were set to be impermeable. The coordinate system, model size, model grid, and boundary conditions are shown in the attached figure. Figure 3 shown.

[0060] The slurry density was selected as 1×10 3 kg / m 3 The slurry dynamic viscosity is 1×10 -3 Pa·s, the roughness coefficient is 1.0, the calculation time is 6000s, and the numerical simulation is performed using 3DEC 7.0 software. The results of the slurry flow rate per width and slurry pressure distribution in the crack at the end of the calculation are shown in the attached figure. Figure 4 , Attachment Figure 5 As shown in the figure, the slurry flow has stabilized at this time, and the slurry pressure decreases evenly along the flow direction; the single-width flow rate at each point is the same, about 4.16×10-3 m 2 / s. According to the calculation method of slurry injection rate, the slurry injection rate is calculated using formula (3-9) in step D to be 0.083m 3 / s, which is consistent with the calculation result of the cubic law (Formula (3-5)), indicating that the calculation method of slurry injection rate is accurate and reliable.

[0061] Based on the slurry mix ratio, literature and monitoring data, the corresponding relationship between slurry density and slurry viscosity is determined through comprehensive analysis, as shown in the attached figure. Figure 6 During the simulation, the corresponding slurry viscosity is calculated by linear interpolation according to the slurry density at each moment, as shown in the attached figure. Figure 7 As shown in the table.

[0062] Based on the monitoring data, the relevant parameters of the fracture roughness calculation formula (Formula (3-8)) are obtained by trial calculation method through parameter inversion: α = -0.58, β = -1.5, then

[0063]

[0064] According to formula (3-11), the change process of crack roughness coefficient over time is calculated as shown in the attached figure. Figure 8 As shown in the table.

[0065] Through numerical simulation, the grouting rate and cumulative injection volume of the third grouting section were calculated and compared with the monitoring results. The results are shown in the attached figure. Figure 9 , Attachment Figure 10 As shown. Figure 9 The analysis shows that the numerical simulation results of grouting injection rate are basically consistent with the monitoring results. Figure 10 The numerical simulation result for the cumulative injection volume was 2942.84 L, while the monitoring result was 2875.53 L, with a relative error of only 2.34%. This comparison demonstrates that the numerical model, calculation parameters, boundary conditions, and other computational factors and software methods used in this study can provide relatively accurate simulation results for the slurry diffusion process in curtain grouting.

[0066] The above content is a further detailed description of the present invention in combination with specific implementation methods. It cannot be considered that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, simple modifications and replacements made without departing from the concept of the present invention should be deemed to fall within the scope of protection of the present invention.

Claims

1. A method for calculating the injection rate and cumulative injection volume of slurry for dam toe plate curtain grouting, comprising the following steps: A. First, calculate the direction vector flowing into the crack from each side of the regular octagon; taking the AB side as an example, obtain the coordinates of points A, B, and I, and calculate the coordinate vector and , for the vector and Perform cross product to obtain the normal vector perpendicular to the crack surface and passing through point A , and then the vector and Perform a cross product and take the unit vector of the cross product result to obtain the direction vector flowing from AB into the crack ; B. Then calculate the flow rate into the crack from each side of the regular octagon; Taking the AB side as an example, obtain the coordinates of points A and B and calculate the length of the AB side , get the single width flow vector at the center point of unit 1 to which the AB side belongs ; For single-width traffic and the direction vector of the AB edge flowing into the crack Perform dot product to obtain the single width flow rate flowing into the crack from the AB side, and multiply the single width flow rate by the length of the AB side. Multiply them together to get the flow rate flowing into the crack from the AB side; C. Then, using the Bingham grout flow equation for a single inclined fracture, the following derivation assumptions are made: ① The grout flows in a smooth fracture with a gap width of b; ② The upper, left, and right boundaries of the fracture are pressure-free, and the lower boundary is impermeable. An analytical formula for the fracture grouting rate is established and imported into the calculation. The flow rates flowing into the fracture from each side are accumulated to obtain the grout flow rate injected into the fracture. D. Then the flow rate injected into each fracture is accumulated to obtain the slurry injection rate; Through the above process, the calculation formula of slurry injection rate is obtained as follows: Where, is the grouting injection rate at time t; n represents the number of fracture surfaces intersecting with the grouting hole; m k is the number of sides of the polygonal cross section formed by the intersection of the kth fracture surface and the grouting hole; is the single width flow vector corresponding to the jth side of the kth polygonal section; is the unit normal vector corresponding to the jth edge of the kth polygonal section; is the length of the jth side of the kth polygonal section; E. Based on the slurry injection rate calculated according to the above steps, the cumulative injection volume of the slurry can be obtained by using the integration principle.

2. The method for calculating the injection rate and cumulative injection volume of dam toe plate curtain grouting according to claim 1, characterized in that: The cumulative injection amount of the slurry in step E is as follows: Where V is the cumulative injection volume; T is the total grouting time; Q i , Q i-1 t i , t i-1 Slurry injection rate at the time.

3. The method for calculating the injection rate and cumulative injection volume of dam toe plate curtain grouting according to claim 1 is characterized by: The analytical formula for the fracture grouting injection volume in step C is as follows: where r0 is the radius of the grouting hole, τ0, ν, and ρ are the initial shear strength, kinematic viscosity coefficient, and density of the slurry, respectively; β is the inclination angle of the crack; ℎ0 and ℎ1 are the grouting hole pressure head and hydrostatic pressure head, respectively.

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