An integrated calculation method for grouting diffusion and pressure dissipation processes in fractured rock masses

Abstract

This invention relates to the field of numerical simulation, specifically disclosing an integrated calculation method for the grout diffusion and pressure dissipation processes in fractured rock masses. The method discretizes the fractured region into a finite number of equally spaced annular elements and calculates the grout diffusion process using a time-progressive approach. During the calculation, the position of the grout diffusion front is tracked continuously. The method introduces grout flow control equations and fracture deformation control equations, iteratively solving the pressure and velocity fields at each time step. Ultimately, it achieves accurate calculation considering the grout diffusion and pressure dissipation processes in fractured rock masses, providing reliable reference data for grouting design in fractured rock masses and significantly improving the prediction accuracy of grouting effects.

Description

Technical Field

[0001] This invention relates to the field of numerical simulation calculation, and in particular to an integrated calculation method for the grouting diffusion and pressure dissipation process in fractured rock masses. Background Technology

[0002] The information disclosed in this background section is intended only to enhance understanding of the overall background of the invention and is not necessarily to be construed as an admission or in any way implying that such information constitutes prior art known to those skilled in the art.

[0003] Fracts within the surrounding rock are the primary water-bearing and water-conducting spaces in underground engineering, and have become a major risk source for sudden water inrush disasters during construction. Grouting, with its mechanism of injecting, filling, and cementing grout into fissures to improve the seepage prevention performance of the rock mass, has become the most commonly used method for controlling such disasters. Grouting treatment essentially involves two continuous dynamic processes: the grout filling and diffusion process, where the grout enters the water-rich fissures under grouting pressure and propagates forward; and the subsequent pressure dissipation and diffusion process, where the fissures attempt to close under in-situ stress upon completion of grouting, while residual pressure promotes the continuous diffusion of the grout. Although these two processes occur sequentially, they are both profoundly influenced by the grout-rock coupling effect and the time-varying rheological properties of the grout.

[0004] Accurate prediction of the grout diffusion process in rock mass fissure grouting projects is a prerequisite for scientific grouting design. Only based on accurate grout-rock mass coupling relationships can key grouting parameters such as grout diffusion radius and grouting pressure be obtained accurately. Current calculations of the grout diffusion process in underground engineering rock mass fissure grouting suffer from significant discrepancies between the calculated grout diffusion radius and grouting pressure values ​​and the actual engineering conditions, making it difficult to predict the grout diffusion process within rock mass fissures. Summary of the Invention

[0005] To address the aforementioned problems, this invention proposes an integrated calculation method for the diffusion and pressure dissipation processes of grouting in fractured rock masses. This method effectively solves the difficulty in predicting grout pressure, fracture aperture, and grouting radius during the diffusion and pressure dissipation processes of grouting in fractured rock masses, providing more reliable reference data for grouting design in fractured rock masses. Specifically, the technical solution of this invention is as follows.

[0006] An integrated calculation method for the grouting diffusion and pressure dissipation process in fractured rock masses includes the following steps:

[0007] (1) Set the duration of the grouting stage in the fractured rock mass to T1= j Δ t,j =1, 2, 3..., set the duration of the pressure dissipation stage after the grouting stage is completed to T2= J Δ t, J =1, 2, 3...

[0008] (2) Calculate the grouting stage number 1 j Δ t Viscosity of the slurry μ ( j Δ t and yield stress .

[0009] (3) Calculate the grouting stage ( j- 1)Δ t ~ j Δ t Grouting volume within a time period G Based on this, the grout diffusion radius of the initial iterative state in the grouting stage is calculated. Then, taking the grouting hole as the center, starting from the edge of the grouting hole, with a radius increment Δ... r The slurry diffusion region is discretized into several annular units, so as to... i , i +1 represents the number at the inner or outer boundary of a certain ring-shaped unit. i =1, 2, 3...

[0010] (4) Calculate the crack aperture at the boundary of the ring element. The average crack aperture of the annular unit Based on this, the average crack aperture change of the annular unit is calculated. , n This indicates the number of iterations.

[0011] (5) Based on the above calculate( j- 1)Δ t ~ j Δ t Change in volume of ring-shaped unit cracks over time period Then, in conjunction with the above The calculated and updated slurry diffusion radius is: .

[0012] (6) Calculate the slurry flow rate at the boundary of each annular unit within the slurry diffusion area. and slurry flow rate Thus, the average slurry flow velocity of the annular unit is obtained. .

[0013] (7) Calculate the slurry pressure at the boundary of each annular unit within the slurry diffusion area. Based on this, the crack aperture at the boundary of each annular unit is calculated and updated. .

[0014] (8) Using the above Replace the above step (4) Repeat steps (4) to (7) for the next iteration and iterate until the control index converges.

[0015] (9) Return to step (2) to calculate the next moment until the grouting is completed, and obtain the grout diffusion radius at the end of the grouting stage. convergence value Grout pressure at the boundary of each annular unit convergence value Crack aperture at the boundary of each annular unit convergence value .

[0016] (10) Calculate the pressure dissipation stage. J Δ t Viscosity of the slurry μ ( J Δ t and yield stress .

[0017] (11) Based on the above step (10), calculate the initial iterative state of the pressure dissipation stage (i.e., the number of iterations). m =1) Slurry pressure at the boundary of each annular unit within the slurry diffusion area Based on this, the crack aperture at the boundary of each annular unit within the slurry diffusion area during the pressure dissipation stage is calculated and updated. and the change in fracture aperture .

[0018] (12) Then calculate the number of iterations. m When ≥2, the volume change of the annular unit caused by pressure dissipation. Then, the slurry diffusion radius during the pressure dissipation process is calculated accordingly. Update the circular boundary node number that is closest to the slurry diffusion front during the pressure dissipation stage. .

[0019] (13) Calculate the slurry flow velocity at the boundary of each annular unit during the pressure dissipation process. and the average flow velocity of the annular unit Based on this, the slurry pressure at the boundary of the annular unit was calculated and updated to... Update the crack aperture at the boundary of the annular unit to The average crack aperture of the annular element is updated to .

[0020] (14) According to the above Perform the calculation for the next iteration step to obtain the updated values ​​of slurry flow velocity and slurry pressure at the boundary of each annular unit during the pressure dissipation stage. Repeat steps (12) to (13) for iterative calculation until the control index converges.

[0021] (15) Return to step (10) to perform the calculation for the next moment until the flow velocity at the boundary of each annular unit in the slurry diffusion region is 0, and the calculation of the pressure dissipation stage is completed.

[0022] Furthermore, in step (2), the viscosity of the slurry... Initial yield stress Calculate using the following formulas (1) and (2) respectively:

[0023] (1).

[0024] (2).

[0025] In the above formulas (1) and (2), the... The initial viscosity of the injected grout. The viscosity of the injected slurry increases over time. The initial yield stress of the injected grout. The initial yield stress of the injected grout increases with time as a function of time.

[0026] Further, in step (3), the grouting volume G Calculated using the following formula (3), where q ( t (This refers to the grouting volume relative to time.) t The function.

[0027] q ( t (This refers to the grouting volume relative to time.) t The function.

[0028] (3).

[0029] Further, in step (3), the slurry diffusion radius Calculate using the following formula (4):

[0030] (4).

[0031] In the above formula (4), the The circular boundary of the slurry diffusion front is numbered. This represents the initial aperture of the fractures in the grouted rock mass. express( j -1)∆t The grout diffusion radius at time 1, as stated at the start of grouting. equal to the radius of the grouting hole .

[0032] Furthermore, in step (4), the crack aperture... Average fracture aperture Change in average fracture aperture Calculate using the following formula (5):

[0033] (5).

[0034] In the above formula (5), the... express( j -1)Δ t Crack aperture at the boundary of a certain annular unit at a given time The convergence value. It should be noted that in the initial iteration state (i.e., n When =1), since the slurry is considered to be entirely used for the expansion of the diffusion radius, the crack aperture does not change. Therefore, in the initial iteration state... .

[0035] Furthermore, in step (5), the change volume of the crack Calculate using the following formula (6):

[0036] (6).

[0037] In the above formula (6), the , These are the radii of the inner and outer boundaries of the ring unit, respectively. The radius of the grouting hole, the As described in step (5), the calculation method is shown in formula (7) below. It should be noted that, as mentioned earlier, in the initial iteration state (i.e.... n When =1), the .

[0038] Further, in step (5), the slurry diffusion radius Calculate using the following formula (7):

[0039] (7).

[0040] In the above formula (7), the Indicates the first n The sum of the volumes of grout filling the cracks in each annular unit during the subsequent iteration calculation. , As shown in steps (3) and (4) respectively, the calculation methods are as shown in formulas (4) and (5) above.

[0041] Further, in step (6), the slurry flow rate Calculate using the following formula (8):

[0042] (8).

[0043] In the above formula (8), Representative except The total grouting volume of the remaining annular units outside the corresponding annular unit. G As described in step (3), the calculation method is as shown in formula (3) above. This indicates the grout flow rate at the grouting hole.

[0044] Further, in step (6), the slurry flow rate Calculate using the following formula (9):

[0045] (9).

[0046] In the above formula (9), the The slurry flow rate at the boundary of each annular unit is calculated as shown in formula (8) above. The calculation is as shown in the above formula (6).

[0047] Further, in step (6), the average flow rate of the slurry Calculate using the following formula (10):

[0048] (10).

[0049] In the above formula (10), the , These represent the slurry flow velocities at the inner and outer boundaries of a certain annular unit, respectively.

[0050] Further, in step (7), the slurry pressure Calculate using the following formulas (11) and (12):

[0051] (11).

[0052] (12).

[0053] In the above formulas (11) and (12), the... The hydrostatic pressure in the fissure, the , As shown in step (2), the calculation methods are as shown in formulas (1) and (2) above, respectively. As shown in step (4), the calculation method is as shown in formula (5) above. As shown in step (6), the calculation method is as shown in the above formula (9).

[0054] Furthermore, in step (7), the crack aperture... Calculate using the following formula (13):

[0055] (13).

[0056] In the above formula (13), the... The pressure at the boundary of the annular unit described in step (7) is calculated using the formulas (11) and (12) above. The critical pressure for crack deformation. The normal elastic coefficient of the rock mass: Where D is the grouting influence range and E is the elastic modulus of the rock mass. As mentioned above, This represents the initial aperture of the fractures in the grouting rock mass.

[0057] Further, in step (8), the control indicators include , They are calculated using the following formulas (14) and (15), respectively:

[0058] (14);

[0059] (15).

[0060] In the above formulas (14) and (15), the control indicators This represents the relative error in the volume change of the annular element crack in the current iteration compared to the previous iteration, wherein the... As shown in step (5), its sum The calculation method is as described in formula (6) above. The control indicators... This represents the relative error of the slurry pressure change at the boundary of the first annular unit in the current iteration compared to the previous iteration; , which indicates the first n In the next iteration, the slurry pressure at the boundary of the first annular unit at the current and previous time steps is calculated; similarly... The aforementioned , The calculation method is the same as the above formulas (11) and (12).

[0061] Furthermore, when the stated , When the control index converges, the iterative calculation for this moment is considered complete. Then, as described in step (9): return to step (2) to proceed to the next moment (i.e., the ( ) ) j +1)Δ t Calculation of time.

[0062] Further, in step (10), the μ ( J Δ t ), τ 0 ( J Δ t ) Calculated using the following formula (16):

[0063] (16).

[0064] In the above formula (16), the... The viscosity of the grout at the end of the grouting stage. The viscosity of the injected slurry increases over time. This represents the initial yield stress of the grout at the end of the grouting stage. k 𝜏 This represents the viscosity growth factor of the injected slurry over time.

[0065] Further, in step (11), the slurry pressure Calculate using the following formula (17):

[0066] (17).

[0067] In the above formula (17), the pressure dissipation begins at the initial iteration state (i.e., J When =1, m When =1), the Therefore, the initial iteration state at the start of pressure dissipation... , The crack aperture at the boundary of the annular unit at the end of the grouting stage The convergence value, This represents the initial yield stress of the grout at the end of the grouting stage.

[0068] Further, in step (11), the crack aperture... ;in: The critical pressure for crack deformation. The normal elastic coefficient of the rock mass: D represents the grouting influence range, and E represents the elastic modulus of the rock mass. As shown in step (11), the calculation method is as shown in the above formula (17).

[0069] Furthermore, in step (11), the change in the crack aperture... .in, This refers to the average value of the crack aperture convergence value at the inner and outer boundaries of the annular unit during the grouting stage. The calculation method is the same as step (9) above.

[0070] Further, in step (12), the volume change amount Calculate using the following formula (18):

[0071] (18).

[0072] In the above formula (17), the... , , These represent the changes in the diffusion radius of the slurry at the inner and outer boundaries of the annular unit during the pressure dissipation stage, and the changes in the average crack aperture of the annular unit, respectively. , These represent the crack aperture and average crack aperture at the inner boundary of each annular unit in the grout diffusion zone within the cracks caused by pressure dissipation, respectively. J When =1, in the initial iteration state of the pressure dissipation stage, the diffusion radius distribution is the same as that in the grouting diffusion stage, that is... , .

[0073] Furthermore, in step (12), the slurry diffusion radius during the pressure dissipation process is... Calculate using the following formula (19):

[0074] (19).

[0075] In the above formula (19), the... , The calculation method is shown in formula (18). This represents the sum of the volume changes of each annular unit caused by pressure dissipation. express J ∆ t The slurry diffusion radius in the initial iteration state during the pressure dissipation phase.

[0076] Furthermore, in step (12), the circular boundary node closest to the slurry diffusion front during the pressure dissipation stage is numbered. [ ] is the left rounding symbol. express J ∆ t The slurry diffusion radius during the pressure dissipation process at a given time. The convergence value. The radius of the grouting hole is represented by Δ. r As shown in step (3).

[0077] Furthermore, in step (13), the slurry flow rate at the boundary of each annular unit during the pressure dissipation process... Calculate using the following formula (20):

[0078] , of which: (20).

[0079]

[0080] In the above formula (20), the... As shown in step (12), the calculation method is as shown in formula (18). This represents the diffusion radius of the slurry at the boundary of the annular unit during the dissipation phase. The calculation method is shown in formula (18). As shown in step (12), the calculation method is as shown in formula (19) above. As shown in step (12).

[0081] Further, in step (13), the average flow rate Calculate using the following formula (21):

[0082] (twenty one).

[0083] Further, in step (13), the slurry pressure Calculate using the following formulas (22) and (23):

[0084] (twenty two).

[0085] (twenty three).

[0086] In the above formula (22), the... μ ( J Δ t ), τ 0 ( J Δ t As described in step (10), the calculation method is shown in formula (16). As described in step (13), the calculation method is as shown in the above formula (20). The hydrostatic pressure in the fissure is expressed in the same formula (11) above.

[0087] Furthermore, in step (13), the crack aperture... Calculate using the following formula (24):

[0088] (twenty four).

[0089] In the above formula (24), the... As described in step (13), the calculation method is as shown in formula (23) above. The critical pressure for crack deformation. The normal elastic coefficient of the rock mass: Where D is the grouting influence range and E is the elastic modulus of the rock mass.

[0090] Further, in step (13), the average crack aperture of the annular unit Calculate using the following formula (25):

[0091] (25).

[0092] Furthermore, in step (14), the control index includes: the relative error of the change volume of the annular unit crack in the current iteration compared to the previous iteration. The relative error of the change in slurry pressure at the inner boundary of the first annular unit. For reference, see formulas (14) and (15) above. Specifically: the above , Calculate using the following formulas (26) and (27).

[0093] (26);

[0094] (27).

[0095] Further, in step (14), the control index , When the control index converges, the iterative calculation at this moment is considered complete.

[0096] Furthermore, in step (15), when the flow velocity at the boundary of each annular unit of the slurry diffusion region... At that time, the calculation result is obtained: the slurry diffusion radius mentioned in step (12). convergence value The slurry pressure mentioned in step (13) convergence value With fracture aperture convergence value The calculation of the pressure dissipation stage ends, which means the calculation of this method is completed.

[0097] Compared with the prior art, the present invention has at least the following beneficial technical effects:

[0098] In rock mass fissure grouting projects, the diffusion process of grout within the fissures directly determines the success or failure of the grouting project. Therefore, accurate prediction of the grout diffusion process in rock mass fissures is a prerequisite for scientific grouting design. In particular, accurately predicting the grout diffusion range and grout pressure distribution is of great significance for grouting projects. However, current calculations of the grout diffusion process in underground engineering rock mass fissure grouting suffer from significant discrepancies between the calculated grout diffusion radius and grout pressure values ​​and the actual engineering conditions, making it difficult to predict the grout diffusion process in rock mass fissures. To address this, on the one hand, the calculation method proposed in this invention not only considers the grout-rock mass coupling effect but also introduces the dual time-varying characteristics of grout viscosity and yield stress based on the grout diffusion theoretical calculation model, thereby effectively overcoming the problem of insufficient accuracy in the calculation results. On the other hand, this invention proposes a pressure dissipation model calculation method based on the interaction between the elastic closure of the rock mass on both sides of the fissure and the grout yield stress after grouting is stopped. The pressure dissipation process of grout in rock fissures is a complex fluid-structure interaction process involving elastic deformation of the rock mass and solidification of the grout. Since the grout flow velocity is very small after the grouting is completed and the external power source is lost, this invention performs iterative calculations with a flow velocity of 0 in the initial iteration state at the initial moment of pressure dissipation. The grout pressure in the initial iteration state at the initial moment of pressure dissipation is calculated from the flow velocity and related quantities such as the fissure aperture and diffusion radius obtained from the active grouting stage. Then, the fissure aperture distribution in this state is obtained. Due to the change in fissure aperture, the rock mass on both sides of the fissure squeezes the grout to generate a new flow velocity and increases the grout diffusion radius. The calculation continues in the next iteration step with the newly obtained flow velocity, fissure aperture and diffusion radius. After reaching the convergence state, the calculation of the next time step is carried out until the grout stops flowing, and the calculation of the pressure dissipation stage is completed. The computational model proposed in this invention not only reveals the deformation mechanism of fracture closure and the formation mechanism of "residual pressure" within the fracture during pressure dissipation, but also scientifically simulates and predicts the diffusion process of grout in two continuous processes: grout diffusion and pressure dissipation. It provides more reliable and accurate reference data on the diffusion range and pressure distribution of grout after grouting is stopped in engineering, and significantly improves the prediction accuracy of grouting effect in fractured rock masses. Attached Figure Description

[0099] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0100] Figure 1 The viscosity of the slurry in the following examples is... and yield stress With time Δ t The relationship diagram of the changes.

[0101] Figure 2 The following is a schematic diagram of the distribution of the ring units in the embodiments.

[0102] Figure 3 The following examples show the diffusion radius of the slurry over time under different initial crack openings.

[0103] Figure 4 The following examples show the spatial distribution of grout pressure within the fractures corresponding to different initial fracture openings.

[0104] Figure 5 The following is a spatial distribution diagram of the fracture aperture corresponding to different initial fracture apertures in the embodiments.

[0105] Figure 6 The following examples show the slurry pressure distribution after the pressure dissipation stage for different initial crack openings.

[0106] Figure 7 The following examples show the spatial distribution of the final crack aperture within the crack under different initial crack apertures. Detailed Implementation

[0107] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0108] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms “comprising” and / or “including” are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0109] For ease of description, the words "up," "down," "left," and "right" appearing in this invention only indicate that they are consistent with the up, down, left, and right directions of the accompanying drawings themselves. They do not limit the structure and are merely for the purpose of facilitating the description of this invention and simplifying the description. They do not indicate or imply that the device or component referred to needs to have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0110] The method for calculating the rheological relationship of grout during the grouting process of fractured rock mass in submarine tunnels according to the present invention will now be further explained with reference to the accompanying drawings and specific embodiments.

[0111] This embodiment uses a granite micro-fracture grouting and water plugging project for a subway in a certain city as an example. The water-rich fractured rock mass suffered severe water leakage, with large-area, rain-like, and stream-like leakage phenomena occurring in the tunnel arch and sidewalls. Grouting was used to seal the fracture water. Ordinary single-component cement grout was used as the grouting material, with a cement grout mix ratio of W / C=1.0, and the grouting volume... q ( t Set to: q ( t =50L / min, initial aperture of rock mass fracture b 0 Four grouting thicknesses were selected: 0.5mm, 0.4mm, 0.3mm, and 0.2mm. The grouting influence range D=5m, the rock mass elastic modulus E=80GPa, and the grouting hole radius... The critical deformation pressure of the fracture is equal to the initial geostress. hydrostatic pressure Then, calculations are performed on the grouting diffusion process and pressure dissipation process of the fractured rock mass, specifically including the following steps:

[0112] (1) Set a uniform time increment ∆ during the grouting diffusion and pressure dissipation stage of fractured rock mass. t =0.1s. Where: the grouting stage duration is set to T1= j Δ t =300s, obtained j =1, 2, 3...3000.

[0113] (2) Calculate the first number using the following formulas (1) and (2) respectively. j Δ t Viscosity of the slurry μ ( j Δ t and yield stress τ 0 ( j Δ t ):

[0114] (1).

[0115] (2).

[0116] In the above formulas (2) and (3), the initial viscosity of the injected slurry is... The viscosity of the injected slurry increases with time. Initial yield stress of the injected grout The growth rate of the initial yield stress of the injected grout over time The viscosity of the slurry was calculated. and yield stress The relationships that change over time are as follows: Figure 1 The middle left section is shown (with time T1 as the dividing line).

[0117] Then, the duration of the grouting stage is calculated according to the following formula (3). j- 1)Δ t ~ j Δ t Grouting volume within a time period G :

[0118] (3).

[0119] Substituting each parameter into the above formula (3), we obtain the ( j- 1)Δ t ~ j Δ t Grouting volume within a time period .

[0120] (3) At the grouting volume G Based on this, the initial iterative state (i.e., the number of iterations) of the grouting stage is calculated according to the following formula (4). n =1) Slurry diffusion radius In the initial iteration state, the slurry is considered to be used entirely for the expansion of the diffusion radius.

[0121] (4).

[0122] In the above formula (4), the The number indicates the circular boundary of the slurry front. This represents the initial aperture of the fractures in the grouted rock mass. express( j -1)∆ t The grout diffusion radius at time 1, as stated at the start of grouting. equal to the radius of the grouting hole .

[0123] Then, taking the grouting hole as the center, starting from the edge of the grouting hole, increment the radius... The slurry diffusion region is discretized into several annular units, and... i , i +1 represents the number at the inner or outer boundary of a certain ring-shaped unit. i =1, 2, 3..., such as Figure 2 As shown.

[0124] (4) Calculate the crack aperture at the boundary of the annular unit using the following formula (5). The average crack aperture of the annular unit Based on this, the average crack aperture change of the annular unit is calculated. , n This indicates the number of iterations. n =1, 2, 3...

[0125] (5).

[0126] In the above formula (5), the... express( j -1)Δ t Crack aperture at the boundary of a certain annular unit at a given time The convergence value. It should be noted that in the initial iteration state (i.e., n When =1), since the slurry is considered to be entirely used for the expansion of the diffusion radius, the crack aperture does not change. Therefore, in the initial iteration state... .

[0127] (5) The change in average crack aperture of the annular unit obtained in the previous step. And calculate using the following formula (6) j- 1)Δ t ~ j Δ t Change in volume of the ring-shaped unit crack within a time period (i.e., within 0.1s). :

[0128] (6).

[0129] In the above formula (6), the , These are the radii of the inner and outer boundaries of the ring unit, respectively. The radius of the grouting hole, the As described in step (5), the calculation method is shown in formula (7) below. It should be noted that since the slurry is considered entirely for the expansion of the diffusion radius, the crack opening does not change. Therefore, in the initial iteration state (i.e.... n When =1), the .

[0130] Then, based on the average crack opening of the annular unit obtained in step (4) above, And in conjunction with the following formula (7), the updated slurry diffusion radius is calculated as follows: :

[0131] (7).

[0132] In the above formula (7), the Indicates the first nThe sum of the volumes of grout filling the cracks in each annular unit during the next iteration calculation, the , As shown in steps (3) and (4) respectively, the calculation methods are as shown in formulas (4) and (5) above. Different initial crack openings are calculated. The diffusion radius of the slurry over time like Figure 3 As shown.

[0133] (6) Calculate the slurry flow rate at the boundary of each annular unit within the slurry diffusion area. and slurry flow rate Thus, the average slurry flow velocity of the annular unit is obtained. Wherein: the slurry flow rate Calculate using the following formula (8):

[0134] (8).

[0135] In the above formula (8), Representative except The total grouting volume of the remaining annular units outside the corresponding annular unit. G The grouting volume mentioned in step (3) is calculated using the formula (3) above. This indicates the grout flow rate at the grouting hole. Based on the aforementioned calculations, the grouting volume... , The result obtained after substituting the parameters. Used for the next step of slurry flow rate The calculation.

[0136] Then, the average fracture aperture is obtained by using the following formula (9) and in combination with the above step (4). Calculate the slurry flow rate :

[0137] (9).

[0138] In the above formula (9), the The slurry flow rate at the boundary of each annular unit is calculated as shown in formula (8) above. The calculation is as shown in the above formula (6).

[0139] The average flow velocity of the annular unit is then calculated using the following formula (10). , wherein , These represent the slurry flow velocities at the inner and outer boundaries of a certain annular unit, respectively.

[0140] (10).

[0141] (7) Calculate the slurry pressure at the boundary of each annular unit within the slurry diffusion area. Based on this, the crack aperture at the boundary of each annular unit is calculated and updated. . Specifically:

[0142] First, the slurry pressure is calculated using the following formulas (11) and (12). :

[0143] (11).

[0144] (12).

[0145] In the above formulas (11) and (12), the... This represents the hydrostatic pressure within the fracture, as previously stated. The , As shown in step (2), the calculation methods are as shown in formulas (1) and (2) above, respectively. As shown in step (4), the calculation method is as shown in formula (5) above. As shown in step (6), the calculation method is as shown in the above formula (9).

[0146] Then, based on the above... And calculate the updated crack aperture at the boundary of each annular unit by combining the following formula (13). :

[0147] (13).

[0148] In the above formula (13), the... The pressure at the boundary of the annular unit described in step (7) is calculated using the formulas (11) and (12) above. p l The critical pressure for crack deformation. The normal elastic coefficient of the rock mass: Where D is the grouting influence range and E is the elastic modulus of the rock mass, we obtain As mentioned earlier, This represents the initial aperture of the fractures in the grouting rock mass.

[0149] (8) Using the above Replace the above step (4) Repeat steps (4) to (7) for the next iteration and iterate until the control index converges. , Specifically, iterative calculation n =100 iterations, obtaining the relative error of the change volume of the annular element crack in the current iteration compared to the previous iteration. The relative error between this iteration and the previous iteration in the calculation of the slurry pressure change at the boundary of the first annular unit. The iteration calculation is considered complete at this moment when the control index converges.

[0150] Among them, the The following formula (14) is used to calculate the... Calculate using the following formula (15).

[0151] (14);

[0152] (15).

[0153] In the above formulas (14) and (15), the... As shown in step (5), its sum The calculation method is as described in formula (6) above. , which indicates the first n In the next iteration, the slurry pressure at the boundary of the first annular unit at the current and previous time steps is calculated; similarly... The aforementioned , The calculation method is the same as the above formulas (11) and (12).

[0154] (9) Return to step (2) to proceed to the next moment (i.e., the () j +1)Δ t The calculation of the time (i.e., the end time of the grouting stage) continues until the grouting is completed, thus obtaining the end time of the grouting stage (i.e., the end time of the grouting stage). j +1)Δ t The slurry diffusion radius at 300s (time = 300s) convergence value Grout pressure at the boundary of each annular unit convergence value Crack aperture at the inner boundary of each annular unit convergence value Each as Figure 4 , Figure 5 As shown.

[0155] (10) The duration of the pressure dissipation stage after the grouting stage is set as follows: ，J =1, 2, 3... Calculate the first... in the pressure dissipation process according to the following formula (16). J Δ t Viscosity of the slurry Yield stress :

[0156] (16).

[0157] In the above formula (16), the viscosity of the grout at the end of the grouting stage is... The viscosity of the injected slurry increases with time. The initial yield stress of the grout at the end of the grouting stage. The growth rate of the initial yield stress of the injected grout over time. After inputting the parameters, the viscosity of the slurry is obtained. Yield stress Relationships changing over time, such as Figure 1 The middle right section (in terms of time) (This is the dividing line).

[0158] (11) Based on the calculation results of step (10) above, calculate the initial iterative state of the pressure dissipation stage (i.e., the number of iterations). m =1) Slurry pressure at the boundary of each annular unit within the slurry diffusion area Based on this, the crack aperture at the boundary of each annular unit within the slurry diffusion area during the pressure dissipation stage is calculated and updated. and the change in fracture aperture Specifically, this includes:

[0159] First, calculate the slurry pressure according to the following formula (17). :

[0160] (17).

[0161] In the above formula (17), the pressure dissipation begins at the initial iteration state (i.e., J When =1, m When =1), the Therefore, the initial iteration state at the start of pressure dissipation... ,in: The crack aperture at the boundary of the annular unit at the end of the grouting stage The convergence value is shown in step (9) above. The initial yield stress of the grout at the end of the grouting stage is shown in the above formula (16).

[0162] Then, based on the slurry pressure obtained in the previous step... Calculate the crack aperture. ;in: The critical pressure for crack deformation. The normal elastic coefficient of the rock mass: D represents the grouting influence range, and E represents the elastic modulus of the rock mass. .

[0163] (12) Then calculate the number of iterations. m When ≥2, the volume change of the annular unit caused by pressure dissipation. Then, the slurry diffusion radius during the pressure dissipation process is calculated accordingly. Update the circular boundary node number that is closest to the slurry diffusion front during the pressure dissipation stage. . Specifically:

[0164] First, calculate the volume change according to the following formula (18). :

[0165] (18).

[0166] In the above formula (17), the... , , These represent the changes in the diffusion radius of the slurry at the outer and inner boundaries of the annular unit during the pressure dissipation stage, and the changes in the average crack aperture of the annular unit, respectively. , These represent the crack aperture and average crack aperture at the inner boundary of each annular unit in the grout diffusion zone within the cracks caused by pressure dissipation, respectively. J When =1, in the initial iteration state of the pressure dissipation stage, the diffusion radius distribution is the same as that in the grouting diffusion stage, that is... , .

[0167] Then, based on the previous step... The diffusion radius of the slurry during the pressure dissipation process is calculated using the following formula (19). .

[0168] (19).

[0169] In the above formula (19), the... , The calculation method is shown in formula (18). This represents the sum of the volume changes of each annular unit caused by pressure dissipation. express J ∆ t= ∆ t The slurry diffusion radius in the initial iteration state during the pressure dissipation phase.

[0170] Then, calculate the circular boundary node number. [ ] is the left rounding symbol. express J ∆ t The slurry diffusion radius during the pressure dissipation process at a given time. The convergence value. The radius of the grouting hole is represented by Δ. r As shown in step (3), the value is taken as = 0.2m. Substitute the values ​​of each parameter, for example, in J ∆ t =350s, At that time, , .

[0171] (13) Calculate the slurry flow velocity at the boundary of each annular unit during the pressure dissipation process. and the average flow velocity of the annular unit Based on this, the slurry pressure at the boundary of the annular unit was calculated and updated to... Update the crack aperture at the boundary of the annular unit to The average crack aperture of the annular element is updated to . Specifically:

[0172] First, the slurry velocity at the boundary of each annular unit during the pressure dissipation process is calculated according to the following formula (20). :

[0173] (20).

[0174] In the above formula (20), the... As shown in step (12), the calculation method is as shown in formula (18). This represents the diffusion radius of the slurry at the boundary of the annular unit during the dissipation phase. The calculation method is shown in formula (18). As shown in step (12), the calculation method is as shown in formula (19) above. As shown in step (12).

[0175] Then, based on the calculation results of the previous step, the average flow velocity is calculated using the following formula (21). :

[0176] (twenty one).

[0177] Then, the slurry pressure is calculated according to the following formulas (22) and (23). :

[0178] (twenty two).

[0179] (twenty three).

[0180] In the above formula (22), the... , As described in step (10), the calculation method is shown in formula (16). As described in step (13), the calculation method is as shown in the above formula (20). This represents the hydrostatic pressure in the fracture, as previously mentioned, and its value is 20 kPa.

[0181] Then, the fracture aperture is calculated according to the following formula (24). :

[0182] (twenty four).

[0183] In the above formula (24), the... As described in step (13), the calculation method is as shown in formula (23) above. The critical pressure for crack deformation, as mentioned earlier, is 0.8 MPa. The normal elastic coefficient of the rock mass: D represents the grouting influence range, and E represents the elastic modulus of the rock mass. .

[0184] Then, the average crack aperture of the annular unit is calculated according to the following formula (25). :

[0185] (25).

[0186] (14) Using the above Instead of the crack aperture at the inner boundary of the annular unit in the above formula (18), Then proceed to the next iteration step and repeat steps (12) to (13) for iterative calculation. m =After 100 iterations, until the control index converges. This control index includes the relative error of the change volume of the ring-shaped element crack in the current iteration compared to the previous iteration. The relative error of the change in slurry pressure at the inner boundary of the first annular unit. For reference, see formulas (14) and (15) above. Specifically: the above , Calculate using the following formulas (26) and (27).

[0187] (26);

[0188] (27).

[0189] (15) Return to step (10) above to proceed to the next moment (i.e. ( J +1)Δ t The calculation of () when the calculation reaches ( J +1)Δ t =350s, the flow velocity at the boundary of each annular unit in the slurry diffusion region is 0, and the calculation result is: the slurry diffusion radius mentioned in step (12) is obtained. convergence value The slurry pressure mentioned in step (13) convergence value With fracture aperture convergence value The calculation results are as follows Figure 6 , Figure 7 As shown, the calculation of the pressure dissipation stage ends, which means the calculation of this method is complete. Based on the above calculation results, it can be used to more accurately predict the grout diffusion range, fracture deformation and grout pressure distribution after grouting, providing more reliable and accurate reference data for grouting design of fractured rock masses, and significantly improving the prediction accuracy of grouting effect of fractured rock masses.

[0190] Finally, it should be noted that any modifications, equivalent substitutions, or improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention. Although specific embodiments of this invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of this invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of this invention are still within the scope of protection of this invention.

Claims

1. An integrated calculation method for the grouting diffusion and pressure dissipation process in fractured rock masses, characterized in that, Includes the following steps: (1) Set the duration of the grouting stage of the fractured rock mass to 1. ，j =1, 2, 3..., setting the duration of the pressure dissipation phase after the grouting stage is completed to... ，J =1, 2, 3...; (2) Perform iterative calculations on the grouting stage until the end of the stage to obtain: grout diffusion radius convergence value Grout pressure at the boundary of each annular unit convergence value Crack aperture at the boundary of each annular unit convergence value ; (3) Calculate the pressure dissipation stage. Viscosity of the slurry and yield stress ; (4) Based on the above step (3), calculate the initial iterative state of the pressure dissipation stage, i.e., the number of iterations. m When =1, the slurry pressure at the boundary of each annular unit within the slurry diffusion region is... Based on this, the crack aperture at the boundary of each annular unit within the slurry diffusion area during the pressure dissipation stage is calculated and updated. and the change in fracture aperture ; (5) Then calculate the number of iterations. m When ≥2, the volume change of the annular unit caused by pressure dissipation. Then, the slurry diffusion radius during the pressure dissipation process is calculated accordingly. Update the circular boundary node number that is closest to the slurry diffusion front during the pressure dissipation phase. ; (6) Calculate the slurry flow velocity at the boundary of each annular unit during the pressure dissipation process. and the average flow velocity of the annular unit Based on this, the slurry pressure at the boundary of the annular unit was calculated and updated to... Update the crack aperture at the boundary of the annular unit to The average crack aperture of the annular element is updated to ; (7) According to the above Perform the calculation for the next iteration step to obtain the updated values ​​of slurry flow velocity and slurry pressure at the boundary of each annular unit during the pressure dissipation stage. Repeat steps (5) to (6) for iterative calculation until the control index converges. (8) Return to step (3) to perform the calculation for the next moment until the flow velocity at the boundary of each annular unit in the slurry diffusion region is 0, and the calculation of the pressure dissipation stage is completed.

2. The integrated calculation method for grouting diffusion and pressure dissipation process in fractured rock mass according to claim 1, characterized in that, Step (2) involves iterative calculations for the grouting stage, including the following steps: (2.1) Calculate the first grouting stage Viscosity of the slurry and yield stress ; (2.2) Calculate the pulp stage ( j- 1)Δ t ~ j Δ t Grouting volume within a time period G Based on this, the grout diffusion radius of the initial iterative state in the grouting stage is calculated. Then, taking the grouting hole as the center, starting from the edge of the grouting hole, increment by radius... The slurry diffusion region is discretized into several annular units, so as to... i , i +1 represents the number at the inner or outer boundary of a certain ring-shaped unit. i =1, 2, 3...; (2.3) Calculate the crack aperture at the boundary of the ring element. The average crack aperture of the annular unit Based on this, the average crack aperture change of the annular unit is calculated. , n Indicates the number of iterations; (2.4) Based on the above calculate( j- 1)Δ t ~ j Δ t Change in volume of ring-shaped unit cracks over time period Then, in conjunction with the above The calculated and updated slurry diffusion radius is: ; (2.5) Calculate the slurry flow rate at the boundary of each annular unit within the slurry diffusion area. and slurry flow rate Thus, the average slurry flow velocity of the annular unit is obtained. ; (2.6) Calculate the slurry pressure at the boundary of each annular unit within the slurry diffusion region. Based on this, the crack aperture at the boundary of each annular unit is calculated and updated. ; (2.7) Using the above Replace the above step (4) , and repeat steps (2.3) to (2.6) for the next iteration, and iterate until the control index converges; (2.8) Return to step (2) to calculate the next moment until the grouting is completed, and obtain the grout diffusion radius at the end of the grouting stage. convergence value Grout pressure at the boundary of each annular unit convergence value Crack aperture at the boundary of each annular unit convergence value .

3. The integrated calculation method for grouting diffusion and pressure dissipation process in fractured rock mass according to claim 2, characterized in that, In step (2.1), the viscosity of the slurry Initial yield stress Calculate using the following formulas (1) and (2) respectively: （1）； （2）； In the above formulas (1) and (2), the... The initial viscosity of the injected grout. The viscosity of the injected slurry increases over time; the... The initial yield stress of the injected grout. The initial yield stress of the injected grout increases with time as a function of time. Alternatively, in step (2.2), the grouting volume... G Calculated using the following formula (3), where q ( t (This refers to the grouting volume relative to time.) t The function; （3）； Alternatively, in step (2.2), the slurry diffusion radius... Calculate using the following formula (4): (4) ； In the above formula (4), the The circular boundary of the slurry diffusion front is numbered. This represents the initial aperture of the fractures in the grouted rock mass. express The grout diffusion radius at time 1, as stated at the start of grouting. equal to the radius of the grouting hole .

4. The integrated calculation method for grouting diffusion and pressure dissipation process in fractured rock mass according to claim 2, characterized in that, In step (2.3), the crack aperture... Average fracture aperture Change in average fracture aperture Calculate using the following formula (5): （5）； In the above formula (5), the... express Crack aperture at the boundary of a certain annular unit at a given time The convergence value; the value described in the initial iteration state. ; Alternatively, in step (2.4), the change in crack volume... Calculate using the following formula (6): （6）； In the above formula (6), the , These are the radii of the inner and outer boundaries of the ring unit, respectively; Let be the radius of the grouting hole. In the initial iteration state, the... ; Alternatively, in step (2.4), the slurry diffusion radius... Calculate using the following formula (7): （7）； In the above formula (7), the Indicates the first n The sum of the volumes of grout filling the cracks in each annular unit during the next iteration calculation; Alternatively, in step (2.5), the slurry flow rate... Calculate using the following formula (8): （8）； In the above formula (8), Representative except The total grouting volume of the remaining annular units other than the corresponding annular unit; the Indicates the grout flow rate at the grouting hole; Alternatively, in step (2.5), the slurry flow rate Calculate using the following formula (9): （9）； In the above formula (9), the The slurry flow rate at the boundary of each annular unit; Alternatively, in step (2.5), the average flow rate of the slurry... Calculate using the following formula (10): （10）； In the above formula (10), the , These represent the slurry flow velocities at the inner and outer boundaries of a certain annular unit, respectively.

5. The integrated calculation method for grouting diffusion and pressure dissipation process in fractured rock mass according to claim 2, characterized in that, In step (2.6), the slurry pressure Calculate using the following formulas (11) and (12): （11）； （12）； In the above formulas (11) and (12), the... This represents the hydrostatic pressure within the fracture. Alternatively, in step (2.6), the crack aperture... Calculate using the following formula (13): （13）； In the above formula (13), the... The critical pressure for crack deformation. The normal elastic coefficient of the rock mass: Where D is the grouting influence range and E is the elastic modulus of the rock mass; The initial aperture of the fracture in the grouted rock mass; Alternatively, in step (2.7), the control indicators include , They are calculated using the following formulas (14) and (15), respectively: （14）； （15）； In the above formulas (14) and (15), the control indicators The control index represents the relative error of the change volume of the ring-shaped element crack in the current iteration compared to the previous iteration. This represents the relative error of the slurry pressure change at the boundary of the first annular unit in the current iteration compared to the previous iteration; , which indicates the first n In the next iteration calculation, the slurry pressure at the boundary of the first annular unit at the current moment and the previous moment; ; Or, when the stated , When the control index converges, the iterative calculation for this moment is considered complete; then, as described in step (2.8), return to step (2.1) to perform the calculation for the next moment.

6. The integrated calculation method for grouting diffusion and pressure dissipation process in fractured rock mass according to claim 2, characterized in that, In step (3), the , Calculate using the following formula (16): （16）； In the above formula (16), the... The viscosity of the grout at the end of the grouting stage. The viscosity of the injected slurry increases over time; the... The initial yield stress of the grout at the end of the grouting stage; k 𝜏 This represents the viscosity growth factor of the injected slurry over time.

7. The integrated calculation method for grouting diffusion and pressure dissipation process in fractured rock mass according to claim 2, characterized in that, In step (4), the slurry pressure Calculate using the following formula (17): （17）； In the above formula (17), under the initial iteration state at the start of pressure dissipation, the... Therefore, the initial iteration state at the start of pressure dissipation... , The crack aperture at the boundary of the annular unit at the end of the grouting stage The convergence value, The initial yield stress of the grout at the end of the grouting stage; Alternatively, in step (4), the change in crack aperture... ;in, .

8. The integrated calculation method for grouting diffusion and pressure dissipation process in fractured rock mass according to claim 2, characterized in that, In step (5), the volume change amount Calculate using the following formula (18): （18）； In the above formula (17), the... , , These represent the changes in the diffusion radius of the slurry at the inner and outer boundaries of the annular unit during the pressure dissipation stage, and the changes in the average crack aperture of the annular unit, respectively. , These represent the crack aperture and average crack aperture at the boundary of each annular unit in the slurry diffusion zone within the crack caused by pressure dissipation, respectively. when J When =1, in the initial iteration state of the pressure dissipation stage, the diffusion radius distribution is the same as that in the grouting diffusion stage, that is... , ; Alternatively, in step (5), the slurry diffusion radius during the pressure dissipation process... Calculate using the following formula (19): （19）； In the above formula (19), the... This represents the sum of the volume changes of each annular unit caused by pressure dissipation; the... express The slurry diffusion radius in the initial iterative state during the pressure dissipation phase at any given moment; Alternatively, in step (5), the circular boundary node closest to the slurry diffusion front during the pressure dissipation stage is numbered. [ ] is the left rounding symbol. express The slurry diffusion radius during the pressure dissipation process at a given time. The convergence value; This indicates the radius of the grouting hole.

9. The integrated calculation method for grouting diffusion and pressure dissipation process in fractured rock mass according to claim 2, characterized in that, In step (6), the slurry flow velocity at the boundary of each annular unit during the pressure dissipation process... Calculate using the following formula (20): （20）； Alternatively, in step (6), the average flow velocity Calculate using the following formula (21): （21）； Alternatively, in step (6), the slurry pressure Calculate using the following formulas (22) and (23): （22）； （23）； Alternatively, in step (6), the crack aperture... Calculate using the following formula (24): （24）； In the above formula (24), the... The critical pressure for crack deformation. The normal elastic coefficient of the rock mass: Where D is the grouting influence range and E is the elastic modulus of the rock mass; Alternatively, in step (6), the average crack opening of the annular unit Calculate using the following formula (25): （25）。 10. The integrated calculation method for grouting diffusion and pressure dissipation process in fractured rock mass according to claim 2, characterized in that, In step (7), the control index includes: the relative error of the change volume of the annular unit crack in the current iteration compared with the previous iteration. The relative error of the change in slurry pressure at the inner boundary of the first annular unit. It is calculated using the following formulas (26) and (27); （26）； （27）； Alternatively, the control indicators described in step (7) , When the control index converges, the iterative calculation at this moment is considered complete; or, in step (8), when the flow velocity at the boundary of each annular unit in the slurry diffusion region... Then, the calculation result is obtained: the slurry diffusion radius mentioned in step (5) convergence value The slurry pressure mentioned in step (6) convergence value With fracture aperture convergence value The calculation of the pressure dissipation stage ends, which means the calculation of this method is completed.

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