Fractured rock mass surrounding rock grouting reinforcement design method based on multi-parameter coupling

Abstract

The invention provides a fractured rock mass surrounding rock grouting reinforcement design method based on multi-parameter coupling, and relates to the technical field of surrounding rock grouting reinforcement. By establishing a multi-parameter coupling joint probability distribution model, spatial structure characteristics of a main fracture and branch fractures and a dynamic evolution process of grouting pressure induced fractures are accurately described; statistical inference and dynamic correction of fracture parameters are realized; differential reinforcement is implemented for different fracture levels by adopting a sectional grouting strategy, and meanwhile, an optimal combination of grouting pressure and time is scientifically determined by combining physical constraint conditions and an optimization algorithm. According to the method, the grouting reinforcement precision and efficiency are effectively improved, slurry waste and construction risks are reduced, the stability and construction safety of the surrounding rock are guaranteed, data inference and scheme optimization can be conducted without a large amount of field data, and therefore the reliability of the rock mass surrounding rock grouting reinforcement technology is greatly improved, the application range of the rock mass surrounding rock grouting reinforcement technology is greatly widened, and the method is suitable for popularization and application. And the reinforcement requirement in a complex engineering environment is met.

Description

Technical Field

[0001] This invention relates to the field of surrounding rock grouting reinforcement technology, specifically to a design method for grouting reinforcement of fractured rock masses based on multi-parameter coupling. Background Technology

[0002] In tunnel excavation, underground mining, and foundation engineering construction, the surrounding rock often exhibits complex fracture systems, leading to reduced stability and structural damage, severely impacting project safety and construction progress. Traditional grouting reinforcement methods rely heavily on empirical parameters and single fracture characteristics, neglecting the multi-parameter coupling relationship between main and branch fractures, as well as the dynamic influence of grouting pressure on fracture induction. Furthermore, the difficulty in accurately measuring the parameters of branch fractures makes it challenging to precisely predict and control the grouting effect, thus reducing the overall grouting effectiveness. In addition, existing technologies typically fail to effectively reflect the number and size of fractures during grouting and their nonlinear response characteristics over time, which affects the scientific validity and engineering applicability of reinforcement schemes in complex rock environments.

[0003] In the prior art, CN120508175A discloses an adaptive grouting control and sealing method based on real-time monitoring of mining-induced fractures, relating to the fields of mine safety engineering and hydrogeology. By coordinating the grouting mechanism, data monitoring system, data acquisition and processing module, and adaptive control module, automation and intelligence of grouting protection can be achieved. By introducing the fracture roughness coefficient and time-dependent viscosity, the flow resistance of rough fractures and the time-varying rheological characteristics of the grout are quantified, reducing the calculation error of the grout diffusion radius. Although this scheme can perform adaptive adjustments, it relies on a complex sensing system and real-time field data. When the collected sensor data is insufficient, it is difficult to systematically invert the fracture evolution law, thus limiting the system's accuracy and applicability.

[0004] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0005] The purpose of this invention is to provide a design method for grouting reinforcement of fractured rock masses based on multi-parameter coupling, so as to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A design method for grouting reinforcement of fractured rock mass surrounding rock based on multi-parameter coupling, the specific steps of which include: S1: Collect surrounding rock samples with different rock mass types and fractures. Based on the fracture classification method, divide the fractures on the surrounding rock samples into main fractures and branch fractures, obtain the fracture parameters of the main fractures and branch fractures of the surrounding rock samples, and use them as the first observation data. S2: Grouting tests were conducted on the surrounding rock samples at a fixed grouting pressure, and grouting tests were conducted on the surrounding rock samples at different pressures. After the tests were completed, the fracture parameters of the new branch fractures generated by grouting in the surrounding rock samples were collected and used as the second observation data. S3: Based on statistical analysis and joint probability distribution methods, the first and second observation data are processed respectively to construct a first joint probability distribution model corresponding to the rock mass type and about the main fracture and branch fracture, and a second joint probability distribution model about the grouting pressure and branch fracture; S4: Collect the rock mass type and fracture parameters of the main fracture in the surrounding rock of the area to be grouted. Based on the rock mass type of the surrounding rock in the area to be grouted, select the corresponding first joint probability distribution model to obtain the fracture parameters of the branch fractures. Then, formulate a segmented grouting strategy according to the rock mass type of the surrounding rock, the fracture parameters of the main fracture, and the fracture parameters of the branch fractures. S5: Based on the second joint probability distribution model and grouting strategy corresponding to the rock mass type of the surrounding rock in the area to be grouted, the fracture parameters of the branch fractures are modified. The optimization objective is to minimize the total number of branch fractures. The optimization algorithm is used to solve the problem and obtain the grouting pressure and grouting time of the segmented grouting strategy at different stages, thereby optimizing the segmented grouting strategy.

[0007] Preferably, the fracture parameters include the number of fractures, the fracture length, and the fracture aperture; The construction logic of the first joint probability distribution model is as follows: Statistical analysis was performed on the fracture length of the main fracture to obtain its probability distribution type; A Poisson distribution was fitted to the number of branch fractures to establish a distribution function between the number of branch fractures and the fracture length of the main fracture. Edge probability distributions were fitted to the fracture length and fracture aperture of the branch fractures to obtain the distribution functions between the fracture length and fracture aperture of the branch fractures and the fracture length of the main fracture, and the Copula function was used for coupling. Using the distribution function between the number of branch fractures and the length of the main fracture as the conditional probability, and combining it with the coupled joint distribution, a complete first joint probability distribution model is obtained to reflect the influence of the main fracture on the branch fractures.

[0008] Preferably, the distribution function between the number of branch fractures and the length of the main fracture is expressed as: ,in This indicates the number of branched fractures. Indicates the length of the main fracture; The distribution functions of the fracture length and fracture aperture of the branch fractures and the fracture length of the main fractures are expressed as follows: , ,in , These represent the fracture length and fracture aperture of the branch fracture, respectively. After coupling using Copula functions, the joint distribution of the fracture length and aperture of the branch fractures with the fracture length of the main fracture is expressed as follows: ; The complete first joint probability distribution model is expressed as: ; In the formula This represents the correlation parameter of the Copula function in the first joint probability distribution model.

[0009] Preferably, the construction logic of the second joint probability distribution model is as follows: The time cumulative effect of grouting pressure on new branch fractures is introduced. A nonlinear response model of grouting pressure and new branch fractures is established based on fluid dynamics to obtain the expected value of the number of new branch fractures changing with time under the action of grouting pressure. Using the expected value of the number of new branch fractures changing over time as the mean parameter of the Poisson distribution, we obtain the distribution function between the expected value of the number of new branch fractures changing over time and the grouting pressure. The edge probability distribution of the new branch fracture length and fracture aperture is fitted to obtain the distribution functions of the new branch fracture length, fracture aperture and grouting pressure, and the Copula function is used for coupling. Using the distribution function between the expected value of the number of new branch fractures changing over time and the grouting pressure as the conditional probability, and combining it with the coupled joint distribution, a complete second joint probability distribution model is obtained to reflect the influence of grouting pressure on new branch fractures.

[0010] Preferably, the nonlinear response model of the grouting pressure to the new branch fracture is expressed as: ; In the formula Indicates in ~ The expected number of new branching fractures during this period. , These represent the start and end times of the grouting process, respectively. , These represent the grouting pressure and the critical pressure of the surrounding rock fissures, respectively. , The model parameters represent the nonlinear response model. Represents the time infinitesimal element; The distribution function relating the expected number of new branch fractures over time to grouting pressure is expressed as: The distribution functions of the new branch fracture length, fracture aperture, and grouting pressure are expressed as follows: , ; The complete second joint probability distribution model is expressed as: ; In the formula This represents the correlation parameter of the Copula function in the second joint probability distribution model.

[0011] Preferably, the segmented grouting strategy includes two consecutive stages: low-pressure grouting and high-pressure grouting. The low-pressure grouting stage is used to fill the branch fractures, and the high-pressure grouting stage is used to fill the main fractures. Timing is taken from the start of grouting. The number of new branch fractures generated during the low-pressure grouting stage is expressed as follows: , The term "end of low-pressure grouting" indicates the time of completion. The number of new branch fractures generated during the high-pressure grouting stage is expressed as: , Indicates the end time of high-pressure grouting; The fracture parameters of the branch fractures are corrected, that is, the number of branch fractures is corrected. After low-pressure grouting and high-pressure grouting, the total number of branch fractures is expressed as: ; In the formula This indicates the total number of branched fractures.

[0012] Preferably, the physical constraints that need to be satisfied when solving the problem using an optimization algorithm include: After the low-pressure grouting stage is completed, the grouting volume of the low-pressure grouting stage is greater than the total volume of the branch fractures, and the branch fractures are completely filled. The corresponding expression is: ; After the high-pressure grouting stage is completed, the grouting volume of the high-pressure grouting stage is greater than the total volume of the main fracture, and the main fracture is completely filled. The corresponding expression is: ; Meanwhile, the total grouting time should not exceed the preset time threshold: ; In the formula , These represent the grouting flow rates in the low-pressure grouting stage and the high-pressure grouting stage, respectively, and are directly proportional to the grouting pressure in the low-pressure grouting stage and the high-pressure grouting stage, respectively. , These represent the total volume of the branch fracture and the total volume of the main fracture, respectively. This indicates the preset time threshold.

[0013] Preferably, the total volume of the branch fracture is obtained by combining the fracture length and fracture aperture of the branch fracture with the thickness of the surrounding rock in the grouting area, and the calculation method is as follows: ; The total volume of the main fracture is obtained by combining the fracture length and fracture aperture of the main fracture with the thickness of the surrounding rock in the grouting area. The calculation method is as follows: ; In the formula Indicates the thickness of the surrounding rock. , These represent the fracture length and fracture aperture of the main fracture, respectively.

[0014] Compared with the prior art, the beneficial effects of the present invention are: This invention establishes a multi-parameter coupled joint probability distribution model to accurately characterize the spatial structural features of main and branch fractures and the dynamic evolution process of grouting pressure-induced fractures, achieving statistical inference and dynamic correction of fracture parameters. A segmented grouting strategy is employed to implement differentiated reinforcement for different fracture levels. Simultaneously, by combining physical constraints and optimization algorithms, the optimal combination of grouting pressure and time is scientifically determined. This method effectively improves the accuracy and efficiency of grouting reinforcement, reduces grout waste and construction risks, ensures the stability of the surrounding rock and construction safety, and allows for data inference and scheme optimization without requiring extensive field data. This significantly enhances the reliability and applicability of rock mass grouting reinforcement technology, meeting the reinforcement needs of complex engineering environments. Attached Figure Description

[0015] Figure 1 This is a schematic diagram of the overall method flow of the present invention. Detailed Implementation

[0016] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0017] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0018] Example: Please see Figure 1 The present invention provides a technical solution: A design method for grouting reinforcement of fractured rock mass surrounding rock based on multi-parameter coupling, the specific steps of which include: S1: Collect surrounding rock samples of different rock types with fractures. Based on the fracture classification method, classify the fractures on the surrounding rock samples into main fractures and branch fractures, and obtain the fracture parameters of the main fractures and branch fractures in the surrounding rock samples. The fracture parameters include the number of fractures, fracture length, and fracture aperture, and use them as the first observation data. It can be seen that the first observation data reflects the relationship between branch fractures and main fractures under natural conditions (such as weathering, rain erosion, etc.).

[0019] Main fractures refer to dominant, large-scale, and highly penetrating fractures, typically manifesting as major fracture surfaces or fracture zones in rock masses. They are key controlling factors for the overall mechanical behavior and seepage characteristics of the rock mass. Branch fractures, on the other hand, are smaller-scale fractures branching from main fractures. They are numerous, densely distributed, and form a network structure, affecting grouting permeability and local stability of the surrounding rock. For fracture classification methods, the definitions of both should be determined based on expert experience regarding size and spatial distribution. In this embodiment, using visual observation or CT scanning, fractures longer than 50% of the longest side of the specimen and penetrating the entire specimen are identified as main fractures. Fractures connected to main fractures but shorter than 20% of their length, and exhibiting a clear branching structure in scanned images or mechanical tests, are identified as branch fractures.

[0020] In this step, collecting surrounding rock samples of different rock mass types can cover diverse geological conditions, avoid the limitations of a single rock mass type that may lead to model limitations, and thus improve the applicability and prediction accuracy of subsequent statistical models.

[0021] S2: Grouting tests were conducted on the surrounding rock samples at a fixed grouting pressure, and grouting tests were also conducted on the surrounding rock samples at different pressures. After the tests were completed, the fracture parameters of the new branch fractures generated by grouting were collected and used as the second observation data. It can be seen that the second observation data reflects the relationship between the branch fractures and the external force under the action of external force.

[0022] In this step, by controlling the grouting pressure to apply external force, the actual grouting conditions are simulated, the influence of grouting pressure on the induction and propagation of branch cracks is observed and quantified, and the parameters of the new branch cracks induced by grouting are collected. This can reveal the causal relationship and dynamic mechanism of crack evolution, making the subsequent model closer to the actual field situation and improving the representativeness and applicability of the project.

[0023] S3: Based on statistical analysis and joint probability distribution methods, the first and second observation data are processed respectively to construct a first joint probability distribution model corresponding to the rock mass type and about the main fracture and branch fracture, and a second joint probability distribution model about the grouting pressure and branch fracture.

[0024] The construction logic of the first joint probability distribution model is as follows: Statistical analysis was performed on the fracture length of the main fracture to obtain its probability distribution type; A Poisson distribution was fitted to the number of branch fractures to establish a distribution function relating the number of branch fractures to the length of the main fracture. This distribution function is expressed as: ,in This indicates the number of branched fractures. Indicates the length of the main fracture; Marginal probability distributions were fitted to the fracture length and aperture of the branch fractures to obtain the distribution functions between the fracture length and aperture of the branch fractures and the fracture length of the main fracture. Copula functions were then used for coupling. The distribution functions between the fracture length and aperture of the branch fractures and the fracture length of the main fracture are expressed as follows: , ,in , Let represent the fracture length and fracture aperture of the branch fracture, respectively. After coupling using a Copula function, the joint distribution of the fracture length and fracture aperture of the branch fracture with the fracture length of the main fracture is expressed as: ; Using the distribution function between the number of branch fractures and the length of the main fracture as the conditional probability, and combining it with the coupled joint distribution, a complete first joint probability distribution model is obtained to reflect the influence of the main fracture on the branch fractures. The complete first joint probability distribution model is expressed as follows: ; In the formula This represents the correlation parameter of the Copula function in the first joint probability distribution model.

[0025] Understandably, the number of branch fractures is a discrete random variable (non-negative integer), reflecting the "number of events" of fracture generation per unit space or around the main fracture. It exhibits statistical characteristics similar to the occurrence of random events and is suitable for fitting with a counting probability distribution. Therefore, the Poisson distribution is used to characterize the random "occurrence rate" of fracture generation. In contrast, the fracture aperture and length of branch fractures describe their physical dimensions and are more constrained by material properties, stress state, and fracture propagation dynamics. They exhibit a continuous spectrum and are interdependent, belonging to two continuous random variables, typically following continuous distributions (commonly normal and log-normal distributions). Therefore, a marginal probability distribution is used for fitting. Furthermore, in a fracture system, the number determines how many branch fractures exist, while length and aperture are geometric descriptions of these fractures. The distribution of length and aperture only exists under the condition that fractures "appear." That is, the number is the counting result of whether fractures "generate," a first-occurring event, while length and aperture are the specific manifestations of fractures after generation, subsequent variables. Therefore, the conditional probability form can clearly express the causal chain of "first generating quantity, then distributing length and aperture based on that quantity". This approach is consistent with the physical generation mechanism of rock mass fractures and the hierarchical logic of statistical modeling, which helps to improve the accuracy and engineering applicability of the model.

[0026] The construction logic of the second joint probability distribution model is as follows: The time-cumulative effect of grouting pressure on new branch fractures is introduced. Based on fluid dynamics, a nonlinear response model of grouting pressure and new branch fractures is established to obtain the expected value of the number of new branch fractures changing with time under grouting pressure. The nonlinear response model of grouting pressure and new branch fractures is expressed as follows: ; In the formula Indicates in ~ The expected number of new branching fractures during this period. , These represent the start time and the end time, respectively. , These represent the grouting pressure and the critical pressure of the surrounding rock fissures, respectively. , The model parameters represent the nonlinear response model. Represents the time infinitesimal element; Using the expected value of the number of new branch fractures changing over time as the mean parameter of the Poisson distribution, we obtain the distribution function between the expected value of the number of new branch fractures changing over time and the grouting pressure. Marginal probability distributions were fitted to the fracture length and fracture aperture of the new branch fractures to obtain the distribution functions of the fracture length, fracture aperture, and grouting pressure, respectively. These functions were then coupled using a Copula function. The distribution function of the expected value of the number of new branch fractures changing over time and the grouting pressure is expressed as follows: The distribution functions of the new branch fracture length, fracture aperture, and grouting pressure are expressed as follows: , ; Using the distribution function between the expected value of the number of new branch fractures changing over time and the grouting pressure as the conditional probability, and combining it with the coupled joint distribution, a complete second joint probability distribution model is obtained to reflect the influence of grouting pressure on new branch fractures.

[0027] The complete second joint probability distribution model is expressed as: ; In the formula This represents the correlation parameter of the Copula function in the second joint probability distribution model.

[0028] As can be seen from the construction logic of the second joint probability distribution model, it is similar to that of the first joint probability distribution model. The difference lies in that the branch fractures and main fractures in the first joint probability distribution model are naturally formed, so the corresponding fracture parameters will not change in a short period of time and can be regarded as constant values. However, in the second joint probability distribution model, new branch fractures are generated by grouting pressure, and the corresponding fracture parameters are variables. Grouting pressure is not an instantaneous action, but a dynamic process that acts over time. Fracture induction is a cumulative effect of pressure action, which depends not only on the current pressure but also on historical pressure. Therefore, a nonlinear response model of grouting pressure and new branch fractures is introduced to reflect this time-cumulative effect.

[0029] As can be seen from the expression of the nonlinear response model, cracks are only significantly generated when the grouting pressure exceeds the critical pressure of the surrounding rock. When the pressure is below the threshold, the response quickly approaches zero, indicating that there is basically no crack induction. It is a time accumulation factor used to describe the time accumulation effect of grouting pressure on branch fractures. That is, under the stimulation of early grouting pressure, the impact on the rock mass is small and it is not easy to induce new branch fractures. As the grouting pressure acts for a longer time, the impact on the rock mass gradually increases, and it becomes easier to induce new branch fractures.

[0030] For the first and second joint probability distribution models, after construction, the hold-out method or k-fold cross-validation method can be used to evaluate the accuracy and generalization ability of the model prediction. Based on the fitted distribution, the confidence intervals (such as the 95% confidence interval) of each parameter and joint probability can be calculated to provide uncertainty quantification indicators for subsequent grouting design. At the same time, by analyzing the model residuals, systematic biases can be identified, and the model structure or parameters can be adjusted to improve the model fitting quality.

[0031] S4: Collect the rock mass type and fracture parameters of the main fracture in the surrounding rock of the area to be grouted. Based on the rock mass type of the surrounding rock in the area to be grouted, select the corresponding first joint probability distribution model to obtain the fracture parameters of the branch fractures. Then, formulate a segmented grouting strategy according to the rock mass type of the surrounding rock, the fracture parameters of the main fracture, and the fracture parameters of the branch fractures.

[0032] The segmented grouting strategy includes two consecutive stages: low-pressure grouting and high-pressure grouting. The low-pressure grouting stage is used to fill branch fractures, while the high-pressure grouting stage is used to fill main fractures.

[0033] Understandably, to improve the effectiveness of grouting reinforcement, it is necessary to fully fill the small branch fractures. Therefore, during the low-pressure grouting stage, it is necessary to maintain grouting at a long time and low pressure to allow the grout to fully penetrate and fill the branch fractures. After the branch fractures are fully filled, short-time, high-pressure grouting is required to ensure that the main fractures are fully filled, thereby achieving reinforcement and stability of the overall surrounding rock structure. The critical pressure of the fracture can be determined on-site based on the rock mass type. For example, the critical pressure of granite is 8~10 MPa, and the critical pressure of sandstone is 3~8 MPa. The specific range can be determined by collecting surrounding rock samples on-site and conducting triaxial fracture tests, and then incorporating the theoretical minimum value into the nonlinear response model. Ideally, the grouting pressure during the low-pressure grouting stage should be less than the theoretical minimum critical pressure of the rock mass fractures, allowing for thorough filling through prolonged grouting. However, in practical engineering applications, the total project time is limited, and the grouting pressures in both stages are usually set between the theoretical minimum and maximum critical pressures of the fractures to prevent the project progress from becoming too slow.

[0034] By controlling the pressure and grouting time in stages, the reinforcement requirements of different crack levels can be precisely controlled, ensuring the overall stability and long-term durability of the surrounding rock, reducing sudden damage to the surrounding rock and construction safety hazards, and facilitating real-time monitoring and adjustment of grouting parameters at the construction site, thereby improving the level of construction management.

[0035] S5: Based on the second joint probability distribution model and grouting strategy corresponding to the rock mass type of the surrounding rock in the area to be grouted, the fracture parameters of the branch fractures are modified. The optimization objective is to minimize the total number of branch fractures. The optimization algorithm is used to solve the problem and obtain the grouting pressure and grouting time of the segmented grouting strategy at different stages, thereby optimizing the segmented grouting strategy.

[0036] Timing is taken from the start of grouting. The number of new branch fractures generated during the low-pressure grouting stage is expressed as follows: , The term "end of low-pressure grouting" indicates the time of completion. The number of new branch fractures generated during the high-pressure grouting stage is expressed as: , Indicates the end time of high-pressure grouting; The fracture parameters of the branch fractures are corrected, that is, the number of branch fractures is corrected. After low-pressure grouting and high-pressure grouting, the total number of branch fractures is expressed as: ; In the formula This indicates the total number of branched fractures.

[0037] When using optimization algorithms to solve the problem, the physical constraints that need to be satisfied include: After the low-pressure grouting stage is completed, the grouting volume of the low-pressure grouting stage is greater than the total volume of the branch fractures, and the branch fractures are completely filled. The corresponding expression is: ; After the high-pressure grouting stage is completed, the grouting volume of the high-pressure grouting stage is greater than the total volume of the main fracture, and the main fracture is completely filled. The corresponding expression is: ; Meanwhile, the total grouting time should not exceed the preset time threshold: ; In the formula , These represent the grouting flow rates in the low-pressure grouting stage and the high-pressure grouting stage, respectively, and are directly proportional to the grouting pressure in the low-pressure grouting stage and the high-pressure grouting stage, respectively. , These represent the total volume of the branch fracture and the total volume of the main fracture, respectively. This represents the preset time threshold, which is derived from the specific project timeline.

[0038] From the correction logic of the fracture parameters of the branch fracture, it can be seen that the total number of fractures in the branch fracture mainly consists of three parts. Indicates the naturally formed part. This refers to branched cracks that occur during low-pressure grouting. This refers to branched fissures generated during high-pressure grouting. The naturally formed portion is much larger than the latter two types, while the branched fissures generated are the fewest due to the shorter grouting time and weaker cumulative effect over time.

[0039] Therefore, it can be seen from the expression of physical constraints that the main purpose of low-pressure grouting is to fill the branch cracks, and the grouting volume needs to be greater than the total volume of the branch cracks. However, in the high-pressure grouting stage, since there are fewer newly generated branch cracks and their volume is much smaller than that of the main cracks, they are ignored to simplify the calculation. Only the grouting volume needs to be greater than the total volume of the main cracks.

[0040] The total volume of the branch fracture is obtained by considering the fracture length and fracture aperture, combined with the thickness of the surrounding rock in the grouting area. The calculation method is as follows: ; The total volume of the main fracture is obtained by combining the fracture length and fracture aperture of the main fracture with the thickness of the surrounding rock in the grouting area. The calculation method is as follows: ; In the formula Indicates the thickness of the surrounding rock. , These represent the fracture length and fracture aperture of the main fracture, respectively. The fracture length, fracture aperture, and surrounding rock thickness of the main fracture are relatively easy to measure and can be obtained directly on-site. However, the fracture length and fracture aperture of the branch fractures are difficult to measure, so they need to be inferred using models.

[0041] Understandably, fractures are typically constrained by bedding, joints, or structural planes in rock strata. Fracture height is often similar to the thickness of the rock strata or the spacing of joints, exhibiting certain scale boundaries. For example, in sedimentary rocks or shale, fractures usually develop along bedding planes, and their height is "constrained" by the rock stratum thickness, resulting in a relatively small range of variation. Furthermore, direct measurement of fracture height is often difficult for rock specimens or engineering sites, especially given the limited information in the fracture height direction. Therefore, in engineering practice, rock stratum thickness or specimen dimensions are often used as fixed values ​​for height to simplify volume calculations. This simplification has minimal impact on volume estimation in most engineering scenarios, reducing the dimensionality of random variables, lowering model complexity, and facilitating parameter estimation and calculation.

[0042] In this step, the optimization objective is to minimize the total number of branch cracks. This is combined with physical constraints such as grouting volume, time, and pressure: the low-pressure grouting volume must cover the total volume of the branch cracks, and the high-pressure grouting volume must cover the total volume of the main cracks to ensure that the grouting is fully filled; the total grouting time is controlled to not exceed the preset threshold to meet the construction cycle requirements and prevent the construction period from being extended or resources from being wasted. This scientifically seeks the optimal combination of grouting pressure and grouting time at different stages, taking into account both the reinforcement effect and construction efficiency, and avoiding excessive crack expansion caused by excessive grouting pressure or insufficient reinforcement caused by excessively low pressure.

[0043] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0044] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0045] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0046] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A design method for grouting reinforcement of fractured rock mass surrounding rock based on multi-parameter coupling, characterized in that, The specific steps include: S1: Collect surrounding rock samples with different rock mass types and fractures. Based on the fracture classification method, divide the fractures on the surrounding rock samples into main fractures and branch fractures, obtain the fracture parameters of the main fractures and branch fractures of the surrounding rock samples, and use them as the first observation data. S2: Grouting tests with different pressures were conducted on each surrounding rock sample. After the test, the fracture parameters of the new branch fractures generated by the grouting were collected and used as the second observation data. S3: Based on statistical analysis and joint probability distribution methods, the first and second observation data are processed respectively to construct a first joint probability distribution model corresponding to the rock mass type and about the main fracture and branch fracture, and a second joint probability distribution model about the grouting pressure and branch fracture; S4: Collect the rock mass type and fracture parameters of the main fracture in the surrounding rock of the area to be grouted. Based on the rock mass type of the surrounding rock in the area to be grouted, select the corresponding first joint probability distribution model to obtain the fracture parameters of the branch fractures. Then, formulate a segmented grouting strategy according to the rock mass type of the surrounding rock, the fracture parameters of the main fracture, and the fracture parameters of the branch fractures. S5: Based on the second joint probability distribution model and grouting strategy corresponding to the rock mass type of the surrounding rock in the area to be grouted, the fracture parameters of the branch fractures are modified. The optimization objective is to minimize the total number of branch fractures. The optimization algorithm is used to solve the problem and obtain the grouting pressure and grouting time of the segmented grouting strategy at different stages, thereby optimizing the segmented grouting strategy.

2. The design method for grouting reinforcement of fractured rock mass based on multi-parameter coupling according to claim 1, characterized in that: The fracture parameters include the number of fractures, the length of fractures, and the fracture aperture. The construction logic of the first joint probability distribution model is as follows: Statistical analysis was performed on the fracture length of the main fracture to obtain its probability distribution type; A Poisson distribution was fitted to the number of branch fractures to establish a distribution function between the number of branch fractures and the fracture length of the main fracture. Edge probability distributions were fitted to the fracture length and fracture aperture of the branch fractures to obtain the distribution functions between the fracture length and fracture aperture of the branch fractures and the fracture length of the main fracture, and the Copula function was used for coupling. Using the distribution function between the number of branch fractures and the length of the main fracture as the conditional probability, and combining it with the coupled joint distribution, a complete first joint probability distribution model is obtained to reflect the influence of the main fracture on the branch fractures.

3. The design method for grouting reinforcement of fractured rock mass based on multi-parameter coupling according to claim 2, characterized in that: The distribution function between the number of branch fractures and the length of the main fracture is expressed as: ,in This indicates the number of branched fractures. Indicates the length of the main fracture; The distribution functions of the fracture length and fracture aperture of the branch fractures and the fracture length of the main fractures are expressed as follows: , ,in , These represent the fracture length and fracture aperture of the branch fracture, respectively. After coupling using Copula functions, the joint distribution of the fracture length and aperture of the branch fractures with the fracture length of the main fracture is expressed as follows: ； The complete first joint probability distribution model is expressed as: ； In the formula This represents the correlation parameter of the Copula function in the first joint probability distribution model.

4. The design method for grouting reinforcement of fractured rock mass based on multi-parameter coupling according to claim 1, characterized in that: The construction logic of the second joint probability distribution model is as follows: The time cumulative effect of grouting pressure on new branch fractures is introduced. A nonlinear response model of grouting pressure and new branch fractures is established based on fluid dynamics to obtain the expected value of the number of new branch fractures changing with time under the action of grouting pressure. Using the expected value of the number of new branch fractures changing over time as the mean parameter of the Poisson distribution, we obtain the distribution function between the expected value of the number of new branch fractures changing over time and the grouting pressure. The edge probability distribution of the new branch fracture length and fracture aperture is fitted to obtain the distribution functions of the new branch fracture length, fracture aperture and grouting pressure, and the Copula function is used for coupling. Using the distribution function between the expected value of the number of new branch fractures changing over time and the grouting pressure as the conditional probability, and combining it with the coupled joint distribution, a complete second joint probability distribution model is obtained to reflect the influence of grouting pressure on new branch fractures.

5. The design method for grouting reinforcement of fractured rock mass based on multi-parameter coupling according to claim 4, characterized in that: The nonlinear response model of the grouting pressure to the new branch fracture is expressed as follows: ； In the formula Indicates in ~ The expected number of new branching fractures during this period. , These represent the start and end times of the grouting process, respectively. , These represent the grouting pressure and the critical pressure of the surrounding rock fractures, respectively. , The model parameters represent the nonlinear response model. Represents the time infinitesimal element; The distribution function relating the expected number of new branch fractures over time to grouting pressure is expressed as: The distribution functions of the new branch fracture length, fracture aperture, and grouting pressure are expressed as follows: , ; The complete second joint probability distribution model is expressed as: ； In the formula This represents the correlation parameter of the Copula function in the second joint probability distribution model.

6. The design method for grouting reinforcement of fractured rock mass based on multi-parameter coupling according to claim 5, characterized in that: The segmented grouting strategy includes two continuous stages: low-pressure grouting and high-pressure grouting. The low-pressure grouting stage is used to fill the branch fractures, and the high-pressure grouting stage is used to fill the main fractures. Timing is taken from the start of grouting. The number of new branch fractures generated during the low-pressure grouting stage is expressed as follows: , The term "end of low-pressure grouting" indicates the time of completion. The number of new branch fractures generated during the high-pressure grouting stage is expressed as: , Indicates the end time of high-pressure grouting; The fracture parameters of the branch fractures are corrected, that is, the number of branch fractures is corrected. After low-pressure grouting and high-pressure grouting, the total number of branch fractures is expressed as: ； In the formula This indicates the total number of branched fractures.

7. The design method for grouting reinforcement of fractured rock mass based on multi-parameter coupling according to claim 6, characterized in that: When solving using optimization algorithms, the following physical constraints must be satisfied: After the low-pressure grouting stage is completed, the grouting volume of the low-pressure grouting stage is greater than the total volume of the branch fractures, and the branch fractures are completely filled. The corresponding expression is: ； After the high-pressure grouting stage is completed, the grouting volume of the high-pressure grouting stage is greater than the total volume of the main fracture, and the main fracture is completely filled. The corresponding expression is: ； Meanwhile, the total grouting time should not exceed the preset time threshold: ； In the formula , These represent the grouting flow rates in the low-pressure grouting stage and the high-pressure grouting stage, respectively, and are directly proportional to the grouting pressure in the low-pressure grouting stage and the high-pressure grouting stage, respectively. , These represent the total volume of the branch fracture and the total volume of the main fracture, respectively. This indicates the preset time threshold.

8. The design method for grouting reinforcement of fractured rock mass based on multi-parameter coupling according to claim 7, characterized in that: The total volume of the branch fractures is obtained by combining the fracture length and fracture aperture of the branch fractures with the thickness of the surrounding rock in the grouting area. The calculation method is as follows: ； The total volume of the main fracture is obtained by combining the fracture length and fracture aperture of the main fracture with the thickness of the surrounding rock in the grouting area. The calculation method is as follows: ； In the formula Indicates the thickness of the surrounding rock. , These represent the fracture length and fracture aperture of the main fracture, respectively.

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