A method for grouting reinforcement design of fractured rock mass surrounding rock based on multi-parameter coupling

Abstract

The application provides a fissure rock mass surrounding rock grouting reinforcement design method based on multi-parameter coupling, relates to the surrounding rock grouting reinforcement technical field, and accurately depicts the spatial structure characteristics of the main fissure and the branch fissure and the dynamic evolution process of the fissure induced by grouting pressure by establishing a multi-parameter coupling joint probability distribution model, realizes the statistical inference and dynamic correction of the fissure parameters, adopts a sectional grouting strategy to implement differential reinforcement for different fissure levels, simultaneously combines physical constraint conditions and an optimization algorithm, and scientifically determines the optimal combination of the grouting pressure and time. The method effectively improves the precision and efficiency of the grouting reinforcement, reduces the slurry waste and construction risk, guarantees the stability of the surrounding rock and the construction safety, and can perform data inference and scheme optimization without a large amount of field data, so that the reliability and application range of the rock mass surrounding rock grouting reinforcement technology are greatly enhanced, and the reinforcement demand under the complex engineering environment is met.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of surrounding rock grouting reinforcement, in particular to a fissured rock mass surrounding rock grouting reinforcement design method based on multi-parameter coupling. BACKGROUND

[0002] During the construction process of tunnel excavation, underground mining and foundation engineering, the surrounding rock of rock mass often leads to reduced stability and structural damage of the surrounding rock due to the presence of complex fissure systems, which seriously affects the safety and construction progress of the project. Traditional grouting reinforcement methods rely on empirical parameters and single fissure characteristics, ignoring the multi-parameter coupling relationship between the main fissure and branch fissure and the dynamic influence of grouting pressure on fissure induction. Moreover, due to the difficulty in accurately measuring the parameters of branch fissures, the grouting effect is difficult to accurately predict and control, which reduces the overall grouting effect. In addition, the existing technology cannot effectively reflect the nonlinear response characteristics of the number, size and time variation of fissures during grouting, which affects the scientificity and engineering applicability of the reinforcement scheme in complex rock mass environment.

[0003] In the prior art, the publication number CN120508175A discloses a self-adaptive grouting regulation and control sealing method based on real-time monitoring of mining fissures, which relates to the technical field of mine safety engineering and hydrogeology. Through the cooperative work of the grouting mechanism, data monitoring system, data acquisition and processing module and self-adaptive control module, the automation and intelligentization of grouting protection can be realized. By introducing the roughness coefficient of fissures and time-dependent viscosity, the flow resistance of rough fissures and the time-varying characteristics of slurry rheology are quantified, and the calculation error of slurry diffusion radius is reduced. Although this scheme can be self-adaptively adjusted, it relies on a complex sensing system and real-time data on site, and it is difficult to systematically invert the fissure evolution law when the collected sensing data is insufficient, thus limiting the accuracy and applicability of the system.

[0004] The above information disclosed in the background section is only used to enhance the understanding of the background of the present disclosure, and therefore it can include information that does not constitute prior art known to those of ordinary skill in the art. SUMMARY

[0005] The present application aims to provide a fissured rock mass surrounding rock grouting reinforcement design method based on multi-parameter coupling to solve the problems raised in the background.

[0006] To achieve the above-mentioned purpose, the present application provides the following technical solutions:

[0007] A fissured rock mass surrounding rock grouting reinforcement design method based on multi-parameter coupling, the specific steps comprising:

[0008] S1: Collecting surrounding rock samples of different rock mass types and with fissures, classifying the fissures on the surrounding rock samples into main fissures and branch fissures based on a fissure classification method, obtaining fissure parameters of the main fissures and the branch fissures on the surrounding rock samples, and taking the fissure parameters as first observation data;

[0009] S2: Carrying out grouting tests on the surrounding rock samples at a fixed grouting pressure, and carrying out grouting tests on the surrounding rock samples at different pressures, collecting fissure parameters of new branch fissures generated in the surrounding rock samples due to grouting after the tests are completed, and taking the fissure parameters as second observation data;

[0010] S3: Processing the first observation data and the second observation data based on statistical analysis and joint probability distribution method, respectively, constructing a first joint probability distribution model corresponding to the rock mass type and about the main fissures and the branch fissures, and a second joint probability distribution model about the grouting pressure and the branch fissures;

[0011] S4: Collecting the rock mass type and the fissure parameters of the main fissures of the surrounding rock in the area to be grouted, selecting the corresponding first joint probability distribution model to obtain the fissure parameters of the branch fissures based on the rock mass type of the surrounding rock in the area to be grouted, and formulating a segmented grouting strategy according to the rock mass type of the surrounding rock, the fissure parameters of the main fissures, and the fissure parameters of the branch fissures, respectively;

[0012] S5: Based on the second joint probability distribution model corresponding to the rock mass type of the surrounding rock in the area to be grouted and the grouting strategy, correcting the fissure parameters of the branch fissures, taking the minimization of the total number of the branch fissures as an optimization objective, and solving by using an optimization algorithm to obtain the grouting pressure and the grouting time of the segmented grouting strategy at different stages, and realizing the optimization of the segmented grouting strategy.

[0013] Preferably, the fissure parameters include the number of fissures, the length of fissures, and the opening of fissures;

[0014] The construction logic of the first joint probability distribution model is as follows:

[0015] Statistical analysis is performed on the length of the main fissures to obtain the probability distribution type thereof;

[0016] Poisson distribution fitting is performed on the number of branch fissures to establish a distribution function between the number of branch fissures and the length of main fissures;

[0017] Edge probability distribution fitting is performed on the length and opening of branch fissures to obtain distribution functions between the length and opening of branch fissures and the length of main fissures, respectively, and coupling is performed by using a Copula function;

[0018] 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.

[0019] 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;

[0020] 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.

[0021] 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:

[0022] ;

[0023] The complete first joint probability distribution model is expressed as:

[0024] ;

[0025] In the formula This represents the correlation parameter of the Copula function in the first joint probability distribution model.

[0026] Preferably, the construction logic of the second joint probability distribution model is as follows:

[0027] 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.

[0028] 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.

[0029] 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.

[0030] The distribution function between the expected value of the crack number of the new branch crack over time and the grouting pressure is taken as the conditional probability, and the complete second joint probability distribution model is obtained by combining the coupled joint distribution, so as to reflect the influence of the grouting pressure on the new branch crack.

[0031] Preferably, the nonlinear response model of the grouting pressure and the new branch crack is expressed as:

[0032] ;

[0033] In the formula, represents the start time of grouting and the end time of grouting, respectively, ~ The expected value of the crack number of the new branch crack over time in this time period, 、 represents the start time of grouting and the end time of grouting, respectively, 、 represents the grouting pressure and the crack critical pressure of the surrounding rock, respectively, 、 represents the model parameters of the nonlinear response model, represents a time element;

[0034] The distribution function between the expected value of the crack number of the new branch crack over time and the grouting pressure is expressed as: The distribution functions between the crack length and the crack opening of the new branch crack and the grouting pressure are respectively expressed as: 、 ;

[0035] The complete second joint probability distribution model is expressed as:

[0036] ;

[0037] In the formula, represents the correlation parameter of the Copula function in the second joint probability distribution model.

[0038] Preferably, the segmented grouting strategy includes two continuous stages of low-pressure grouting and high-pressure grouting, the low-pressure grouting stage is used for filling the branch crack, and the high-pressure grouting stage is used for filling the main crack;

[0039] From the start of grouting, the crack number of the new branch crack generated in the low-pressure grouting stage is expressed as , represents the end time of low-pressure grouting, and the crack number of the new branch crack generated in the high-pressure grouting stage is expressed as , represents the end time of high-pressure grouting;

[0040] The fracture parameters of the branch fissure are corrected, that is, the correction of the number of branch fissures, and after low-pressure grouting and high-pressure grouting, the total number of branch fissures is expressed as:

[0041] ;

[0042] In the formula, The total number of branch fissures is represented.

[0043] Preferably, when solving by using an optimization algorithm, the physical constraints to be met include:

[0044] After the end of the low-pressure grouting stage, the grouting volume of the low-pressure grouting stage is greater than the total volume of the branch fissure, and the branch fissure is completely filled, and the corresponding expression is:

[0045] ;

[0046] After the end of the high-pressure grouting stage, the grouting volume of the high-pressure grouting stage is greater than the total volume of the main fissure, and the main fissure is completely filled, and the corresponding expression is:

[0047] ;

[0048] At the same time, the total grouting time should not exceed the preset time threshold:

[0049] ;

[0050] In the formula, , The grouting flow of the low-pressure grouting stage and the high-pressure grouting stage is proportional to the grouting pressure, , The total volume of the branch fissure and the total volume of the main fissure, Indicates the preset time threshold.

[0051] Preferably, the total volume of the branch fissure is obtained from the fissure length, fissure opening of the branch fissure, and the surrounding rock thickness of the grouting area, and the calculation method is:

[0052] ;

[0053] The total volume of the main fissure is obtained from the fissure length, fissure opening of the main fissure, and the surrounding rock thickness of the grouting area, and the calculation method is:

[0054] ;

[0055] In the formula, Indicates the surrounding rock thickness, , respectively represent the fracture length and the fracture opening of the main fracture.

[0056] Compared with the prior art, the application has the beneficial effects that:

[0057] The application accurately depicts the spatial structure characteristics of the main fracture and branch fracture and the dynamic evolution process of the fracture induced by grouting pressure by establishing a joint probability distribution model coupled with multiple parameters, realizes statistical inference and dynamic correction of the fracture parameters, and scientifically determines the optimal combination of grouting pressure and time by adopting a segmented grouting strategy to implement differential reinforcement for different fracture levels and combining physical constraint conditions and optimization algorithms. The method effectively improves the accuracy and efficiency of grouting reinforcement, reduces the waste of grouting fluid and construction risks, guarantees the stability of surrounding rock and construction safety, and does not require a large amount of field data for data inference and scheme optimization, thereby greatly enhancing the reliability and application range of the rock mass surrounding rock grouting reinforcement technology and meeting the reinforcement requirements in complex engineering environments. BRIEF DESCRIPTION OF DRAWINGS

[0058] Figure 1 It is a whole method flowchart of the application. DETAILED DESCRIPTION

[0059] To make the purpose, technical scheme and advantages of the application clearer and more apparent, the application is further described in detail below with reference to specific embodiments.

[0060] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the application should be understood as the usual meaning understood by those skilled in the art to which the application belongs. The terms "first", "second" and similar words used in the application do not represent any order, quantity or importance, but are only used to distinguish different components. The terms "include" or "contain" and similar words mean that the elements or objects before the words cover the elements or objects listed after the words and their equivalents, without excluding other elements or objects. The terms "connect" or "connected" and similar words are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. The terms "up", "down", "left", "right" and the like only represent relative positional relationships, which may change accordingly when the absolute position of the described object changes.

[0061] Embodiment:

[0062] Please refer to Figure 1 The application provides a technical scheme:

[0063] A grouting reinforcement design method for fractured rock mass surrounding rock based on multi-parameter coupling, the specific steps comprising:

[0064] S1: Collect surrounding rock samples of different rock mass types with fissures, classify the fissures on the surrounding rock samples into main fissures and branch fissures based on a fissure classification method, obtain fissure parameters of the main fissures and branch fissures on the surrounding rock samples, the fissure parameters including fissure number, fissure length, and fissure opening, and take the fissure parameters as first observation data. It can be seen that the first observation data reflects the relationship between the branch fissures and the main fissures under natural conditions (such as weathering, rain erosion, etc.).

[0065] The main fissure refers to a crack that plays a leading role, has a larger scale, and has a stronger penetration, and is usually manifested as a main fracture surface or a crack zone in the rock mass, and is a key control factor of the overall mechanical behavior and seepage characteristics of the rock mass. The branch fissure refers to a smaller scale crack branched from the main fissure, which has a smaller scale than the main fissure, a large number, a dense distribution, and a network structure, and affects grouting permeability and local stability of the surrounding rock. For the fissure classification method, the definitions of the two should be determined based on the size, spatial distribution, and other expert experiences. In this embodiment, visual observation or CT scanning is used to determine that a crack with a length greater than 50% of the longest side of the test piece and penetrating the test piece is a main fissure, and a crack connected with the main fissure but with a length less than 20% of the length of the main fissure and showing a clear branch structure in the scanning image or mechanical test is a branch fissure.

[0066] In this step, surrounding rock samples of different rock mass types are collected, which can cover diversified geological conditions and avoid the limitation of a single rock mass type, thereby improving the application range and prediction accuracy of the subsequent statistical model.

[0067] S2: Perform grouting tests on the surrounding rock samples at a fixed grouting pressure, and perform grouting tests on the surrounding rock samples at different pressures. After the tests are completed, collect fissure parameters of new branch fissures generated by grouting, and take the fissure parameters as second observation data. It can be seen that the second observation data reflects the relationship between the branch fissures and the external force under the action of the external force.

[0068] In this step, the external force is applied by controlling the grouting pressure to simulate the actual grouting working condition, observe and quantify the influence of the grouting pressure on the induction and expansion of the branch fissures, collect the parameters of the new branch fissures induced by grouting, and reveal the causal relationship and dynamic mechanism of the fissure evolution, so that the subsequent model is closer to the actual site, and the engineering representativeness and applicability are improved.

[0069] S3: Process the first observation data and the second observation data based on statistical analysis and joint probability distribution method, and construct a first joint probability distribution model corresponding to the rock mass type and about the main fissures and the branch fissures, and a second joint probability distribution model about the grouting pressure and the branch fissures.

[0070] The construction logic of the first joint probability distribution model is:

[0071] The probability distribution type of the main fracture length is obtained by statistical analysis of the main fracture length;

[0072] The number of branch fractures is fitted by Poisson distribution, and a distribution function between the number of branch fractures and the length of main fracture is established, and the distribution function between the number of branch fractures and the length of main fracture is expressed as: wherein represents the number of branch fractures, represents the length of main fracture;

[0073] The edge probability distribution of the length and aperture of branch fracture is fitted, and the distribution functions between the length and aperture of branch fracture and the length of main fracture are obtained, and the coupling is performed by using Copula function, and the distribution functions between the length and aperture of branch fracture and the length of main fracture are expressed as: , wherein , respectively represent the length and aperture of branch fracture, and the joint distribution between the length and aperture of branch fracture and the length of main fracture after coupling by using Copula function is expressed as:

[0074] ;

[0075] The complete first joint probability distribution model is obtained by taking the distribution function between the number of branch fractures and the length of main fracture as a conditional probability and combining the coupled joint distribution, so as to reflect the influence of main fracture on branch fracture, and the complete first joint probability distribution model is expressed as:

[0076] ;

[0077] wherein represents the correlation parameter of Copula function in the first joint probability distribution model.

[0078] It can be understood that, for the number of branch fissures, it is a discrete random variable (non-negative integer), which reflects the "number of events" of generating fissures around the unit space or the main fissure, has similar statistical characteristics of "random event occurrence", and is suitable for fitting with a counting probability distribution. Therefore, the Poisson distribution is adopted to describe the random "occurrence rate" of fissure generation. The fissure aperture and length of the branch fissure are used to describe the physical size of the branch fissure, which is more restricted by material properties, stress state and fissure propagation dynamics, and shows a continuous spectrum and a mutual dependence relationship, which are two continuous random variables and usually subject to a continuous distribution (commonly normal distribution, lognormal distribution, etc.). Therefore, an edge probability distribution is adopted for fitting. Further, in the fissure system, the number determines how many branch fissures exist, and the length and aperture are the geometric descriptions of these fissures. Only under the condition of "fissure occurrence", there is a distribution of length and aperture, i.e., the number is the counting result of "fissure generation", which is the first event, and the length and aperture are the specific forms of the generated fissure, which are the second event. Therefore, the conditional probability form can clearly express the causal chain of "generating the number first, and then distributing the length and aperture on the basis of the number", which is consistent with the physical generation mechanism of rock mass fissure and the hierarchical logic of statistical modeling, and is helpful to improve the accuracy and engineering applicability of the model.

[0079] The construction logic of the second joint probability distribution model is:

[0080] The time cumulative effect of grouting pressure on new branch fissures is introduced, a nonlinear response model of grouting pressure and new branch fissures is established based on fluid dynamics, so as to obtain the expected value of the number of new branch fissures changing with time under the action of grouting pressure. The nonlinear response model of grouting pressure and new branch fissures is expressed as:

[0081] ;

[0082] In the formula, E (N (t) | P (t) ) represents the expected value of the number of new branch fissures in the time interval [t, t + dt] under the action of grouting pressure, ~ represents the expected value of the number of new branch fissures in the time interval [t, t + dt] under the action of grouting pressure, ~ the expected value of the number of new branch fissures in the time interval [t, t + dt] under the action of grouting pressure, 、 respectively represent the starting time and the ending time, 、 respectively represent the grouting pressure and the critical pressure of the surrounding rock fissure, 、 represent the model parameters of the nonlinear response model, represent the time infinitesimal;

[0083] 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.

[0084] 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: , ;

[0085] 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.

[0086] The complete second joint probability distribution model is expressed as:

[0087] ;

[0088] In the formula This represents the correlation parameter of the Copula function in the second joint probability distribution model.

[0089] 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.

[0090] 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. A time accumulation factor belongs to one, used to describe the time accumulation effect of grouting pressure on inducing branch fissures, that is, under the stimulation of early grouting pressure, the influence on rock mass is small, and it is not easy to induce new branch fissures, with the increase of grouting pressure action time, the influence on rock mass gradually increases, and it becomes easier to induce new branch fissures.

[0091] For the first joint probability distribution model and the second joint probability distribution model, after the construction is completed, the leave-one-out method or the k-fold cross-validation method can be used to evaluate the accuracy and generalization ability of the model prediction, and based on the fitting distribution, the confidence interval (such as 95% confidence interval) of each parameter and joint probability is calculated, which provides uncertainty quantification index for subsequent grouting design, and also can identify systematic bias by analyzing model residual, adjust model structure or parameter, so as to improve the fitting quality of model.

[0092] S4: Collect the rock mass type and fissure parameters of the surrounding rock of the area to be grouted, based on the rock mass type of the surrounding rock of the area to be grouted, select the corresponding first joint probability distribution model to obtain the fissure parameters of the branch fissure, and formulate a segmented grouting strategy according to the rock mass type of the surrounding rock, the fissure parameters of the main fissure and the fissure parameters of the branch fissure respectively.

[0093] The segmented grouting strategy includes two continuous stages of low-pressure grouting and high-pressure grouting, the low-pressure grouting stage is used to fill the branch fissure, and the high-pressure grouting stage is used to fill the main fissure.

[0094] It can be understood that in order to improve the effect of grouting reinforcement, it is necessary to fully fill the small branch fissure, therefore, in the low-pressure grouting stage, long-time and low-pressure grouting is needed to make the grout fully penetrate and fill into the branch fissure, and after the branch fissure is fully filled, short-time and high-pressure grouting is needed to make the main fissure be fully filled, so as to realize the reinforcement and stability of the overall structure of the surrounding rock. The critical pressure of the fissure can be determined by the rock mass type of the surrounding rock in the field, for example, the critical pressure of granite is 8~10MPa, and the critical pressure of sandstone is 3~8MPa, the specific range can be determined by triaxial fracture test on the collected surrounding rock samples, and the theoretical minimum value is brought into the In an ideal case, the grouting pressure in the low-pressure grouting stage should be less than the theoretical minimum value of the critical pressure of the rock mass fissure, and then the grouting is filled for a long time. But in actual engineering application, the total engineering time is limited, and the grouting pressure of the two stages is usually set between the theoretical minimum value and the theoretical maximum value of the critical pressure of the fissure, so as to keep the engineering progress not too slow.

[0095] By controlling the pressure and grouting time in different stages, the reinforcement requirements of different fracture levels can be accurately controlled, the overall stability and long-term durability of the surrounding rock are ensured, the sudden destruction of the surrounding rock and the construction safety hazards are reduced, the grouting parameters can be monitored and adjusted in real time on the construction site, and the construction management level is improved.

[0096] S5: Based on the second joint probability distribution model corresponding to the rock type of the surrounding rock in the region to be grouted and the grouting strategy, the fracture parameters of the branch fracture are corrected, the total number of branch fractures is minimized as the optimization objective, and an optimization algorithm is used to solve, to obtain the grouting pressure and grouting time of the segmented grouting strategy at different stages, and to realize the optimization of the segmented grouting strategy.

[0097] From the start of grouting, the number of new branch fractures generated in the low-pressure grouting stage is represented as , represents the end time of low-pressure grouting, and the number of new branch fractures generated in the high-pressure grouting stage is represented as , represents the end time of high-pressure grouting.

[0098] The fracture parameters of the branch fracture are corrected, that is, the correction of the number of branch fractures, and after low-pressure grouting and high-pressure grouting, the total number of branch fractures is represented as:

[0099] ;

[0100] In the formula, represents the total number of branch fractures.

[0101] When using an optimization algorithm to solve, the physical constraints to be met include:

[0102] After the end of the low-pressure grouting stage, 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, and the corresponding expression is:

[0103] ;

[0104] After the end of the high-pressure grouting stage, 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, and the corresponding expression is:

[0105] ;

[0106] At the same time, the total grouting time should not exceed the preset time threshold:

[0107] ;

[0108] In the formula, , respectively represent the grouting flow in the low-pressure grouting stage and the high-pressure grouting stage, which are proportional to the grouting pressure in the low-pressure grouting stage and the high-pressure grouting stage, 、 respectively represent the total volume of the branch fissure and the total volume of the main fissure, represents a preset time threshold, which is obtained according to a specific engineering period.

[0109] As can be seen from the correction logic of the fissure parameters of the branch fissure, the total number of the branch fissure mainly includes three parts, represents a naturally formed part, represents a branch fissure generated in the low-pressure grouting, represents a branch fissure generated in the high-pressure grouting. The naturally formed part is far greater than the last two, and because the time of high-pressure grouting is shorter, the time accumulation effect is also weaker, so the branch fissure generated is the least.

[0110] Therefore, as can be seen from the expression of the physical constraint, the main purpose in the low-pressure grouting stage is to fill the branch fissure, and the grouting volume needs to be greater than the total volume of the branch fissure, and in the high-pressure grouting stage, because the newly generated branch fissure is less, and the volume is far less than the volume of the main fissure, therefore, in order to simplify the calculation, it is ignored, and only the grouting volume greater than the total volume of the main fissure is considered.

[0111] The total volume of the branch fissure is obtained from the fissure length, fissure opening of the branch fissure, and the surrounding rock thickness of the grouting area, and the calculation method is:

[0112] ;

[0113] The total volume of the main fissure is obtained from the fissure length, fissure opening of the main fissure, and the surrounding rock thickness of the grouting area, and the calculation method is:

[0114] ;

[0115] In the formula, represents the surrounding rock thickness, 、 respectively represent the fissure length and the fissure opening of the main fissure. The fissure length, the fissure opening of the main fissure, and the surrounding rock thickness are relatively easy to measure and can be directly measured on site, but the fissure length and the fissure opening of the branch fissure are difficult to measure, so a model needs to be used for speculation.

[0116] It can be understood that the fissure is usually limited by the bedding, joint or structural plane of the rock stratum, the fissure height is usually similar to the rock stratum thickness or joint spacing, and has a certain scale boundary. For example, in a sedimentary rock stratum or shale, the fissure usually develops along the bedding plane, and the height is “clamped” by the rock stratum thickness, and the change range is relatively small. Moreover, for a rock mass test piece or an engineering site, direct measurement of the fissure height is often difficult, especially the information in the fissure height direction is limited, so in engineering practice, the rock stratum thickness or the test piece size is often used as a fixed value of the height to simplify the volume calculation. This simplification has little effect on the volume estimation in most engineering scenarios, can reduce the dimension of random variables, reduce the model complexity, and facilitate parameter estimation and calculation.

[0117] In this step, the total number of branch fissures is minimized as the optimization objective, combined with physical constraints such as grouting volume, time and pressure: the low-pressure grouting volume needs to cover the total volume of the branch fissure, the high-pressure grouting volume needs to cover the total volume of the main fissure, and the grouting filling is ensured; the total grouting time is controlled to be not more than a preset threshold, the construction period requirement is met, and the extension of the construction period or the waste of resources is prevented, so as to scientifically seek the optimal combination of grouting pressure and grouting time at different stages, take into account the reinforcement effect and construction efficiency, and avoid excessive expansion of the fissure caused by high grouting pressure or insufficient reinforcement caused by low grouting pressure.

[0118] The above formulas are all dimensionless numerical calculations, the formulas are obtained by software simulation of a large amount of data to obtain a formula closest to the actual situation, and the preset parameters in the formulas are set by a person skilled in the art according to the actual situation.

[0119] The above embodiments can be realized wholly or partially by software, hardware, firmware or any combination thereof. When realized by software, the above embodiments can be realized wholly or partially in the form of a computer program product. Those skilled in the art can realize that the units and algorithm steps of the examples described in conjunction with the embodiments disclosed herein can be realized by electronic hardware or a combination of computer software and electronic hardware. Whether the functions are realized by hardware or software methods depends on the specific application and design constraints of the technical solutions.

[0120] The units described as separate components can or can not be physically separated, and the components shown as units can or can not be physical units, and can be located in one place or distributed on multiple network units. Part or all of the units can be selected according to actual needs to achieve the purpose of the embodiments.

[0121] The above is merely specific embodiments of the present application, but the protection scope of the present application is not limited thereto, and any person skilled in the art can easily think of changes or replacements within the technical range disclosed in the present application, which should be covered within the protection scope of the present application.

Claims

1. A multi-parameter coupling-based fissure rock mass surrounding rock grouting reinforcement design method, characterized in that, The specific steps include: S1: Collecting surrounding rock samples of different rock mass types and with fissures, classifying the fissures on the surrounding rock samples into main fissures and branch fissures based on a fissure classification method, obtaining fissure parameters of the main fissures and the branch fissures of the surrounding rock samples, and taking the fissure parameters as first observation data, wherein the fissure parameters include fissure quantity, fissure length and fissure opening; S2: Carrying out grouting tests on each surrounding rock sample under different pressures, collecting fissure parameters of new branch fissures generated by grouting after the test is completed, and taking the fissure parameters as second observation data; S3: Processing the first observation data and the second observation data based on statistical analysis and joint probability distribution method, respectively, constructing a first joint probability distribution model corresponding to the rock mass type and about the main fissures and the branch fissures, and a second joint probability distribution model about the grouting pressure and the branch fissures; The construction logic of the first joint probability distribution model is as follows: Statistical analysis is performed on the fissure length of the main fissures to obtain the probability distribution type thereof; Poisson distribution fitting is performed on the fissure quantity of the branch fissures to establish a distribution function between the fissure quantity of the branch fissures and the fissure length of the main fissures; Edge probability distribution fitting is performed on the fissure length and the fissure opening of the branch fissures to respectively obtain distribution functions between the fissure length and the fissure opening of the branch fissures and the fissure length of the main fissures, and coupling is performed by using a Copula function; Taking the distribution function between the fissure quantity of the branch fissures and the fissure length of the main fissures as a conditional probability, the complete first joint probability distribution model is obtained by combining the coupled joint distribution, so as to reflect the influence of the main fissures on the branch fissures; The construction logic of the second joint probability distribution model is as follows: The time cumulative effect of the grouting pressure on the new branch fissures is introduced, a nonlinear response model of the grouting pressure and the new branch fissures is established based on fluid dynamics, so as to obtain an expected value of the fissure quantity of the new branch fissures changing with time under the action of the grouting pressure; The expected value of the fissure quantity of the new branch fissures changing with time is taken as a mean value parameter of Poisson distribution, so as to obtain a distribution function between the expected value of the fissure quantity of the new branch fissures changing with time and the grouting pressure; Edge probability distribution fitting is performed on the fissure length and the fissure opening of the new branch fissures to respectively obtain distribution functions between the fissure length and the fissure opening of the new branch fissures and the grouting pressure, and coupling is performed by using a Copula function; Taking the distribution function between the expected value of the fissure quantity of the new branch fissures changing with time and the grouting pressure as a conditional probability, the complete second joint probability distribution model is obtained by combining the coupled joint distribution, so as to reflect the influence of the grouting pressure on the new branch fissures; S4: Collecting the rock mass type and the fissure parameters of the main fissures of the surrounding rock in a region to be grouted, selecting a corresponding first joint probability distribution model to obtain the fissure parameters of the branch fissures based on the rock mass type of the surrounding rock in the region to be grouted, and formulating a segmented grouting strategy according to the rock mass type of the surrounding rock, the fissure parameters of the main fissures and the fissure parameters of the branch fissures, respectively. S5: Based on the second joint probability distribution model corresponding to the rock mass type of the surrounding rock of the grouting area to be grouted and the grouting strategy, the fracture parameters of the branch fracture are corrected, the total number of branch fractures is minimized as an optimization objective, and an optimization algorithm is used to solve, to obtain the grouting pressure and grouting time of the staged grouting strategy at different stages, and to realize the optimization of the staged grouting strategy.

2. The multi-parameter coupling-based fissure rock mass surrounding rock grouting reinforcement design method according to claim 1, characterized in that: The distribution function between the number of fractures of the branch fractures and the fracture length of the main fracture is expressed as: wherein represents the number of fractures of the branch fractures, represents the fracture length of the main fracture; The distribution functions between the fracture length of the branch fracture and the fracture length of the main fracture and between the fracture aperture of the branch fracture and the fracture length of the main fracture are respectively represented as: , wherein , respectively represent the fracture length of the branch fracture and the fracture aperture. After coupling by using the Copula function, the joint distribution between the fracture length, the fracture aperture of the branch fracture and the fracture length of the main fracture is represented as: The complete first joint probability distribution model is represented as: In the formula denotes the correlation parameter of the Copula function in the first joint probability distribution model.

3. The multi-parameter coupling-based fissure rock mass surrounding rock grouting reinforcement design method according to claim 2, characterized in that: The nonlinear response model of the grouting pressure and the new branch fracture is represented as: In the formula indicates the start time and the end time of grouting, respectively The expected value of the number of new branch fractures in this time period, indicates the start time and the end time of grouting, respectively indicates the grouting pressure and the fracture critical pressure of the surrounding rock, respectively indicates the model parameters of the nonlinear response model indicates a time infinitesimal​​​​​ The distribution function between the expected value of the number of new branch fractures and the grouting pressure over time is expressed as: The distribution functions between the fracture length and the fracture opening of the new branch fractures and the grouting pressure are expressed as: , ; The complete second joint probability distribution model is represented as: In the formula denotes the correlation parameter of the Copula function in the second joint probability distribution model.

4. The multi-parameter coupling-based fissure rock mass surrounding rock grouting reinforcement design method according to claim 3, characterized in that: The staged grouting strategy includes two continuous stages of low-pressure grouting and high-pressure grouting, the low-pressure grouting stage is used for filling the branch fracture, and the high-pressure grouting stage is used for filling the main fracture; The number of fractures of the new branch fractures generated in the low-pressure grouting stage is represented as , represents the end time of the low-pressure grouting, the number of fractures of the new branch fractures generated in the high-pressure grouting stage is represented as , represents the end time of the high-pressure grouting; The correction of the fracture parameters of the branch fracture is the correction of the number of branch fractures, and after low-pressure grouting and high-pressure grouting, the total number of branch fractures is represented as: In the formula represents the total number of fractures including branch fractures.

5. The multi-parameter coupling-based fissure rock mass surrounding rock grouting reinforcement design method according to claim 4, characterized in that: When the optimization algorithm is used to solve, the following physical constraints are met: After the low-pressure grouting stage ends, the grouting volume of the low-pressure grouting stage is greater than the total volume of the branch fracture, and the branch fracture is completely filled, and the corresponding expression is: After the high-pressure grouting stage ends, 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, and the corresponding expression is: At the same time, the total grouting time should not exceed the preset time threshold: In the formula , respectively represent the grouting flow in the low-pressure grouting stage and the high-pressure grouting stage, which are proportional to the grouting pressure in the low-pressure grouting stage and the high-pressure grouting stage, , respectively represent the total volume of the branch fissure and the total volume of the main fissure, represents a preset time threshold.

6. The multi-parameter coupling-based fissure rock mass surrounding rock grouting reinforcement design method according to claim 5, characterized in that: The total volume of the branch fracture is obtained from the fracture length, the fracture aperture of the branch fracture, and the surrounding rock thickness of the grouting area surrounding rock, and the calculation method is: The total volume of the main fracture is obtained from the fracture length, the fracture aperture of the main fracture, and the surrounding rock thickness of the grouting area surrounding rock, and the calculation method is: In the formula represents the thickness of the surrounding rock, , respectively represent the fracture length and the fracture aperture of the main fracture.

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