Method for long-term stability of rock mass with bolted joint considering long-term effect

Abstract

The application relates to the technical field of rock mechanics and geotechnical engineering, and discloses a method for long-term stability of rock mass with anchored joints considering long-term effect. The method comprises the following steps: establishing two mechanical models of separate bearing mode and joint bearing mode, respectively simulating different states of independent loading and collaborative work of rock mass and anchoring structure, obtaining and inputting historical monitoring data of joint surface displacement, anchor rod stress and surrounding rock deformation, and calculating stress distribution, displacement development and anchor rod stress state under each mode. The calculation results are compared with the corresponding monitoring data for multi-parameter verification, and the model parameters are adjusted according to the results until the verification is passed. The method deepens the understanding of the interaction mechanism of rock anchors under long-term load through double model comparison, and realizes the iteration verification and correction of the model with the help of historical monitoring data, so that the rationality and prediction credibility of long-term stability evaluation are improved.

Description

Technical Field

[0001] This invention relates to the fields of rock mechanics and geotechnical engineering, specifically to a method for long-term stability of anchored jointed rock masses considering long-term effects. Background Technology

[0002] In geotechnical engineering, the long-term stability analysis of anchored jointed rock masses typically employs a single mechanical model. These models, based on fixed constitutive relations and interaction assumptions, simplify the rock mass and anchored structure into a homogeneous composite or perform linear load distribution calculations. The analytical results directly depend on the initial assumptions of the model and fail to provide a comparative perspective under different mechanical mechanisms.

[0003] The main drawbacks of existing technologies lie in the implicit nature of the model's mechanical mechanisms and the limitations of the verification methods. A single model cannot encompass the various possible states between the rock mass and the anchor bolt, ranging from independent load-bearing to coordinated deformation, leading to potential systematic biases in the prediction of long-term stress, displacement, and anchor bolt force evolution. Furthermore, conventional methods lack a rigorous process for systematically verifying and iteratively correcting the model using long-term, multi-dimensional monitoring data. Model parameters are often fixed once set, making it unreliable to ensure their accurate reflection of the structure's aging behavior under long-term loads.

[0004] An analytical framework is needed to explicitly compare different mechanical action modes in order to identify the true interaction mechanism between the rock mass and the anchored structure under long-term loads. Furthermore, a multi-parameter quantitative verification and iterative parameter correction method based on long-term monitoring data needs to be developed to ensure that the mechanical model accurately reflects the long-term mechanical behavior of the engineering structure. Summary of the Invention

[0005] The purpose of this invention is to provide a method for the long-term stability of anchored jointed rock masses that takes into account long-term effects, so as to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides a method for long-term stability of anchored jointed rock masses considering long-term effects, the method comprising:

[0007] Acquire historical monitoring data of anchored jointed rock mass under long-term load, including joint surface displacement, anchor stress value and surrounding rock deformation;

[0008] Mechanical analysis models for separate load-bearing mode and combined load-bearing mode are constructed; the separate load-bearing mode refers to the mode in which the jointed rock mass and the anchoring structure bear the load independently, and the combined load-bearing mode refers to the mode in which the jointed rock mass and the anchoring structure work together to bear the load.

[0009] Historical monitoring data were input into the mechanical analysis models of separate bearing mode and combined bearing mode respectively, and the stress distribution, displacement development and anchor stress state of joint surface under each mode were calculated.

[0010] The stress distribution, displacement development, and anchor bolt stress state calculated under separate and combined load-bearing modes were compared with the corresponding historical monitoring data to verify the rationality of the mechanical analysis model.

[0011] If the verification results are consistent, the simulation platform is built and the model is confirmed to be valid; if the verification results are inconsistent, the model parameters are adjusted and the comparison verification is carried out again until the model verification is successful.

[0012] Preferably, the construction of the mechanical analysis model for the separate load-bearing mode and the combined load-bearing mode includes the following sub-steps:

[0013] For anchored jointed rock masses, a constitutive model reflecting the shear slip and opening behavior of joint surfaces is established based on the geometric characteristics and mechanical parameters of the joint surfaces.

[0014] The anchoring structure is simulated as an elastic-plastic rod element, and its constitutive relation includes an elastic stage, a yielding stage, and a strengthening stage. The anchoring structure is connected to the jointed rock mass through interface bonding elements.

[0015] In the separate bearing mode, jointed rock mass unit groups and anchored structure unit groups are set separately. The interaction between the two is only transmitted through the interface bonding unit to transfer shear force, without considering the joint sharing of normal force.

[0016] In the joint bearing mode, the jointed rock mass unit group and the anchored structural unit group are connected by shared nodes or strong constraints, so that the two can coordinate deformation and share the load in both normal and tangential directions.

[0017] Preferably, the specific steps for calculating the stress distribution, displacement development, and anchor bolt stress state of the joint surface under each mode include:

[0018] Apply long-term load boundary conditions consistent with actual engineering to the established mechanical analysis model. The long-term loads include continuous ground stress, water pressure, and time-varying engineering disturbance forces.

[0019] The model is iteratively solved over a long time step by using the finite element numerical calculation method to obtain the normal stress and shear stress at each calculation point on the joint surface, thus forming a stress distribution cloud map.

[0020] During the iterative solution process, the cumulative displacement of the key control points of the joint surface is recorded at each time step, and the relationship curve of displacement over time is generated.

[0021] During the iterative solution process, the axial stress values ​​of each anchorage structural unit at each time step are recorded synchronously to generate a sequence of anchor stress changes over time.

[0022] Preferably, the rationality of the verification mechanical analysis model is based on the following: the deviation between the calculated stress distribution result and the stress measurement point value in the historical monitoring data is within 10%; the calculated displacement development curve is consistent with the trend of the historical displacement monitoring curve and the displacement value deviation at key time points is within 5%; and the correlation coefficient between the calculated anchor bolt stress state sequence and the historical anchor bolt stress monitoring value is greater than 0.95.

[0023] Preferably, after the comparative analysis and model validation stage, an interface treatment measure impact analysis stage is also included; the interface treatment measure impact analysis stage includes the following steps:

[0024] Based on the proven and effective mechanical analysis model of the joint bearing mode, the interface between the joint surface and the anchoring structure in the anchored jointed rock mass is selected;

[0025] Different treatment measures are set for the interface between the joint surface and the anchoring structure. The treatment measures include embedding shear connectors at the interface and setting flexible pads.

[0026] In the model, for the interface of the implanted shear connector, the material properties of the interface bonding unit are modified to high-strength bonding material, and its shear stiffness and normal stiffness are adjusted.

[0027] In the model, for the interface with the flexible pad layer, the material properties of the interface bonding unit are modified to low modulus elastic material, and it is given specific compression and shear properties.

[0028] Numerical calculations were performed on models employing different interface treatments by applying the same long-term load sequence.

[0029] The overall displacement field of the jointed rock mass, the relative slip of the joint surface, and the peak stress in the anchoring structure were extracted under different interface treatment measures.

[0030] The effects of different interface treatment measures on the stress and deformation law of jointed rock mass and the joint bearing mechanism of rock mass and anchoring structure are compared and analyzed.

[0031] Preferably, the specific method for comparing and analyzing the effects of different interface treatment measures on the stress and deformation law of jointed rock mass and the joint bearing mechanism of rock mass and anchorage structure is as follows: taking the model results without interface treatment measures as a benchmark, calculate the percentage reduction of the overall displacement of jointed rock mass, the rate of change of the maximum relative slip of joint surface, and the reduction ratio of the maximum stress peak in anchorage structure after adopting the two measures of implanting shear connectors and setting flexible cushion layer.

[0032] Preferably, after the comparative analysis and model verification stage, a stage for analyzing the interaction between the surrounding rock and the anchoring structure is also included; the stage for analyzing the interaction between the surrounding rock and the anchoring structure includes the following steps:

[0033] Based on the proven and effective mechanical analysis model of the combined bearing mode, the mechanical parameters of the surrounding rock region in the model are changed to simulate the surrounding rock conditions of different strength levels.

[0034] Under each surrounding rock condition, long-term loads were applied to the model, and numerical calculations were performed.

[0035] Calculate and extract the distribution range of the plastic zone of the surrounding rock, the stress transfer path of the contact surface between the surrounding rock and the jointed rock mass, and the distribution law of the axial force of the anchoring structure along the length in the model corresponding to each surrounding rock condition;

[0036] Based on the distribution range of the plastic zone of the surrounding rock, the stress transmission path, and the axial force distribution law of the anchoring structure, the overall joint bearing mechanism of the surrounding rock and the anchoring structure caused by the change in the strength of the surrounding rock is analyzed.

[0037] Preferably, the analysis of the overall joint bearing mechanism of the surrounding rock and anchorage structure caused by the change in surrounding rock strength includes: defining the negative correlation between the range of the plastic zone of the surrounding rock and the strength of the surrounding rock; describing the phenomenon that the stress transmission path gradually concentrates towards the anchorage structure as the strength of the surrounding rock decreases; and clarifying the law that the position of the peak axial force of the anchorage structure migrates with the change in the strength of the surrounding rock.

[0038] Preferably, the interaction analysis stage between the surrounding rock and the anchoring structure further includes a sub-stage for analyzing the impact of cavities and grouting; the sub-stage for analyzing the impact of cavities and grouting includes the following steps:

[0039] On the contact surface between the surrounding rock and the jointed rock mass, a portion of the area is selected, and the interface constraints of the portion of the area are deleted or set to extremely low stiffness to simulate the void defect of the contact surface.

[0040] Long-term loads were applied to a model containing void defects, and numerical calculations were performed to analyze the stress concentration phenomenon in the jointed rock mass surrounding the void region and the additional bending stress of the anchoring structure.

[0041] For models containing void defects, simulated grouting material is filled into the void areas, and the grouting material is assigned material property parameters that change over time to simulate the hardening process of the grout.

[0042] The same long-term load was applied to the model after grouting, and numerical calculations were performed in stages.

[0043] Extract data on the evolution of stress concentration in the void area, stress redistribution on the contact surface, and changes in additional stress in the anchoring structure during the process of grout performance changes.

[0044] Based on the evolution data of stress concentration in the extracted cavity area, the stress redistribution data of the contact surface, and the variation data of the additional stress of the anchoring structure, the law of force transmission mechanism between the surrounding rock and the anchoring structure with the change of grouting filling material performance is analyzed.

[0045] Preferably, the method for analyzing the force transmission mechanism between the surrounding rock and the anchoring structure as the performance of the grouting filling material changes is as follows: the calculation time is divided into the unhardened stage, the partially hardened stage, and the fully hardened stage of the grout body. The maximum principal stress value, the average compressive stress value of the contact surface, and the maximum additional bending stress value of the anchoring structure of the jointed rock mass surrounding the cavity area are compared in each stage. Correspondence curves between the performance parameters of the grouting material and the maximum principal stress value, the average compressive stress value of the contact surface, and the maximum additional bending stress value of the anchoring structure of the jointed rock mass surrounding the cavity area are established.

[0046] Compared with the prior art, the beneficial effects of the present invention are:

[0047] By constructing and parallelizing two mechanical models with different physical foundations—a "separate load-bearing mode" and a "joint load-bearing mode"—this approach changes the traditional single-model analytical paradigm. The two models are based on the fundamental assumptions that the rock mass and the anchored structure independently bear loads, and that their coordinated deformation works together. This dual-model architecture transforms the key interaction mechanisms in long-term mechanical behavior from implicit parameters within the model into comparable analytical objects. The analysis process can output a comprehensive view of the differences in stress distribution, displacement development, and anchor stress state under the two typical mechanisms. This allows the assessment of the long-term stability of anchored jointed rock masses to no longer rely on the presupposed conclusions of a single model, but rather, through mechanism comparison, deepen the understanding of the possible dominant response modes and evolution paths of the structure under long-term loads, enhancing the depth and explanatory power of the analysis.

[0048] A multi-parameter synchronous verification and closed-loop iterative process based on long-term historical monitoring data is employed to rigorously and quantitatively verify the model's calculation results. This process requires that the stress field, displacement field, and anchor bolt stress state output by the model must be consistent with the corresponding data obtained from long-term on-site monitoring in terms of evolution patterns. When the calculation results do not match the monitoring data, the system will trigger adjustments to the model parameters and recalculate and verify, forming a closed loop of "calculation-verification-correction." This directly anchors the reliability of the mechanical model to the long-term, real response data of the engineering entity. It forces the model parameters to undergo the test and screening of historical data, thereby enabling the final determined model and its parameters to more accurately reflect the long-term mechanical characteristics under specific engineering geological conditions and load histories, improving the objectivity and credibility of long-term stability prediction. Attached Figure Description

[0049] Figure 1This is a schematic diagram illustrating the working principle of the long-term stability method for anchored jointed rock masses considering long-term effects as described in this invention.

[0050] Figure 2 This is a flowchart of the numerical solution and result extraction process;

[0051] Figure 3 A flowchart for the impact analysis of different interface processing measures;

[0052] Figure 4 A biaxial bar chart showing the area of ​​the plastic zone and the peak position of the anchor bolt axial force in anchored jointed rock mass under different surrounding rock strengths;

[0053] Figure 5 A biaxial line graph showing the changes in compressive stress at the contact surface and additional bending stress of the anchor rod during grouting of jointed rock cavities for anchoring. Detailed Implementation

[0054] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0055] Please see Figure 1 This invention provides a method for assessing the long-term stability of anchored jointed rock masses considering long-term effects. The method includes: a comparative analysis and model verification stage to obtain historical monitoring data of the target anchored jointed rock mass under long-term loads. This data should cover the displacement of the joint surfaces, the stress values ​​of the anchor bolts, and the deformation of the surrounding rock. Two mechanical analysis models are constructed: one is a separate bearing mode, in which the jointed rock mass and the anchoring structure are considered as independently load-bearing systems; the other is a combined bearing mode, in which the jointed rock mass and the anchoring structure are considered as a cooperating whole, jointly bearing the load. Next, the historical monitoring data are input into these two mechanical analysis models respectively, and the stress distribution, displacement development history, and anchor bolt stress state of the joint surfaces under each mode are calculated. The stress distribution, displacement development, and anchor bolt stress state calculated by the model are compared with the corresponding historical monitoring data to verify the rationality of the constructed mechanical analysis model. If the comparison results are consistent, the simulation platform is considered to be successfully built and the model is valid; if the comparison results are inconsistent, the input parameters of the model need to be adjusted, and the aforementioned calculation and comparison verification process needs to be repeated until the model calculation results and monitoring data reach an acceptable level of consistency.

[0056] In one embodiment of the present invention, see [reference] Figure 2For anchored jointed rock masses, a constitutive model reflecting the shear slip and opening behavior of the joint surfaces is established based on the geometric characteristics and mechanical parameters of the joint surfaces. Simultaneously, the anchoring structure is simulated as an elasto-plastic rod element, whose constitutive relations include elastic, yielding, and strengthening stages. The anchoring structure is connected to the jointed rock mass through interface bonding elements. In the separate load-bearing mode, jointed rock mass element groups and anchoring structure element groups are set separately. The interaction between these two groups only transmits shear force through interface bonding elements, without considering the joint sharing of normal forces. In the joint load-bearing mode, the jointed rock mass element groups and anchoring structure element groups are connected through shared nodes or strong constraints, enabling them to deform in a coordinated manner and share the load in both normal and tangential directions. Long-term load boundary conditions consistent with actual engineering are applied to the constructed mechanical analysis model. These long-term loads include continuous ground stress, water pressure, and time-varying engineering disturbance forces. The model is iteratively solved over a long time step using the finite element method to obtain the normal and shear stresses at each calculation point on the joint surface, forming a stress distribution cloud map. During the iterative solution process, the cumulative displacement values ​​of key control points on the joint surface are recorded at each time step, generating a curve showing the relationship between displacement and time. Simultaneously, the axial stress values ​​of each anchoring structural element are recorded at each time step, generating a sequence of anchor stress changes over time.

[0057] In practical implementation, taking a rock slope anchoring project with a single continuous joint surface as an example scenario, it is necessary to establish a constitutive model reflecting the shear slip and opening behavior of the joint surface based on its geometric characteristics such as undulation angle and roughness, as well as mechanical parameters such as basic friction angle and peak shear strength. In some embodiments, this constitutive relationship can consider the nonlinear relationship between the peak shear strength and normal stress of the joint surface, and the relationship between shear stress and shear displacement can be expressed piecewise as follows: In the elastic stage, the shear stress... With shear displacement The relationship is linear; after exceeding the peak strength, it enters the softening stage, and the shear stress decreases with increasing displacement to the residual strength. It can be understood that this constitutive model is the basis for simulating the long-term behavior of jointed rock masses.

[0058] In practical implementation, the anchoring structure is simulated as an elasto-plastic rod element. The constitutive relationship of the anchoring structure includes an elastic stage, a yielding stage, and a strengthening stage. The anchoring structure is connected to the jointed rock mass through interface bonding elements, which are used to simulate the mechanical behavior of the grouting material or resin. Their characteristics include bond stiffness and ultimate bond strength. In the separate load-bearing mode, jointed rock mass element groups and anchoring structure element groups are set separately. The interaction between the jointed rock mass element groups and the anchoring structure element groups is only through the interface bonding elements, transferring shear force without considering the joint sharing of normal forces. This means that in the normal direction, the deformation of the jointed rock mass and the deformation of the anchoring structure are calculated independently. In the joint load-bearing mode, the jointed rock mass element groups and the anchoring structure element groups are connected through shared nodes or strong constraints, allowing the jointed rock mass and the anchoring structure to deform in a coordinated manner and share the load in both the normal and tangential directions. This connection method forces the continuity of displacement at the contact point.

[0059] In practical implementation, long-term load boundary conditions consistent with actual engineering are applied to the constructed mechanical analysis model. These long-term loads include sustained ground stress, water pressure, and time-varying engineering disturbance forces. In the example scenario, sustained ground stress is determined by the rock mass's self-weight and tectonic stress field; water pressure is set based on the groundwater level and the permeability characteristics of the joint surfaces; and time-varying engineering disturbance forces can be simulated as cyclic loads added to the slope crest or long-term, slowly increasing surcharges. The model is iteratively solved using the finite element method with long time steps. During the solution process, the normal stress at each calculation point on the joint surface is obtained. With shear stress This generates a stress distribution cloud map. In some embodiments, iterative solutions with long time steps need to consider the creep characteristics of the rock mass and anchorage structure, setting the material parameters in the model as time-dependent functions. Optionally, viscoelastic or viscoplastic constitutive models can be used to characterize long-term effects.

[0060] In practical implementation, during the iterative solution process, it is necessary to record the cumulative displacement values ​​of key control points on the joint surface at each time step. These key control points can be located in the middle of the joint surface or at potential slip locations, thus generating a displacement-time relationship curve. Simultaneously, the axial stress values ​​of each anchored structural unit are recorded at each time step, generating a sequence of anchor stress changes over time. It can be understood that the displacement-time curve and stress-time sequence are direct data for assessing long-term stability. Comparing the displacement development curves and anchor stress sequences obtained from the separate bearing mode with the corresponding results under the combined bearing mode reveals a systematic difference in the long-term deformation trends and stress responses between the two modes. The cumulative displacement value of the joint surface under the combined bearing mode is generally smaller than the corresponding value under the separate bearing mode, while the peak axial force shared by the anchor in the combined bearing mode is usually higher. This data comparison reveals the impact of the bearing mode assumption on the long-term stability assessment conclusions.

[0061] In one embodiment of the present invention, the first verification criterion is that the deviation between the calculated stress distribution result and the stress measurement point values ​​in the historical monitoring data needs to be within 10%. Specifically, this involves extracting the normal stress and shear stress values ​​calculated by the model at the spatial coordinates corresponding to the locations of the numerical model grid nodes and the on-site stress monitoring points, and comparing them one by one with the historical monitoring values ​​recorded by the stress sensor at the same location at the same time. In some embodiments, for multiple stress monitoring points, the deviation... The calculation can be performed for all valid measurement points. Defined as the average of the ratios of the absolute values ​​of the differences between the calculated and monitored stress values ​​at all measuring points to the absolute values ​​of the corresponding monitored values, this average value must be less than 0.1. This standard ensures the static reliability of the model in terms of spatial stress field distribution.

[0062] In practical implementation, the second verification criterion is that the calculated displacement development curve and the historical displacement monitoring curve show consistent trends, and the deviation of the displacement value at key time points is within 5%. Specifically, this involves extracting the displacement-time history data of nodes or units corresponding to the on-site displacement monitoring points from the model calculation results, and comparing the model-calculated displacement curve and the historical monitoring displacement curve on the same coordinate system. The judgment of trend consistency needs to be based on the overall shape of the curves, such as whether they both exhibit characteristics of initial rapid growth, subsequent creep stabilization, or continuous slow growth. The deviation of the displacement value at key time points refers to the relative error between the model-calculated displacement value and the monitored displacement value at specific time points selected during long-term monitoring that have engineering significance; this error must be controlled within 5%. In some embodiments, the selection of key time points needs to cover the characteristic stages of load changes and deformation development.

[0063] In practical implementation, the third verification criterion is that the correlation coefficient between the calculated anchor bolt stress state sequence and the historical anchor bolt stress monitoring values ​​is greater than 0.95. Specifically, the axial stress sequence of each anchor bolt at different calculation time steps is output from the model calculation results. Simultaneously, the stress monitoring value sequence recorded by the stress gauge on the corresponding anchor bolt at the same time is obtained. Both sets of sequences must have the same time length and sampling interval. (Anchor bolt stress sequence correlation coefficient) The calculation formula is:

[0064]

[0065] in: Representing the The model calculates the stress values ​​at each time point. Representing the The monitored stress values ​​at each time point and These represent the means of the two sequences, respectively. This represents the total number of data points. It's understandable that the correlation coefficient standard focuses on evaluating the degree to which the model matches the actual situation in simulating the dynamic response of anchor stress over time. Optionally, if the model uses separate bearing mode and combined bearing mode, the calculation results for both modes need to be verified using the three criteria mentioned above, and the verification results should be compared with historical monitoring data. The data shows that only the calculation results under the combined bearing mode can simultaneously meet all three criteria of stress deviation, displacement deviation, and correlation coefficient. The displacement development curve trend or anchor stress correlation coefficient under the separate bearing mode may differ significantly from the monitoring data. This data comparison directly supports the rationality of the combined bearing mode in simulating long-term effects.

[0066] In one embodiment of the present invention, see [reference] Figure 3 In practical implementation, based on the validated and effective mechanical analysis model of the joint bearing mode, the interface region where the joint surface intersects with the anchoring structure in the anchored jointed rock mass is selected as the analysis object. Different treatment measures are set for the interface between the joint surface and the anchoring structure, including the implantation of shear connectors and the setting of flexible cushion layers. In the model, for the interface where shear connectors are planned to be implanted, the material properties of the original interface bonding unit are modified, defining the material properties as high-strength bonding materials, and the shear stiffness and normal stiffness parameters of the interface bonding unit are adjusted to the corresponding high value range. In the model, for the interface where flexible cushion layers are planned to be set, the material properties of the original interface bonding unit are modified, defining the material properties as low-modulus elastic materials, and assigning low-modulus elastic material compressive and shear performance parameters. It can be understood that modifying material properties is a direct way to simulate the mechanical response of different interface treatment measures.

[0067] In practical implementation, numerical calculations were performed on models employing different interface treatment measures, using the same long-term load sequence as the original verification stage. The long-term load sequence included constant confining pressure and periodically varying train vibration loads. The overall displacement field of the jointed rock mass, the relative slip of the joint surfaces, and the peak stress in the anchoring structure were extracted from the model after implementing the shear connector implantation measure. Simultaneously, the overall displacement field of the jointed rock mass, the relative slip of the joint surfaces, and the peak stress in the anchoring structure were extracted from the model after implementing the flexible cushion layer measure. Meanwhile, the corresponding calculation results of the original combined bearing mode model without any interface treatment measures were retained as a benchmark. The effects of different interface treatment measures on the stress-deformation law of the jointed rock mass and the combined bearing mechanism of the rock mass and anchoring structure were compared and analyzed. Specifically, using the model results without interface treatment measures as a benchmark, the percentage reduction in the overall displacement of the jointed rock mass, the rate of change of the maximum relative slip of the joint surfaces, and the reduction ratio of the maximum peak stress in the anchoring structure were calculated after implementing the shear connector implantation and the flexible cushion layer measures.

[0068] In some embodiments, the rate of change of the maximum relative slip of the joint surface formula:

[0069]

[0070] in: This represents the maximum relative slip of the joint surfaces in the untreated model. This represents the maximum relative slip of the joint surface in the model after adopting a certain interface treatment measure. The reduction ratio of the maximum stress peak in the anchored structure can be calculated in a similar manner. Data shows that after implanting shear connectors, the rate of change of the maximum relative slip of the joint surface is negative, indicating an increase in slip, while the reduction ratio of the maximum stress peak in the anchored structure is positive. After setting a flexible cushion layer, the percentage reduction of the overall displacement of the jointed rock mass is positive, but the rate of change of the maximum relative slip of the joint surface may show a slight positive value. This data comparison reveals the differentiated impact of different interface treatment measures on the internal force and deformation distribution mechanism of the combined bearing system. Implanting shear connectors mainly changes the shear force transmission path and may lead to the relief of anchor stress concentration, while setting a flexible cushion layer mainly affects the overall deformation by adjusting the normal contact state.

[0071] In one embodiment of the present invention, in a specific implementation, based on a proven and effective mechanical analysis model of the combined bearing mode, the mechanical parameters of the surrounding rock region in the model are changed to simulate surrounding rock conditions of different strength levels. The changes in the surrounding rock mechanical parameters mainly involve systematically adjusting the cohesion, internal friction angle, and deformation modulus of the rock mass, thereby defining three typical working conditions: high-strength surrounding rock conditions, medium-strength surrounding rock conditions, and low-strength surrounding rock conditions. Under each surrounding rock condition, the same long-term load is applied to the model, including the initial geostress field, seepage water pressure, and long-term dynamic load transmitted from the operating equipment, followed by numerical calculations. The distribution range of the plastic zone of the surrounding rock, the stress transmission path at the contact surface between the surrounding rock and the jointed rock mass, and the distribution law of the axial force of the anchoring structure along the length of the anchor rod are calculated and extracted in the model corresponding to each surrounding rock condition.

[0072] In practical implementation, based on the extracted distribution range of the plastic zone of the surrounding rock, the stress transmission path, and the axial force distribution law of the anchoring structure, the overall joint bearing mechanism of the surrounding rock and anchoring structure caused by changes in surrounding rock strength is analyzed. The analysis includes defining the negative correlation between the range of the plastic zone and the surrounding rock strength, describing the phenomenon that the stress transmission path gradually concentrates towards the anchoring structure as the surrounding rock strength decreases, and clarifying the law of migration of the peak position of the axial force in the anchoring structure with changes in surrounding rock strength. The negative correlation between the range of the plastic zone and the surrounding rock strength can be expressed by quantitative indicators. In some embodiments, a comprehensive index of surrounding rock strength is defined. Its cohesion with the rock mass and internal friction angle Positive correlation; the range of the plastic region is based on the total area of ​​the plastic unit. The relationship between the two measures can be characterized as follows:

[0073]

[0074] in: and These are positive coefficients related to the model geometry and loads. This is a natural constant. It can be understood that this relationship quantifies the trend of damage area expansion caused by the weakening of the surrounding rock's own bearing capacity. The phenomenon of stress transmission paths concentrating towards the anchoring structure is manifested in the fact that as the strength grade of the surrounding rock changes from high to low, the proportion of compressive stress flow transmitted through the surrounding rock's own skeleton decreases, while the proportion of stress flow transmitted through the anchoring structure increases significantly. Specifically, the law governing the migration of the peak axial force position of the anchoring structure with changes in surrounding rock strength is as follows: in high-strength surrounding rock, the peak axial force point is close to the joint surface; in medium- and low-strength surrounding rock, the peak axial force point shifts towards the deeper parts of the surrounding rock.

[0075] To clearly present the analysis results, please refer to Table 1, which summarizes the key data under different surrounding rock strength conditions.

[0076] Table 1: Comparison of Combined Bearing Characteristics under Different Surrounding Rock Strength Conditions

[0077]

[0078] Understandably, the data in the table visually compares the calculation results under different working conditions. The data shows that the area of ​​the plastic zone in the surrounding rock increases monotonically as the surrounding rock strength decreases. The peak position of the anchor bolt axial force gradually moves away from the joint surface and into the surrounding rock as the surrounding rock strength decreases. This data comparison indicates that in weak surrounding rock, a longer anchorage section is required to mobilize the resistance of the deep, stable rock mass. The change in stress transfer path concentration qualitatively reveals the evolution of the combined bearing mechanism: a transition from surrounding rock-dominated bearing to anchorage structure-dominated bearing. In some embodiments, optionally, the comprehensive index of surrounding rock strength... Can be adopted The calculation is simplified using the form of [formula missing]. Alternatively, the extent of the plastic region can also be measured by the volume enclosed by the plastic strain contour lines.

[0079] See Figure 4This is a biaxial bar chart showing the area of ​​the plastic zone and the peak position of the anchor bolt axial force under different surrounding rock strengths in anchored jointed rock masses. It is a biaxial grouped bar chart, displaying the area of ​​the plastic zone (left axis) and the peak position of the anchor bolt axial force (right axis) under high-strength, medium-strength, and low-strength surrounding rock conditions, corresponding to a comparison of key indicators in the surrounding rock characteristic analysis stage. The lower the surrounding rock strength, the more severe the plastic damage, and the anchor bolt needs to extend deeper to mobilize the resistance of the stabilizing rock mass. It is used to quantify the rock mass damage and anchor bolt stress characteristics under different surrounding rock strengths, and is a core basis for analyzing the combined bearing mechanism of surrounding rock and anchorage, guiding the optimized design of anchor bolt length and arrangement in engineering projects. In the long-term stability analysis of anchored jointed rock masses, this type of chart is a key tool for evaluating the collaborative working ability of the surrounding rock and anchorage structure, and can intuitively reveal the influence of surrounding rock strength on engineering safety.

[0080] In one embodiment of the present invention, in a specific implementation, a portion of the contact surface between the surrounding rock and the jointed rock mass is selected to simulate contact surface void defects. Specifically, this involves identifying a section of the contact surface unit between the surrounding rock and the jointed rock mass located at the tunnel shoulder in the numerical model, deleting the interface constraints of this selected area, or setting it to extremely low stiffness to simulate void defects caused by construction quality or geological reasons. Long-term loads consistent with the engineering background are applied to the model containing void defects for numerical calculation. The long-term loads include additional stress caused by mining and groundwater seepage pressure. The stress concentration phenomenon in the jointed rock mass surrounding the void area and the additional bending stress caused by the lack of local support in the anchoring structure are analyzed.

[0081] In practical implementation, for models containing voids, simulated grouting material is filled into the void areas to simulate the hardening process of the grout. The low-stiffness elements representing the voids in the model are replaced with elements simulating the grouting material. Time-varying material property parameters are assigned to the grouting material, such as its elastic modulus. It can be defined as time The growth function:

[0082]

[0083] in: The elastic modulus of the initial liquid grout. This represents the final elastic modulus of the grout after it has fully hardened. This parameter controls the hardening rate. It can be understood that this function characterizes the performance evolution of the grout from a fluid state to a solid state. The same long-term load is applied to the grout-filled model, and numerical calculations are performed in stages. The division of the calculation stages must correspond to the characteristic time points of the grout material performance changes.

[0084] In practical implementation, data on the evolution of stress concentration in the jointed rock mass surrounding the cavity area, stress redistribution at the contact surface between the surrounding rock and the jointed rock mass, and changes in the additional bending stress of the anchoring structure are extracted during the performance changes of the grout. Based on the extracted data on the evolution of stress concentration in the cavity area, stress redistribution at the contact surface, and changes in the additional stress of the anchoring structure, the law of force transmission mechanism between the surrounding rock and the anchoring structure as the performance of the grouting filling material changes is analyzed. The specific method is as follows: the calculation time is divided into the unhardened stage of the grout, the partially hardened stage of the grout, and the fully hardened stage of the grout. The maximum principal stress value of the jointed rock mass surrounding the cavity area, the average compressive stress value of the contact surface between the surrounding rock and the jointed rock mass, and the maximum additional bending stress value of the anchoring structure are compared in each stage. Correspondence curves between the performance parameters of the grouting material and the maximum principal stress value of the jointed rock mass surrounding the cavity area, the average compressive stress value of the contact surface between the surrounding rock and the jointed rock mass, and the maximum additional bending stress value of the anchoring structure are established.

[0085] Data shows that during the unhardened stage of the grout, the maximum principal stress of the jointed rock mass surrounding the cavity area remains high, while the average compressive stress at the contact surface between the surrounding rock and the jointed rock mass is low, and the maximum additional bending stress of the anchoring structure is significant. As the calculation progresses into the partially hardened stage of the grout, the maximum principal stress of the jointed rock mass surrounding the cavity area begins to decrease, the average compressive stress at the contact surface between the surrounding rock and the jointed rock mass gradually increases, and the maximum additional bending stress of the anchoring structure decreases simultaneously. During the fully hardened stage of the grout, the maximum principal stress of the jointed rock mass surrounding the cavity area drops to a level close to that of the complete contact surface, the average compressive stress at the contact surface between the surrounding rock and the jointed rock mass returns to the normal range, and the maximum additional bending stress of the anchoring structure essentially disappears. This data comparison clearly reveals that grouting filling, by gradually restoring the force transmission function of the contact surface, effectively alleviates stress concentration and redirects the load back to the path shared by the surrounding rock and the rock mass, thereby improving the stress state of the anchoring structure. In some embodiments, optionally, the strength parameters of the grouting material, such as cohesion and internal friction angle, can also be set as similar time-varying functions.

[0086] See Figure 5 This is a biaxial line graph showing the changes in compressive stress at the contact surface and additional bending stress of the anchor bolt during grouting of cavities in anchored jointed rock masses. It illustrates the trends of average compressive stress at the contact surface (left axis) and additional bending stress of the anchor bolt (right axis) over the grouting period (0-25 days), corresponding to the evaluation of the grouting reinforcement effect in the force transmission mechanism analysis stage. The two are significantly negatively correlated, indicating that the grouting hardening process transforms the load transmission mechanism from "anchor bolt bearing alone" to "shared load by surrounding rock, grout body, and rock mass." Such graphs are crucial tools for verifying the feasibility of grouting reinforcement technology in the long-term stability analysis of anchored jointed rock masses, visually revealing the improvement patterns of the mechanical state during grouting.

[0087] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0088] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for long-term stability of anchored jointed rock masses considering long-term effects, characterized in that, This includes a comparative analysis and model validation phase; the comparative analysis and model validation phase includes the following steps: Acquire historical monitoring data of anchored jointed rock mass under long-term load, including joint surface displacement, anchor stress value and surrounding rock deformation; Mechanical analysis models for separate load-bearing mode and combined load-bearing mode are constructed; the separate load-bearing mode refers to the mode in which the jointed rock mass and the anchoring structure bear the load independently, and the combined load-bearing mode refers to the mode in which the jointed rock mass and the anchoring structure work together to bear the load. Historical monitoring data were input into the mechanical analysis models of separate bearing mode and combined bearing mode respectively, and the stress distribution, displacement development and anchor stress state of joint surface under each mode were calculated. The stress distribution, displacement development, and anchor bolt stress state calculated under separate and combined load-bearing modes were compared with the corresponding historical monitoring data to verify the rationality of the mechanical analysis model. If the verification results are consistent, the simulation platform is built and the model is confirmed to be valid; if the verification results are inconsistent, the model parameters are adjusted and the comparison verification is performed again until the model verification is successful. The rationality of the mechanical analysis model is verified as follows: the deviation between the calculated stress distribution results and the stress measurement points in the historical monitoring data is within 10%; the calculated displacement development curve is consistent with the trend of the historical displacement monitoring curve and the displacement value at key time points is within 5%; and the correlation coefficient between the calculated anchor bolt stress state sequence and the historical anchor bolt stress monitoring values ​​is greater than 0.

95. Following the comparative analysis and model validation phase, an impact analysis phase on interface treatment measures is also included; this impact analysis phase includes the following steps: Based on the proven and effective mechanical analysis model of the joint bearing mode, the interface between the joint surface and the anchoring structure in the anchored jointed rock mass is selected; Different treatment measures are set for the interface between the joint surface and the anchoring structure. The treatment measures include embedding shear connectors at the interface and setting flexible pads. In the model, for the interface of the implanted shear connector, the material properties of the interface bonding unit are modified to high-strength bonding material, and its shear stiffness and normal stiffness are adjusted. In the model, for the interface with the flexible pad layer, the material properties of the interface bonding unit are modified to low modulus elastic material, and it is given specific compression and shear properties. Numerical calculations were performed on models employing different interface treatments by applying the same long-term load sequence. The overall displacement field of the jointed rock mass, the relative slip of the joint surface, and the peak stress in the anchoring structure were extracted under different interface treatment measures. The effects of different interface treatment measures on the stress and deformation law of jointed rock mass and the joint bearing mechanism of rock mass and anchoring structure are compared and analyzed.

2. The method for long-term stability of anchored jointed rock mass considering long-term effects according to claim 1, characterized in that, The construction of the mechanical analysis models for separate load-bearing modes and combined load-bearing modes includes the following sub-steps: For anchored jointed rock masses, a constitutive model reflecting the shear slip and opening behavior of joint surfaces is established based on the geometric characteristics and mechanical parameters of the joint surfaces. The anchoring structure is simulated as an elastic-plastic rod element, and its constitutive relation includes an elastic stage, a yielding stage, and a strengthening stage. The anchoring structure is connected to the jointed rock mass through interface bonding elements. In the separate bearing mode, jointed rock mass unit groups and anchored structure unit groups are set separately. The interaction between the two is only transmitted through the interface bonding unit to transfer shear force, without considering the joint sharing of normal force. In the joint bearing mode, the jointed rock mass unit group and the anchored structural unit group are connected by shared nodes or strong constraints, so that the two can coordinate deformation and share the load in both normal and tangential directions.

3. The method for long-term stability of anchored jointed rock mass considering long-term effects according to claim 1, characterized in that, The calculations yield the stress distribution, displacement development, and anchor bolt stress state of the joint surface under each mode. The specific steps include: Apply long-term load boundary conditions consistent with actual engineering to the established mechanical analysis model. The long-term loads include continuous ground stress, water pressure, and time-varying engineering disturbance forces. The model is iteratively solved over a long time step by using the finite element numerical calculation method to obtain the normal stress and shear stress at each calculation point on the joint surface, thus forming a stress distribution cloud map. During the iterative solution process, the cumulative displacement of the key control points of the joint surface is recorded at each time step, and the relationship curve of displacement over time is generated. During the iterative solution process, the axial stress values ​​of each anchorage structural unit at each time step are recorded synchronously to generate a sequence of anchor stress changes over time.

4. The method for long-term stability of anchored jointed rock mass considering long-term effects according to claim 1, characterized in that, The comparative analysis of the effects of different interface treatment measures on the stress and deformation law of jointed rock mass and the joint bearing mechanism of rock mass and anchorage structure is conducted as follows: taking the model results without interface treatment measures as a benchmark, the percentage reduction of the overall displacement of jointed rock mass, the rate of change of the maximum relative slip of the joint surface, and the reduction ratio of the maximum stress peak in the anchorage structure are calculated after adopting the two measures of implanting shear connectors and setting flexible cushion layers.

5. A method for long-term stability of anchored jointed rock mass considering long-term effects according to claim 1, characterized in that, Following the comparative analysis and model verification stage, the analysis also includes a stage of interaction analysis between the surrounding rock and the anchoring structure; this stage includes the following steps: Based on the proven and effective mechanical analysis model of the combined bearing mode, the mechanical parameters of the surrounding rock region in the model are changed to simulate the surrounding rock conditions of different strength levels. Under each surrounding rock condition, long-term loads were applied to the model, and numerical calculations were performed. Calculate and extract the distribution range of the plastic zone of the surrounding rock, the stress transfer path of the contact surface between the surrounding rock and the jointed rock mass, and the distribution law of the axial force of the anchoring structure along the length in the model corresponding to each surrounding rock condition; Based on the distribution range of the plastic zone of the surrounding rock, the stress transmission path, and the axial force distribution law of the anchoring structure, the overall joint bearing mechanism of the surrounding rock and the anchoring structure caused by the change in the strength of the surrounding rock is analyzed.

6. A method for long-term stability of anchored jointed rock mass considering long-term effects according to claim 5, characterized in that, The analysis of the overall joint bearing mechanism of the surrounding rock and anchorage structure caused by changes in surrounding rock strength includes: defining the negative correlation between the range of the plastic zone of the surrounding rock and the strength of the surrounding rock; describing the phenomenon that the stress transmission path gradually concentrates towards the anchorage structure as the strength of the surrounding rock decreases; and clarifying the law that the peak position of the axial force of the anchorage structure migrates with changes in the strength of the surrounding rock.

7. A method for long-term stability of anchored jointed rock mass considering long-term effects according to claim 6, characterized in that, The analysis stage of the interaction between the surrounding rock and the anchoring structure also includes a sub-stage of analyzing the impact of cavities and grouting; the sub-stage of analyzing the impact of cavities and grouting includes the following steps: On the contact surface between the surrounding rock and the jointed rock mass, a portion of the area is selected, and the interface constraints of the portion of the area are deleted or set to extremely low stiffness to simulate the void defect of the contact surface. Long-term loads were applied to a model containing void defects, and numerical calculations were performed to analyze the stress concentration phenomenon in the jointed rock mass surrounding the void region and the additional bending stress of the anchoring structure. For models containing void defects, simulated grouting material is filled into the void areas, and the grouting material is assigned material property parameters that change over time to simulate the hardening process of the grout. The same long-term load was applied to the model after grouting, and numerical calculations were performed in stages. Extract data on the evolution of stress concentration in the void area, stress redistribution on the contact surface, and changes in additional stress in the anchoring structure during the process of grout performance changes. Based on the evolution data of stress concentration in the extracted cavity area, the stress redistribution data of the contact surface, and the variation data of the additional stress of the anchoring structure, the law of force transmission mechanism between the surrounding rock and the anchoring structure with the change of grouting filling material performance is analyzed.

8. A method for long-term stability of anchored jointed rock mass considering long-term effects according to claim 7, characterized in that, The analysis of the force transmission mechanism between the surrounding rock and the anchoring structure varies with the performance of the grouting filling material. The specific method is as follows: the calculation time is divided into the unhardened stage, the partially hardened stage and the fully hardened stage of the grout body. The maximum principal stress value, the average compressive stress value of the contact surface and the maximum additional bending stress value of the anchoring structure of the jointed rock mass around the cavity area are compared in each stage. Correspondence curves between the performance parameters of the grouting material and the maximum principal stress value, the average compressive stress value of the contact surface and the maximum additional bending stress value of the jointed rock mass around the cavity area and the anchoring structure are established.

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