A method for analyzing multi-field coupling creep characteristics of rock mass with anchor joint

Abstract

This invention relates to the fields of rock mechanics and underground engineering, specifically a method for analyzing the multi-field coupled creep characteristics of anchored jointed rock masses. The method includes: preparing anchored rock mass samples corroded by inorganic salts and containing different joint orientations; installing anchor bolts with different prestressing; conducting graded loading creep compression experiments, simultaneously acquiring axial deformation and acoustic emission signals; plotting creep time-history curves based on deformation data; determining long-term strength and creep stages using the steady-state creep rate method; calibrating the crack initiation and propagation process at each creep stage using acoustic emission signals; analyzing the differences in crack development and anchorage failure responses under different inorganic salt compositions, concentrations, joint orientations, and prestressing conditions to determine the degree of influence of each factor on the anchor bolt support effect at each creep stage. This method, by coupling chemical corrosion and prestressing, achieves simultaneous quantitative analysis of macroscopic creep characteristics and microscopic damage evolution, improving the accuracy of long-term strength prediction and understanding of anchorage failure mechanisms.

Description

Technical Field

[0001] This invention relates to the fields of rock mechanics and underground engineering, and in particular to a method for analyzing the multi-field coupled creep characteristics of anchored jointed rock masses. Background Technology

[0002] Studies on the creep characteristics of conventionally anchored jointed rock masses mostly focus on rock samples in natural conditions or under single-aquatic environments, with anchor bolt support typically employing unstressed or fixed anchoring methods. Creep experiments collect axial deformation data to plot time-history curves, relying on experience to determine creep stages and estimate long-term strength. Acoustic emission monitoring technology has been used to monitor rock fracture processes, but it mainly focuses on counting or locating fracture events, without systematically linking it to the entire creep process. Existing methods are insufficient to reflect the complex conditions in actual engineering projects where underground rock masses are exposed to corrosive groundwater or seawater environments for extended periods, as well as the complex working conditions of active prestressed support with anchor bolts.

[0003] Existing technical solutions have shortcomings. They neglect the long-term effects of inorganic salt corrosion on the mineral composition and structural weakening of rock masses, as well as the bonding performance of the anchor bolt-rock mass interface, leading to inaccurate predictions of the aging deformation and failure of engineering rock masses. The attenuation law of the prestressed anchor bolt's support effect during creep is not quantitatively considered, and the anchoring design lacks parameter basis under multi-field coupling. Macroscopic creep analysis relies on subjective diagrams or empirical formulas, resulting in low accuracy and poor consistency in determining long-term strength. Furthermore, acoustic emission signal acquisition is disconnected from creep stage analysis, making it impossible to correlate crack evolution processes to specific creep stages, and the microscopic mechanism of anchoring failure remains unclear.

[0004] To address the long-term mechanical behavior of jointed rock masses under the coupled effects of inorganic salt corrosion and prestressed anchoring, an analytical method is needed to accurately characterize creep properties and reveal internal damage patterns. This method must integrate the interactive effects of chemical and stress fields and achieve a synchronous dynamic correlation between macroscopic creep parameters and microscopic fracture events. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of existing technologies and propose a method for analyzing the multi-field coupled creep characteristics of anchored jointed rock masses.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: a method for analyzing the multi-field coupled creep characteristics of anchored jointed rock masses, comprising:

[0007] Inorganic salt-corroded anchored jointed rock mass samples with different joint orientations were prepared, and anchor rods with different prestresses were installed in the anchored jointed rock mass samples.

[0008] A graded loading creep compression test was conducted on the anchored jointed rock mass sample, and the axial deformation data and time data of the anchored jointed rock mass sample were collected in real time.

[0009] Acoustic emission monitoring equipment was used to collect the acoustic emission signals of the anchored jointed rock mass sample during the creep compression test in real time;

[0010] Based on the axial deformation data and time data, the creep deformation time history curves of the anchored jointed rock mass specimens were plotted.

[0011] The long-term strength and creep stage of the anchored jointed rock mass specimen were determined by analyzing the creep deformation time history curve based on the steady-state creep rate method.

[0012] The initiation and propagation process of cracks in the anchored jointed rock mass sample during each stage of creep was determined based on the acoustic emission signal.

[0013] The differences in response between crack development patterns and anchorage failure characteristics under different inorganic salt compositions, concentrations, joint orientations, and prestressed anchor conditions were analyzed.

[0014] Based on the response differences of the anchoring failure characteristics, the degree of influence of different influencing factors on the anchor support effect in each stage of creep of the anchored jointed rock mass is determined.

[0015] As a further aspect of the present invention, the step of performing a graded loading creep compression test on the anchored jointed rock mass sample specifically involves:

[0016] Axial compressive loads are applied to the anchored jointed rock mass specimen in stages according to a preset stress level sequence;

[0017] At each stress level, the axial compressive load is kept constant and the loading continues until the creep deformation rate of the anchored jointed rock mass specimen reaches a relatively stable state.

[0018] Record the axial deformation and time data of the anchored jointed rock mass specimens from the start of loading to the deformation stabilization process at each stress level;

[0019] When the anchored jointed rock mass sample enters the accelerated creep stage or undergoes macroscopic failure, the graded loading creep compression test is terminated.

[0020] As a further aspect of the present invention, the use of acoustic emission monitoring equipment to collect acoustic emission signals of the anchored jointed rock mass sample in real time during the creep compression test specifically includes:

[0021] An array of acoustic emission sensors is arranged on the surface of the anchored jointed rock mass sample, ensuring that the sensors and the sample surface are acoustically connected through a coupling agent;

[0022] Throughout the entire process of the graded loading creep compression experiment, electrical signals converted by the acoustic emission sensor array are continuously received;

[0023] The received electrical signal is amplified and filtered to remove environmental noise and interference from the equipment's inherent frequency.

[0024] Set a threshold voltage to trigger an acoustic emission event. When the signal amplitude exceeds the threshold voltage, record the time as the occurrence time of the acoustic emission event and collect the waveform data of the acoustic emission event.

[0025] Multiple parameters, including arrival time, rise time, duration, amplitude, energy, and count, of acoustic emission events are extracted from the acquired waveform data.

[0026] Based on the arrival time difference of the same event received by different sensors in the acoustic emission sensor array, the source location coordinates of the acoustic emission event inside the anchored jointed rock mass sample are calculated by a positioning algorithm.

[0027] As a further aspect of the present invention, the step of plotting the creep deformation time history curve of the anchored jointed rock mass sample based on the axial deformation data and time data specifically involves:

[0028] The axial deformation data collected at each stress level are paired with the corresponding acquisition time data to form a data point sequence at each stress level.

[0029] In the time-deformation coordinate system, all data points are plotted sequentially, and a smooth curve is used to connect consecutive data points under the same stress level.

[0030] On the creep deformation time history curve, mark the loading start time and the unloading or the start of the next loading level for each stress level;

[0031] Based on the long-term strength determined by the steady-state creep rate method, mark the time and deformation amount corresponding to the critical stress point on the creep deformation time history curve.

[0032] Based on the identified creep stage, different line types or colors are used to distinguish and mark the curve segments corresponding to the decay creep stage, steady-state creep stage, and accelerated creep stage on the creep deformation time history curve.

[0033] As a further aspect of the present invention, the step of analyzing the creep deformation time history curve based on the steady-state creep rate method to determine the long-term strength and creep stage of the anchored jointed rock mass sample specifically involves:

[0034] Calculate the steady-state creep rate of the creep deformation time history curve at each constant stress level;

[0035] Plot a curve showing the relationship between stress level and steady-state creep rate, with the stress level as the abscissa and the steady-state creep rate as the ordinate.

[0036] Determine the critical stress point on the relationship curve where the steady-state creep rate changes abruptly;

[0037] The stress value corresponding to the critical stress point is defined as the long-term strength of the anchored jointed rock mass specimen.

[0038] Based on the morphological characteristics of the creep deformation time history curve and the change in the steady-state creep rate, the creep process is divided into a decay creep stage, a steady-state creep stage, and an accelerated creep stage.

[0039] As a further aspect of the present invention, the step of calibrating the crack initiation and propagation process of the anchored jointed rock mass sample in each stage of creep based on the acoustic emission signal specifically includes:

[0040] The acoustic emission signals collected by the acoustic emission monitoring device are processed to extract the number of acoustic emission events, acoustic emission energy, and acoustic emission amplitude parameters.

[0041] The time series of the number of acoustic emission events, acoustic emission energy, and acoustic emission amplitude parameters are synchronously compared and analyzed with the creep deformation time history curve.

[0042] The time point at which the acoustic emission parameters first showed a significant sudden increase was identified, and this time point was marked as the initiation time of the microcracks inside the anchored jointed rock mass sample.

[0043] By tracking the sustained activity of acoustic emission parameters after the crack initiation time, the spatiotemporal distribution of acoustic emission events is correlated with the macroscopic deformation stages of the anchored jointed rock mass sample to calibrate the crack propagation path and propagation rate.

[0044] As a further aspect of the present invention, the analysis of the response differences between crack development patterns and anchorage failure characteristics under different inorganic salt compositions, concentrations, joint orientations, and prestressed anchor conditions specifically includes:

[0045] The anchored jointed rock mass samples under different experimental conditions were grouped, and each group of samples maintained the same conditions except for the target influencing factors.

[0046] Comparative analysis was conducted on the differences in the spatial distribution morphology of cracks determined by the location coordinates of acoustic emission event sources under different inorganic salt compositions, as well as the differences in the debonding rate between the anchor bolt and the rock mass interface reflected by the anchor bolt strain data.

[0047] The differences in the cumulative release of acoustic emission energy parameters during creep under different inorganic salt concentrations, as well as the differences in the duration of the steady-state creep stage determined by the creep deformation time history curve, were compared and analyzed.

[0048] Comparative analysis was conducted on the differences in crack propagation paths and spatial geometric relationships of precast joint surfaces under different joint orientations, as well as the differences in the relationship between the macroscopic failure modes of the specimens and the angle between the anchor bolt axis.

[0049] Comparative analysis was conducted on the differences in the proportion of elastic deformation in the axial deformation data before reaching long-term strength under different prestressed anchor conditions, as well as the differences in the timing of the peak occurrence of acoustic emission event rate during the accelerated creep stage.

[0050] As a further aspect of the present invention, the determination of the degree of influence of different influencing factors on the anchor bolt support effect at each stage of creep in the anchored jointed rock mass based on the response differences of the anchoring failure characteristics specifically includes:

[0051] The stress levels required for the anchored jointed rock mass samples to reach long-term strength under different inorganic salt compositions were compared and analyzed, as well as the creep stages corresponding to the debonding or fracture of the anchor rods.

[0052] The steady-state creep rate of the anchored jointed rock mass samples was compared and analyzed under different inorganic salt concentrations, as well as the differences in the severity of crack propagation and the level of acoustic emission energy release.

[0053] A comparative analysis was conducted to examine the differences in the proportion of slip deformation along the joint surface in the total creep deformation of the anchored jointed rock mass samples under different joint orientations.

[0054] A comparative analysis was conducted to examine the time delay differences in the transition from the steady-state creep stage to the accelerated creep stage of the anchored jointed rock mass specimen under different prestressed anchor conditions.

[0055] Based on the differences in stress level, creep stage, steady-state creep rate, crack propagation severity and acoustic emission energy release level, the proportion of slip deformation in total creep deformation, and time delay, the influence weights of different influencing factors on the anchor bolt support effect are quantified. A formula for calculating the influence weights is expressed as follows:

[0056] ;

[0057] in, This represents the influence weight of the j-th influencing factor. Represents the normalized importance coefficient of the i-th comparison parameter. This represents the standardized difference value of the i-th comparison parameter under the j-th influencing factor. To compare the total number of parameters, This represents the total number of influencing factors.

[0058] As a further aspect of the present invention, the method further includes:

[0059] Based on the creep deformation data obtained from the graded loading creep compression experiment, the rheological deformation characteristic curve of the anchored rock mass is fitted.

[0060] Based on the aforementioned rheological deformation characteristic curves, the main deformation mechanisms of the anchored rock mass evolving from stable rheology to accelerated rheology are analyzed.

[0061] The weakening of rock mechanical properties caused by inorganic salt corrosion is defined as the corrosion damage variable;

[0062] The decrease in bearing capacity caused by the initiation and propagation of microcracks inside the rock during creep is defined as the creep damage variable;

[0063] A nonlinear damage evolution function is established based on the combined effects of the corrosion damage variable and the creep damage variable.

[0064] As a further aspect of the present invention, the establishment of the nonlinear damage evolution function based on the combined effect of the corrosion damage variable and the creep damage variable specifically involves:

[0065] The corrosion damage variable is defined as a negative exponential function that is related to the inorganic salt corrosion time and the concentration of the corrosive medium.

[0066] The creep damage variable is defined as a negative exponential function that is related to creep time and stress level;

[0067] A coupling function is used to associate the corrosion damage variable with the creep damage variable to form a total damage variable that reflects the synergistic damage effect of corrosion and creep.

[0068] The total damage variable is incorporated into the viscoelastic mechanical parameters characterizing the rheological properties of rocks, such that the viscoelastic mechanical parameters gradually weaken as the total damage variable increases.

[0069] Compared with the prior art, the advantages and positive effects of the present invention are as follows:

[0070] Rock samples with different joint orientations were pretreated with inorganic salt solutions of specific compositions and concentrations, and anchor bolts with different prestresses were installed. This scheme reproduces the real stress-chemical coupling field of chemical corrosion environment and active support in underground engineering. By comparing and analyzing the creep response under different corrosion conditions and prestress levels, the long-term weakening mechanism of the chemical solution on the rock matrix and anchor-rock interface can be directly revealed. At the same time, the time-dependent decay law of prestress in controlling joint slip and inhibiting deformation during creep can be clarified. This provides a key experimental basis for the long-term performance evaluation and parameter design of anchoring systems in complex environments.

[0071] The steady-state creep rate method was applied to process the axial deformation time history curve, and acoustic emission signals were simultaneously acquired throughout the process. The steady-state creep rate method objectively determines the transition between long-term strength and creep stages by identifying the inflection point of the creep rate, improving the accuracy and consistency of parameter determination. Simultaneous acoustic emission monitoring enabled dynamic calibration of the initiation, propagation, and convergence processes of microcracks within each creep stage, directly linking macroscopic deformation stages with microscopic damage events. This correlation reveals the micromechanical process of damage accumulation and eventual interface failure in the anchoring system during creep, deepening the understanding of the aging failure mechanism of anchor bolt support.

[0072] Based on the above correlation analysis, the acoustic emission characteristics and creep curve response patterns under different corrosion factors, joint orientations, and prestress levels were analyzed. By systematically comparing multiple sets of experimental data, the influence of various factors on the anchor support effect at different stages of creep can be quantitatively distinguished, and the dominant factors and key failure links controlling long-term stability can be identified. This provides a micromechanical basis for establishing a creep constitutive model and anchorage design theory under multi-field coupling conditions. Attached Figure Description

[0073] Figure 1 This is a flowchart of the multi-field coupled creep characteristic analysis method for anchored jointed rock masses described in this invention;

[0074] Figure 2 This is a flowchart of acoustic emission signal acquisition and processing.

[0075] Figure 3 A comparative diagram showing the effects of different influencing factors on the creep characteristics of anchored jointed rock masses;

[0076] Figure 4 A weighted comparison chart of factors influencing the creep characteristics of anchored jointed rock masses;

[0077] Figure 5 The time history curves of axial strain versus creep deformation obtained in a graded loading creep compression test of anchored jointed rock mass. Detailed Implementation

[0078] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0079] In the description of this invention, it should be understood that the terms "length," "width," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientation or positional relationships, are based on the orientation or positional relationships shown in the accompanying drawings and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, in the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0080] See Figure 1 A multi-field coupled creep characteristic analysis method for anchored jointed rock masses is proposed. The overall implementation scheme includes preparing inorganic salt-corroded anchored jointed rock mass samples with different joint orientations, installing anchors with different prestresses in these samples, conducting graded loading creep compression tests on the anchored jointed rock mass samples, acquiring axial deformation data and time data of the samples in real time, and simultaneously using acoustic emission monitoring equipment to acquire acoustic emission signals during the creep compression test process. Based on the axial deformation data and time data, a creep deformation time history curve of the anchored jointed rock mass samples is plotted. Based on the steady-state creep rate method, the creep deformation time history curves were analyzed to determine the long-term strength and creep stage of the anchored jointed rock mass specimens. The crack initiation and propagation process of the anchored jointed rock mass specimens in each creep stage was calibrated according to the acoustic emission signal. The response differences of crack development law and anchorage failure characteristics under different inorganic salt compositions, different inorganic salt concentrations, different joint orientations and different prestressed anchor bolt conditions were analyzed. Based on the response differences of anchorage failure characteristics, the degree of influence of different influencing factors on the anchor bolt support effect in each creep stage of the anchored jointed rock mass was determined.

[0081] See Figure 2In one embodiment of the present invention, the prepared inorganic salt-corroded anchored jointed rock mass specimen is placed at the center of the pressure plate of a rigid press. The loading control system of the press applies axial compressive loads to the anchored jointed rock mass specimen step by step according to a preset stress level sequence. An exemplary stress level sequence is set to apply axial stresses equivalent to 30%, 45%, 60%, 75%, and 90% of the estimated uniaxial compressive strength in sequence. At each stress level, the servo control system maintains a constant axial compressive load, and the loading continues until the creep deformation rate of the anchored jointed rock mass specimen changes by less than 0.001 mm per hour over a continuous 24-hour period. At this point, the creep deformation rate is considered to have reached a relatively stable state. The data acquisition system records the axial deformation data and time data of the anchored jointed rock mass specimen from the start of loading to deformation stabilization at a frequency of once per second for each stress level. When the anchored jointed rock mass specimen enters the accelerated creep stage, characterized by a continuously increasing and irreversible axial deformation rate, or when macroscopic damage occurs in the specimen with visible through cracks, the control system automatically terminates the graded loading creep compression experiment.

[0082] In some embodiments, the implementation of the acoustic emission monitoring equipment is synchronized with the graded loading process. In a specific implementation, eight acoustic emission sensors are arranged in a spatial array on the surface of the anchored jointed rock mass sample. The sensor positions cover all sides and ends of the sample, ensuring complete acoustic connection between each acoustic emission sensor and the surface of the anchored jointed rock mass sample via a dedicated acoustic coupling agent to reduce signal attenuation. Throughout the loading and constant load processes of the graded loading creep compression experiment, the acoustic emission signal acquisition host continuously receives the analog electrical signals converted by the acoustic emission sensor array. The received analog electrical signals are pre-amplified and bandpass filtered. The bandpass filter is set to filter out environmental mechanical noise below 20 kHz and inherent high-frequency interference from the equipment above 1 MHz. The threshold voltage for triggering an acoustic emission event is set to 40 dB. When the signal amplitude exceeds the threshold voltage, the acquisition system records this moment as the occurrence time of the acoustic emission event and acquires the complete waveform data of the acoustic emission event at a sampling rate of 10 MHz per second. From the acquired waveform data, multiple parameters such as arrival time, rise time, duration, amplitude, energy, and count are extracted for each acoustic emission event using a built-in algorithm. Based on the arrival time difference of the same event received by sensors at different spatial locations in the acoustic emission sensor array, the source position coordinates of the acoustic emission event in the three-dimensional space inside the anchored jointed rock mass sample are calculated by a time difference-based positioning algorithm.

[0083] It is understandable that the implementation of graded loading creep compression experiments and acoustic emission signal acquisition is a highly integrated and synchronized process. In practice, the press control unit, deformation measurement unit, and acoustic emission acquisition unit are synchronized by a unified central clock source, achieving millisecond-level synchronization accuracy. At the instant of each load application, the loading control system sends a marker signal to the data recording system, which is simultaneously recorded by the acoustic emission system to ensure precise alignment between the axial deformation data time series and the acoustic emission event time series in subsequent analysis. In practice, the acoustic emission event localization algorithm requires pre-input of the precise geometric dimensions of the anchored jointed rock sample and the three-dimensional coordinates of each acoustic emission sensor in the sample coordinate system. The propagation speed of the acoustic emission wave in the rock material is calibrated before the experiment using a lead-breaking test.

[0084] Optionally, for staged loading creep compression tests, a safety monitoring mechanism can be set up in the specific implementation. When the anchored jointed rock mass sample fails to reach deformation stability and enter accelerated creep under a certain stress level for an extended period, the system can automatically determine and prompt whether to proceed to the next loading stage or terminate the experiment based on a preset maximum constant load time threshold, such as 720 hours. In the specific implementation, the parameter settings for acoustic emission signal acquisition can be adjusted according to the material and size of the anchored jointed rock mass sample. For more active samples, the trigger threshold can be appropriately increased to reduce the amount of data, while for samples with weaker signals, the threshold needs to be lowered and the preamplification gain increased.

[0085] In one embodiment of the present invention, the axial deformation data and corresponding acquisition time data recorded by the data acquisition system at each stress level are exported in text file format. A data processing program is used to pair the axial deformation data at each stress level with the corresponding acquisition time data, forming an independent data point sequence for each stress level. A data point sequence includes all time points from the start of load application to the load change or end of the experiment, along with their corresponding axial deformation amounts. In a time-deformation coordinate system, a plotting program sequentially plots the data points at all stress levels, with the time axis in hours or seconds and the deformation axis in millimeters. A smooth curve generated using a cubic spline interpolation algorithm connects continuous data points at the same stress level to visually reflect the continuous process of creep deformation.

[0086] In some embodiments, information is labeled on the completed creep deformation time history curve. Specifically, the plotting program marks key time points on the creep deformation time history curve with vertical dashed lines based on the start time of each stress level loading and the time of unloading or entering the next loading level recorded in the experimental log, and labels the corresponding stress level values ​​above the dashed lines. Based on the long-term strength independently calculated using the steady-state creep rate method, the time and deformation amount corresponding to the critical stress point are located on the creep deformation time history curve and marked with a prominent symbol such as a pentagram at the corresponding position on the curve, along with the text annotation "Long-term strength: XXMPa". Based on the identified creep stage division results, the plotting program uses different line types or colors to distinguish and label the curve segments corresponding to the decaying creep stage, steady-state creep stage, and accelerated creep stage on the creep deformation time history curve. For example, the decaying creep stage curve segment is represented by a dashed line, the steady-state creep stage by a solid line, and the accelerated creep stage by a thick solid line, or by blue, green, and red respectively.

[0087] It is understandable that the process of plotting and labeling creep deformation time history curves requires maintaining a precise correspondence between data and graphics. In practice, the plotting program executes a coordinate mapping function to ensure that the mapping relationship from the original data timestamps to the graphic time axis is distortion-free. The function form is as follows:

[0088] ;

[0089] in: This represents the position on the graph's coordinate axes. Represents the original time data. It is a scaling factor used to adapt to the display range of the graphics. The offset is used to adjust the starting point of the time. In practice, in order to conduct effective data comparison, multiple sets of creep deformation time history curves under different experimental conditions are plotted on the same graph. Each set of curves is distinguished by different legends, and the horizontal and vertical axes use a uniform scale to directly compare the overall shape of the curves under different conditions, the position of the long-term strength corresponding point, and the length of each creep stage.

[0090] Optionally, the creep deformation time history curve can be plotted with richer supplementary information. In practice, the plotting program can simultaneously plot a stepped curve showing the change of axial stress over time below the curve, allowing the creep deformation history to be compared with the loading history. In practice, for different marked creep stages, the program can automatically calculate and display the duration of each stage, the total deformation of that stage, and the average deformation rate in text boxes on the map. Optionally, the generated high-resolution creep deformation time history curve can be exported as a vector graphic for scaling and editing in subsequent reports or publications.

[0091] In one embodiment of the present invention, the data processing program reads the plotted creep deformation time history curve data, identifies the time period in which the deformation rate is basically constant for each curve segment under a constant stress level, calculates the ratio of the axial deformation increment to the time increment within this time period, and defines this ratio as the steady-state creep rate under that stress level. A formula for calculating the steady-state creep rate is as follows:

[0092] ;

[0093] in: Represents the steady-state creep rate. This represents the increment of axial deformation over a selected steady-state time period. This represents the corresponding time increment. Using the calculated stress level as the x-axis and the corresponding steady-state creep rate as the y-axis, a curve relating stress level and steady-state creep rate is plotted in a double logarithmic or rectangular coordinate system. On this curve, by observing changes in the curve's slope or identifying turning points in the data, the critical stress point where the steady-state creep rate abruptly changes is determined. This abrupt change is manifested as a leap in the steady-state creep rate value with increasing stress level. The stress value corresponding to the critical stress point is directly defined as the long-term strength of the anchored jointed rock mass specimen under the current experimental conditions. Based on the morphological characteristics of the creep deformation time history curve and the changes in the steady-state creep rate, the complete creep process is divided into three stages: the decay creep stage corresponds to the initial curve segment where the deformation rate continuously decreases over time; the steady-state creep stage corresponds to the curve segment where the deformation rate fluctuates around a certain constant value; and the accelerated creep stage corresponds to the final curve segment where the deformation rate continuously increases until failure.

[0094] In some embodiments, the initiation and propagation of cracks in anchored jointed rock mass samples during each stage of creep are calibrated based on acoustic emission signals. This process is achieved through correlation analysis with time series. Specifically, the raw waveform data collected by the acoustic emission monitoring equipment is processed, and the count, energy, and amplitude parameters of each acoustic emission event are extracted. Time series of acoustic emission event rate, cumulative acoustic emission energy, and acoustic emission amplitude distribution are generated according to the chronological order of event occurrence. The acoustic emission event rate time series, cumulative acoustic emission energy time series, and creep deformation time history curve of the anchored jointed rock mass sample are synchronously compared and analyzed, ensuring strict alignment of the three on the time axis. The time point at which a significant surge occurs in the acoustic emission event rate or cumulative acoustic emission energy time series is identified. A significant surge is defined as a value exceeding five times the average level of the previous stage within a short time window. This identified time point is designated as the initiation time of microcracks within the anchored jointed rock mass sample. By tracking the continuous active process of acoustic emission event rate after crack initiation and combining the three-dimensional spatial distribution of acoustic emission event source coordinates, the spatial aggregation and evolution of acoustic emission events is correlated with the macroscopic deformation stage of anchored jointed rock mass samples, thereby calibrating the crack propagation path and propagation rate. The propagation path is indicated by the spatial center movement trajectory of the acoustic emission event cluster, and the propagation rate is calculated by the expansion distance of the event cluster in the spatial range per unit time.

[0095] It is understandable that determining long-term strength and calibrating crack development requires comprehensive multi-source data. In practice, the relationship curve between stress level and steady-state creep rate can be plotted using a piecewise fitting method, fitting different functions before and after the critical stress point, with the critical stress point being the intersection of the two fitted functions. In practice, the time point of the first significant increase in acoustic emission parameters may correspond to the turning point of the creep curve from the decaying creep stage to the steady-state creep stage, or it may occur within the steady-state creep stage. This difference in correspondence can be used to analyze the differences in damage mechanisms under different influencing factors. Optionally, for the calibration of crack propagation paths, a three-dimensional spatial distribution animation of acoustic emission events can be plotted in practice to dynamically display the spatial evolution of micro-fracture events throughout the entire process from crack initiation to macroscopic failure, thereby revealing the crack propagation process more intuitively. Optionally, the ratio of the average frequency or rise time to the amplitude of acoustic emission events can be introduced as auxiliary parameters to distinguish different fracture modes that may exist during crack propagation, such as tension fracture or shear fracture.

[0096] See Figure 3This is a comparative chart showing the effects of different influencing factors on the creep characteristics of anchored jointed rock masses. This biaxial grouped bar chart quantifies and compares the influence of four factors—inorganic salt composition and concentration, joint orientation, and prestressed anchors—on the creep characteristics of anchored jointed rock masses using two core indicators: steady-state creep rate (blue, left axis) and anchorage failure time (green, right axis). High-prestressed anchors have the most significant creep-inhibiting effect; therefore, it is recommended to prioritize the use of prestressed anchors with a strength of 15 MPa or higher in complex conditions such as high corrosion and oblique joints. When the inorganic salt concentration is ≥15% or the joint orientation is ≥45°, the anchorage failure time warning threshold should be lowered from 100 hours to 70 hours, and maintenance should be scheduled in advance. The chart quantifies the interaction effects of multiple factors, verifying the scientific validity of the "multi-field coupled creep characteristic analysis method" and providing data support for subsequent engineering applications.

[0097] In one embodiment of the present invention, anchored jointed rock mass samples under different experimental conditions are grouped. Each group of samples maintains consistent conditions except for the target influencing factor. For example, four control groups can be set up: Group A (sodium chloride solution corrosion), Group B (sodium sulfate solution corrosion), Group C (sodium chloride solution of different concentrations), and Group D (different joint dip angles). The differences in the spatial distribution morphology of cracks determined by the coordinates of the acoustic emission event source are compared and analyzed under different inorganic salt compositions. The spatial distribution morphology of cracks is quantified by the three-dimensional ellipsoid fitting parameters of the acoustic emission event point cloud. At the same time, the differences in the debonding rate of the anchor bolt and rock mass interface reflected by the anchor bolt strain data are compared and analyzed. The debonding rate is calculated by the rate of change of anchor bolt strain during the constant load stage. The differences in the cumulative release of acoustic emission energy parameters during the creep process are compared and analyzed under different inorganic salt concentrations. At the same time, the differences in the duration of the steady-state creep stage determined by the creep deformation time history curve are compared and analyzed. The differences in the spatial geometric relationship between crack propagation paths and precast joint surfaces under different joint orientations were compared and analyzed. This was assessed by calculating the average distance between the set of newly formed crack event points and the equation of the precast joint surface. Simultaneously, the differences in the relationship between the macroscopic failure modes of the specimens and the angle between the anchor bolt axis were compared. The differences in the proportion of elastic deformation in the axial deformation data before reaching long-term strength were also compared and analyzed under different prestressed anchor bolt conditions. The proportion of elastic deformation was calculated using unloading and rebound test data. Furthermore, the differences in the timing of the peak acoustic emission event rate during the accelerated creep stage were compared. See Table 1.

[0098] Table 1: Grouping and Comparison Parameters of Influencing Factors

[0099] Experimental group number Factors affecting the target Fixed conditions Main comparison parameter 1 Main comparison parameter 2 G1 Inorganic salt components Same concentration, joint occurrence, and prestress. Crack spatial distribution ellipsoidal eccentricity Anchor bolt interface debonding rate G2 Inorganic salt concentration Same composition, joint occurrence, and prestress. Accumulated acoustic emission energy Steady-state creep phase duration G3 Jointed birth Corrosion conditions and prestress are the same Average distance from crack point set to joint surface Angle between the failure surface and the anchor bolt axis G4 Anchor prestressing Corrosion conditions and joint occurrence are the same Elastic deformation ratio Acceleration phase acoustic emission peak moment

[0100] In some embodiments, the influence of different influencing factors on the anchor bolt support effect at each stage of creep in anchored jointed rock mass is determined based on the response differences of anchor failure characteristics. Specifically, the differences in stress levels required for anchored jointed rock mass samples to reach long-term strength under different inorganic salt compositions, and the differences in creep stages corresponding to anchor bolt debonding or fracture, are compared and analyzed. The differences in steady-state creep rates of anchored jointed rock mass samples under different inorganic salt concentrations, as well as the differences in the severity of crack propagation and the level of acoustic emission energy release, are also compared and analyzed. The differences in the proportion of slip deformation along the joint surface in the total creep deformation of anchored jointed rock mass samples under different joint orientations are compared and analyzed; the proportion of slip deformation is obtained through surface displacement field decomposition measured by digital image correlation technology. The differences in the time delay of anchored jointed rock mass samples transitioning from the steady-state creep stage to the accelerated creep stage under different prestressed anchor bolt conditions are also compared and analyzed. The influence weights of various factors on the anchor bolt support effect are quantified by considering differences in stress level, creep stage, steady-state creep rate, crack propagation severity and acoustic emission energy release level, the proportion of slip deformation in total creep deformation, and time delay. A multi-factor normalized weighted processing method is used. One formula for calculating the influence weights is as follows:

[0101] ;

[0102] in: This represents the influence weight of the j-th influencing factor. Represents the normalized importance coefficient of the i-th comparison parameter. This represents the standardized difference value of the i-th comparison parameter under the j-th influencing factor. To compare the total number of parameters, This represents the total number of influencing factors.

[0103] It is understandable that analyzing response differences and quantifying their impact constitutes a systematic data processing procedure. In practice, all comparison parameters must be dimensionless or standardized to eliminate the influence of different dimensions; for example, range standardization can be used to transform the original difference values ​​to the [0,1] interval. In practice, the importance coefficients of each comparison parameter... The impact can be predetermined using expert scoring or the analytic hierarchy process (AHP). Optionally, to more intuitively demonstrate the degree of influence, radar charts or bar charts can be generated during implementation to visualize the standardized differences of each influencing factor across different comparison parameters. Alternatively, the quantified impact weights can be further used to construct predictive models to predict the changing trends of creep life or long-term strength of anchored jointed rock masses under the influence of different composite factors.

[0104] See Figure 4This is a weighted comparison chart of factors influencing the creep characteristics of anchored jointed rock masses. The bar chart shows the total influence weight (0-0.8) of four core influencing factors on the creep characteristics of anchored jointed rock masses, reflecting the relative importance of each factor in the multi-field coupled creep process. Under complex working conditions, creep should be suppressed primarily by increasing the anchor prestress (e.g., above 15 MPa), followed by targeted measures to address the adverse effects of inorganic salt corrosion and joint orientation. In scenarios with high-concentration CaSO4 corrosion and 45° oblique joints, anchor prestress should be used as a core control indicator to ensure the long-term stability of the support system. The quantification of weights provides a basis for subsequent experimental design, allowing more resources to be invested in the study of the coupling effect between anchor prestress and inorganic salt corrosion.

[0105] In one embodiment of the present invention, steady-state creep deformation data and corresponding stress data of multiple sets of anchored jointed rock mass samples under different constant stress levels are summarized, and nonlinear regression fitting is performed using rheological constitutive models such as the Burgers model and the Nishihara model to obtain model parameter curves describing the rheological deformation characteristics of the anchored rock mass. Based on the rheological deformation characteristic curves obtained by fitting, the variation law of curve parameters with stress level is analyzed, such as the decay law of viscosity coefficient or the change of yield threshold of plastic element, so as to infer the main deformation mechanism of the anchored rock mass from steady rheological evolution to accelerated rheological evolution, such as viscous flow dominance, microcrack accumulation dominance, or joint surface slip dominance. The weakening of macroscopic mechanical properties caused by the dissolution of rock matrix and cement and the increase of porosity due to inorganic salt corrosion is defined as corrosion damage variable. The decrease in bearing capacity caused by the initiation, expansion and connection of microcracks inside the rock during creep is defined as creep damage variable. A nonlinear damage evolution function is established to allow the corrosion damage variable and the creep damage variable to interact through a coupling function.

[0106] In some embodiments, establishing a nonlinear damage evolution function that combines corrosion damage variables and creep damage variables involves specific mathematical definitions and coupling processes. In a specific implementation, the corrosion damage variable is defined as a negative exponential function related to the inorganic salt corrosion time and the concentration of the corrosive medium; for example, one expression is:

[0107] ;

[0108] in: Represents corrosion damage variables. It is a material constant reflecting the corrosion resistance of rock mass materials. Represents the concentration of the corrosive medium. This represents the corrosion time. The creep damage variable is defined as a negative exponential function related to creep time and stress level; for example, one expression could be:

[0109] ;

[0110] in: Represents creep damage variables. It is a material constant reflecting the creep sensitivity of rock mass. Represents the applied stress level. Represents the uniaxial compressive strength of the rock mass. This represents the duration of the creep load. A coupling function is used to combine the corrosion damage variables. With creep damage variables By correlating these factors, a total damage variable reflecting the synergistic damage effect of corrosion and creep is constructed. One coupling method is:

[0111] ;

[0112] in: , , The coupling coefficient is used to characterize the independent contributions of corrosion damage and creep damage, as well as their interactive strengthening effect. The total damage variable... Introduced into viscoelastic mechanical parameters characterizing the rheological properties of rocks, for example, modifying the sticky pot viscosity parameter in the Burgers model to... ,in, These are the initial viscosity parameters for the sticky pot. Let be the viscosity parameters of the sticky pot after damage coupling. This makes the viscoelastic mechanical parameters change with the total damage variable. Its influence gradually weakens as it grows.

[0113] It is understandable that the establishment of the damage evolution function needs to be based on calibration using experimental data. In practical implementation, corrosion damage variables... Material constants in The rate of decrease in static elastic modulus or uniaxial compressive strength of rock samples after corrosion can be determined by comparing the rates of decrease in static elastic modulus or uniaxial compressive strength between uncorroded and samples after different corrosion times. In practical applications, creep damage variables... Material constants in and coupling coefficient , , It needs to be calibrated using an iterative inversion algorithm to incorporate the total damage variable. The modified rheological constitutive model theoretical curves achieve the best fit with the creep deformation time history curves obtained from graded loading creep experiments. Optional, total damage variable... The evolution process can be correlated with the cumulative energy of acoustic emission or the number of events, and the damage state can be independently verified by the temporal changes of acoustic emission parameters.

[0114] See Figure 5This is a time-history curve of axial strain versus creep deformation obtained from a graded loading creep compression test on anchored jointed rock mass. The curve was plotted using collected axial deformation and time data and is used for subsequent analysis of long-term strength and creep stages. By analyzing the slope of the steady-state creep stage, the long-term strength of the anchored jointed rock mass can be determined, which is also the basis for dividing the creep stages. The deformation characteristics of the curve can be used to fit Burgers et al. rheological constitutive models, and then analyze the coupling effect of corrosion damage and creep damage. For example, in the accelerated creep stage, the increase in the total damage variable leads to a rapid weakening of the viscoelastic mechanical parameters of the rheological model. The abrupt change point of the steady-state creep rate can determine the long-term strength of the anchored jointed rock mass, providing a key indicator for the long-term stability design of anchor bolt support in underground engineering.

[0115] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments that can be applied to other fields. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method for analyzing the multi-field coupled creep characteristics of anchored jointed rock masses, characterized in that, Includes the following steps: Inorganic salt-corroded anchored jointed rock mass samples with different joint orientations were prepared, and anchor rods with different prestresses were installed in the anchored jointed rock mass samples. A graded loading creep compression test was conducted on the anchored jointed rock mass sample, and the axial deformation data and time data of the anchored jointed rock mass sample were collected in real time. Acoustic emission monitoring equipment was used to collect the acoustic emission signals of the anchored jointed rock mass sample during the creep compression test in real time; Based on the axial deformation data and time data, the creep deformation time history curves of the anchored jointed rock mass specimens were plotted. The long-term strength and creep stage of the anchored jointed rock mass specimen were determined by analyzing the creep deformation time history curve based on the steady-state creep rate method. The initiation and propagation process of cracks in the anchored jointed rock mass sample during each stage of creep was determined based on the acoustic emission signal. The differences in response between crack development patterns and anchorage failure characteristics under different inorganic salt compositions, concentrations, joint orientations, and prestressed anchor conditions were analyzed. Based on the response differences of the anchoring failure characteristics, the degree of influence of different influencing factors on the anchor support effect in each stage of creep of the anchored jointed rock mass is determined, specifically as follows: The stress levels required for the anchored jointed rock mass samples to reach long-term strength under different inorganic salt compositions were compared and analyzed, as well as the creep stages corresponding to the debonding or fracture of the anchor rods. The steady-state creep rate of the anchored jointed rock mass samples was compared and analyzed under different inorganic salt concentrations, as well as the differences in the severity of crack propagation and the level of acoustic emission energy release. A comparative analysis was conducted to examine the differences in the proportion of slip deformation along the joint surface in the total creep deformation of the anchored jointed rock mass samples under different joint orientations. A comparative analysis was conducted to examine the time delay differences in the transition from the steady-state creep stage to the accelerated creep stage of the anchored jointed rock mass specimen under different prestressed anchor conditions. Based on the differences in stress level, creep stage, steady-state creep rate, crack propagation severity and acoustic emission energy release level, the proportion of slip deformation in total creep deformation, and time delay, the influence weights of different influencing factors on the anchor support effect are quantified. A formula for calculating the influence weights is expressed as follows: ； in, This represents the influence weight of the j-th influencing factor. Represents the normalized importance coefficient of the i-th comparison parameter. This represents the standardized difference value of the i-th comparison parameter under the j-th influencing factor. To compare the total number of parameters, This represents the total number of influencing factors.

2. The method for analyzing the multi-field coupled creep characteristics of anchored jointed rock mass according to claim 1, characterized in that, The step-load creep compression test on the anchored jointed rock mass sample is specifically as follows: Axial compressive loads are applied to the anchored jointed rock mass specimen in stages according to a preset stress level sequence; At each stress level, the axial compressive load is kept constant and the loading continues until the creep deformation rate of the anchored jointed rock mass specimen reaches a relatively stable state. Record the axial deformation and time data of the anchored jointed rock mass specimens from the start of loading to the deformation stabilization process at each stress level; When the anchored jointed rock mass sample enters the accelerated creep stage or undergoes macroscopic failure, the graded loading creep compression test is terminated.

3. The method for analyzing the multi-field coupled creep characteristics of anchored jointed rock mass according to claim 2, characterized in that, The method of using acoustic emission monitoring equipment to collect acoustic emission signals of the anchored jointed rock mass sample in real time during the creep compression test is as follows: An array of acoustic emission sensors is arranged on the surface of the anchored jointed rock mass sample, ensuring that the sensors and the sample surface are acoustically connected through a coupling agent; Throughout the entire process of the graded loading creep compression experiment, electrical signals converted by the acoustic emission sensor array are continuously received; The received electrical signal is amplified and filtered to remove environmental noise and interference from the equipment's inherent frequency. Set a threshold voltage to trigger an acoustic emission event. When the signal amplitude exceeds the threshold voltage, record the time as the occurrence time of the acoustic emission event and collect the waveform data of the acoustic emission event. Multiple parameters, including arrival time, rise time, duration, amplitude, energy, and count, of acoustic emission events are extracted from the acquired waveform data. Based on the arrival time difference of the same event received by different sensors in the acoustic emission sensor array, the source location coordinates of the acoustic emission event inside the anchored jointed rock mass sample are calculated by a positioning algorithm.

4. The method for analyzing the multi-field coupled creep characteristics of anchored jointed rock mass according to claim 3, characterized in that, The creep deformation time history curve of the anchored jointed rock mass sample is plotted based on the axial deformation data and time data, specifically as follows: The axial deformation data collected at each stress level are paired with the corresponding acquisition time data to form a data point sequence at each stress level. In the time-deformation coordinate system, all data points are plotted sequentially, and a smooth curve is used to connect consecutive data points under the same stress level. On the creep deformation time history curve, mark the loading start time and the unloading or the start of the next loading level for each stress level; Based on the long-term strength determined by the steady-state creep rate method, mark the time and deformation amount corresponding to the critical stress point on the creep deformation time history curve. Based on the identified creep stage, different line types or colors are used to distinguish and mark the curve segments corresponding to the decay creep stage, steady-state creep stage, and accelerated creep stage on the creep deformation time history curve.

5. The method for analyzing the multi-field coupled creep characteristics of anchored jointed rock mass according to claim 4, characterized in that, The analysis of the creep deformation time history curve based on the steady-state creep rate method to determine the long-term strength and creep stage of the anchored jointed rock mass sample is as follows: Calculate the steady-state creep rate of the creep deformation time history curve at each constant stress level; Plot a curve showing the relationship between stress level and steady-state creep rate, with the stress level as the abscissa and the steady-state creep rate as the ordinate. Determine the critical stress point on the relationship curve where the steady-state creep rate changes abruptly; The stress value corresponding to the critical stress point is defined as the long-term strength of the anchored jointed rock mass specimen. Based on the morphological characteristics of the creep deformation time history curve and the change in the steady-state creep rate, the creep process is divided into a decay creep stage, a steady-state creep stage, and an accelerated creep stage.

6. The method for analyzing the multi-field coupled creep characteristics of anchored jointed rock mass according to claim 5, characterized in that, The process of calibrating the crack initiation and propagation of the anchored jointed rock mass sample in each stage of creep based on the acoustic emission signal is specifically as follows: The acoustic emission signals collected by the acoustic emission monitoring device are processed to extract the number of acoustic emission events, acoustic emission energy, and acoustic emission amplitude parameters. The time series of the number of acoustic emission events, acoustic emission energy, and acoustic emission amplitude parameters are synchronously compared and analyzed with the creep deformation time history curve. The time point at which the acoustic emission parameters first showed a significant sudden increase was identified, and this time point was marked as the initiation time of the microcracks inside the anchored jointed rock mass sample. By tracking the sustained activity of acoustic emission parameters after the crack initiation time, the spatiotemporal distribution of acoustic emission events is correlated with the macroscopic deformation stages of the anchored jointed rock mass sample to calibrate the crack propagation path and propagation rate.

7. The method for analyzing the multi-field coupled creep characteristics of anchored jointed rock mass according to claim 6, characterized in that, The analysis examines the differences in crack development patterns and anchorage failure characteristics under conditions of different inorganic salt compositions, concentrations, joint orientations, and prestressed anchor bolts. Specifically: The anchored jointed rock mass samples under different experimental conditions were grouped, and each group of samples maintained the same conditions except for the target influencing factors. Comparative analysis was conducted on the differences in the spatial distribution morphology of cracks determined by the location coordinates of acoustic emission event sources under different inorganic salt compositions, as well as the differences in the debonding rate between the anchor bolt and the rock mass interface reflected by the anchor bolt strain data. The differences in the cumulative release of acoustic emission energy parameters during creep under different inorganic salt concentrations, as well as the differences in the duration of the steady-state creep stage determined by the creep deformation time history curve, were compared and analyzed. Comparative analysis was conducted on the differences in crack propagation paths and spatial geometric relationships of precast joint surfaces under different joint orientations, as well as the differences in the relationship between the macroscopic failure modes of the specimens and the angle between the anchor bolt axis. Comparative analysis was conducted on the differences in the proportion of elastic deformation in the axial deformation data before reaching long-term strength under different prestressed anchor conditions, as well as the differences in the timing of the peak occurrence of acoustic emission event rate during the accelerated creep stage.

8. The method for analyzing the multi-field coupled creep characteristics of anchored jointed rock mass according to claim 7, characterized in that, Also includes: Based on the creep deformation data obtained from the graded loading creep compression experiment, the rheological deformation characteristic curve of the anchored rock mass is fitted. Based on the aforementioned rheological deformation characteristic curves, the main deformation mechanisms of the anchored rock mass evolving from stable rheology to accelerated rheology are analyzed. The weakening of rock mechanical properties caused by inorganic salt corrosion is defined as the corrosion damage variable; The decrease in bearing capacity caused by the initiation and propagation of microcracks inside the rock during creep is defined as the creep damage variable; A nonlinear damage evolution function is established based on the combined effects of the corrosion damage variable and the creep damage variable.

9. The method for analyzing the multi-field coupled creep characteristics of anchored jointed rock mass according to claim 8, characterized in that, The establishment of the nonlinear damage evolution function based on the combined effect of the corrosion damage variable and the creep damage variable is specifically as follows: The corrosion damage variable is defined as a negative exponential function that is related to the inorganic salt corrosion time and the concentration of the corrosive medium. The creep damage variable is defined as a negative exponential function that is related to creep time and stress level; A coupling function is used to associate the corrosion damage variable with the creep damage variable to form a total damage variable that reflects the synergistic damage effect of corrosion and creep. The total damage variable is incorporated into the viscoelastic mechanical parameters characterizing the rheological properties of rocks, such that the viscoelastic mechanical parameters gradually weaken as the total damage variable increases.

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