Method and device for predicting stability trend of dangerous rock mass based on long-period displacement monitoring

Abstract

This invention discloses a method and device for predicting the stability trend of unstable rock masses based on long-period displacement monitoring, relating to the field of safety monitoring and geological disaster early warning technology for water conservancy and hydropower projects. The method includes: setting up fixed monitoring points and periodically measuring the spacing to obtain displacement monitoring data for at least 5 years and 10 periods; calculating the cumulative displacement and time variables using the initial measurement spacing as a zero baseline to obtain a cumulative displacement-time series; constructing and fitting a logarithmic decay trend prediction model to determine the deformation rate decay coefficient, initial displacement deviation correction term, and determination coefficient; extrapolating the model to obtain the cumulative displacement increment for a preset extrapolation time; calculating the average deformation rate over the past year and comparing it with a preset grading threshold to determine the stability level; and outputting a trend prediction report containing the determination coefficient, cumulative displacement increment, and stability level. This method quantifies the long-term deformation decay law of unstable rock masses and can provide future displacement increments and grading early warning conclusions.

Description

Technical Field

[0001] This invention relates to the field of safety monitoring and geological disaster early warning technology for water conservancy and hydropower projects. More specifically, this invention relates to a method and device for predicting the stability trend of unstable rock masses based on long-period displacement monitoring. This invention is particularly applicable to the long-term deformation trend analysis and instability risk prediction of unstable rock masses, landslides, and overburden landslides on steep slopes in reservoir areas. Background Technology

[0002] Unstable rock masses and landslides are common geological hazards in hydropower reservoir areas, characterized by their suddenness and destructive power, threatening the safety of dam structures, navigation safety, and the load-bearing structures at the toe of the slope. A certain hydropower station reservoir area contains an exceptionally large unstable rock mass with a volume of millions of cubic meters. Multiple open cracks have developed along its rear edge, with the largest crack reaching several meters in width. This mass has been in a state of instability for a long time, and making quantitative predictions about its long-term deformation is fundamental to reservoir area safety management.

[0003] Currently, the evaluation of the stability of unstable rock masses at engineering sites mainly relies on three technical approaches. The first is on-site geological surveys and qualitative judgment based on experience, classifying the development degree of the unstable rock mass according to relevant industry standards based on apparent characteristics such as the degree of crack development and rockfall phenomena. The second is short-period displacement monitoring, which involves setting up benchmark points on the unstable rock mass and periodically reading displacement values, directly comparing the current change range with the warning value. The third is numerical simulation methods, using the finite element method and discrete element method to conduct mechanical analysis of the unstable rock mass.

[0004] The most direct existing technology corresponding to the core inventive point of this invention is the second approach mentioned above. The practical method of this approach is as follows: benchmark points are set on both sides of the crack at the rear edge of the unstable rock mass. The distance between the two points is measured with a steel ruler. After obtaining the reading each period, the change in the current period is subtracted from the previous period's reading. Then, the change in the current period is compared with an experienced warning value; if it exceeds the limit, an alarm is triggered. The technical logic of this approach stops at a single-point threshold judgment of "whether the deformation in the current period exceeds the limit." The continuous reading sequence accumulated over many years is only kept as a ledger and is not organized into a time function that can be extrapolated. Based on this approach, the industry has also introduced common time series methods such as grey models and exponential models to fit the trend of displacement data.

[0005] This leads to two pressing technical problems. First, existing short-cycle displacement monitoring only compares the deformation amplitude in the current period and fails to establish a quantitative evolutionary relationship that can be extrapolated between cumulative displacement and time. Because the single-period change simultaneously incorporates measurement errors, reversible fluctuations caused by seasonal rainfall and temperature, and actual irreversible creep, the flaw lies in the fact that single-period difference cannot separate the irreversible component from the fluctuations. Therefore, it is difficult to distinguish between the initial compaction settlement and the later creep sliding, and it is also impossible to provide a quantitative prediction of the cumulative displacement increment over the next few years. Engineering reinforcement and emergency evacuation lack a quantifiable time window. Second, existing general trend analysis methods such as grey models and exponential models are not adapted to the decay characteristics of unstable rock masses, which are characterized by "rapid initial deformation and subsequent stabilization." Because power-law decay is too fast and exponential decay is too slow, their residuals exhibit systematic deviations at both ends of long-cycle sequences. Furthermore, the output of these methods is merely a fitted curve, not linked to a goodness-of-fit index to form a criterion. Therefore, it is difficult to provide actionable identification conclusions when unstable rock masses deviate from the decay pattern and enter an accelerated creep stage. Summary of the Invention

[0006] The technical problem this invention aims to solve is that existing short-cycle displacement monitoring only compares the deformation amplitude in the current period and does not establish a quantitative evolution relationship that can be extrapolated between cumulative displacement and time. It is difficult to distinguish between initial compaction settlement and later creep and sliding, and it is also impossible to give a quantitative expectation of future cumulative displacement increment. Existing general trend prediction methods are not adapted to the decay characteristics of rapid initial deformation and subsequent stabilization of unstable rock masses, and they are not linked with the goodness-of-fit index to form a criterion, making it difficult to identify situations where unstable rock masses deviate from the decay law and enter the accelerated creep stage.

[0007] To address the aforementioned technical problems, this invention provides a method for predicting the stability trend of unstable rock masses based on long-period displacement monitoring, comprising:

[0008] Fixed monitoring points, including fixed reference points on the side of the mountain and moving points on the side of the unstable rock mass, are set up on the unstable rock mass. The distance between the fixed reference points and the moving points is measured periodically to obtain displacement monitoring data for no less than 5 years and no less than 10 periods.

[0009] Using the initial measurement interval as the zero baseline, the cumulative displacement and the time variable in years are calculated period by period to obtain the cumulative displacement-time series;

[0010] The cumulative displacement is characterized by the sum of the product of the deformation rate decay coefficient and the natural logarithm of the time variable plus 1 and the initial displacement deviation correction term. A logarithmic decay trend prediction model is constructed, and the cumulative displacement-time series is fitted by least squares regression to determine the deformation rate decay coefficient, the initial displacement deviation correction term, and the coefficient of determination.

[0011] Extrapolation is performed based on the logarithmic decay trend prediction model to obtain the cumulative displacement increment since the latest monitoring time after a preset extrapolation period.

[0012] The average deformation rate over the past year is calculated based on the cumulative displacement-time series, and the average deformation rate over the past year is compared with a preset grading threshold to determine the stability level.

[0013] The output includes a trend prediction report containing the determination coefficient, the cumulative displacement increment, and the stability level.

[0014] Further, the cumulative displacement is characterized by the sum of the product of the deformation rate attenuation coefficient and the natural logarithm of the time variable plus 1, and the initial displacement deviation correction term. A logarithmic attenuation trend prediction model is constructed, and the cumulative displacement-time series is fitted using least squares regression to determine the deformation rate attenuation coefficient, the initial displacement deviation correction term, and the coefficient of determination. This includes: taking the natural logarithm of the time variable for each period in the cumulative displacement-time series after adding 1, obtaining a sequence of transformed independent variables; constructing a regression sample set using the sequence of transformed independent variables as independent variables and the cumulative displacement as dependent variable; and solving for the deformation rate attenuation coefficient and the initial displacement deviation correction term by minimizing the sum of squared residuals. Positive term; calculate the coefficient of determination based on the sum of squared residuals and the sum of squared total deviations of the regression sample set; when the coefficient of determination is not less than the preset goodness-of-fit threshold, determine that the logarithmic decay trend prediction model is fit and allowed for extrapolation; when the coefficient of determination is less than the preset goodness-of-fit threshold, determine that the dispersion of the cumulative displacement-time series exceeds the limit, check whether the fixed monitoring point has experienced local collapse, measurement error or deformation stage change, extend the collection period of the displacement monitoring data and refit until the coefficient of determination is not less than the preset goodness-of-fit threshold, and obtain the deformation rate decay coefficient, the initial displacement deviation correction term and the coefficient of determination.

[0015] Further, the step of constructing a regression sample set using the transformed independent variable sequence as the independent variable and the cumulative displacement as the dependent variable, and solving for the deformation rate attenuation coefficient and the initial displacement deviation correction term by minimizing the sum of squared residuals, includes: solving the regression sample set by minimizing the sum of squared residuals to obtain initial values ​​for the initial deformation rate attenuation coefficient and the initial displacement deviation correction term; calculating the fitting residuals of each sample point in the regression sample set relative to the initial values ​​of the initial deformation rate attenuation coefficient and the initial displacement deviation correction term, and calculating the standard deviation of the fitting residuals; identifying sample points whose absolute value of the fitting residuals is greater than a preset multiple of the standard deviation as abrupt sample points, and removing the abrupt sample points from the regression sample set to obtain a corrected regression sample set; resolving the corrected regression sample set by minimizing the sum of squared residuals to obtain the deformation rate attenuation coefficient and the initial displacement deviation correction term; when the relative change of the deformation rate attenuation coefficient relative to the initial deformation rate attenuation coefficient is greater than a preset convergence threshold, repeating the removal and resolving steps for the corrected regression sample set until the relative change is not greater than the preset convergence threshold.

[0016] Further, the extrapolation based on the logarithmic decay trend prediction model to obtain the cumulative displacement increment from the current latest monitoring time over a preset extrapolation period includes: taking the time variable corresponding to the current latest monitoring time as the extrapolation starting point, and the sum of the extrapolation starting point and the preset extrapolation period as the extrapolation ending point, wherein the preset extrapolation period is 3 to 5 years; multiplying the deformation rate decay coefficient by the difference between the natural logarithm of the extrapolation ending point plus 1 and the natural logarithm of the extrapolation starting point plus 1 to obtain the cumulative displacement increment; and adding the cumulative displacement corresponding to the extrapolation starting point to the cumulative displacement increment to obtain the predicted cumulative displacement of the extrapolation ending point.

[0017] Further, after multiplying the deformation rate attenuation coefficient by the difference between the natural logarithm of the extrapolated endpoint plus 1 and the natural logarithm of the extrapolated starting point plus 1 to obtain the cumulative displacement increment, the method further includes: dividing the deformation rate attenuation coefficient by the value of the extrapolated endpoint plus 1 to obtain the predicted instantaneous deformation rate at the end of the year; calculating the difference between the predicted instantaneous deformation rate at the end of the year and the average deformation rate of the past year to obtain the deformation rate evolution difference; when the deformation rate evolution difference is less than zero, determining that the deformation of the unstable rock mass is in a convergent decay creep state; when the deformation rate evolution difference is not less than zero, refitting the cumulative displacement-time series using an exponential trend model with the time variable as the exponential term independent variable to obtain the exponential model determination coefficient; when the exponential model determination coefficient is greater than the determination coefficient, determining that the deformation of the unstable rock mass deviates from the logarithmic decay law, and adjusting the stability level to the accelerated instability precursor level.

[0018] Further, the step of calculating the average deformation rate over the past year based on the cumulative displacement-time series, and comparing the average deformation rate over the past year with a preset grading threshold to determine the stability level includes: the preset grading threshold includes a first threshold, a second threshold, and a third threshold that increase sequentially, wherein the first threshold is 2 mm per year, the second threshold is 5 mm per year, and the third threshold is 10 mm per year; when the average deformation rate over the past year is not greater than the first threshold, the stability level is determined to be a stable level; when the average deformation rate over the past year is greater than the first threshold but not greater than the second threshold, the stability level is determined to be a weak creep level; when the average deformation rate over the past year is greater than the second threshold but not greater than the third threshold, the stability level is determined to be a moderate creep level; and when the average deformation rate over the past year is greater than the third threshold, the stability level is determined to be an accelerated instability precursor level.

[0019] Furthermore, the method also includes: when there is a disaster-bearing object below the unstable rock mass, reducing the first threshold, the second threshold, and the third threshold by a reduction factor of 50%, and then comparing them with the average deformation rate over the past year; when the deformation rate attenuation coefficient is greater than a preset attenuation coefficient adjustment threshold and the determination coefficient is greater than a preset goodness adjustment threshold, increasing the stability level by one level; and writing the increased stability level into the trend prediction report.

[0020] Furthermore, the step of setting up fixed monitoring points on the unstable rock mass, including fixed reference points on the mountain side and moving points on the unstable rock mass side, and periodically measuring the distance between the fixed reference points and the moving points to obtain displacement monitoring data for no less than 5 years and no less than 10 periods, includes: setting up no less than 3 fixed monitoring points on both sides of the main crack at the rear edge of the unstable rock mass; setting the fixed reference point on the mountain side of each fixed monitoring point on a fixed pile on the stable bedrock of the mountain, and setting the moving point on the unstable rock mass side on a moving pile at the edge of the main crack at the rear edge; setting up two measurement directions for each fixed monitoring point, one perpendicular to the direction of the main crack at the rear edge and one parallel to the direction of the main crack at the rear edge, and obtaining the opening displacement and shear displacement of the main crack at the rear edge, respectively; measuring the distance between the fixed reference points and the moving points using a steel ruler or displacement sensor, with a measurement accuracy of no less than 1 mm; performing the measurement at a frequency of no less than 2 periods per year, and accumulating no less than 10 periods of displacement monitoring data.

[0021] Furthermore, the method further includes: when the number of periods of the displacement monitoring data is less than 10, using leave-one-out cross-validation to evaluate the stability of the logarithmic decay trend prediction model and obtain the cross-validation error; when the cross-validation error is greater than 15%, extending the acquisition period of the displacement monitoring data until the cross-validation error is no greater than 15%.

[0022] This invention also provides a device for predicting the stability trend of unstable rock masses based on long-period displacement monitoring, comprising:

[0023] The monitoring point deployment and data acquisition module 501 is used to deploy fixed monitoring points on the dangerous rock mass, including fixed reference points on the mountain side and moving points on the dangerous rock mass side, periodically measure the distance between the fixed reference points and the moving points, and obtain displacement monitoring data for no less than 5 years and no less than 10 periods.

[0024] The cumulative displacement sequence generation module 502 is used to calculate the cumulative displacement and the time variable in years on a periodic basis, with the interval of the first measurement as the zero reference, to obtain the cumulative displacement-time series.

[0025] The logarithmic decay model fitting module 503 is used to characterize the cumulative displacement by the sum of the product of the deformation rate decay coefficient and the natural logarithm of the time variable plus 1 and the initial displacement deviation correction term, construct a logarithmic decay trend prediction model, perform least squares regression fitting on the cumulative displacement-time series, and determine the deformation rate decay coefficient, the initial displacement deviation correction term, and the determination coefficient.

[0026] The displacement increment extrapolation module 504 is used to extrapolate based on the logarithmic decay trend prediction model to obtain the cumulative displacement increment since the latest monitoring time after a preset extrapolation time.

[0027] The stability level determination module 505 is used to calculate the average deformation rate of the past year based on the cumulative displacement-time series, compare the average deformation rate of the past year with a preset classification threshold, and determine the stability level.

[0028] The prediction report output module 506 is used to output a trend prediction report that includes the determination coefficient, the cumulative displacement increment, and the stability level.

[0029] The technical effects of this invention are as follows:

[0030] By adopting a logarithmic decay trend prediction model that characterizes the cumulative displacement by summing the product of the deformation rate decay coefficient and the natural logarithm of the time variable plus one, along with the initial displacement deviation correction term, and extrapolating the cumulative displacement increment based on the logarithmic difference between the extrapolation start point and the extrapolation end point, the accumulated reading sequence over many years is organized into an extrapolable time function. Measurement errors and seasonal reversible fluctuations are averaged out in the least squares sense, and the irreversible creep component is extracted separately as the decay coefficient. This solves the problems of existing short-period displacement monitoring that do not establish an extrapolable quantitative evolution relationship, are difficult to distinguish between compaction settlement and creep sliding, and cannot provide a quantitative expectation of future cumulative displacement increments. This enables engineering reinforcement and emergency evacuation to obtain a quantitative time window measured in millimeters. Because the constructed model is of the same order of decay rate as the physical process of fissure compaction-friction interlocking rebalancing of unstable rock mass, and uses the coefficient of determination as the goodness-of-fit threshold and the evolution difference between the predicted instantaneous deformation rate at the end of the year and the average deformation rate over the past year as the criterion, it solves the problem that general trend methods are not adapted to the decay characteristics of unstable rock mass and are not linked with the goodness of fit, making it difficult to identify the accelerated creep stage. This allows situations where unstable rock mass deviates from the decay law to be automatically marked and directly mapped as accelerated instability precursor levels. Attached Figure Description

[0031] Figure 1 This is a schematic diagram of the overall process of the method for predicting the stability trend of unstable rock masses based on long-period displacement monitoring provided in an embodiment of the present invention.

[0032] Figure 2 This is a flowchart illustrating the steps of constructing a logarithmic decay trend prediction model and performing least squares regression fitting, as provided in an embodiment of the present invention.

[0033] Figure 3 A flowchart illustrating the cumulative displacement increment extrapolation step provided in an embodiment of the present invention;

[0034] Figure 4 A flowchart illustrating the stability level determination steps provided in an embodiment of the present invention;

[0035] Figure 5 This is a schematic diagram of the module structure of the unstable rock mass stability trend prediction device based on long-period displacement monitoring provided in an embodiment of the present invention. Detailed Implementation

[0036] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments, but the implementation of the present invention is not limited thereto.

[0037] Example 1

[0038] like Figure 1 As shown in the figure, this embodiment provides a method for predicting the stability trend of unstable rock masses based on long-period displacement monitoring, including:

[0039] S1. Set up fixed monitoring points on the unstable rock mass, including fixed reference points on the side of the mountain and moving points on the side of the unstable rock mass, periodically measure the distance between the fixed reference points and the moving points, and obtain displacement monitoring data for no less than 5 years and no less than 10 periods.

[0040] A fixed reference point is set on the stable bedrock on one side of the mountain behind the unstable rock mass, and a moving point is set on one side of the unstable rock mass itself. These two points form a set of benchmarks, and the measured changes in the distance reflect the relative displacement of the unstable rock mass relative to the stable mountain. Measuring instruments can include steel rulers, vernier calipers, or displacement sensors. The data collection period is limited to at least 5 years and at least 10 periods. The technical significance of this is that the annual deformation of the unstable rock mass is often on the order of millimeters, while the error of a single-period measurement and seasonal reversible fluctuations are also on the order of millimeters. Only when the sequence length covers multiple complete hydrological and temperature cycles does the irreversible creep component exhibit a stable monotonic trend in the sequence. In other embodiments, the displacement monitoring data can also be obtained by automatic aiming with a total station or continuous acquisition using a crack gauge.

[0041] Specifically, the typical unstable rock masses targeted by this invention are often isolated columnar or tower-shaped structures with three sides exposed, spanning elevations of one to two hundred meters. Their rear edges are frequently cut by regional faults, and multiple open cracks develop at the top, with the widest crack reaching several meters. Rural roads, shrublands, or other disaster-prone areas are often distributed below the toe of the slope. The stability of these unstable rock masses is affected by a combination of their own weight, weathering and erosion, and the periodic rise and fall of reservoir water levels. The softening and buoyancy effects of reservoir water level fluctuations on the rock mass at the toe exhibit a clear annual periodicity. It is precisely because these effects include both irreversible components that accumulate monotonically over time and reversible components that fluctuate seasonally that the measurement sequence must cover several complete annual cycles.

[0042] It is worth noting that the collection of displacement monitoring data should maintain consistency in measurement conditions as much as possible. This includes the same group of operators performing the measurements according to the same measurement procedures, using the same measuring instruments and calibrating the instruments before each measurement period, and taking the arithmetic mean of the readings three times at the same benchmark position during each measurement period. Optionally, if a point needs to be redrawn due to unclear benchmark markings in a certain period, this period should be marked as a benchmark change period in the data log, and the first reading after redrawing the point should be used as the new zero benchmark for subsequent sequences of that measurement point, to avoid misinterpreting the abrupt changes in readings caused by benchmark changes as actual displacement.

[0043] S2. Using the initial measurement interval as the zero baseline, calculate the cumulative displacement and the time variable in years period by period to obtain the cumulative displacement-time series.

[0044] Zero-base conversion and time variable conversion can be achieved using conventional difference calculations and date conversion methods in the art, and this invention does not limit this to any particular method. In one embodiment, the time variable is converted by dividing the number of calendar days between the current measurement date and the first measurement date by 365.25, and then rounded to two decimal places.

[0045] S3. The cumulative displacement is characterized by the sum of the product of the deformation rate attenuation coefficient and the natural logarithm of the time variable plus one, and the initial displacement deviation correction term. A logarithmic attenuation trend prediction model is constructed, and the cumulative displacement-time series is fitted by least squares regression to determine the deformation rate attenuation coefficient, the initial displacement deviation correction term, and the coefficient of determination.

[0046] The logarithmic decay trend prediction model can be expressed as equation (1):

[0047] (1)

[0048] In equation (1), S(t) represents the cumulative displacement at time t, in millimeters; t represents the time variable in years, with the first measurement time as the zero point, and t≥0; represents the deformation rate attenuation coefficient, in millimeters, reflecting the rate at which the deformation of the unstable rock mass decays over time; b represents the initial displacement deviation correction term, in millimeters, used to correct the systematic deviation of the initial measurement; ln represents the natural logarithm.

[0049] In this embodiment of the invention, the logarithmic decay trend prediction model is a two-parameter trend model with the natural logarithm of the time variable plus one as the sole independent variable and the cumulative displacement as the dependent variable. Unlike common time series methods such as grey models and exponential models, this model does not select a fitting function based on the statistical form of the data, but rather derives the function form from the deformation physical process of the unstable rock mass itself: its independent variable is the logarithm rather than time itself, precisely to ensure that the derivative of the model with respect to time decays in a reciprocal law, thus corresponding segment by segment in terms of rate magnitude to the three-stage evolution of the rock and soil mass after being subjected to stress: "rapid compression—slow creep—tend to stability". The deformation rate decay coefficient... The initial displacement deviation correction term b carries the system deviation of the first measurement, while the two do not overlap in physical meaning. This division of labor of parameters is the premise for the subsequent extrapolation to eliminate the system deviation.

[0050] The model form shown in equation (1) is chosen because during the compaction and closure of the fractures and the rearrangement of the boulders in the unstable rock mass, the deformation rate is approximately inversely proportional to the time elapsed: in the early stage of deformation, the debris and weathering products filling the fractures are rapidly compacted under their own weight, and the boulders rotate and rearrange, exhibiting a large displacement rate; as the compaction process gradually completes, the frictional interlocking between the boulders reaches a new mechanical equilibrium, the available pore volume for compression decreases according to the remaining amount, and the deformation rate decreases accordingly. The derivative of equation (1) with respect to time is... This decay rate decreases reciprocally with time, exhibiting the same decay rate as the aforementioned physical process. In contrast, the power-law decay is faster than this physical process, while the exponential decay is slower, with their residuals showing a systematic deviation at the beginning and end of the long-period sequence. Because the selected model is of the same order as the compaction-rebalancing process, the irreversible components in the multi-year reading sequence can be represented by a single coefficient. The measurement error and seasonal reversible fluctuations are averaged to zero mean residuals in the least squares sense, thus solving the problem that existing short-cycle displacement monitoring only compares the deformation amplitude in the current period and cannot separate the irreversible creep component from the fluctuations.

[0051] Furthermore, the reciprocal law can be explained more specifically from the perspective of the available compressible pore volume. Assume that the pore volume that can be further compacted within the fractures at the rear edge of the unstable rock mass is a constant value at the initial moment. The pore volume consumed per unit time during the compaction process is proportional to the remaining pore volume at that time. Therefore, the remaining pore volume decreases reciprocally with time, while the cumulative displacement is a linear function of the consumed pore volume, thus the cumulative displacement increases logarithmically with time. This derivation shows that equation (1) is not an empirical fit, but a direct result of compaction dynamics. This also explains why the same model form can be applied to both limestone unstable rock masses and loose deposit landslides—the difference between the two lies only in the initial compressible pore volume, and this difference is precisely determined by the coefficient... The value of reflects.

[0052] Deformation rate attenuation coefficient The value reflects the rock mass stiffness and the degree of development of structural planes. In engineering practice, the typical value range is 5 mm to 40 mm: for unstable limestone rock masses with good integrity. The value is relatively small, and the landslide deposits are loosely structured. The value is too large; A value that is too small indicates that the overall deformation is limited and the amount of sequence information is insufficient to support extrapolation. If the value is too large, it indicates that the initial deformation rate is fast and the measurement cycle needs to be shortened to capture the stage transition.

[0053] By introducing the aforementioned logarithmic decay trend prediction model, this invention achieves the following technical effects. First, the qualitative descriptions of "basically stable" and "underly stable" in traditional evaluations are replaced by quantitative predictions measured in millimeters. For example, it can directly give "the cumulative displacement increment over the next 5 years is approximately 7.1 millimeters, with an annual average of approximately 1.4 millimeters." The prediction results are quantifiable, comparable, and reproducible. Second, since all historical periods participate in parameter estimation, the impact of accidental reading errors in any period on the parameters is averaged across the periods, thus transforming long-term ledger data from archived information into calculable engineering assets. Third, the model contains only two undetermined parameters, provides a closed-form solution, requires no input of rock mechanics parameters, and does not require finite element or discrete element numerical simulation software. It can be completed on ordinary computing equipment at the engineering site and has the potential to be adapted to scenarios such as highway high slopes and mine spoil heaps.

[0054] In one example, 24 monitoring readings from 2015 to 2023 were taken from a fixed monitoring point at the main crack at the rear edge of a super-large unstable rock mass in the reservoir area of ​​a hydropower station. The data were fitted according to formula (1) to obtain... =16.8 mm, b=-5.2 mm, R 2 =0.91, the displacement of the unstable rock mass increased by an average of about 7 to 8 mm per year in the first 3 years, and by an average of about 1 to 2 mm per year in the following 2 years, which is consistent with the attenuation law described in equation (1). In this example, if the same sequence is fitted in exponential form, its coefficient of determination is lower than that in logarithmic form, and the residuals show a systematic deviation of the same sign at the end of the sequence, which confirms the necessity of choosing the model form.

[0055] S4. Extrapolate based on the logarithmic decay trend prediction model to obtain the cumulative displacement increment since the latest monitoring time after a preset extrapolation period.

[0056] Extrapolation essentially involves taking the difference between the values ​​of equation (1) over a period of time following the latest monitoring moment. Its technical significance lies in the fact that, since the model parameters are constrained by all historical periods, the extrapolation result no longer depends on the single-point reading at the end of the period, and the random error of the final reading will not be directly amplified into the prediction error. Because the extrapolation measures the logarithmic difference between two moments rather than the absolute value, the initial displacement deviation correction term b is eliminated in the difference. Therefore, the systematic deviation of the initial measurement does not affect the predicted cumulative displacement increment, thus solving the problem that existing methods cannot provide a quantitative expectation of the future cumulative displacement increment. The specific calculation method for extrapolation is explained in Example 4.

[0057] In one example, the time variable corresponding to the latest monitoring time is set to 8.50 years, and the preset extrapolation duration is 5 years, according to the example above. Extrapolating from 16.8 mm, the cumulative displacement increment over the next 5 years is approximately 7.1 mm, corresponding to a predicted cumulative displacement of approximately 63.1 mm at the extrapolation endpoint.

[0058] S5. Calculate the average deformation rate over the past year based on the cumulative displacement-time series, compare the average deformation rate over the past year with a preset grading threshold, and determine the stability level.

[0059] The average deformation rate over the past year is calculated using formula (2):

[0060] V=S(t0)-S(t0-1)(2)

[0061] In equation (2), v represents the average deformation rate over the past year, in millimeters per year; S(t) represents the cumulative displacement at time t, in millimeters (defined as in equation (1)); t0 represents the time variable corresponding to the latest monitoring time, in years. The specific threshold division of the grading criteria is elaborated in Example 6. In other embodiments, the average deformation rate over the past year can also be determined by the slope obtained by linear regression of the cumulative displacement of each period over the past year against the time variable.

[0062] It should be noted that the two readings in equation (2) that are one year apart should preferably be taken from the same hydrological season. Specifically, when two readings are taken each year and are arranged in the wet season and dry season respectively, the readings should be paired by subtracting the readings of the previous year from the readings of the wet season of this year, or by subtracting the readings of the previous year from the readings of the dry season of this year, to avoid directly subtracting the readings of the dry season six months ago from the readings of the wet season. The reason for this stipulation is that the reversible displacement component caused by the rise and fall of reservoir water level and temperature changes has an annual periodicity. Pairing and subtracting in the same season can make the reversible components cancel each other out in the difference, and the resulting rate is closer to the true irreversible deformation rate. When more than two readings are obtained in the same year, the difference between the arithmetic mean of the readings of this year and the arithmetic mean of the readings of the previous year can be taken as the average deformation rate of the past year.

[0063] S6. Output a trend prediction report containing the determination coefficient, the cumulative displacement increment, and the stability level.

[0064] The arrangement and presentation of the report can be achieved using tables, fitted curves, and text templates, which are conventional methods in the field. This invention does not limit the scope of the report.

[0065] In one implementation, the trend prediction report may include five parts: a raw monitoring data table, listing the measurement date, interval readings, and cumulative displacement of each fixed monitoring point period by period; a fitted curve graph, plotting the measured points and the fitted curve obtained by equation (1) with time variable as the horizontal axis and cumulative displacement as the vertical axis; a model parameter column, listing the deformation rate attenuation coefficient, the initial displacement deviation correction term, and the determination coefficient; a prediction result column, listing the cumulative displacement increment, the predicted cumulative displacement of the extrapolated endpoint, and the average deformation rate over the past year; and a stability level column, listing the stability level and the corresponding monitoring frequency recommendation. Optionally, the trend prediction report may also be tabulated separately for each fixed monitoring point and accompanied by a multi-point comparison curve graph, so that engineering management personnel can determine whether the deformation shows a consistent trend on the unstable rock mass or is concentrated only in individual parts.

[0066] Example 2

[0067] like Figure 2 As shown, based on Example 1, this example further defines S3. The step of characterizing the cumulative displacement by the sum of the product of the deformation rate attenuation coefficient and the natural logarithm of the time variable plus one, and the initial displacement deviation correction term, and constructing a logarithmic attenuation trend prediction model, performing least squares regression fitting on the cumulative displacement-time series, and determining the deformation rate attenuation coefficient, the initial displacement deviation correction term, and the coefficient of determination, includes:

[0068] S3.1. Add one to the time variable of each period in the cumulative displacement-time series and take the natural logarithm to obtain the sequence of transformed independent variables.

[0069] The technical significance of this transformation lies in converting the nonlinear relationship shown in equation (1) into a linear relationship with respect to the parameters: Let the independent variable of the transformation be x. i =ln(t i +1) Then the cumulative displacement with respect to x i Linear, parameters The slope and intercept of this linear relationship are represented by 'b', thus enabling the parameter solution to have a closed-form solution, eliminating the need for iterative optimization, and reducing the computational load to a level that can be completed on ordinary computing equipment in an engineering field, without the need for numerical simulation software. In the formula, x... i t represents the independent variable of the transformation in period i; i The time variable for period i is represented in years; i represents the monitoring period number, ranging from 1 to n; n represents the number of valid monitoring periods.

[0070] It should be understood that adding one to the time variable instead of directly taking the logarithm of time is to ensure that the transformation variable corresponding to the first period (when the time variable is zero) is zero rather than negative infinity, thus guaranteeing that the data points in the first period can participate in the regression without being excluded by numerical singularities. This treatment also ensures that the initial displacement deviation correction term b is physically exactly equal to the cumulative displacement prediction value of the model at the first period, facilitating comparison and verification with the measured zero baseline.

[0071] S3.2. Using the transformed independent variable sequence as the independent variable and the cumulative displacement as the dependent variable to form a regression sample set, the deformation rate attenuation coefficient and the initial displacement deviation correction term are solved by minimizing the sum of squared residuals.

[0072] The objective is to minimize the sum of squared residuals as shown in equation (3):

[0073] (3)

[0074] In equation (3), Indicates The sum of squared residuals with b as the independent variable; denoted by , representing the deformation rate attenuation coefficient, in millimeters, reflecting the rate of attenuation of the rock mass deformation over time (defined as in equation (1)); b represents the initial displacement deviation correction term, in millimeters, used to correct the systematic deviation of the initial measurement (defined as in equation (1)); ln represents the natural logarithm (defined as in equation (1)); i represents the monitoring period number, ranging from 1 to n; n represents the number of valid monitoring periods; S i This represents the cumulative displacement in the i-th period, in millimeters. The solution method is explained in Example 3.

[0075] Specifically, equation (3) is applied to... Taking the partial derivative with b and setting it to zero, we obtain a system of two linear normal equations: the first of which is the sum of the products of the transformed independent variable and the cumulative displacement in each period equal to... The first is the product of the sum of squares of the independent variables in each period plus the product of b and the sum of the independent variables in each period; the second is the sum of the cumulative displacements in each period equal to... The product of the sum of the independent variables in each period and the product of b and the number of periods is added. The coefficient matrix of this system of equations is non-singular when the independent variables in each period are not all equal, so the solution exists uniquely. Since the condition number of the coefficient matrix improves with the number of periods, this further illustrates from a numerical perspective that the restriction of no less than 10 collection periods is not merely a statistical requirement.

[0076] S3.3. Calculate the coefficient of determination based on the sum of squared residuals and the sum of squared total deviations of the regression sample set.

[0077] The coefficient of determination is calculated according to formula (4):

[0078] (4)

[0079] In equation (4), R 2 denoted by the coefficient of determination; i represents the monitoring period number, which ranges from 1 to n (defined as in equation (3)); n represents the number of valid monitoring periods (defined as in equation (3)). This represents the model-fitted value of the cumulative displacement in period i, in millimeters; This represents the arithmetic mean of the cumulative displacement over the periods, expressed in millimeters.

[0080] S3.4. When the determination coefficient is not less than the preset goodness-of-fit threshold, the logarithmic decay trend prediction model is deemed to be fit and allowed for extrapolation.

[0081] The preset goodness-of-fit threshold ranges from 0.80 to 0.90, with 0.85 used in practice. If the threshold is too low, sequences with large dispersion will be judged as acceptable, resulting in insufficient confidence in the extrapolation results; if the threshold is too high, normal measurement noise can cause acceptable sequences to be mistakenly judged as unacceptable, repeatedly extending the acquisition cycle and delaying early warning opportunities. The reason for setting the coefficient of determination as an entry condition for extrapolation rather than merely as a reference indicator in the report is that a low coefficient of determination has two causes—measurement dispersion or the rock mass itself deviating from the decay law, both of which render the extrapolation without a physical basis. By setting the goodness-of-fit threshold as an entry condition, sequences that do not meet the decay law premise will not be extrapolated to a formally complete but physically distorted predicted value, thus avoiding the shortcomings of general trend methods that only output a fitted curve without linkage to the goodness-of-fit.

[0082] In this embodiment of the invention, the goodness-of-fit threshold is essentially a "physical premise check" rather than a simple statistical significance test. The technical principle is as follows: the physical premise for equation (1) to hold is that the unstable rock mass is in a compaction-rebalancing stage. Once this premise is broken—for example, by the penetration of rear-edge cracks or the formation of a slip surface—the cumulative displacement will change from logarithmic growth to linear or even accelerated growth—the deviation between the data points and the logarithmic curve will no longer be zero-mean random noise, but a systematic deviation. This systematic deviation will directly manifest as a significant decrease in the coefficient of determination. Therefore, using the coefficient of determination as an entry condition is equivalent to automatically verifying whether the "attenuation law still holds" before each extrapolation. This is the technical contribution of this invention in upgrading the goodness-of-fit index from a post-evaluation parameter to a pre-judgment criterion.

[0083] The resulting technical advantage is that, within the same calculation process, the model performs both trend prediction and self-testing of its applicability, sharing the same set of parameters without requiring a separate discriminant model or human intervention. In engineering applications, managers only need to read the coefficient of determination column in the report to determine the reliability of the current period's predictions, without needing a background in regression analysis.

[0084] Let's take a real-world example. The 24-period sequence fitting of a certain limestone unstable rock mass measurement point yielded a coefficient of determination of 0.91, higher than the threshold, and its extrapolation conclusion was adopted. Similarly, the 9-year sequence fitting of a certain overburden landslide measurement point yielded a coefficient of determination of 0.89, also higher than the threshold, and its extrapolation conclusion was adopted. However, if a measurement point experiences a baseline jump due to a change in its benchmark location midway through the process, its coefficient of determination may drop below 0.6. In this case, the system does not output an extrapolation conclusion but instead prompts for verification of the measurement point, thus avoiding providing seemingly accurate predictions on sequences with discontinuous benchmarks.

[0085] S3.5. When the determination coefficient is less than the preset goodness-of-fit threshold, it is determined that the dispersion of the cumulative displacement-time series exceeds the limit. Check whether the fixed monitoring point has experienced local collapse, measurement error or deformation stage change. Extend the acquisition period of the displacement monitoring data and refit until the determination coefficient is not less than the preset goodness-of-fit threshold, and obtain the deformation rate attenuation coefficient, the initial displacement deviation correction term and the determination coefficient.

[0086] The verification points for the three types of causes are different: local collapse is manifested by a sudden jump in the reading of a single monitoring point while the readings of other monitoring points in the same group remain stable; measurement error is manifested by the deviation of the reading being an integer multiple of the minimum scale value of the measuring instrument; and the transformation of the deformation stage is manifested by the residuals having the same sign and increasing absolute value in several periods at the end.

[0087] Preferably, the above verification can be performed in the following order to improve efficiency. First, perform a cross-point horizontal comparison. If only one measuring point in the same period shows an abnormal reading while the readings of other measuring points in the same group are stable, it should be treated as a local collapse. On-site verification should be performed to check whether the benchmark stake of the measuring point is loose and whether there are any fallen blocks around it. If multiple measuring points in the same period deviate in the same direction, the measurement conditions of that period may be problematic. It should be checked whether the operators or measuring instruments were changed in that period. Next, perform a residual sign sequence check. If the residual signs are randomly distributed in the sequence, it indicates that the deviation is caused by random noise, which can be improved by extending the acquisition cycle. If the residual signs are consecutively the same in the last segment and the absolute value increases monotonically, it should be judged as a transformation stage. At this time, the acquisition cycle should not be simply extended, but the deviation judgment process described in Example 5 should be followed.

[0088] Example 3

[0089] Based on Example 2, this example further defines S3.2. The step of constructing a regression sample set using the transformed independent variable sequence as the independent variable and the cumulative displacement as the dependent variable, and solving for the deformation rate attenuation coefficient and the initial displacement deviation correction term by minimizing the sum of squared residuals, includes:

[0090] S3.2.1. Solve the regression sample set by minimizing the sum of squared residuals to obtain the initial values ​​of the initial deformation rate attenuation coefficient and the initial displacement deviation correction term.

[0091] The initial deformation rate attenuation coefficient is denoted as The unit is millimeters; the initial value of the initial displacement deviation correction term is denoted as b1, with the unit being millimeters. Both are derived from equation (3). The normal equation system is obtained by taking the partial derivatives of b and setting the partial derivatives to zero.

[0092] S3.2.2. Calculate the fitting residuals of each sample point in the regression sample set relative to the initial deformation rate attenuation coefficient and the initial value of the initial displacement deviation correction term, and calculate the standard deviation of the fitting residuals.

[0093] The fitting residual of the i-th sample point is denoted as e. i The unit is millimeters, equal to the cumulative displacement of period i and the displacement of that period according to... The difference between the fitted values ​​calculated by b1; the standard deviation of the fitted residuals is denoted as b1. The unit is millimeters.

[0094] S3.2.3. The sample points whose absolute value of the fitting residual is greater than a preset multiple of the standard deviation are identified as mutation sample points, and the mutation sample points are removed from the regression sample set to obtain the corrected regression sample set.

[0095] The criterion for mutation sample points is as shown in equation (5):

[0096] (5)

[0097] In equation (5), e i This represents the fitting residual for the i-th sample point, in millimeters. The standard deviation of the fitted residuals is expressed in millimeters; k represents the preset factor, a dimensionless quantity with a value ranging from 2 to 3, and 2.5 is used in practice. If the value of k is too small, a large number of sample points with normal fluctuations will be eliminated, the effective period will decrease, and the statistical significance of long-period series will be weakened; if the value of k is too large, the true jump readings cannot be identified, and the attenuation coefficient will be skewed by single-point anomalies.

[0098] In this embodiment of the invention, the abrupt change sample point refers to a sample point whose reading deviation does not originate from the actual deformation of the unstable rock mass, but rather from changes in the measurement process or the state of the benchmark itself. The fundamental difference between this and the aforementioned "deformation stage transition" in terms of data form is that the abrupt change sample point is an isolated, single-period deviation that can revert to its original trend afterward, while the deformation stage transition is a continuous, multi-period, and irreversible trend change. The abrupt change sample point removal mechanism is designed based on this morphological difference—it judges each point according to the relative relationship between the residual and the residual standard deviation, removing only isolated deviation points without changing the overall trend of the sequence.

[0099] The reason for setting up a mutation sample point removal step within the solution process is that local collapses and reading errors in the benchmark measurement can cause deviations far exceeding normal fluctuations in individual periods. Since the least squares criterion squares the residuals, the impact of a single jump reading on the parameters is amplified by the square, resulting in a systematically larger decay coefficient fitted by the unremoved sequence and a risky extrapolation result. Because the anomaly is judged based on the relative relationship between the residuals and the standard deviation rather than a fixed threshold, the criterion automatically adapts to the measurement noise level of different monitoring points, thereby eliminating the interference of single-point anomalies on trend prediction without losing the value of long-term data.

[0100] The specific implementation process can be described as follows. The system first calculates the fitting residuals of all sample points according to the initial parameters obtained in S3.2.1 and calculates their standard deviation. Then, it judges each point according to Equation (5), marks the hit sample points as mutation sample points and removes them from the regression sample set. At the same time, it retains the original reading of the point and the removed mark in the data ledger for review. To avoid excessive reduction of the effective period, an upper limit for the single-round removal ratio can be optionally set. When the number of mutation sample points hit in a single round exceeds 10% of the total period, the removal is suspended and a prompt is given that the overall dispersion of the sequence is too high. The process is then transferred to the verification process described in S3.5. In addition, if the removed sample point happens to be the first or last period of the sequence, an additional prompt should be given. Removing the first period will change the physical meaning of the zero baseline, and removing the last period will weaken the reliability of the average deformation rate over the past year. In both cases, it is advisable to manually review and decide whether to adopt the removal result.

[0101] Through the above mechanism, this invention achieves the following technical effects. First, parameter estimation is no longer sensitive to isolated anomaly readings, and the estimated value of the attenuation coefficient is closer to the true level of irreversible deformation, avoiding the situation where extrapolation results are too large due to single-point anomalies, leading to false alarms of high-level warnings. Second, the elimination criterion uses the residual standard deviation as the scale rather than the absolute displacement, allowing the same set of criteria to be directly applied to different measuring points with large differences in measurement noise levels and even different engineering scenarios, without the need for point-by-point parameter tuning. Third, the eliminated sample points are recorded in the ledger, making the anomaly readings themselves clues for on-site verification, thus allowing problems in the measurement process and problems in the unstable rock mass itself to be located separately.

[0102] In one example, the monitoring point in the above example showed a sudden increase of approximately 2.4 mm in the reading of the first period in year 5.1 compared to the adjacent period. The absolute value of its residual was approximately 3.1 times the standard deviation, and it was identified as a mutation point and removed. This point subsequently returned to the normal trend in subsequent periods. Before removal, the deformation rate attenuation coefficient obtained from the fitting of this measurement point was approximately 18.5 mm, and the coefficient of determination was approximately 0.83, which was below the goodness-of-fit threshold. After removal, the deformation rate attenuation coefficient was corrected to 16.8 mm, and the coefficient of determination increased to 0.91. The sequence changed from unacceptable to acceptable, and extrapolation proceeded normally. This comparison illustrates the direct impact of the mutation point removal process on the model's usability.

[0103] S3.2.4. Resolve the modified regression sample set by minimizing the sum of squared residuals to obtain the deformation rate attenuation coefficient and the initial displacement deviation correction term.

[0104] The deformation rate attenuation coefficient obtained by resolving is denoted as The unit is millimeters, which is the final unit used. value.

[0105] S3.2.5. When the relative change of the deformation rate attenuation coefficient relative to the initial deformation rate attenuation coefficient is greater than the preset convergence threshold, the elimination and re-solution are repeated on the modified regression sample set until the relative change is not greater than the preset convergence threshold.

[0106] The convergence criterion is as shown in equation (6):

[0107] (6)

[0108] In equation (6), This represents the deformation rate attenuation coefficient obtained from the recalculation, in millimeters, which is the final value used. value; This represents the initial deformation rate attenuation coefficient, in millimeters. This represents the preset convergence threshold, which is a dimensionless quantity with a value range of 0.01 to 0.05, and is set to 0.02 in practice. The significance of setting the convergence criterion is that the standard deviation of the residuals will decrease after a single round of elimination. Sample points that were not originally within the limit may exceed the limit under the new standard deviation, and the process needs to be repeated until the parameters no longer change significantly, in order to avoid parameter drift introduced by the elimination process itself.

[0109] Furthermore, in engineering practice, this iterative process typically converges within two to three rounds. To prevent the iteration from failing to terminate on extremely discrete sequences, a maximum number of iterations can be set, for example, five rounds as the upper limit; if the upper limit is reached but the relative change is still greater than the preset convergence threshold, the sequence is determined to be unsuitable for logarithmic decay trend prediction, and the process proceeds to the verification and extended acquisition cycle described in S3.5.

[0110] Example 4

[0111] like Figure 3 As shown, based on Example 1, this example further defines S4. The extrapolation based on the logarithmic decay trend prediction model to obtain the cumulative displacement increment since the latest monitoring time after a preset extrapolation period includes:

[0112] S4.1. The time variable corresponding to the latest monitoring time is taken as the extrapolation starting point, and the sum of the extrapolation starting point and the preset extrapolation duration is taken as the extrapolation ending point. The preset extrapolation duration is 3 to 5 years.

[0113] The extrapolation endpoint is denoted as t. e The unit is years, which is equal to the sum of t0 and the preset extrapolation duration. The preset extrapolation duration of 3 to 5 years is based on the following: when the duration is less than half the length of the existing monitoring sequence, the extrapolation interval falls within the effective constraint range of the model parameters; if the duration is too short, the predicted increment is on the same order of magnitude as the measurement accuracy and has no decision significance; if the duration is too long, the extrapolation interval is far from the sample interval, and the uncertainty of parameter estimation is amplified by the flat section of the logarithmic curve.

[0114] Optionally, when the length of the existing monitoring sequence is significantly greater than 10 years, the preset extrapolation time can be set to the upper limit within the range of 3 to 5 years; when the sequence length is only slightly more than 5 years, the lower limit should be used. It should be noted that the design and implementation cycle of the reinforcement scheme that is of concern to engineering decisions is usually also on the order of 3 to 5 years, so the setting of this extrapolation time takes into account both the extrapolation reliability of the model and the time scale of engineering decisions.

[0115] S4.2. Multiply the deformation rate attenuation coefficient by the difference between the natural logarithm of the extrapolated endpoint plus one and the natural logarithm of the extrapolated starting point plus one to obtain the cumulative displacement increment.

[0116] The cumulative displacement increment is calculated according to formula (7):

[0117] (7)

[0118] In equation (7), This represents the cumulative displacement increment over the extrapolated period, in millimeters. The deformation rate attenuation coefficient is expressed in millimeters, reflecting the rate of attenuation of the deformation of the unstable rock mass over time (defined as in equation (1)); ln represents the natural logarithm (defined as in equation (1)); t e The extrapolation endpoint is represented in years and is equal to the sum of t0 and the preset extrapolation duration; t0 represents the time variable corresponding to the latest monitoring time, in years (defined as in equation (2)). Equation (7) does not contain b, that is, the initial displacement deviation correction term is eliminated when the difference is made between the two times. Therefore, the systematic deviation of the first measurement is not transmitted to the predicted increment. This is the direct benefit of defining the predicted quantity as an increment rather than an absolute displacement.

[0119] In this embodiment of the invention, the cumulative displacement increment refers to the relative displacement of the unstable rock mass after a preset extrapolation period from the latest monitoring time. Physically, this corresponds to the deformation released by the further compaction of the rear edge cracks and the continued rearrangement of the boulders during this period. Compared to directly extrapolating the absolute cumulative displacement, the technical principle of using the increment as the prediction quantity is as follows: the value of the absolute cumulative displacement depends on the selection of the zero benchmark, which is determined by the initial measurement. The systematic deviation of the initial measurement and the deviation of the initial point location will shift all absolute values. The increment is the difference between the values ​​taken by the same model at two different times, and the aforementioned shifts are completely canceled out in the difference calculation. This property allows for direct horizontal comparison of predicted increments between different measuring points and different projects, whereas absolute cumulative displacement does not possess this comparability.

[0120] Equation (7) also shows that the cumulative displacement increment decreases as the extrapolation starting point increases—for the same extrapolation time, the longer the sequence and the later the extrapolation starting point, the smaller the predicted increment. This mathematical property is consistent with the physical fact that the deformation of the unstable rock mass gradually converges, which also means that this method will automatically give increasingly convergent prediction conclusions as the monitoring years accumulate, without the need for manual adjustment of the model form or parameters.

[0121] In one example, t0 is 8.50 years, and the preset extrapolation duration is 5 years, then t e Given a period of 13.50 years, ln(14.50)≈2.674, (9.50)≈2.251, the difference between the two is approximately 0.423. =16.8 mm It is approximately 7.1 millimeters.

[0122] S4.3. Add the cumulative displacement corresponding to the extrapolation starting point to the cumulative displacement increment to obtain the predicted cumulative displacement of the extrapolation ending point.

[0123] In the example above, the cumulative displacement corresponding to the extrapolation starting point is approximately 56.0 mm. Adding this to the 7.1 mm, the predicted cumulative displacement of the extrapolation ending point is approximately 63.1 mm. To verify the effectiveness of the extrapolation, a backtesting prediction can be performed: when only the first four periods of data are accumulated at this monitoring point, the model is fitted using this method and extrapolated over five years. The resulting predicted cumulative displacement is approximately 47.5 mm, while the measured value at that time is approximately 52.5 mm, with a relative error of approximately 9.5%. This indicates that the model has usable extrapolation capabilities even with short sequences.

[0124] It is worth noting that the data from the first four periods used in the above retrospective prediction only covers approximately 1.07 years, which does not yet meet the requirement of S1 that the data collection period be no less than 5 years and the number of periods be no less than 10. The resulting deformation rate attenuation coefficient is approximately 17.2 mm, and the initial displacement deviation correction term is approximately 4.8 mm, which is numerically close to the 16.8 mm obtained using the complete 24-period sequence. This indicates that the parameter estimation of the logarithmic decay trend prediction model has good robustness. Even so, extrapolation under short-sequence conditions should still be performed using leave-one-out cross-validation as described in Example 9 before it can be used.

[0125] Example 5

[0126] Based on Example 4, after multiplying the deformation rate attenuation coefficient by the difference between the natural logarithm of the extrapolated endpoint plus one and the natural logarithm of the extrapolated starting point plus one to obtain the cumulative displacement increment, the method further includes:

[0127] S4.2.1. Divide the deformation rate attenuation coefficient by the value after adding one to the extrapolation endpoint to obtain the predicted instantaneous deformation rate at the end of the year.

[0128] The predicted instantaneous deformation rate at the end of the year is calculated according to formula (8):

[0129] (8)

[0130] In equation (8), v e This indicates the predicted instantaneous deformation rate at the end of the year, expressed in millimeters per year. The deformation rate attenuation coefficient, expressed in millimeters, reflects the rate attenuation of deformation of the unstable rock mass over time (defined as in equation (1)); t e The extrapolation endpoint is represented in years and is equal to the sum of t0 and the preset extrapolation duration (defined as in equation (7)). Equation (8) is the derivative of equation (1) at the extrapolation endpoint, characterizing the instantaneous deformation rate of the unstable rock mass at the end of the predicted period. In the example above, v e Approximately 1.16 millimeters per year.

[0131] S4.2.2. Calculate the difference between the predicted instantaneous deformation rate at the end of the year and the average deformation rate over the past year to obtain the deformation rate evolution difference.

[0132] In this embodiment of the invention, the deformation rate evolution difference refers to the algebraic difference between the future terminal instantaneous rate predicted by the model and the current measured rate. Its sign, rather than its absolute value, carries the discriminative information: a negative difference indicates that the rate is still in a decreasing channel, while a positive or zero difference indicates that the rate is no longer decreasing. The deformation rate evolution difference is expressed in millimeters per year and is obtained by subtracting the value obtained from equation (2) from the value obtained from equation (8).

[0133] S4.2.3. When the difference in deformation rate evolution is less than zero, it is determined that the deformation of the unstable rock mass is in a convergent decay creep state.

[0134] Specifically, being in a convergent decay creep state means that the compaction process of the trailing edge crack is still ongoing and the friction interlocking structure has not been destroyed. In this case, the stability level can be determined according to the grading criteria described in Example 6, without the need to initiate an additional discrimination process. It should be noted that when the measured rate is temporarily lower than the model smoothing value due to seasonal factors, the difference in deformation rate evolution may also be positive. This situation does not directly constitute a deviation from the conclusion and still needs to be verified by S4.2.4 and S4.2.5 before it can be determined. In the above example, the predicted instantaneous deformation rate at the end of the year is about 1.16 mm per year, and the average deformation rate in the past year is about 0.8 mm per year. The difference between the two is about positive 0.36 mm per year, which is not less than zero. Therefore, it enters the exponential trend model verification stage. The coefficient of determination of the exponential model obtained by performing exponential fitting on the same sequence is about 0.74, which is lower than the 0.91 obtained by logarithmic fitting. The second-order condition is not met, so it is not judged as a deviation from the logarithmic decay law. This measuring point still maintains the stability level as described in Example 6.

[0135] S4.2.4. When the difference in the deformation rate evolution is not less than zero, the cumulative displacement-time series is refitted using an exponential trend model with the time variable as the independent variable of the exponential term to obtain the coefficient of determination of the exponential model.

[0136] The exponential trend model uses time as the independent variable of the exponential term. Its two undetermined parameters are solved using the minimum residual sum of squares criterion, which is isomorphic to equation (3), and the coefficients of determination of the exponential model are calculated in a manner isomorphic to equation (4). To avoid symbol confusion, the two undetermined parameters of the exponential trend model are denoted as... With b', where b' represents the displacement magnitude coefficient of the exponential trend model, in millimeters; b' represents the growth rate coefficient of the exponential trend model, in annually.

[0137] In practice, the solution to the exponential trend model can also be transformed into linear regression through variable transformation: after taking the natural logarithm of the cumulative displacement, perform a linear regression with the time variable, and the resulting slope is the growth rate coefficient b', and the natural exponent of the resulting intercept is the displacement amplitude coefficient. When there are non-positive cumulative displacement readings in the sequence, a common positive translation can be applied to the entire sequence first, and then the logarithm can be taken. When calculating the coefficient of determination of the exponential model, the original reading before translation can be used as the benchmark to ensure that the coefficients of determination of the two models are comparable on the same scale.

[0138] S4.2.5. When the coefficient of determination of the exponential model is greater than the coefficient of determination, it is determined that the deformation of the unstable rock mass deviates from the logarithmic decay law, and the stability level is adjusted to the accelerated instability precursor level.

[0139] The reason for using the comparison of the coefficients of determination of the two models as the deviation criterion is that the logarithmic and exponential forms mathematically correspond to two types of evolution: decreasing and increasing rates, respectively. The goodness of fit between the two on the same sequence reflects whether the sequence is in the decay or acceleration phase. Since the difference in deformation rate evolution is not less than zero, it means that the instantaneous rate predicted by the model at the end is not lower than the current measured rate, which contradicts the decay law itself. This condition constitutes a necessary indication of deviation. Furthermore, by using the goodness of fit of the exponential model as cross-validation, the misjudgment of occasional differences caused by measurement noise as accelerated creep is avoided. Thus, while maintaining the sensitivity of the criterion, false alarms are suppressed, solving the problem that general trend methods are difficult to identify when a dangerous rock mass enters the accelerated creep stage. A grade adjustment conclusion can be given months to years before accelerated instability.

[0140] In this embodiment of the invention, the aforementioned "evolutionary difference indication—exponential model verification" constitutes a dual-condition criterion. Its technical definition is: using the rate evolution direction as the primary screening condition and the relative goodness of fit of the model form as the secondary confirmation condition, a deviation is determined when both conditions are simultaneously met. The technical principle of this criterion is that each level of condition compensates for the other's shortcomings—using only the primary condition, occasional rate bounces caused by measurement noise might be misjudged as acceleration; using only the secondary condition, the exponential model, which may already have a slightly higher coefficient of determination on short or weakly decaying sequences, would also lead to misjudgment. After the two levels are concatenated, a deviation conclusion is only output when both the rate evolution direction and the model form selection point to acceleration.

[0141] The resulting technical benefits are threefold. First, the entire computational load required for the determination is merely a single additional linear regression, without introducing any new sensing devices or human experience parameters, resulting in virtually zero engineering implementation costs. Second, the determination conclusion directly maps to the accelerated instability precursor level, seamlessly integrating with the four-level classification system described in Example 6, eliminating the need for a separate response procedure. Third, because this criterion applies to the overall shape of the cumulative displacement sequence rather than a single period reading, its triggering time is earlier than the triggering time of the rate-type criterion "annual deformation rate exceeds the third threshold," thus allowing for several months to several years' lead time for engineering reinforcement or personnel evacuation.

[0142] Let's take an example to illustrate its function. Suppose that the cumulative displacement sequence of a certain unstable rock mass measuring point in the previous few years follows a logarithmic decay law with a coefficient of determination of 0.92; thereafter, due to the combined effects of continuous heavy rainfall and a sudden drop in reservoir water level, the rear edge cracks are partially connected, and the measured values ​​of the last four consecutive periods of the sequence are all higher than the logarithmic curve, with the deviation increasing period by period. Before the deviation occurred, the average deformation rate of the past year calculated according to formula (2) was 3.2 mm per year, which was at the weak creep level. The predicted instantaneous deformation rate at the end of the year calculated according to formula (8) was 1.4 mm per year. The difference in deformation rate evolution was -1.8 mm per year, which was less than zero, and it was judged to be a convergent decay creep state. After two more observations, the measured average deformation rate of the past year climbed to 5.8 mm per year, while the predicted instantaneous deformation rate at the end of the year was still 1.4 mm per year. The difference in deformation rate evolution turned to positive 4.4 mm per year, which was not less than zero, and the first-level condition was met. The coefficient of determination of the exponential model obtained by performing exponential fitting on the same sequence was 0.95, which was higher than the 0.88 of the logarithmic fitting. The second-level condition was also met. The system then determined that the dangerous rock mass deviated from the logarithmic decay law and directly adjusted the stability level from the medium creep level obtained by the rate to the accelerated instability precursor level. Based on this, the personnel below the slope foot were evacuated and engineering reinforcement was carried out.

[0143] Example 6

[0144] like Figure 4 As shown, based on Example 1, this example further defines S5. The step of calculating the average deformation rate over the past year based on the cumulative displacement-time series, comparing the average deformation rate over the past year with a preset grading threshold to determine the stability level includes:

[0145] S5.1. The preset grading thresholds include a first threshold, a second threshold, and a third threshold that increase sequentially, wherein the first threshold is 2 mm per year, the second threshold is 5 mm per year, and the third threshold is 10 mm per year.

[0146] The values ​​of the Level III thresholds are determined with reference to the recommended values ​​in the relevant industry regulations for dam and reservoir bank deformation monitoring, and in combination with statistics from years of engineering practice in this field. Statistics show that about 95% of unstable rock masses in a stable state have an annual deformation rate of less than 2 mm per year.

[0147] In this embodiment of the invention, the preset grading threshold constitutes a four-segment rate band divided by three boundary values. Each rate band corresponds to a stability level and a set of monitoring and response measures. The technical principle of this threshold system is that there is a stable correspondence between the deformation rate of a rock mass and its creep stage—the annual deformation rate of a rock mass in the compaction and convergence stage remains stable below the millimeter level over many years of monitoring; after entering the steady-state creep stage, the rate rises to the millimeter level; and after entering the accelerated creep stage, the rate will cross the ten-millimeter level in a short period of time and continue to climb. The three boundary values ​​are taken from the rate ranges of the above-mentioned stage transitions, so the grading conclusion is not only a division of numerical ranges, but also corresponds to a clear deformation mechanics stage.

[0148] S5.2. When the average deformation rate over the past year is not greater than the first threshold, the stability level is determined to be a stable level.

[0149] The corresponding measure is to maintain the regular monitoring frequency, with one to two measurements per year.

[0150] S5.3. When the average deformation rate over the past year is greater than the first threshold and not greater than the second threshold, the stability level is determined to be a weak creep level.

[0151] The corresponding measures include increasing the measurement frequency to once every six months and strengthening on-site inspections. The focus of on-site inspections is on changes in the width of the main crack at the rear edge, whether the filling material in the crack has been squeezed out, whether new falling blocks have appeared on the free face of the unstable rock mass, and whether new accumulations have appeared at the toe of the slope.

[0152] S5.4. When the average deformation rate over the past year is greater than the second threshold but not greater than the third threshold, the stability level is determined to be a medium creep level.

[0153] The corresponding measures are to add automated monitoring equipment and activate emergency response plans. The added automated monitoring equipment may include crack gauges or fissure gauges deployed across the cracks, satellite positioning monitoring piers deployed on the top of the unstable rock mass, and ground-based synthetic aperture radar facing the free face. The sampling frequency can be increased to once a day or even continuous collection, so as to obtain a daily-scale encrypted sequence in addition to the annual-scale sequence measured manually. It should be noted that when the encrypted sequence collected by the automated equipment is used in the calculation of this method, it should still be thinned to data points of the same scale as the manual sequence according to the rule of no less than 2 periods per year, so as to ensure that the dimensions of the time variable are consistent with Equation (1).

[0154] S5.5. When the average deformation rate over the past year is greater than the third threshold, the stability level is determined to be an accelerated instability precursor level.

[0155] The corresponding measures include evacuating personnel from below the slope and reinforcing the structure. In other implementation methods, the measures corresponding to each level can also be automatically triggered by the engineering management system according to a preset response strategy table.

[0156] By adopting the above-mentioned four-level classification system, the technical effects of this invention are as follows: the early warning conclusion no longer stops at the binary judgment of "whether it exceeds a certain early warning value", but gives a level conclusion that is bound to the disposal measures one by one. Engineering managers do not need to interpret the engineering meaning of the displacement value themselves and can directly take corresponding measures. At the same time, since the four-level boundary values ​​are fixed and public, the evaluation conclusions between different dangerous rock masses and different years have horizontal and vertical comparability, which makes it easy to prioritize the treatment of multiple dangerous rock masses within a reservoir area.

[0157] In the example above, the average deformation rate of this monitoring point over the past year was approximately 0.8 mm per year, which is below the first threshold and is therefore classified as stable. Maintaining the regular monitoring frequency is sufficient, and no engineering reinforcement is required. As a contrast, if another monitoring point on the same unstable rock mass has an average deformation rate of 3.5 mm per year over the past year, it falls between the first and second thresholds and is classified as having weak creep. The measurement frequency for this monitoring point should be increased to once every six months. Therefore, different parts of the same unstable rock mass may yield different stability levels. In engineering practice, it is advisable to take the highest level among all monitoring points as the overall stability level of the unstable rock mass.

[0158] Example 7

[0159] Based on Example 6, the method further includes:

[0160] Step A. When there is a disaster-bearing object below the unstable rock mass, the first threshold, the second threshold, and the third threshold are all reduced by a reduction factor of 50%, and then compared with the average deformation rate of the past year.

[0161] The disaster-affected areas include dam intakes, main transportation routes, and residential areas. The reduced classification thresholds are 1 mm / year, 2.5 mm / year, and 5 mm / year, respectively. The reduction factor of 50% is based on the fact that the existence of disaster-affected areas does not change the deformation pattern of the unstable rock mass itself, but rather changes the acceptable risk level under the same deformation rate. Therefore, shifting the threshold zone downward by a uniform proportion can increase the lead time for early warning without disrupting the relative relationship of the four-level criteria.

[0162] Specifically, whether a disaster-bearing object meets the threshold reduction trigger condition can be determined based on its spatial relationship with the unstable rock mass: when the disaster-bearing object is located directly below the free face of the unstable rock mass, and its horizontal distance from the toe of the slope is less than 1.5 times the elevation difference of the unstable rock mass, it is considered to be within the influence range of the landslide and rockfall, triggering threshold reduction; otherwise, it is not triggered. The reason for using 1.5 times the elevation difference as the criterion is that the maximum horizontal throwing distance of the collapsed body after instability is roughly proportional to its falling elevation difference. Optionally, when multiple types of disaster-bearing objects exist simultaneously below the same unstable rock mass, as long as any one of them falls within the aforementioned influence range, all three thresholds will be reduced.

[0163] Step B. When the deformation rate attenuation coefficient is greater than the preset attenuation coefficient adjustment threshold and the determination coefficient is greater than the preset goodness adjustment threshold, the stability level is increased by one level.

[0164] The preset threshold for adjusting the attenuation coefficient ranges from 25 mm to 35 mm, with 30 mm used in practice; the preset threshold for adjusting the goodness of fit ranges from 0.93 to 0.97, with 0.95 used in practice. The physical meaning of this combination of conditions is: a large attenuation coefficient and high goodness of fit indicate that the overall deformation of the unstable rock mass is large and the deformation pattern is stable and reliable. Even if the current annual deformation rate is low, its cumulative deformation base and subsequent releaseable deformation are still higher than other unstable rock masses with the same rate, therefore the alert level should be raised.

[0165] Furthermore, the reason for requiring both conditions to be met simultaneously, rather than judging solely by the deformation rate attenuation coefficient, is that a large attenuation coefficient may also stem from sequence dispersion or the existence of unidentified mutation sample points. In such cases, the coefficient does not represent the true magnitude of deformation. Only when the coefficient of determination is simultaneously higher than the adjustment threshold, i.e., the sequence truly conforms to the logarithmic decay law, can a large attenuation coefficient be interpreted as a true large deformation. For example: a measurement point has a deformation rate attenuation coefficient of 32 mm, a coefficient of determination of 0.96, and an average deformation rate of 1.5 mm per year over the past year. According to the criteria in Example 6, it should be classified as a stable level. However, because both adjustment conditions are met, it is upgraded to a weak creep level, and the measurement frequency is correspondingly increased to once every six months. Another measurement point, although having a deformation rate attenuation coefficient of 33 mm, has a coefficient of determination of only 0.86, which does not reach the adjustment threshold. Therefore, the level is not upgraded, and the cause of its sequence dispersion is checked according to the process described in Example 2.

[0166] Step C. Write the revised stability level into the trend forecast report.

[0167] It should be noted that when the threshold reduction described in step A and the level increase described in step B are applied simultaneously, the base level should first be obtained by comparing the reduced threshold, and then the level should be increased based on that base level. The two measures take effect sequentially and do not substitute for each other. Once the level is increased to the level of accelerated instability precursor, no further increases will be made.

[0168] Example 8

[0169] Based on Example 1, this example further defines S1. The step of setting up fixed monitoring points on the unstable rock mass, including fixed reference points on the mountainside and moving points on the unstable rock mass side, and periodically measuring the distance between the fixed reference points and the moving points to obtain displacement monitoring data for no less than 5 years and no less than 10 periods, includes:

[0170] S1.1. At least three fixed monitoring points shall be set up on both sides of the main crack at the rear edge of the unstable rock mass.

[0171] The rear edge main crack is the part where the relative displacement between the unstable rock mass and the parent rock is most concentrated. Placing it here can obtain the highest signal-to-noise ratio; placing no less than 3 cracks can identify single-point local collapses through mutual verification of multi-point readings.

[0172] In this embodiment of the invention, the fixed monitoring point is a benchmark measurement unit consisting of a fixed reference point and a moving point located on both sides of the main crack. The object of measurement is not the absolute spatial coordinates of the unstable rock mass, but rather the relative displacement of the unstable rock mass relative to the stable parent rock behind it. Compared with absolute coordinate monitoring methods such as satellite positioning and total stations, the benchmark measurement unit is not affected by external factors such as base station settlement, atmospheric refraction, and satellite ephemeris errors. Its measurement accuracy depends only on the stability of the measuring instrument itself and the benchmark marker, making it particularly suitable for long-term monitoring scenarios that require consistent measurement conditions over many years.

[0173] S1.2. Set the fixed reference point on the mountain side of each fixed monitoring point as a fixed pile on the stable bedrock of the mountain, and set the moving point on the dangerous rock mass side as a moving pile at the edge of the main crack at the rear edge.

[0174] Specifically, both fixed and movable piles should be cast in concrete and embedded in the bedrock to a certain depth. A metal marker with a cross engraving should be placed on the top of the pile to ensure consistent alignment during each measurement period. Fixed piles should be installed on intact bedrock behind the main crack, unaffected by the crack's cutting effect, with a horizontal distance from the main crack preferably greater than half the crack's depth to avoid the crack's influence zone. Movable piles should be installed on the side of the unstable rock mass, as close as possible to the free face, but in a location where they will not become unstable due to weathering and rockfall.

[0175] S1.3. Set two measurement directions for each fixed monitoring point: one perpendicular to the direction of the trailing edge main crack and the other parallel to the direction of the trailing edge main crack, and obtain the opening displacement and shear displacement of the trailing edge main crack respectively.

[0176] The significance of setting two orthogonal measurement directions is that the instability modes of unstable rock masses include toppling and sliding. The former is mainly characterized by crack opening, while the latter is mainly characterized by shear along the crack surface. Reading from a single direction will miss one of these components. In other embodiments, a third measurement direction perpendicular to the horizontal plane can also be added to obtain the settlement component.

[0177] The technical principle of the bidirectional measurement is that the relative displacement of the unstable rock mass relative to the parent rock is a vector, and the measurement obtained along only one direction is the projection of this vector in that direction. When there is an angle between the actual displacement direction and the measurement direction, the projected value is systematically smaller than the actual displacement, and the degree of underestimation increases with the increase of the angle. Moreover, the actual displacement direction of the unstable rock mass is often difficult to predict in the early stage of monitoring and may change with the process of crack penetration. After setting two mutually orthogonal measurement directions, the square root of the sum of the squares of the two projected values ​​is the modulus of the displacement vector in that plane. Therefore, no matter how the actual displacement direction changes, it will not be systematically underestimated. More importantly, the change of the ratio of the two components over time is itself an indicator of the evolution of the instability mode—the opening component is dominant and the proportion is stable, indicating a toppling evolution; the proportion of the shear component increases periodically, indicating that a slip surface is forming. This should be verified in conjunction with the deviation judgment process described in Example 5.

[0178] The resulting technical effect is that, without increasing the cost of measurement equipment, the same set of benchmark points can simultaneously provide displacement magnitude information and instability mode information, enabling trend prediction conclusions and instability mechanism judgments to be completed on the same set of data, thus avoiding systematic underestimation of deformation due to improper selection of measurement direction.

[0179] S1.4. Use a steel ruler or displacement sensor to measure the distance between the fixed reference point and the moving point, with a measurement accuracy of not less than 1 mm.

[0180] The measurement accuracy should be no less than 1 mm, which is the lower limit matching the first threshold of 2 mm per year for the stability level criterion. When the accuracy is lower than this value, the resolution of a single period reading is insufficient to support the classification of the annual deformation rate. Optionally, when using a steel ruler for measurement, its accuracy can reach the order of 0.5 mm. In this case, it is advisable to repeat the measurement three times at the same interval during each period and take the arithmetic mean to further reduce the error of random readings. When there is a disaster-bearing object under the unstable rock mass and the threshold reduction needs to be performed according to Example 7, the first threshold is reduced to 1 mm per year. In this case, a displacement sensor or vernier caliper with higher accuracy should be used first.

[0181] S1.5. Measure at a frequency of no less than 2 periods per year, and accumulate no less than 10 periods of displacement monitoring data.

[0182] At least two sampling periods are usually arranged each year, one during the high-water season and one during the low-water season, so that the reversible components caused by the rise and fall of reservoir water levels are sampled symmetrically throughout the year.

[0183] Furthermore, the specific time periods for the two phases of measurement should be fixed in the first monitoring year and remain consistent in subsequent years, for example, fixed in March and August each year. The reason for emphasizing the interannual consistency of the measurement period is that the reversible displacement component caused by reservoir water level and temperature has an annual periodicity. Only when sampling at the same phase in each year can the reversible component cancel each other out in interannual comparisons. If the measurement period of a certain year is offset, the reversible component contained in the reading of that period will not be comparable to that of other years, and a false trend will be formed in the residual. Taking the long-term benchmarking observation of a landslide in a certain overburden layer as an example, the benchmarking observation has been carried out continuously since the reservoir was impounded. The measurements are carried out twice a year, in wet and dry seasons, and three types of quantities are recorded at the same time: the benchmark height on the mountain side, the benchmark height on the riverbed side, and the distance between the two benchmarks. It is precisely because of the long-term consistency of the measurement period that the distance sequence over the past ten years has shown a clearly discernible logarithmic decay pattern.

[0184] Example 9

[0185] Based on Example 1, the method further includes:

[0186] Step D. When the number of periods of the displacement monitoring data is less than 10, the stability of the logarithmic decay trend prediction model is evaluated by leave-one-out cross-validation to obtain the cross-validation error.

[0187] Leave-one-out cross-validation involves successively leaving out one period's data, fitting the model with the remaining periods, and predicting the cumulative displacement of the left-out period. The average of the relative deviations between the predicted and measured values ​​for each period is the cross-validation error.

[0188] The specific implementation process is as follows: Let the effective monitoring period be n. Then, take each period from period 1 to period n as the leaveout period. Each time, use the data of the remaining n-1 periods to fit a set of parameters according to formula (3). Then, use the set of parameters to calculate the cumulative displacement prediction value under the time variable corresponding to the leaveout period according to formula (1). Divide the absolute value of the difference between the prediction value and the actual cumulative displacement of the period by the actual cumulative displacement of the period to obtain the relative deviation of the period. Take the arithmetic mean of the relative deviations of all n periods to obtain the cross-validation error. It should be noted that when the actual cumulative displacement of a certain period is close to zero (e.g., the first period), the denominator of the relative deviation is too small, which will cause the result of that period to be distorted. Therefore, when calculating the cross-validation error, it is advisable to exclude the periods with actual cumulative displacement less than twice the measurement accuracy from the average.

[0189] Step E. When the cross-validation error is greater than 15%, extend the acquisition period of the displacement monitoring data until the cross-validation error is no greater than 15%.

[0190] The 15% threshold is on the same order of magnitude as the approximately 9.5% relative error obtained from backtracking prediction in Example 4. Taking this threshold means that the out-of-sample performance of the model is not inferior to the typical level under long sequence conditions.

[0191] The technical significance of cross-validation error lies in measuring the model's predictive ability for data points not previously fitted, i.e., out-of-sample generalization ability. The coefficient of determination measures the model's fit to existing data; the shorter the sequence and the more periods the parameters represent, the more easily the coefficient of determination can be artificially inflated. Leave-one-out cross-validation, however, uses unseen data points for each test and is therefore unaffected by this effect. Using both in combination allows for a more prudent assessment of model usability before reaching 10 periods. For example, a newly established monitoring point accumulates 8 periods of readings, resulting in a coefficient of determination of 0.94, seemingly excellent. However, the leave-one-out cross-validation error is 18.7%, exceeding the 15% threshold, indicating that while the sequence is internally consistent, its prediction of new data points is unstable. After continuing observation to the 12th period, the coefficient of determination becomes 0.90, and the cross-validation error drops to 11.2%. Only then can the extrapolation conclusion be output using this method.

[0192] Example 10

[0193] like Figure 5 As shown, this embodiment provides a device for predicting the stability trend of unstable rock masses based on long-period displacement monitoring, including:

[0194] The monitoring point deployment and data acquisition module 501 is used to deploy fixed monitoring points on the dangerous rock mass, including fixed reference points on the mountain side and moving points on the dangerous rock mass side, periodically measure the distance between the fixed reference points and the moving points, and obtain displacement monitoring data for no less than 5 years and no less than 10 periods.

[0195] The cumulative displacement sequence generation module 502 is used to calculate the cumulative displacement and the time variable in years on a periodic basis, with the interval of the first measurement as the zero reference, to obtain the cumulative displacement-time series.

[0196] The logarithmic decay model fitting module 503 is used to characterize the cumulative displacement by the sum of the product of the deformation rate decay coefficient and the natural logarithm of the time variable plus one, and the initial displacement deviation correction term, to construct a logarithmic decay trend prediction model, and to perform least squares regression fitting on the cumulative displacement-time series to determine the deformation rate decay coefficient, the initial displacement deviation correction term, and the determination coefficient.

[0197] The displacement increment extrapolation module 504 is used to extrapolate based on the logarithmic decay trend prediction model to obtain the cumulative displacement increment since the latest monitoring time after a preset extrapolation time.

[0198] The stability level determination module 505 is used to calculate the average deformation rate of the past year based on the cumulative displacement-time series, compare the average deformation rate of the past year with a preset classification threshold, and determine the stability level.

[0199] The prediction report output module 506 is used to output a trend prediction report that includes the determination coefficient, the cumulative displacement increment, and the stability level.

[0200] The modules described above can be deployed on general-purpose computing devices at the engineering site, and the modules are connected serially according to the data flow direction.

[0201] Specifically, the monitoring point deployment and data acquisition module 501 includes a monitoring point ledger subunit and a reading entry subunit. The monitoring point ledger subunit stores the number, pile location description, measurement direction, measuring instrument model, and measurement accuracy of each fixed monitoring point. The reading entry subunit receives the spacing readings obtained from manual measurements or the spacing data returned by automated monitoring equipment, and performs integrity and range rationality checks on each period's readings. Readings that fail the checks are marked but not automatically discarded. The cumulative displacement sequence generation module 502 reads all period readings from the reading entry subunit, calculates the difference for each monitoring point using the first period's reading as the zero baseline, and converts the time variable according to the measurement date, outputting a cumulative displacement-time sequence set indexed by the monitoring points.

[0202] The logarithmic decay model fitting module 503 is the core calculation module of this device. Its implementation includes a transformation subunit, a solution subunit, and a goodness-of-dominance subunit: the transformation subunit performs the logarithmic transformation described in S3.1; the solution subunit performs the least squares solution and iterative elimination of abrupt sample points as described in S3.2 to S3.2.5, and writes the eliminated sample points back to the measurement point log; the goodness-of-dominance subunit performs the determination coefficient calculation and threshold discrimination as described in S3.3 to S3.5, and only sends an allow-extrapolation signal to the displacement increment extrapolation module 504 when the discrimination passes. The displacement increment extrapolation module 504 receives the deformation rate decay coefficient and the allow-extrapolation signal, performs extrapolation calculations according to S4.1 to S4.3, and, when the deviation judgment function is configured, further performs the rate evolution difference calculation and exponential trend model verification as described in S4.2.1 to S4.2.5.

[0203] The stability level determination module 505 incorporates a four-level threshold configuration table and a reduction switch: the four-level threshold configuration table stores the first threshold, the second threshold, and the third threshold, along with their corresponding level names and monitoring response measures; the reduction switch is configured one by one according to whether there is a disaster-bearing object beneath each unstable rock mass, and when the switch is set, a reduction coefficient is uniformly applied to the three thresholds. This module also receives the deformation rate attenuation coefficient and determination coefficient from the logarithmic attenuation model fitting module 503, and performs level adjustment discrimination accordingly. The prediction report output module 506 collects the outputs of the above modules, organizes them into a structured report according to the two levels of measuring points and unstable rock masses, and exports it.

[0204] It should be noted that the above module division is a logical division based on function. In terms of physical implementation, the modules can be integrated into the same computing device or deployed in a distributed manner—for example, the monitoring point deployment and data acquisition module 501 can be deployed on the field terminal, while the remaining modules can be deployed on the management center server, with the two transmitting cumulative displacement-time series data through a data interface. Furthermore, the functions of each module of the device can also be carried by a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the methods described in the foregoing embodiments.

[0205] This method is not limited to limestone-type unstable rock masses. For a super-large landslide with a volume of tens of millions of cubic meters on the left bank of a hydropower station reservoir, whose landslide material mainly consists of boulders, gravel, and clay, the cumulative displacement data over nine years from one measuring point was fitted using equation (1) to obtain... =15.2mm, R 2 =0.89. This result indicates that the logarithmic decay trend prediction model also has a good fitting effect on the long-period displacement of overburden landslides; the decay coefficient of 15.2 mm for overburden landslides is similar to that of 16.8 mm for limestone unstable rock masses, reflecting the consistency of their deformation rate decay characteristics. Since this method only requires fitting two parameters, has low computational cost, and does not rely on rock mechanics parameters or numerical simulation software, it can be applied to the monitoring of unstable rock masses or landslides in scenarios such as highway high slopes and mine spoil heaps.

[0206] It is worth noting that the benchmark observation of the aforementioned overburden landslide differs slightly from that of limestone unstable rock masses in its layout: two sets of benchmark points are set at the upper and lower edges of the landslide body, respectively. Each set of benchmark points simultaneously records three types of quantities: the benchmark height on the mountain side, the benchmark height on the riverbed side, and the distance between the two benchmarks. The distance between the two benchmarks corresponds to the distance between the fixed reference point and the moving point described in S1. The other two quantities serve as check quantities for whether the benchmark piles themselves have settled or overturned. When the distance between the two benchmarks changes in a certain period while the benchmark heights on both sides change synchronously, the change in the state of the benchmark piles themselves should be suspected first, rather than the actual displacement of the landslide body. The readings for this period are processed according to the abrupt sample point mechanism described in Example 3. Because the input of this method is only a scalar spacing sequence, its adaptability to the layout method is not limited by the specific measuring point structure. As long as a spacing sequence reflecting relative displacement can be obtained stably over a long period, the same calculation process can be applied.

[0207] Furthermore, the applicability to different rock and soil types can be further verified by the distribution of deformation rate attenuation coefficients. In engineering practice, the attenuation coefficients of intact limestone and dolomite rock masses are mostly in the range of 5 mm to 20 mm, while the attenuation coefficients of loosely structured collapsed deposits and landslides with residual slope deposits are mostly in the range of 15 mm to 40 mm. There is a significant overlap between these two ranges, indicating that the attenuation coefficient characterizes the overall magnitude of the compaction process rather than the lithological label itself. Therefore, in engineering sites lacking detailed rock mechanics parameters, the fitted attenuation coefficient can be directly used as a quantitative indicator of the overall deformation magnitude of the rock mass, for lateral ranking and priority determination of treatment among multiple rock masses within the same reservoir area.

[0208] The embodiments described above are merely examples of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. A method for predicting the stability trend of unstable rock masses based on long-period displacement monitoring, characterized in that, include: Fixed monitoring points, including fixed reference points on the side of the mountain and moving points on the side of the unstable rock mass, are set up on the unstable rock mass. The distance between the fixed reference points and the moving points is measured periodically to obtain displacement monitoring data for no less than 5 years and no less than 10 periods. Using the initial measurement interval as the zero baseline, the cumulative displacement and the time variable in years are calculated period by period to obtain the cumulative displacement-time series; The cumulative displacement is characterized by the sum of the product of the deformation rate decay coefficient and the natural logarithm of the time variable plus 1 and the initial displacement deviation correction term. A logarithmic decay trend prediction model is constructed, and the cumulative displacement-time series is fitted by least squares regression to determine the deformation rate decay coefficient, the initial displacement deviation correction term, and the coefficient of determination. Extrapolation is performed based on the logarithmic decay trend prediction model to obtain the cumulative displacement increment since the latest monitoring time after a preset extrapolation period. The average deformation rate over the past year is calculated based on the cumulative displacement-time series, and the average deformation rate over the past year is compared with a preset grading threshold to determine the stability level. The output includes a trend prediction report containing the determination coefficient, the cumulative displacement increment, and the stability level.

2. The method according to claim 1, characterized in that, The cumulative displacement is characterized by the sum of the product of the deformation rate attenuation coefficient and the natural logarithm of the time variable plus 1, and the initial displacement deviation correction term. A logarithmic attenuation trend prediction model is constructed, and the cumulative displacement-time series is fitted with least squares regression to determine the deformation rate attenuation coefficient, the initial displacement deviation correction term, and the coefficient of determination, including: Add 1 to the time variable of each period in the cumulative displacement-time series and take the natural logarithm to obtain the sequence of transformed independent variables; Using the transformed independent variable sequence as the independent variable and the cumulative displacement as the dependent variable to form a regression sample set, the deformation rate attenuation coefficient and the initial displacement deviation correction term are solved by minimizing the sum of squared residuals. The coefficient of determination is calculated based on the sum of squared residuals and the sum of squared total deviations of the regression sample set; When the determination coefficient is not less than the preset goodness-of-fit threshold, the logarithmic decay trend prediction model is deemed to be a qualified fit and can be used for extrapolation. When the coefficient of determination is less than the preset goodness-of-fit threshold, it is determined that the dispersion of the cumulative displacement-time series exceeds the limit. It is then checked whether the fixed monitoring point has experienced local collapse, measurement error, or deformation stage change. The acquisition period of the displacement monitoring data is extended and the data is refitted until the coefficient of determination is not less than the preset goodness-of-fit threshold. The deformation rate attenuation coefficient, the initial displacement deviation correction term, and the coefficient of determination are then obtained.

3. The method according to claim 2, characterized in that, The process of constructing a regression sample set using the transformed independent variable sequence as the independent variable and the cumulative displacement as the dependent variable, and solving for the deformation rate attenuation coefficient and the initial displacement deviation correction term by minimizing the sum of squared residuals, includes: Solve the regression sample set by minimizing the sum of squared residuals to obtain the initial values ​​of the initial deformation rate attenuation coefficient and the initial displacement deviation correction term; Calculate the fitting residuals of each sample point in the regression sample set relative to the initial value of the initial deformation rate attenuation coefficient and the initial value of the initial displacement deviation correction term, and calculate the standard deviation of the fitting residuals; Sample points whose absolute value of the fitting residual is greater than a preset multiple of the standard deviation are identified as mutation sample points. The mutation sample points are removed from the regression sample set to obtain the corrected regression sample set. The modified regression sample set is re-solved by minimizing the sum of squared residuals to obtain the deformation rate attenuation coefficient and the initial displacement deviation correction term. When the relative change of the deformation rate attenuation coefficient with respect to the initial deformation rate attenuation coefficient is greater than the preset convergence threshold, the elimination and re-solution are repeated on the modified regression sample set until the relative change is no greater than the preset convergence threshold.

4. The method according to claim 1, characterized in that, The extrapolation based on the logarithmic decay trend prediction model to obtain the cumulative displacement increment since the latest monitoring time after a preset extrapolation period includes: The extrapolation starts with the time variable corresponding to the latest monitoring time and ends with the sum of the extrapolation start and the preset extrapolation duration, which is 3 to 5 years. The cumulative displacement increment is obtained by multiplying the deformation rate attenuation coefficient by the difference between the natural logarithm of the extrapolated endpoint plus 1 and the natural logarithm of the extrapolated starting point plus 1. The cumulative displacement corresponding to the extrapolation starting point is added to the cumulative displacement increment to obtain the predicted cumulative displacement of the extrapolation ending point.

5. The method according to claim 4, characterized in that, After multiplying the deformation rate attenuation coefficient by the difference between the natural logarithm of the extrapolated endpoint plus 1 and the natural logarithm of the extrapolated starting point plus 1 to obtain the cumulative displacement increment, the method further includes: Divide the deformation rate attenuation coefficient by the value after adding 1 to the extrapolation endpoint to obtain the predicted instantaneous deformation rate at the end of the year. The difference between the predicted instantaneous deformation rate at the end of the year and the average deformation rate over the past year is calculated to obtain the deformation rate evolution difference. When the difference in deformation rate evolution is less than zero, it is determined that the deformation of the unstable rock mass is in a convergent decay creep state. When the difference in the deformation rate evolution is not less than zero, the cumulative displacement-time series is refitted using an exponential trend model with the time variable as the independent variable of the exponential term to obtain the coefficient of determination of the exponential model. When the coefficient of determination of the exponential model is greater than the coefficient of determination, it is determined that the deformation of the unstable rock mass deviates from the logarithmic decay law, and the stability level is adjusted to the accelerated instability precursor level.

6. The method according to claim 1, characterized in that, The step of calculating the average deformation rate over the past year based on the cumulative displacement-time series, comparing the average deformation rate over the past year with a preset classification threshold, and determining the stability level includes: The preset grading thresholds include a first threshold, a second threshold, and a third threshold that increase sequentially, wherein the first threshold is 2 millimeters per year, the second threshold is 5 millimeters per year, and the third threshold is 10 millimeters per year; When the average deformation rate over the past year is not greater than the first threshold, the stability level is determined to be a stable level. When the average deformation rate over the past year is greater than the first threshold and not greater than the second threshold, the stability level is determined to be a weak creep level. When the average deformation rate over the past year is greater than the second threshold but not greater than the third threshold, the stability level is determined to be a medium creep level. When the average deformation rate over the past year is greater than the third threshold, the stability level is determined to be an accelerated instability precursor level.

7. The method according to claim 6, characterized in that, The method further includes: When there is a disaster-bearing object below the unstable rock mass, the first threshold, the second threshold, and the third threshold are all reduced by a reduction factor of 50%, and then compared with the average deformation rate of the past year. When the deformation rate attenuation coefficient is greater than the preset attenuation coefficient adjustment threshold and the determination coefficient is greater than the preset goodness adjustment threshold, the stability level is increased by one level. The revised stability level will be written into the trend forecast report.

8. The method according to claim 1, characterized in that, The method involves setting up fixed monitoring points on the unstable rock mass, including fixed reference points on the mountainside and moving points on the unstable rock mass side. The distance between the fixed reference points and the moving points is periodically measured to obtain displacement monitoring data for no less than 5 years and no less than 10 periods, including: No fewer than three fixed monitoring points shall be set up on both sides of the main crack at the rear edge of the unstable rock mass; The fixed reference point on the mountain side of each of the fixed monitoring points is set as a fixed pile on the stable bedrock of the mountain, and the moving point on the dangerous rock mass side is set as a moving pile at the edge of the main crack at the rear edge. For each of the fixed monitoring points, two measurement directions are set, one perpendicular to the direction of the trailing edge main crack and the other parallel to the direction of the trailing edge main crack, to obtain the opening displacement and shear displacement of the trailing edge main crack respectively; The distance between the fixed reference point and the moving point is measured using a steel ruler or a displacement sensor, with a measurement accuracy of not less than 1 mm. The measurements shall be performed at a frequency of no less than 2 times per year, and the displacement monitoring data shall be accumulated for no less than 10 periods.

9. The method according to claim 1, characterized in that, The method further includes: When the number of periods of the displacement monitoring data is less than 10, the stability of the logarithmic decay trend prediction model is evaluated by leave-one-out cross-validation to obtain the cross-validation error. When the cross-validation error is greater than 15%, the acquisition period of the displacement monitoring data is extended until the cross-validation error is no greater than 15%.

10. A device for predicting the stability trend of unstable rock masses based on long-period displacement monitoring, characterized in that, include: The monitoring point deployment and data acquisition module 501 is used to deploy fixed monitoring points on the dangerous rock mass, including fixed reference points on the mountain side and moving points on the dangerous rock mass side, periodically measure the distance between the fixed reference points and the moving points, and obtain displacement monitoring data for no less than 5 years and no less than 10 periods. The cumulative displacement sequence generation module 502 is used to calculate the cumulative displacement and the time variable in years on a periodic basis, with the interval of the first measurement as the zero reference, to obtain the cumulative displacement-time series. The logarithmic decay model fitting module 503 is used to characterize the cumulative displacement by the sum of the product of the deformation rate decay coefficient and the natural logarithm of the time variable plus 1 and the initial displacement deviation correction term, construct a logarithmic decay trend prediction model, perform least squares regression fitting on the cumulative displacement-time series, and determine the deformation rate decay coefficient, the initial displacement deviation correction term, and the determination coefficient. The displacement increment extrapolation module 504 is used to extrapolate based on the logarithmic decay trend prediction model to obtain the cumulative displacement increment since the latest monitoring time after a preset extrapolation time. The stability level determination module 505 is used to calculate the average deformation rate of the past year based on the cumulative displacement-time series, compare the average deformation rate of the past year with a preset classification threshold, and determine the stability level. The prediction report output module 506 is used to output a trend prediction report that includes the determination coefficient, the cumulative displacement increment, and the stability level.

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