Real-time monitoring method for three-dimensional shape tilt deformation based on GNSS

Abstract

The present application relates to the technical field of slope engineering monitoring, in particular to a three-dimensional shape tilt deformation real-time monitoring method based on GNSS. Static three-dimensional coordinates of each monitoring point of the slope monitoring network before the blasting trigger moment are obtained, and after the blasting, GNSS observation values of each monitoring point at each moment are obtained, three-dimensional instantaneous velocity and acceleration vectors are solved, and the dynamic change of the slope rock mass is captured; since the slope instability is caused by the relative deformation accumulation of the internal rock mass block, therefore, the velocity, acceleration and static coordinate differences between different monitoring points at each moment are integrated to form a relative feature set; the set values are orthogonally projected and decomposed to obtain normal and tangential deformation components, and the deformation direction is determined; the component value features and the preset weight coefficients are fused to construct a relative motion cost matrix, and the optimal solution of the matrix is obtained to obtain a cooperative motion deviation index, the cooperative motion deviation degree is quantified, and through the analysis of the time change trend, the slope stability state can be more accurately judged.

Description

Technical Field

[0001] This invention relates to the field of slope engineering monitoring technology, specifically to a real-time monitoring method for three-dimensional shape tilt deformation based on GNSS. Background Technology

[0002] In fields involving slope engineering, such as mining and civil engineering construction, the stability of slope rock mass is crucial. Under the influence of human factors (such as blasting operations), slope rock mass may undergo tilting deformation. Once the deformation exceeds a certain limit, it may trigger geological disasters such as landslides, posing a significant threat to human safety and engineering construction. Therefore, real-time and accurate deformation monitoring of slope rock mass, and timely understanding of its stability status, is a key link in ensuring the safe operation of engineering projects.

[0003] Global Navigation Satellite System (GNSS) technology boasts advantages such as all-weather operation, high precision, and strong real-time performance, leading to its widespread application in slope deformation monitoring. From a rock mechanics perspective, the rock mass after blasting is not a homogeneous continuum and contains two distinct deformation modes: relatively benign normal deformation and high-risk shear slip deformation. However, existing GNSS-based slope deformation monitoring methods mostly analyze all kinematic information as a single displacement vector, failing to effectively distinguish and quantify the contributions of these two deformation modes. Furthermore, they lack in-depth analysis and effective utilization of the relative motion relationships and collaborative deformation between different monitoring points. Consequently, they struggle to accurately assess the stability of slope rock masses under complex conditions, failing to meet the higher requirements for slope safety monitoring in practical engineering. Summary of the Invention

[0004] To address the shortcomings of existing GNSS-based slope deformation monitoring methods, which often analyze all kinematic information as a single displacement vector, failing to effectively distinguish and quantify the contributions of the two deformation modes, and lacking in-depth analysis and effective utilization of the relative motion relationships and coordinated deformation between different monitoring points, this invention aims to provide a GNSS-based method for real-time monitoring of three-dimensional slope tilt deformation. The specific technical solution adopted is as follows: Obtain the static three-dimensional coordinates of each monitoring point in the slope monitoring network before the blasting trigger moment; after the blasting trigger moment, obtain the GNSS observation values ​​of each monitoring point at each moment to calculate the three-dimensional instantaneous velocity vector and three-dimensional instantaneous acceleration vector at each moment. At each moment, the differences in three-dimensional instantaneous velocity vectors, three-dimensional instantaneous acceleration vectors, and static three-dimensional coordinates between different monitoring points are combined to form a relative feature set between any two monitoring points at each moment. At each moment, the values ​​in the relative feature set between each pair of monitoring points are orthogonally projected and decomposed to obtain the corresponding normal deformation component and tangential deformation component. Based on the numerical characteristics of the normal deformation component and tangential deformation component, and fused with the preset deformation mode weight coefficient, the relative motion cost matrix between monitoring points at each moment is constructed. The relative motion cost matrix at each time point is optimally solved to obtain the cooperative motion deviation index at each time point; based on the temporal changes and temporal relationships of the cooperative motion deviation index at each time point, the stability state of the slope rock mass is evaluated.

[0005] Furthermore, the method for obtaining the relative feature set includes: At each time point, all monitoring points are paired up to obtain all monitoring point pairs; In each monitoring point pair, the difference between the three-dimensional instantaneous velocity vectors of the two monitoring points is taken as the relative velocity vector of the point pair, the difference between the three-dimensional instantaneous acceleration vectors of the two monitoring points is taken as the relative acceleration vector of the point pair, and the difference between the static three-dimensional coordinates of the two monitoring points is taken as the direction vector. The direction vector is normalized and taken as the point-to-baseline unit vector. The relative velocity vector, relative acceleration vector, and baseline unit vector of each monitoring point pair are used to form the set of relative features between each monitoring point pair.

[0006] Furthermore, at each time point, the values ​​in the relative feature set between every two monitoring points are orthogonally projected and decomposed to obtain the corresponding normal deformation component and tangential deformation component, including: For any set of relative features between monitoring point pairs, calculate the scalar projections of the relative velocity vector and relative acceleration vector of the point pairs onto the baseline unit vector of the point pairs. Multiply each of the obtained scalar projections with the baseline unit vector of the point pairs to reconstruct the normal relative velocity component and normal relative acceleration component, which are collectively referred to as the normal deformation component of the monitoring point pair. Based on the differences between the relative velocity vector and relative acceleration vector of the point pair and their respective normal deformation components, the tangential deformation component of the monitoring point pair is determined.

[0007] Furthermore, the method for obtaining the tangential deformation component includes: The vector difference between the relative velocity vector of the point pair and the corresponding normal relative velocity component is calculated as the tangential relative velocity component. The vector difference between the relative acceleration vector of the point pair and the corresponding normal relative acceleration component is calculated as the tangential relative acceleration component. The tangential relative velocity component and the tangential relative acceleration component are collectively referred to as the tangential deformation component of the monitoring point pair.

[0008] Furthermore, the method for obtaining the relative motion cost matrix includes: For any pair of monitoring points, the scalar of the corresponding normal relative velocity component is normalized to obtain the normal relative velocity scalar; the scalar of the corresponding normal relative acceleration component is normalized to obtain the normal relative acceleration scalar; the scalar of the corresponding tangential relative velocity component is normalized to obtain the tangential relative velocity scalar; and the scalar of the tangential relative acceleration component is normalized to obtain the tangential relative acceleration scalar. The relative motion cost of the monitoring point pair is obtained by weighting and fusing the normal relative velocity scalar, normal relative acceleration scalar, tangential relative velocity scalar, and tangential relative acceleration scalar using preset deformation mode weighting coefficients. Using the relative motion cost of each monitoring point pair as the off-diagonal element and the preset maximum value as the diagonal element, a relative motion cost matrix is ​​constructed at that moment.

[0009] Furthermore, the method for obtaining the relative motion cost includes: The preset deformation mode weighting coefficients include preset tangential weighting coefficients and preset normal weighting coefficients; The tangential relative velocity scalar and the tangential relative acceleration scalar are weighted and fused using preset tangential weighting coefficients, and the resulting weighted result is used as the first cost factor. The normal relative velocity scalar and the normal relative acceleration scalar are weighted and fused using preset normal weighting coefficients, and the resulting weighted result is used as the second cost factor. The sum of the first cost factor and the second cost factor is taken as the relative motion cost of the monitoring point pair.

[0010] Furthermore, the method for obtaining the cooperative motion deviation index includes: At each time step, the variance of all off-diagonal elements in the corresponding relative motion cost matrix is ​​calculated and used as the cooperative motion deviation index at each time step.

[0011] Furthermore, the assessment of the stability state of the slope rock mass based on the temporal changes and temporal relationships of the cooperative motion deviation index at various times includes: Based on the temporal variation characteristics of the cooperative motion deviation index at each time point, and combined with the temporal difference between each time point and the blasting trigger time, the logarithmic coordinate decay slope corresponding to each time point is determined. If the absolute value of the logarithmic coordinate decay slope of all times within the neighborhood window at the current time is less than the preset stability threshold, then the lower slope rock mass is determined to have reached a cooperative stability state at the current time, and a safety access decision signal is output.

[0012] Furthermore, the method for obtaining the logarithmic coordinate decay slope includes: Logarithmic coordinate transformation is performed on the cooperative motion deviation index at each time point to obtain the corresponding logarithmic deviation value at each time point. The time difference between each time point and the blasting trigger time is calculated and logarithmic coordinate transformation is performed to obtain the corresponding logarithmic time value at each time point. The logarithmic time value and the logarithmic deviation value at each time point are combined to form the data point pair at each time point. Determine the neighborhood window corresponding to each time step. Within the neighborhood window at each time step, use the logarithmic value of time step as the horizontal axis and the logarithmic value of deviation as the vertical axis to fit a straight line to all pairs of data points at all time steps. Use the slope of the fitted straight line as the logarithmic coordinate decay slope corresponding to each time step.

[0013] Furthermore, the linear fitting employs the least squares method.

[0014] The present invention has the following beneficial effects: The static three-dimensional coordinates of each monitoring point in the slope monitoring network before the blasting trigger moment are obtained, providing a precise initial reference position for subsequent dynamic monitoring. After the blasting trigger moment, GNSS observations of each monitoring point at each moment are obtained, and the three-dimensional instantaneous velocity vector and three-dimensional instantaneous acceleration vector at each moment are calculated, which can capture the dynamic change process of the slope rock mass under the blasting action. Since the overall instability of the slope is the result of the cumulative relative deformation between different rock blocks within it, at each moment, the differences in the three-dimensional instantaneous velocity vector, the differences in the three-dimensional instantaneous acceleration vector, and the differences in the static three-dimensional coordinates between different monitoring points are combined to form a set of relative characteristics between any two monitoring points at each moment. Meanwhile, since a single mixed relative motion vector cannot distinguish the distinctly different mechanical causes behind its risks, orthogonal projection decomposition is performed on the values ​​in the relative feature set between every two monitoring points to obtain the corresponding normal and tangential deformation components. This clearly identifies the direction of slope rock mass deformation. Furthermore, based on the numerical characteristics of the normal and tangential deformation components, and integrated with the preset deformation mode weighting coefficients, a relative motion cost matrix between monitoring points at each time step is constructed. This comprehensively considers the influence of multiple factors on slope deformation, achieving a comprehensive assessment of the slope's relative motion. Finally, a discreteness analysis is performed on the relative motion cost matrix at each time step to obtain the cooperative motion deviation index at each time step. This accurately quantifies the degree of cooperative motion deviation between different monitoring points on the slope. By analyzing the trend of the cooperative motion deviation index over time, it helps to more accurately determine whether the slope's stability is gradually deteriorating or trending towards stability. Attached Figure Description

[0015] To more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is a flowchart of a method for real-time monitoring of three-dimensional shape tilt deformation based on GNSS, provided as an embodiment of the present invention. Detailed Implementation

[0017] To further illustrate the technical means and effects adopted by the present invention to achieve its intended purpose, the following, in conjunction with the accompanying drawings and preferred embodiments, details the specific implementation, structure, features, and effects of a GNSS-based real-time monitoring method for three-dimensional shape tilt deformation proposed according to the present invention. In the following description, different "one embodiment" or "another embodiment" do not necessarily refer to the same embodiment. Furthermore, specific features, structures, or characteristics in one or more embodiments can be combined in any suitable form.

[0018] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0019] The following description, in conjunction with the accompanying drawings, details a specific scheme for a GNSS-based real-time monitoring method for three-dimensional shape tilt deformation provided by the present invention.

[0020] Please see Figure 1 The diagram illustrates a method flowchart for real-time monitoring of three-dimensional shape tilt deformation based on GNSS, according to an embodiment of the present invention. The method includes the following steps: Step S1: Obtain the static three-dimensional coordinates of each monitoring point in the slope monitoring network before the blasting trigger moment; after the blasting trigger moment, obtain the GNSS observation values ​​of each monitoring point at each moment to calculate the three-dimensional instantaneous velocity vector and three-dimensional instantaneous acceleration vector at each moment.

[0021] Since slope instability is the result of the cumulative relative deformation between different rock masses within the slope, rather than the overall motion of the slope as a rigid body, diagnosing its internal deformation mode requires simultaneously obtaining static reference information describing the network geometry and dynamic information describing the motion state of each monitoring point at every moment. Furthermore, the impact of blasting instantly disrupts the original mechanical equilibrium of the slope rock mass, causing it to enter a dynamic relaxation process of internal stress redistribution. From the perspective of rock mechanics, the rock mass after blasting is not a homogeneous continuum, but a block system divided by multiple structural planes and interacting with each other. Its deformation is a comprehensive manifestation of the relative movement of different blocks along the weak structural planes, mainly including two deformation modes with distinctly different properties: one is relatively benign normal deformation, mainly characterized by overall settlement and compression; the other is high-risk shear slip deformation along the structural planes, the latter being the main cause of instability and failure. Therefore, subsequent steps require decomposing the relative movement into components along the direction of the line connecting the monitoring points and perpendicular to that direction. This decomposition must be based on a geometric reference frame that does not change with time. Therefore, the first step is to obtain the values ​​of each monitoring point in the slope monitoring network at the time of blasting triggering ( The static 3D coordinates prior to this: in the GNSS monitoring network (including...) After the monitoring points (usually a quadrilateral network) are deployed and before dynamic monitoring begins, i.e., before the blasting trigger moment, the data of all monitoring points are acquired using a standard, high-precision static measurement method known in the field. ( For monitoring point indexing, The static three-dimensional coordinates in the geocentric coordinate system are calculated once and stored as fixed parameters. The three-dimensional static coordinates are called as an unchanging geometric reference in all subsequent dynamic calculations.

[0022] Based on the required monitoring accuracy and slope environmental conditions, select a suitable GNSS receiver and install it at the chosen monitoring point. Secure the receiver with a sturdy bracket to ensure it does not move or shake during monitoring. During installation, the receiver's antenna should generally be pointed towards an open area of ​​the sky to ensure sufficient satellite signals can be received. This will allow the receiver to acquire data from all visible satellites after the burst triggers. (in For satellite index, number of visible satellites The system synchronously acquires all visible satellite GNSS observations, including carrier phase observations, at a fixed frequency (e.g., 20 Hz, i.e., once every 0.05 seconds). And pseudorange observations.

[0023] Since acceleration is the most direct indicator of changes in the resultant external force acting on a rock mass, it is crucial for capturing the dynamic adjustment process of the intense stress redistribution within the rock mass in the initial stage after blasting. Therefore, the purpose of this step is to calculate the three-dimensional instantaneous acceleration vector of each monitoring point in real time from the most basic GNSS carrier phase observations. .

[0024] The line-of-sight acceleration component in each satellite-receiver line-of-sight direction is calculated by performing a second backward difference on the raw carrier phase observations. : ;in, For the carrier wavelength corresponding to the satellite signal, This is the sampling time interval. Since this calculation requires data from two historical sampling points, in the first two sampling times ( and ), monitoring points Three-dimensional instantaneous acceleration vector Set to zero vector, from the third sampling time ( )start, This step involves continuous calculations. Finally, a set of observation equations is established to solve for the three-dimensional instantaneous acceleration vector. Line-of-sight acceleration component along the line of sight of each satellite and receiver. All In the corresponding line-of-sight unit vector The projection onto the surface; while the line-of-sight unit vector can be calculated in real time based on the satellite's broadcast ephemeris and the receiver's approximate position, and then all... The observation equations of the satellites form a linear overdetermined system of equations. ,in It is composed of line-of-sight vectors from each satellite. 3D geometric matrix It is by Linear acceleration component Composition The observation vector is 3D. Solving this system of equations using the least squares method yields the value of the monitoring point. Three-dimensional instantaneous acceleration vector at time t. .

[0025] Furthermore, velocity is a fundamental kinematic parameter describing the current rate and direction of rock mass movement, and is indispensable for assessing the overall dynamic behavior of the slope. Therefore, the purpose of this step is to obtain the instantaneous velocity vector of each monitoring point in three-dimensional space. .

[0026] Specifically, for monitoring points Using well-known algorithms in the field, such as Real-Time Dynamic Differential (RTK) or Precise Point Positioning (PPP), the high-frequency three-dimensional coordinate time series is calculated. Subsequently, by performing a first-order backward difference operation in time on the coordinate sequence, its position in time was calculated. Three-dimensional instantaneous velocity vector at time t. : Since this calculation requires data from a historical sampling point, at the first sampling moment triggered by the blast ( ), monitoring points Three-dimensional instantaneous velocity vector Set to zero vector, from the second sampling time ( )start, This formula can be used for continuous calculation.

[0027] Step S2: At each moment, the differences in the three-dimensional instantaneous velocity vector, the differences in the three-dimensional instantaneous acceleration vector, and the differences in the static three-dimensional coordinates between different monitoring points are combined to form a relative feature set between any two monitoring points at each moment; at each moment, the values ​​in the relative feature set between each pair of monitoring points are orthogonally projected and decomposed to obtain the corresponding normal deformation component and tangential deformation component; based on the numerical characteristics of the normal deformation component and tangential deformation component, and fused with the preset deformation mode weight coefficient, the relative motion cost matrix between monitoring points at each moment is constructed.

[0028] Given that the overall instability of the slope is the result of the cumulative relative deformation between different rock blocks within it, rather than the translation or rotation of the slope as a rigid body, the absolute motion state of all monitoring points can be converted into basic variables describing the relative motion state between any two monitoring points. This provides direct input for subsequent deformation mode decomposition. Therefore, at each moment, the differences in the three-dimensional instantaneous velocity vectors, the differences in the three-dimensional instantaneous acceleration vectors, and the differences in the static three-dimensional coordinates between different monitoring points are combined to form the set of relative characteristics between any two monitoring points at each moment.

[0029] Preferably, in one embodiment of the present invention, the method for obtaining the relative feature set includes: At each time point, all monitoring points are first paired up to obtain all monitoring point pairs.

[0030] Then, in each monitoring point pair, the difference between the three-dimensional instantaneous velocity vectors of the two monitoring points is taken as the point-to-point relative velocity vector, and the difference between the three-dimensional instantaneous acceleration vectors of the two monitoring points is taken as the point-to-point relative acceleration vector. The point-to-point relative velocity vector and point-to-point relative acceleration vector obtained by calculating the difference can filter out the common mode motion component of the slope as a whole and extract the real relative motion rate and force change trend.

[0031] Meanwhile, the difference between the static three-dimensional coordinates of the two monitoring points is used as the direction vector, and the direction vector is normalized (divided by its own modulus) as the point-to-baseline unit vector. The point-to-baseline unit vector can establish a local spatial reference for the orthogonal decomposition of relative motion, which represents the direction of the static initial spatial connection between the two monitoring points. This direction is the geometric reference for determining whether the rock blocks at the two monitoring points are close to or far from each other. The motion parallel to the connection direction represents normal tensile and compressive deformation, and the motion perpendicular to the connection direction represents tangential shear deformation.

[0032] Finally, the relative velocity vector, relative acceleration vector, and baseline unit vector of each monitoring point pair are combined to form the relative feature set between each monitoring point pair, binding the dynamic relative motion quantity and the static spatial geometric reference, providing a structured input for subsequent analysis.

[0033] However, from the perspective of rock mechanics, the rock mass after blasting is not a homogeneous continuum, but a block system divided by multiple structural planes and interacting with each other. Its deformation is a comprehensive manifestation of the relative movement of different blocks along weak structural planes, mainly including two deformation modes with distinctly different properties: one is relatively benign normal deformation, mainly characterized by overall settlement and compression; the other is high-risk shear slip deformation along structural planes, the latter being the main cause of instability and failure. A mixed relative motion vector cannot distinguish the mechanical causes with distinctly different risk properties behind it. For example, it cannot distinguish whether two blocks are approaching each other (normal compression) or moving away from each other (tangential shear). Therefore, at each moment, the mixed vector in the relative characteristic set between every two monitoring points is orthogonally projected and decomposed along a direction with clear rock mechanics significance to isolate and quantify the contribution of different deformation modes, thereby obtaining the corresponding normal deformation component and tangential deformation component.

[0034] Preferably, in one embodiment of the present invention, the method for obtaining the normal deformation component and the tangential deformation component includes: The normal deformation component is parallel to the point-to-baseline unit vector, which can quantify the degree of compression or stretching between rock blocks. Therefore, by using vector projection, the force and motion in this specific direction can be directly extracted: For any set of relative characteristics between monitoring point pairs, calculate the scalar projections of the point-to-point relative velocity vector and the point-to-point relative acceleration vector onto the point-to-baseline unit vector, and multiply each of the obtained scalar projections with the point-to-point baseline unit vector to reconstruct the normal relative velocity component and the normal relative acceleration component, which are collectively referred to as the normal deformation component of the monitoring point pair.

[0035] Based on the differences between the relative velocity vector and relative acceleration vector of the point pair and their respective normal deformation components, the tangential deformation component of the monitoring point pair is determined: the tangential deformation component is perpendicular to the baseline unit vector of the point pair and represents the motion of mutual displacement or shear slip between the two blocks. It is calculated by subtracting its normal component from the original relative motion vector. Therefore, the vector difference between the relative velocity vector of the point pair and the corresponding normal relative velocity component is calculated as the tangential relative velocity component. The vector difference between the relative acceleration vector of the point pair and the corresponding normal relative acceleration component is calculated as the tangential relative acceleration component. The tangential relative velocity component and the tangential relative acceleration component are collectively referred to as the tangential deformation component of the monitoring point pair.

[0036] In slope engineering, failure modes dominated by shear slip are typically more sudden and destructive than overall settlement or local tension. Therefore, an effective assessment process must be able to prioritize the abnormal activity of tangential deformation modes. However, directly merging various values ​​can cause global compaction movement to mask local shear movement. Therefore, in this embodiment of the invention, after obtaining the normal deformation component and the tangential deformation component, based on their numerical characteristics and fused with the preset deformation mode weighting coefficient, a relative motion cost matrix between monitoring points at each moment is constructed to characterize the relative motion cost between rock blocks and to improve the priority of high-risk tangential modes.

[0037] Preferably, in one embodiment of the present invention, the method for obtaining the relative motion cost matrix includes: For any pair of monitoring points, the scalar of the corresponding normal relative velocity component is normalized to obtain the normal relative velocity scalar. The normal relative velocity scalar reflects the intensity of the tension or compression occurring between the two monitoring points. The larger the value, the faster the distance between the rock masses at the two monitoring points changes, which usually belongs to a benign overall settlement or stress compression process. The scalar of the corresponding normal relative acceleration component is normalized to obtain the normal relative acceleration scalar. The normal relative acceleration scalar reflects the rate of change of the resultant tension and compression between the two monitoring points. The larger the value, the more intense the internal normal stress is redistributing, which belongs to the stress adjustment process after blasting. The scalar of the corresponding tangential relative velocity component is normalized. Normalization yields the tangential relative velocity scalar, which reflects the intensity of shearing or slippage occurring between monitoring points. A larger value indicates strong displacement of the rock mass along the weak or structural plane between the two monitoring points, a direct characteristic of slope instability. Normalization of the tangential relative acceleration component yields the tangential relative acceleration scalar, reflecting the rate of change in the resultant shear force between monitoring points. A larger value indicates that the shear stress on the structural plane is in a state of rapid instability or abrupt change, a core indicator for detecting the initial potential slippage within the rock mass. Specifically, the velocity component represents the current deformation magnitude, the acceleration component represents the subsequent deformation potential, the tangential term characterizes the degree of danger, and the normal term characterizes the normal adjustment status. It should be noted that normalization here can use maximum-minimum value normalization, with the maximum and minimum values ​​selected from all monitoring point pairs.

[0038] Then, the four scalars mentioned above are weighted and fused using preset deformation mode weight coefficients: the preset deformation mode weight coefficients include preset tangential weight coefficients and preset normal weight coefficients. Since the tangential term represents the degree of danger, the preset tangential weight coefficient should be greater than the preset normal weight coefficient. The ratio of the preset tangential weight coefficient to the preset normal weight coefficient can be set between 2 and 10 to ensure the sensitivity of the subsequent calculation process to the tangential mode. In this embodiment of the present invention, the preset tangential weight coefficient is 2 and the preset normal weight coefficient is 1. The specific values ​​are not limited here.

[0039] The tangential relative velocity scalar and tangential relative acceleration scalar are weighted and fused using preset tangential weighting coefficients. The resulting weighted value is used as the first cost factor. This can also be viewed as multiplying the sum of the tangential relative velocity scalar and the tangential relative acceleration scalar by the preset tangential weighting coefficient. The larger the first cost factor, the more significant the performance in the tangential term, the more intense the shear displacement, and the more serious the deviation from the overall cooperative motion state, thus increasing the degree of danger. Similarly, the normal relative velocity scalar and normal relative acceleration scalar are weighted and fused using preset normal weighting coefficients. The resulting weighted value is used as the second cost factor. This can also be viewed as multiplying the sum of the normal relative velocity scalar and the normal relative acceleration scalar by the preset normal weighting coefficient. The larger the second cost factor, the more significant the performance in the normal term, that is, the more significant the non-cooperative deformation in the normal term. The sum of the first cost factor and the second cost factor is taken as the relative motion cost of the monitoring point pair. The relative motion cost reflects the comprehensive deviation between the two monitoring points in the monitoring point pair at each time. The larger the value, the greater the deviation.

[0040] Finally, the relative motion cost of each monitoring point pair is used as the off-diagonal element to fill the corresponding positions in the relative motion cost matrix, where the rows and columns of the relative motion cost matrix are the indices of the monitoring point pairs. A preset maximum value is used as the diagonal element to construct the relative motion cost matrix at that moment. It should be noted that in this embodiment of the invention, the preset maximum value can be set to 10. 6 The purpose of the preset maximum value is to be naturally excluded in subsequent global matching. The specific value can be adjusted according to the implementation scenario, and is not limited here.

[0041] Step S3: Perform a discreteness analysis on the relative motion cost matrix at each time point to obtain the cooperative motion deviation index at each time point; based on the temporal changes and temporal relationships of the cooperative motion deviation index at each time point, assess the stability of the slope rock mass.

[0042] The overall stability of a slope is a systematic manifestation of the interaction of all blocks. Simply summing or averaging local costs can mask key signs of instability due to the offsetting of high and low values. Therefore, an optimization method is used to condense the local, paired relative motion cost matrices into a single, global index describing the "inevitable inherent incoordination that still exists under the current optimal cooperative state." In other words, the optimal solution is performed on the relative motion cost matrix at each time step to obtain the cooperative motion deviation index at that time step.

[0043] Preferably, in one embodiment of the present invention, the method for obtaining the cooperative motion deviation index includes: At each moment, the variance of all off-diagonal elements in the corresponding relative motion cost matrix is ​​calculated as the cooperative motion deviation index at each moment. The cooperative motion deviation index represents the degree of spatial difference in non-cooperative motion at each moment. The larger the value, the higher the degree of non-cooperative motion, which means that the rock blocks are still undergoing violent relative motion, and high-risk deformations such as tangential shear sliding dominate. The stress relaxation inside the rock mass after blasting continues and has not reached a cooperative steady state.

[0044] Given that the indicators at a single moment may change abruptly due to measurement noise or local transient slippage, and that the stress relaxation process inside the rock mass after blasting exhibits a macroscopic trend of gradual decay over time, in this step, the stability state of the slope rock mass can be assessed based on the temporal changes and temporal relationships of the cooperative motion deviation indicators at each moment.

[0045] Preferably, in one embodiment of the present invention, the stability state of the slope rock mass is evaluated based on the temporal changes and temporal relationships of the cooperative motion deviation index at various times, including: Since the rock mass after blasting is a complex system composed of multi-scale blocks and joints, its stress relaxation and energy dissipation processes generally follow a power-law decay law. Therefore, a logarithmic coordinate transformation is performed on the cooperative motion deviation index at each time step to obtain the corresponding logarithmic deviation value at each time step. Similarly, the time difference between each time step and the blasting trigger time is calculated and a logarithmic coordinate transformation is performed to obtain the corresponding logarithmic time value at each time step. The logarithmic time value and the logarithmic deviation value at each time step are combined to form a data point pair at each time step. In this embodiment of the invention, the logarithmic coordinate transformation uses a logarithmic function with the natural constant e as the base. When performing the logarithmic coordinate transformation on the cooperative motion deviation index, to prevent taking the logarithm of 0, the cooperative motion deviation index can be added to a preset minimum positive number, which can be set to 10. -12 .

[0046] Then, the neighborhood window corresponding to each time point is determined. In this embodiment of the invention, the neighborhood window is set to trace back 9 times from each time point, that is, the size of the neighborhood window is 10. Within the neighborhood window of each time point, the logarithmic value of the time point is used as the horizontal axis and the logarithmic value of the deviation is used as the vertical axis. The least squares method (a well-known technique, which will not be elaborated here) is used to fit a straight line to the data point pairs of all time points. The slope of the fitted straight line is used as the logarithmic coordinate decay slope corresponding to each time point. The logarithmic coordinate decay slope is the instantaneous estimate of the power-law decay exponent. In the early stage of the blasting, this slope will be significantly negative. As the stress is gradually released, when the value approaches zero, it indicates that the above-mentioned coordinated relaxation process has ended, and the residual motion of the system has transformed into irregular random disturbances or long-term creep dominated by local factors.

[0047] To ensure the reliability of the judgment, it is necessary to confirm whether the state in which the logarithmic coordinate decay slope approaches 0 is continuous and stable. Therefore, if the absolute value of the logarithmic coordinate decay slope of all times in the neighborhood window at the current time is less than the preset stability threshold, it is determined that the lower slope rock mass has reached a cooperative stable state at the current time, and a safe access decision signal is output.

[0048] It should be noted that, in this embodiment of the invention, the time to be judged refers to the time within the real-time judgment stage, specifically 10 minutes after the blasting trigger time. Within 10 minutes from the start of the blasting trigger time, no stable state judgment is performed; only data collection and calculation are performed. Furthermore, in this embodiment of the invention, the preset stability threshold is not a fixed threshold. It is set as the standard deviation of the logarithmic coordinate decay slope of all times within 5 minutes before each time to be judged. The preset stability threshold is set as the sum of 3 times this standard deviation and the preset minimum tolerance constant (0.01). All the aforementioned values ​​can be adjusted according to the implementation scenario and are not limited here.

[0049] In summary, obtaining the static three-dimensional coordinates of each monitoring point in the slope monitoring network before the blasting trigger provides a precise initial reference position for subsequent dynamic monitoring. After the blasting trigger, acquiring the GNSS observations of each monitoring point at each moment and calculating the three-dimensional instantaneous velocity vector and three-dimensional instantaneous acceleration vector at each moment can capture the dynamic changes of the slope rock mass under blasting. Since the overall instability of the slope is the result of the cumulative relative deformation between different rock blocks within it, at each moment, the differences in the three-dimensional instantaneous velocity vector, the differences in the three-dimensional instantaneous acceleration vector, and the differences in the static three-dimensional coordinates between different monitoring points are combined to form a set of relative characteristics between any two monitoring points at each moment. Meanwhile, since a single mixed relative motion vector cannot distinguish the distinctly different mechanical causes behind its risks, orthogonal projection decomposition is performed on the values ​​in the relative feature set between every two monitoring points to obtain the corresponding normal and tangential deformation components. This clearly identifies the direction of slope rock mass deformation. Furthermore, based on the numerical characteristics of the normal and tangential deformation components, and integrated with the preset deformation mode weighting coefficients, a relative motion cost matrix between monitoring points at each time step is constructed. This comprehensively considers the influence of multiple factors on slope deformation, achieving a comprehensive assessment of the slope's relative motion. Finally, a discreteness analysis is performed on the relative motion cost matrix at each time step to obtain the cooperative motion deviation index at each time step. This accurately quantifies the degree of cooperative motion deviation between different monitoring points on the slope. By analyzing the trend of the cooperative motion deviation index over time, it helps to more accurately determine whether the slope's stability is gradually deteriorating or trending towards stability.

[0050] It should be noted that the order of the above embodiments of the present invention is merely for descriptive purposes and does not represent the superiority or inferiority of the embodiments. The processes depicted in the accompanying drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0051] The various embodiments in this specification are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

Claims

1. A method for real-time monitoring of three-dimensional shape tilt deformation based on GNSS, characterized in that, The method includes: Obtain the static three-dimensional coordinates of each monitoring point in the slope monitoring network before the blasting trigger moment; after the blasting trigger moment, obtain the GNSS observation values ​​of each monitoring point at each moment to calculate the three-dimensional instantaneous velocity vector and three-dimensional instantaneous acceleration vector at each moment. At each moment, the differences in three-dimensional instantaneous velocity vectors, three-dimensional instantaneous acceleration vectors, and static three-dimensional coordinates between different monitoring points are combined to form a relative feature set between any two monitoring points at each moment. At each moment, the values ​​in the relative feature set between each pair of monitoring points are orthogonally projected and decomposed to obtain the corresponding normal deformation component and tangential deformation component. Based on the numerical characteristics of the normal deformation component and tangential deformation component, and fused with the preset deformation mode weight coefficient, the relative motion cost matrix between monitoring points at each moment is constructed. Discreteness analysis is performed on the relative motion cost matrix at each time point to obtain the cooperative motion deviation index at each time point; based on the temporal changes and temporal relationships of the cooperative motion deviation index at each time point, the stability state of the slope rock mass is evaluated.

2. The method for real-time monitoring of three-dimensional shape tilt deformation based on GNSS according to claim 1, characterized in that, The method for obtaining the relative feature set includes: At each time point, all monitoring points are paired up to obtain all monitoring point pairs; In each monitoring point pair, the difference between the three-dimensional instantaneous velocity vectors of the two monitoring points is taken as the relative velocity vector of the point pair, the difference between the three-dimensional instantaneous acceleration vectors of the two monitoring points is taken as the relative acceleration vector of the point pair, and the difference between the static three-dimensional coordinates of the two monitoring points is taken as the direction vector. The direction vector is normalized and taken as the point-to-baseline unit vector. The relative velocity vector, relative acceleration vector, and baseline unit vector of each monitoring point pair are used to form the set of relative features between each monitoring point pair.

3. The method for real-time monitoring of three-dimensional shape tilt deformation based on GNSS according to claim 2, characterized in that, At each time point, the values ​​in the relative feature set between every two monitoring points are orthogonally projected and decomposed to obtain the corresponding normal deformation component and tangential deformation component, including: For any set of relative features between monitoring point pairs, calculate the scalar projections of the relative velocity vector and relative acceleration vector of the point pairs onto the baseline unit vector of the point pairs. Multiply each of the obtained scalar projections with the baseline unit vector of the point pairs to reconstruct the normal relative velocity component and normal relative acceleration component, which are collectively referred to as the normal deformation component of the monitoring point pair. Based on the differences between the relative velocity vector and relative acceleration vector of the point pair and their respective normal deformation components, the tangential deformation component of the monitoring point pair is determined.

4. The method for real-time monitoring of three-dimensional shape tilt deformation based on GNSS according to claim 3, characterized in that, The method for obtaining the tangential deformation component includes: The vector difference between the relative velocity vector of the point pair and the corresponding normal relative velocity component is calculated as the tangential relative velocity component. The vector difference between the relative acceleration vector of the point pair and the corresponding normal relative acceleration component is calculated as the tangential relative acceleration component. The tangential relative velocity component and the tangential relative acceleration component are collectively referred to as the tangential deformation component of the monitoring point pair.

5. The method for real-time monitoring of three-dimensional shape tilt deformation based on GNSS according to claim 4, characterized in that, The method for obtaining the relative motion cost matrix includes: For any pair of monitoring points, the scalar of the corresponding normal relative velocity component is normalized to obtain the normal relative velocity scalar; the scalar of the corresponding normal relative acceleration component is normalized to obtain the normal relative acceleration scalar; the scalar of the corresponding tangential relative velocity component is normalized to obtain the tangential relative velocity scalar; and the scalar of the tangential relative acceleration component is normalized to obtain the tangential relative acceleration scalar. The relative motion cost of the monitoring point pair is obtained by weighting and fusing the normal relative velocity scalar, normal relative acceleration scalar, tangential relative velocity scalar, and tangential relative acceleration scalar using preset deformation mode weighting coefficients. Using the relative motion cost of each monitoring point pair as the off-diagonal element and the preset maximum value as the diagonal element, a relative motion cost matrix is ​​constructed at that moment.

6. The method for real-time monitoring of three-dimensional shape tilt deformation based on GNSS according to claim 5, characterized in that, The method for obtaining the relative motion cost includes: The preset deformation mode weighting coefficients include preset tangential weighting coefficients and preset normal weighting coefficients; The tangential relative velocity scalar and the tangential relative acceleration scalar are weighted and fused using preset tangential weighting coefficients, and the resulting weighted result is used as the first cost factor. The normal relative velocity scalar and the normal relative acceleration scalar are weighted and fused using preset normal weighting coefficients, and the resulting weighted result is used as the second cost factor. The sum of the first cost factor and the second cost factor is taken as the relative motion cost of the monitoring point pair.

7. The method for real-time monitoring of three-dimensional shape tilt deformation based on GNSS according to claim 1, characterized in that, The method for obtaining the coordinated motion deviation index includes: At each time step, the variance of all off-diagonal elements in the corresponding relative motion cost matrix is ​​calculated and used as the cooperative motion deviation index at each time step.

8. The method for real-time monitoring of three-dimensional shape tilt deformation based on GNSS according to claim 1, characterized in that, The assessment of the stability state of the slope rock mass based on the temporal changes and temporal relationships of the cooperative motion deviation index at various times includes: Based on the temporal variation characteristics of the cooperative motion deviation index at each time point, and combined with the temporal difference between each time point and the blasting trigger time, the logarithmic coordinate decay slope corresponding to each time point is determined. If the absolute value of the logarithmic coordinate decay slope of all times within the neighborhood window at the current time is less than the preset stability threshold, then the lower slope rock mass is determined to have reached a cooperative stability state at the current time, and a safety access decision signal is output.

9. A method for real-time monitoring of three-dimensional shape tilt deformation based on GNSS according to claim 8, characterized in that, The method for obtaining the logarithmic coordinate decay slope includes: Logarithmic coordinate transformation is performed on the cooperative motion deviation index at each time point to obtain the corresponding logarithmic deviation value at each time point. The time difference between each time point and the blasting trigger time is calculated and logarithmic coordinate transformation is performed to obtain the corresponding logarithmic time value at each time point. The logarithmic time value and the logarithmic deviation value at each time point are combined to form the data point pair at each time point. Determine the neighborhood window corresponding to each time step. Within the neighborhood window at each time step, use the logarithmic value of time step as the horizontal axis and the logarithmic value of deviation as the vertical axis to fit a straight line to all pairs of data points at all time steps. Use the slope of the fitted straight line as the logarithmic coordinate decay slope corresponding to each time step.

10. A method for real-time monitoring of three-dimensional shape tilt deformation based on GNSS according to claim 9, characterized in that, The linear fitting was performed using the least squares method.

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