A method for predicting the attenuation law of blasting vibration velocity based on regression analysis

Abstract

This invention belongs to the field of blasting vibration prediction technology, specifically disclosing a method for predicting the attenuation law of blasting vibration velocity based on regression analysis. By deploying monitoring points in multiple directions around the blasting source, geological parameters and peak particle vibration velocities are simultaneously collected at each point, constructing segmented propagation paths, identifying a single dominant propagation segment based on data from adjacent monitoring points, and quantifying the independent influence of specific geological conditions on vibration attenuation using single-factor control regression analysis. This achieves decoupling modeling of geological factors and attenuation behavior. Simultaneously, based on the quantification of the independent influence of a single geological condition, a dual-factor dominant propagation segment is identified. Residual analysis is used to subtract known effects and separate the independent contribution of another geological parameter. Finally, multi-factor influence functions are integrated to construct a comprehensive attenuation model. This achieves a progressive modeling approach from single-factor decoupling to multi-factor synergy, significantly improving the accuracy and physical interpretability of blasting vibration prediction in complex heterogeneous strata.

Description

Technical Field

[0001] This invention belongs to the field of blasting vibration prediction technology, and specifically discloses a method for predicting the attenuation law of blasting vibration velocity based on regression analysis. Background Technology

[0002] Blasting technology, as a key construction method in modern tunnel, mine, and various infrastructure projects, effectively breaks up and excavates hard media through controlled energy release, offering significant advantages in improving engineering efficiency and reducing construction costs. However, the propagation of stress waves generated during blasting can induce significant particle vibration effects, potentially causing adverse effects on adjacent structures. Therefore, accurately predicting the propagation law and attenuation characteristics of blasting vibration velocity has become a core technical requirement for ensuring construction safety and achieving green blasting.

[0003] Currently, there are several technical solutions for modeling blasting vibration attenuation. For example, the peak vibration velocity attenuation model of near-blast source particles in tunnel blasting proposed in CN117034422A adopts a two-stage excavation method and blasts the lower section in stages. The vibration response in the surrounding rock and the initial support shotcrete is monitored synchronously using a vibration measurement system. After blasting, the vibration time history data collected in multiple rounds are imported into the analysis software for vector synthesis, spectrum analysis, integral / differential calculation and regression processing to obtain the particle vibration velocity time history curves at different distances. An empirical PPV-R relationship model is established based on the fitting of the exponential decay function.

[0004] Although the above scheme has achieved systematic acquisition and preliminary modeling of field data, its core defect is that it does not explicitly consider the influence of geological parameters on the vibration attenuation process, resulting in the lack of geological adaptability and extrapolation ability of the model. In areas of geological abrupt change, such as crossing faults, weak interlayers or weathering zones, the prediction error increases significantly.

[0005] To further improve prediction accuracy, another Chinese invention patent, CN118939904A, proposes a method for predicting blasting vibrations that considers elevation effects. This method is based on the principle of dimensional analysis and extends the classic Sadovsky formula to derive an improved model in the following form. Where V is the vibration velocity of the blasting particles, K1 is the site coefficient of the blasting area, and K2 is the influence coefficient of topography. The attenuation coefficient is... denoted as the elevation influence coefficient, Q as the maximum single-stage charge during blasting, R as the distance from the blast center, and H as the elevation difference between the blast center and the vibration measurement point.

[0006] While the above scheme considers the influence of geological parameters on vibration attenuation, compressing complex geological parameters into a single scalar parameter K1 essentially packages all geological variations into an empirical coefficient. This approach masks the differentiated effects of various geological elements on wave propagation mechanisms and fails to reveal the independent contributions of each factor. Furthermore, in actual engineering projects, geological bodies often exhibit significant spatial heterogeneity. For example, within the same tunnel section, a continuous transition may occur from intact rock mass to densely jointed zones to fault fracture zones. Using only a uniform K1 value to describe the entire area could lead to overcompensation in geologically stable sections and severe underfitting in abrupt change zones, resulting in an overall model that is effective on average but fails locally.

[0007] Therefore, it can be seen that K1 proposed in the above scheme is a black box parameter, which is difficult to establish a quantitative relationship with specific rock mechanics indicators, thus limiting the physical interpretability of the model. Summary of the Invention

[0008] Therefore, one objective of this application is to provide a method for predicting the attenuation law of blasting vibration velocity based on regression analysis, which effectively solves the problems mentioned in the background art by constructing a refined blasting vibration attenuation model influenced by geological parameters.

[0009] The objective of this invention can be achieved through the following technical solution: A method for predicting the attenuation law of blasting vibration velocity based on regression analysis, comprising the following steps: S1: Multiple monitoring points are set up in segments along different propagation directions with the blasting hole as the center, and geological parameters including at least rock hardness, rock density, and water content are collected at each monitoring point, and the peak vibration velocity of the mass point is collected at each monitoring point during the blasting test.

[0010] S2: In each propagation direction, the path between adjacent monitoring points is formed into a propagation segment. The geological parameters and peak particle vibration velocities collected at the start and end points of each propagation segment are mapped and correlated to establish a data set relating geological parameters and vibration velocities.

[0011] S3: Identify a single dominant propagation segment from the associated data set, and determine the influence of a single geological parameter on the attenuation of blasting vibration velocity based on the peak particle velocity of the propagation segment through univariate regression analysis.

[0012] S4: Further identify the dual dominant propagation segment from the associated data set, and separate the influence of another geological parameter on the attenuation of blasting vibration velocity by subtracting the influence of the known geological parameter from the influence of the single geological parameter already obtained.

[0013] S5: The independent effects of the obtained geological parameters on vibration velocity attenuation are embedded into the improved Sadovsky model.

[0014] Combining all the above technical solutions, the positive effects of this invention are as follows: 1. This invention, by deploying monitoring points in multiple directions around the blast hole, simultaneously collects geological parameters and peak particle vibration velocities at each point, constructs segmented propagation paths, identifies a single dominant propagation segment based on data from adjacent monitoring points, and quantifies the independent influence of specific geological parameters on vibration attenuation using single-factor control regression analysis. This method achieves decoupled modeling of geological factors and attenuation behavior, effectively improving the physical interpretability and accuracy of the blasting vibration prediction model.

[0015] 2. This invention identifies the dual-factor dominant propagation segment based on the quantification of the independent influence of a single geological parameter. By subtracting known effects through residual analysis, the independent contribution of the other geological parameter is separated, and finally, a comprehensive attenuation model is constructed by integrating multi-factor influence functions. This achieves a progressive modeling approach from single-factor decoupling to multi-factor synergy, significantly improving the accuracy and physical interpretability of blasting vibration prediction in complex heterogeneous strata, and supporting refined vibration control and dynamic risk assessment. Attached Figure Description

[0016] The present invention will be further described with reference to the accompanying drawings, but the embodiments in the drawings do not constitute any limitation on the present invention. For those skilled in the art, other drawings can be obtained based on the following drawings without creative effort.

[0017] Figure 1 This is a diagram illustrating the implementation steps of the method of the present invention.

[0018] Figure 2 This is a schematic diagram of the monitoring points arranged in segments according to the distance gradient along the propagation direction with the center of the blast hole as the starting point.

[0019] Figure 3 This is a flowchart illustrating the implementation of further identifying dual-dominant propagation segments within the associated data group in this invention.

[0020] Attached diagram labels: 1—starting point of propagation segment, 2—boundary point, 3—ending point of propagation segment, 4—monitoring point. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] See Figure 1As shown, the present invention proposes a method for predicting the attenuation law of blasting vibration velocity based on regression analysis, including the following steps: S1: Multiple monitoring points are set up in segments along different propagation directions with the blasting hole as the center, and geological parameters including rock hardness, rock density and water content are collected at each monitoring point. During the blasting test, the peak vibration velocity of each monitoring point is collected.

[0023] In a preferred embodiment of the present invention, multiple monitoring points are set up in segments along different propagation directions with the blasting hole as the center. The specific implementation is as follows: Based on the charge amount of the single-hole blasting test and the geological type of the target area, single-hole blasting cases with the same geological type and charge amount are matched from the historical blasting database, and the typical effective influence radius of vibration propagation is extracted from them as the vibration propagation boundary range of this test.

[0024] It should be understood that the single-hole blasting test selected in this invention can effectively eliminate the interference of multi-hole superimposed vibration and detonation timing, obtain pure single-source vibration data, facilitate accurate identification of vibration propagation law and attenuation characteristics, and is the basic test condition for constructing intrinsic attenuation model.

[0025] It should be noted that the geological types mentioned above refer to rock mass units with similar lithology and structural features, such as slightly weathered granite, moderately jointed limestone, or strongly weathered sandstone-mudstone interbedded layers. Matching historical cases with the specified charge amount and geological type is crucial because the charge amount directly determines the vibration source strength and energy radiation level, thereby controlling the spatial range and attenuation gradient of vibration propagation; while the geological type dominates the absorption, scattering, and attenuation rate of stress waves in the medium. This dual constraint ensures that the source strength conditions and medium characteristics of vibration propagation are highly comparable, thus improving the applicability and reliability of historical data in determining predictive boundaries such as the effective radius of influence, and providing a scientific reference benchmark for current blasting tests.

[0026] As a supplementary explanation for the above operations, when matching historical cases based on charge quantity, the borehole diameter and depth parameters must be considered simultaneously to ensure that the borehole diameter and depth of the current test are basically consistent with those of historical cases. This is to ensure the similarity of the geometric characteristics of the explosion source and the energy release mode, thereby effectively controlling the impact of differences in source region effects on the extrapolation of propagation laws and improving the accuracy and engineering applicability of vibration propagation boundary prediction.

[0027] The typical effective influence radius mentioned above is defined as the distance from the peak vibration velocity of a mass point to the safe control threshold, such as the allowable vibration velocity of the building or the regional background vibration level specified in the "Safety Regulations for Blasting" GB6722.

[0028] With the blast hole as the center point, select no fewer than four propagation directions along a radial path in the surrounding space, and the included angles between adjacent propagation directions are evenly distributed.

[0029] The selection of multiple propagation directions aims to comprehensively reflect the spatial heterogeneity of the rock mass and the anisotropy of wave propagation characteristics, avoiding the modeling bias caused by a single path. Selecting only a single propagation direction limits the number of usable propagation segments, resulting in insufficient sample diversity and reduced statistical significance and generalization ability of the model. Therefore, a uniform distribution across multiple directions increases data coverage, improves the robustness of parameter identification, and enhances the reliability of the attenuation model.

[0030] The angles between adjacent propagation directions are evenly distributed and controlled between 60° and 120°. For example, the angles between the four propagation directions are 0°, 90°, 180°, and 270°, which ensures the spatial anisotropy characterization ability and sampling independence of the monitoring data and avoids statistical bias caused by directional clustering.

[0031] Based on the determined vibration propagation boundary range, the maximum effective propagation distance in each propagation direction is obtained, which serves as the outer boundary of the monitoring network in that direction, providing a distance benchmark for subsequent gradient-based deployment of monitoring points.

[0032] Starting from the center of the blast hole, monitoring points are set up in segments along each propagation direction according to the distance gradient based on the maximum effective propagation distance.

[0033] As one possible way to implement the above scheme, the segmented deployment of monitoring points includes the following: extracting blasting vibration monitoring data from matched single-hole blasting cases, obtaining multiple sets of peak particle vibration velocities and corresponding blast center distance data, plotting the data in a double logarithmic coordinate system, and generating a blasting vibration velocity attenuation characteristic curve.

[0034] It is important to understand that the peak mid-volume velocity (PMV) refers to the maximum vibration velocity reached by medium particles per unit time during the propagation of the blasting vibration wave, and is a core indicator for assessing vibration intensity. The blast center distance refers to the straight-line distance from the measuring point to the blast hole, representing the path length of vibration propagation. Blasting vibration velocities typically follow a power-law decay pattern, meaning the vibration velocity decreases rapidly and non-linearly with increasing distance. Plotting the decay curve in a double logarithmic coordinate system transforms the typical power-law decay relationship into a linear form, helping to reveal piecewise decay behavior and providing clear geometric criteria for inflection point detection and zonal modeling, thus improving the accuracy and operability of decay law analysis.

[0035] The inflection point detection of the plotted double logarithmic decay curve is used to identify the transition position from the near-field rapid decay region to the mid-field stable decay region and the position where the vibration velocity decays to the preset safety control threshold. The abscissa values ​​are defined as the near-mid boundary distance and the mid-far boundary distance, respectively.

[0036] It's important to understand that during the propagation of blasting vibrations, the vibration attenuation characteristics vary at different distances due to factors such as geological parameters, medium properties, and energy distribution. Typically, the vibration velocity decreases sharply near the blast source (near-field) because strong wave interference and scattering in this region cause a rapid drop in velocity. As the distance increases and the vibration enters the mid-field region, the influence of these complex factors weakens, and the attenuation trend becomes relatively stable, following a more stable power-law attenuation pattern.

[0037] Furthermore, different buildings or structures have limited maximum vibration velocities they can withstand, and different safety standards apply depending on the building's importance and type. Therefore, it is necessary to determine the distance range within which the vibration velocity drops below a certain safety threshold to ensure that buildings or facilities beyond this distance are not damaged by blasting vibrations. This distance is the distance at which the vibration velocity decays to a preset safety control threshold.

[0038] The aforementioned inflection point detection can use changes in the derivative to find points where the slope of the curve changes significantly.

[0039] For each radiation propagation direction, the propagation path is divided into near zone, middle zone, and far zone by combining the maximum effective propagation distance in that direction with the near-to-middle zone boundary distance and the middle-to-far zone boundary distance.

[0040] The propagation path is divided into near, middle, and far zones by detecting the near-middle and middle-far boundaries using the inflection point detection of the double logarithmic decay curve. The near zone is defined as the propagation segment from the blast hole to the near-middle boundary, corresponding to the high-gradient decay region in the near field. The middle zone is the interval between the near-middle and middle-far boundaries, representing a transitional decay segment where the vibration velocity tends to level off. The far zone refers to the extended path from the middle-far boundary to the maximum effective propagation distance, belonging to the low-amplitude, slow-decaying far-field region. This three-zone division reflects the differences in the propagation mechanism of blasting vibration at different spatial scales: the near zone is dominated by the nonlinear effect of the source region, the middle zone tends to be controlled by geometric diffusion, and the far field is significantly affected by medium damping. Dividing the propagation path into zones provides a spatial zoning basis for the differentiated and refined deployment of monitoring points in subsequent zones.

[0041] See Figure 2 As shown, monitoring points are deployed at a set interval in the near zone of each propagation direction. For example, this interval is usually set to 1 to 3 times the borehole diameter. Monitoring points are deployed in the middle zone at multiples of the near zone interval, and in the far zone at multiples of the middle zone interval.

[0042] It should be explained that the above-mentioned zoning deployment follows the principle of denser monitoring in the near field and sparser monitoring in the far field. This is because the vibration velocity attenuation gradient is large and the dynamic response is complex in the near field, requiring high-density monitoring to capture its rapid changes at high resolution. In the mid-field, the attenuation tends to be gentler, and the monitoring spacing can be set to 1.5 to 2.0 times that of the near field, achieving a reasonable transition in spatial sampling density. In the far field, the vibration amplitude is low and the changes are slow, so further increasing the spacing can effectively save monitoring resources while ensuring the overall trend representation. Compared with uniform deployment along the entire path, this strategy optimizes the allocation of monitoring resources and improves the spatial representativeness and acquisition efficiency of the data while ensuring the accuracy and sensitivity of data in key areas.

[0043] In a further preferred embodiment of the present invention, the geological parameters are collected as follows: at each selected monitoring point, a geological drilling rig is used to perform core drilling, and rock samples are obtained from different depths. The rock samples are tested for hardness using a hardness tester. The hardness values ​​measured at each depth at the same monitoring point are then arithmetically averaged to be used as the rock hardness at that monitoring point, so as to reflect the overall compressive strength of the rock mass at that location.

[0044] Rock samples were taken from cores drilled at monitoring points, their natural mass was measured using an electronic balance, and the rock density was measured using the displacement method.

[0045] When applied to the above operations, the drainage method mentioned is based on Archimedes' principle. The sample is completely immersed in water, and its geometric volume is determined by the volume of water displaced. Then, the density of the rock is obtained by combining the mass and volume of the rock sample with the density formula.

[0046] Rock samples were collected at the monitoring point, and the water content was obtained by crushing the rocks and drying them.

[0047] Applying the above operations, the drying method involves crushing the rock sample to a particle size of less than 2 mm in the laboratory and weighing the initial mass. It was then placed in a constant temperature oven at 105–110°C and dried to constant weight. After cooling, the dry weight was measured. According to the formula Obtain water content .

[0048] It should be noted that this invention uses borehole sampling at each monitoring point to obtain geological parameters. Although this is a minimally invasive operation and introduces small-scale disturbances locally, the impact is negligible—the volume of a single sampling hole is much smaller than the charging space of the main blasting hole, and their sparse distribution is insufficient to alter the overall stress wave propagation path and media continuity of the rock mass. In contrast, non-destructive testing methods such as ground-penetrating radar and elastic wave tomography, while not requiring drilling, are limited by wave field complexity, inversion ambiguity, and resolution, making it difficult to accurately quantify key physical parameters such as hardness, density, and water content of local rock masses. This invention emphasizes segmented, point-by-point, and multi-parameter refined acquisition of geological parameters, aiming to obtain measured geological data with clear spatial correspondences to support decoupling analysis and high-precision modeling of geological factors during vibration attenuation, avoiding misjudgments of mechanisms caused by generalized and averaged site descriptions.

[0049] It should be further explained that rock hardness, rock density, and water content were chosen as geological parameters because rock hardness is an indicator of the rock mass's ability to resist local plastic deformation or fracturing. The higher the hardness, the more efficiently energy propagates in the form of elastic waves, with less geometric diffusion and internal friction dissipation. Therefore, vibration decay is slow and the range of influence is far. The lower the hardness, the more the vibration energy is consumed in the process of propagation due to rock mass fracturing and frictional heat generation, resulting in greater damping and faster vibration decay.

[0050] Density, referring to the mass of a unit volume of rock, is a key physical parameter determining wave impedance. Differences in wave impedance control the reflection and transmission characteristics of stress waves at the interface of the medium. Lower rock density typically corresponds to higher porosity and looser interparticle contact, leading to reduced wave impedance. In such media, vibration easily excites relative displacement between particles, generating significant internal friction mechanisms through particle friction, collisions, and pore fluid interactions, causing wave energy to dissipate rapidly, manifested as accelerated vibration velocity decay.

[0051] Water content characterizes the saturation level of pore water in soil and rock media, directly affecting their damping characteristics and wave propagation behavior. When the water content is high, the pore water generates hydrodynamic pressure under vibrational loads, triggering interaction between the pore fluid and the solid skeleton. This interaction dissipates wave energy through a seepage-skeleton coupling energy dissipation mechanism. Although the high stiffness and low compressibility of water can increase the overall wave velocity, it also significantly enhances the viscous damping effect of the medium, leading to increased energy dissipation of stress waves during propagation, manifested as accelerated vibration velocity decay.

[0052] These three parameters together constitute the basic physical field describing the dynamic response capability of rock mass, and have a significant and quantifiable physical influence on blasting vibration attenuation. Although other geological parameters such as the degree of fracture development and Poisson's ratio are also important, these three parameters are the most fundamental and universal geological parameter indicators. The measurement methods for these three parameters are mature and can be efficiently obtained through field sampling and laboratory testing. The data has a high degree of quantification and low acquisition cost, making them suitable as benchmark indicators for the quantitative characterization of geological parameters in blasting vibration attenuation prediction models.

[0053] In a further preferred embodiment of the present invention, the specific implementation of collecting the peak vibration velocity of the mass point at each monitoring point during the blasting test is as follows: a three-dimensional velocity-type vibration pickup is set up at each monitoring point, with its sensitive axis corresponding to the vertical, radial and tangential directions respectively, to ensure complete capture of the three-dimensional motion components of the vibration wave. The vibration pickup is rigidly anchored and tightly coupled to the rock mass to ensure effective transmission of the vibration signal.

[0054] When the blast is triggered, the vibration pickups at each monitoring point automatically record the three-dimensional vibration time history data. After the blast, the original waveform is filtered, baseline corrected and vector synthesized to calculate the triaxial composite velocity. Then, the maximum triaxial composite velocity in the entire vibration time history is taken as the peak vibration velocity of the corresponding monitoring point.

[0055] It is important to understand that when stress waves propagate to the monitoring point, rock mass particles generate a continuous dynamic response under wave field excitation, and their vibration process manifests as reciprocating motion over a period of time. The vibration pickup records the velocity time history signal of the particle in three orthogonal directions (vertical, radial, and tangential) that changes continuously over time. The three-dimensional composite velocity obtained through vector synthesis reflects the overall amplitude of the particle's instantaneous vibration intensity. The peak vibration velocity of the particle is not an instantaneous reading at any arbitrary moment, but rather the global maximum value of the composite velocity time history curve over the entire vibration duration, characterizing the maximum dynamic disturbance intensity experienced at that location, and is a key indicator for evaluating the blasting vibration effect.

[0056] S2: In each propagation direction, the path between adjacent monitoring points is formed into a propagation segment. The geological parameters and peak particle vibration velocities collected at the start and end points of each propagation segment are mapped and correlated to establish a data set relating geological parameters and vibration velocities.

[0057] S3: Identify a single dominant propagation segment from the associated data set, and determine the influence of a single geological parameter on the attenuation of blasting vibration velocity based on the peak particle velocity of the propagation segment through univariate regression analysis.

[0058] As an optional implementation of the above scheme, the identification of a single dominant propagation segment from the associated data group is carried out as follows: For each propagation segment, the rock hardness, rock density, and water content measured at its starting and ending points are extracted. For each geological parameter, its relative rate of change within the path of that segment is calculated. The relative rate of change is defined as the ratio of the absolute difference between the geological parameter measurement values ​​at the ending and starting points of the propagation segment and the measurement value at its starting point. This reflects the degree of change of the normalized gradient of the geological parameter in that propagation segment, eliminates the influence of dimensions, and facilitates cross-segment comparison.

[0059] The relative change rate of each geological parameter in each propagation segment is compared with the preset allowable change rate. If the relative change rate of only one geological parameter in a certain propagation segment is greater than the allowable change rate, and the relative change rates of all other geological parameters are less than or equal to the allowable change rate, then the propagation segment is classified as a single dominant propagation segment. The geological parameters with relative change rates greater than the allowable change rate are marked as dominant parameters, and the other geological parameters are marked as stable parameters.

[0060] The aforementioned allowable rate of variation reflects the threshold standard for judging whether a geological parameter has changed significantly in the analysis of blasting vibration propagation. It is used to distinguish whether the parameter is a major variable factor or can be regarded as approximately constant within the propagation section. Specifically, the coefficient of variation can be calculated based on the field measured data of similar rock masses, and the upper third value or the mean value plus one standard deviation can be taken as the allowable rate of variation.

[0061] It should be noted that the single dominant propagation segment identified above can be regarded as a quasi-control test sample of the influence of a single geological factor on vibration velocity attenuation under the premise that other variables are kept approximately constant.

[0062] As a supplementary explanation for the above operations, changes in geological parameters within rock masses are usually not simultaneous abrupt changes involving multiple factors. This is because there are often gradual transition zones of physical properties between adjacent sections within the same geological unit. This continuity stems from the stability of the geological formation process and the spatial correlation of the rock mass structure, resulting in parameters such as hardness, density, and water content exhibiting gradual changes within local ranges. Therefore, within short-distance propagation segments, situations often arise where only a single parameter changes significantly while other parameters remain relatively stable, providing an objective geological basis for identifying a single dominant propagation segment.

[0063] As a further optional implementation of the above scheme, the influence of a single geological parameter on the attenuation of blasting vibration velocity is determined as follows: the dominant propagation segments identified in each propagation direction are classified into a set of dominant propagation segments of the same type based on the same main variable parameter and the same stability parameter.

[0064] It is important to understand that single dominant propagation segments are often limited by spatial length and have scarce samples along a single propagation path. Since such segments typically exist only in local geological transition zones, the number of effective segments obtainable along a single direction is limited. Therefore, by integrating propagation segments with the same dominant variable-stability parameter combination in multiple propagation directions, the sample size of control variables can be expanded. This provides sufficient and comparable data support for separating the influence of single geological factors on vibration attenuation, avoiding statistical bias and unreliable modeling due to insufficient samples.

[0065] In the set of dominant propagation segments of the same type, the ratio of the peak particle velocity at the start point to the peak velocity at the end point of each propagation segment is defined as the vibration velocity attenuation ratio, and the unit vibration attenuation rate is calculated in combination with the propagation segment length. In the formula Indicates the unit vibration attenuation rate. , These represent the peak vibration velocities of the particles at the starting and ending points of the propagation segment, respectively. Indicates the length of the propagation segment.

[0066] It should be noted that the energy attenuation of elastic waves generated by blasting in a non-uniform medium is not a linear process, but rather is affected by the cumulative influence of the medium properties of each segment along the path. The local attenuation rate reflects the ability of the medium within that micro-segment to dissipate wave energy. By dividing the long path into multiple propagation segments and calculating the attenuation rate per unit distance of each segment, a discretized characterization of the continuous spatial attenuation process is achieved.

[0067] Explanation of the unit vibration attenuation rate applied to the above operations. While reflecting the degree of attenuation, this method is affected by the segment length. To eliminate interference from the propagation distance and improve the comparability across segments, the velocity ratio divided by the propagation length is not directly used in this process. This is because vibration attenuation exhibits a non-linear exponential law in space. If a linear attenuation rate is used, it will be distorted as it changes with the segment length, making it difficult to reflect the true attenuation characteristics. This operation is equivalent to the logarithmic attenuation coefficient, which can accurately characterize the attenuation intensity per unit distance, eliminate the influence of propagation length on attenuation rate calculation, and improve the comparability and physical consistency between propagation segments of different lengths.

[0068] Based on the distance from the starting point of each propagation segment to the blast hole, and combined with the previously determined near-middle-far zone boundary points, the same type of dominant propagation segment groups are further divided into near-zone propagation segment groups, middle-zone propagation segment groups, and far-zone propagation segment groups.

[0069] In the near-field propagation segment group, the middle-field propagation segment group, and the far-field propagation segment group, a univariate regression model was established with the unit vibration attenuation rate of the propagation segment as the dependent variable and the relative change rate of the principal variable parameter as the independent variable.

[0070] As a supplement to the above operations, the regression function in the single-factor regression model can be linear, power-law, or exponential, aiming to select the mathematical model that best describes the response trend based on the physical relationship between geological parameters and vibration attenuation rate.

[0071] It should be noted that blasting vibrations in the near-field region are dominated by nonlinear mechanisms such as rock fragmentation and plastic deformation, resulting in rapid attenuation; while in the mid-to-far-field region, geometric diffusion and viscous damping dominate, leading to a more stable attenuation. This demonstrates that the attenuation mechanisms differ across regions. By modeling the attenuation in three zones (near-field, mid-field, and far-field), the spatial heterogeneity of the attenuation mechanisms is reflected, avoiding prediction distortion caused by a one-size-fits-all model.

[0072] The regression results of each region are weighted and integrated based on the sample size of each region to obtain the comprehensive influence function of the main variable parameter throughout the entire effective propagation range.

[0073] In the weighted integration process described above, the weights of the regression results for each region (near, middle, and far regions) are usually allocated according to the proportion of their sample size to the total number of samples in the same dominant propagation segment set. The reason for this allocation is that regions with larger sample sizes reflect the geological response data of the region more fully and have higher statistical stability. Assigning higher weights can improve the reliability of the integrated model.

[0074] The influence of the main variable parameters on the attenuation of blasting vibration velocity was determined by fitting the comprehensive influence function using the least squares method.

[0075] Blasting vibration attenuation is influenced by a combination of factors, including explosive charge, distance, geological hardness, density, and water content. The traditional Sadovsky formula struggles to capture these geological differences. The proposed solution, through propagation segment selection and zonal regression, successfully decomposes this complex multi-factor problem into several sub-problems dominated by single factors. This enables the independent quantification of the influence of various geological parameters, a prerequisite for constructing a refined model.

[0076] S4: Further identify the dual dominant propagation segment from the associated data set, and separate the influence of another geological parameter on the attenuation of blasting vibration velocity by subtracting the influence of the known geological parameter from the influence of the single geological parameter already obtained.

[0077] See Figure 3 As shown, in the specific implementation of the above scheme, further identification of dual dominant propagation segments from the associated data group includes the following: after excluding those already classified as single dominant propagation segments, the relative change rate of each geological parameter of all remaining propagation segments is compared with the preset allowable change rate. If a propagation segment meets the following conditions, it is determined to be a dual dominant propagation segment.

[0078] a) There are exactly two geological parameters whose relative rate of change is greater than the allowable rate of change.

[0079] b) One of the geological parameters is the main variable parameter that was previously identified in a single dominant propagation segment.

[0080] c) The relative rate of change of the remaining geological parameters is less than or equal to the allowable rate of change.

[0081] For the identified dual dominant propagation segments, the two geological parameters with relative change rates greater than the allowable change rate are marked as dominant parameters, and the other geological parameters are marked as stable parameters.

[0082] It should be noted that geological conditions in real rock mass environments often exhibit multi-parameter variations, and the independent variation of a single parameter has limitations. By identifying dual-dominant propagation segments, the joint variation patterns among geological factors can be effectively captured, providing measured data support that satisfies the dual-variable dominance condition for quantifying the nonlinear coupling effect between parameters. This process is a natural extension of the single-factor dominant segment analysis, constructing a progressive path from decoupling independent influences to modeling multi-factor interactions, and deepening the understanding of the blasting vibration attenuation mechanism from single-factor response to multi-field coupling.

[0083] In the further implementation of the above scheme, the influence of another geological parameter on the attenuation of blasting vibration velocity is separated by deducting the influence of the known geological parameters, based on the influence of the single geological parameter already obtained. The implementation is as follows: the dual dominant propagation segments identified in each propagation direction are classified according to the same combination of main variable parameters and the same stable parameters to form a set of dual dominant propagation segments of the same type.

[0084] For each propagation segment in a set of similar dual-dominant propagation segments, the unit vibration attenuation rate is calculated, and the residual attenuation rate is obtained after deducting the influence of known geological parameters on vibration attenuation.

[0085] The residual attenuation rate calculated above is the attenuation portion that still needs to be explained after excluding the influence of known geological factors, and it is mainly dominated by another main variable parameter.

[0086] For each propagation segment in a set of similar dual-dominant propagation segments, extract the relative rate of change of the other dominant variable parameter.

[0087] For similar dual-dominant propagation segments, a regression model is established with the residual attenuation rate as the dependent variable and the relative change rate of the other dominant parameter as the independent variable. ,in Indicates the residual attenuation rate. This represents the relative rate of change of the other principal variable parameter. Represents the function to be fitted. This indicates the error term.

[0088] The independent influence function of another principal variable parameter on vibration attenuation was determined by fitting using the least squares method.

[0089] The implementation details for the above operations indicate that the propagation response of stress waves in rock mass can approximately satisfy the superposition principle under certain conditions, meaning the total attenuation effect can be considered a linear combination of contributions from various independent geological factors. Based on this assumption, if the influence of a certain controlling factor has been accurately quantified using measured data, its theoretical contribution can be subtracted from the total attenuation to obtain the residual attenuation rate. This residual amount is essentially a detrending process of the original attenuation signal. As a new dependent variable, its statistical relationship with the geological parameter to be identified more accurately reflects the independent influence of that parameter, effectively eliminating the confounding bias caused by multi-factor collinearity. This provides theoretical feasibility and computational basis for parameter decoupling and independent contribution separation under multi-field coupling.

[0090] As an innovative extension of the aforementioned approach, multiple geological parameters in actual rock masses often exhibit non-independent, synergistic variations. This makes it difficult for traditional regression analysis based on the assumption of independent variables to effectively distinguish the independent contributions of each parameter in decoupled analysis dominated by two factors. Using only a single main effect model would introduce significant confounding bias and prediction errors. Therefore, systematic bias patterns can be identified through error diagnostic analysis, and interaction terms between geological parameters can be introduced to construct an enhanced attenuation model that incorporates coupling effects. This method can capture the nonlinear synergistic mechanism between parameters, improve the physical characterization of vibration attenuation, and significantly enhance the accuracy and robustness of predicting blasting vibration propagation under complex geological conditions.

[0091] Specifically, error diagnosis and whether to introduce interaction terms are performed as follows: After completing the regression modeling of the residual decay rate and another main variable parameter, plot the relationship between the error term and the other main variable parameter.

[0092] If the error is observed to exhibit a systematic trend with another principal variable parameter in the relationship graph, such as a linear or nonlinear increase / decrease, it indicates that the error still contains structural information that can be explained by this parameter, that is, the residual has not been randomized. This means that the current model has missed the synergistic or modulating effect between this parameter and the existing variables. In this case, a multiple regression model with interaction terms should be constructed.

[0093] As an explanation of the above operations, when two geological parameters have a physical coupling mechanism, such as the significant enhancement of attenuation in low-hardness rock masses under high water content, their effects are not independently superimposed but rather exhibit an interactive effect. If only an additive model is established, this nonlinear synergistic effect will be incorrectly attributed to the residuals, causing the residuals to show a trend with parameter changes.

[0094] For example, the expression for a multiple regression model that incorporates interaction terms is: ,in , These represent the relative rates of change of the two main variable parameters. This represents the cross term, used to quantify the coupling effect between parameters. , These represent the independent influence strengths of the two main variable parameters, Indicates the strength and direction of the interaction; positive indicates synergy, and negative indicates antagonism. This is a constant term.

[0095] The above introduces cross terms This coupling mechanism can be explicitly characterized, making the model regression residuals tend to white noise, achieving error randomization, and improving the physical reality and prediction accuracy of the model.

[0096] The multiple regression model was refitted and error diagnosis was performed. After confirming that the model error was randomized, the least squares method was used to complete parameter estimation and determine the complete regression equation including the main effect and interaction effect, so as to obtain the influence of another main variable parameter on the attenuation of blasting vibration velocity.

[0097] S5: The independent effects of the obtained geological parameters on vibration velocity attenuation are embedded into the improved Sadovsky model.

[0098] In the example implementation of the above operation, after obtaining the influence of each geological parameter on the attenuation of blasting vibration velocity through decoupling, the results can be embedded into the improved Sadovsky model. ,in , , These represent the influence of rock hardness, rock density, and water content on the attenuation of blasting vibration velocity, respectively, thus achieving a leap from empirical formulas to mechanism-enhanced models.

[0099] The parameters involved in the above formula are all dimensionless and calculated numerically. The formula is a formula obtained from the most recent real situation by collecting a large amount of data and simulating it with software. The preset parameters in the formula are set by those skilled in the art according to the actual situation.

[0100] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, in the form of a computer program product.

[0101] Those skilled in the art will recognize that the modules and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0102] In addition, the functional modules in the various embodiments of this application can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module.

[0103] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0104] Finally, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for predicting the attenuation law of blasting vibration velocity based on regression analysis, characterized in that, Includes the following steps: S1: Multiple monitoring points are set up in segments along different propagation directions with the blast hole as the center. Geological parameters including at least rock hardness, rock density, and water content are collected at each monitoring point. The peak particle vibration velocity of each monitoring point is also collected during the blasting test. S2: In each propagation direction, the path between adjacent monitoring points is formed into a propagation segment. The geological parameters and peak particle vibration velocities collected at the start and end points of each propagation segment are mapped and correlated to establish a data set relating geological parameters and vibration velocities. S3: Identify a single dominant propagation segment from the associated data set, and determine the influence of a single geological parameter on the attenuation of blasting vibration velocity based on the peak particle velocity of the propagation segment through univariate regression analysis. The dominant propagation segments identified in each propagation direction are categorized into sets of similar dominant propagation segments based on the same main variable parameters and the same stability parameters. For each propagation segment in the set of similar dominant propagation segments, the ratio of the peak particle velocity at the start point to the peak velocity at the end point is defined as the vibration velocity attenuation ratio, and the unit vibration attenuation rate is calculated based on the propagation segment length. In the formula Indicates the unit vibration attenuation rate. , These represent the peak vibration velocities of the particles at the starting and ending points of the propagation segment, respectively. The propagation segment length is represented. Based on the distance from the starting point of each propagation segment to the blast hole and the previously determined near-middle-far boundary points, the same type of dominant propagation segment groups are further divided into near-zone propagation segment groups, middle-zone propagation segment groups, and far-zone propagation segment groups. In the near-zone, middle-zone, and far-zone propagation segment groups, a single-factor regression model is established with the unit vibration attenuation rate as the dependent variable and the relative change rate of the main variable parameter as the independent variable. The regression results of each zone are weighted and integrated according to the sample size of each zone to obtain the comprehensive influence function of the main variable parameter in the entire effective propagation range. The influence of the main variable parameter on the attenuation of blasting vibration velocity is determined by fitting the comprehensive influence function using the least squares method. S4: Further identify the dual dominant propagation segment from the associated data set, and separate the influence of another geological parameter on the attenuation of blasting vibration velocity by subtracting the influence of the known geological parameter, combined with the influence of the single geological parameter already obtained; The dual-dominant propagation segments identified in each propagation direction are categorized into sets of similar dual-dominant propagation segments based on the same combination of principal variable parameters and the same stability parameters. For each propagation segment in the set of similar dual-dominant propagation segments, the unit vibration attenuation rate is calculated, and the residual attenuation rate is obtained after deducting the influence of known geological parameters on vibration attenuation. The relative change rate of the other principal variable parameter is extracted for each propagation segment in the set of similar dual-dominant propagation segments. A regression model is established for the set of similar dual-dominant propagation segments, with the residual attenuation rate as the dependent variable and the relative change rate of the other principal variable parameter as the independent variable. ,in Indicates the residual attenuation rate. This represents the relative rate of change of the other principal variable parameter. Represents the function to be fitted. The error term is represented; the independent influence of another principal variable parameter on vibration attenuation is determined by least squares fitting. S5: The independent effects of the obtained geological parameters on vibration velocity attenuation are embedded into the improved Sadovsky model.

2. The method for predicting the attenuation law of blasting vibration velocity based on regression analysis as described in claim 1, characterized in that: The specific implementation of setting up multiple monitoring points in segments is as follows: Based on the charge amount and geological type of the target area in the single-hole blasting test, single-hole blasting cases with the same geological type and charge amount were matched from the historical blasting database, and the typical effective influence radius of vibration propagation was extracted from them as the vibration propagation boundary range of this test. With the blast hole as the center point, select no less than four propagation directions along a radial path in the surrounding space, and the included angles between adjacent propagation directions are evenly distributed. The maximum effective propagation distance in each propagation direction is obtained based on the defined vibration propagation boundary range; Starting from the center of the blast hole, monitoring points are set up in segments along each propagation direction according to the distance gradient based on the maximum effective propagation distance.

3. The method for predicting the attenuation law of blasting vibration velocity based on regression analysis as described in claim 2, characterized in that: The segmented deployment of monitoring points includes the following: Blasting vibration monitoring data were extracted from matched single-hole blasting cases. Multiple sets of peak particle vibration velocities and corresponding blast center distance data were obtained. The data were plotted as scatter points in a double logarithmic coordinate system to generate a blasting vibration velocity decay characteristic curve. The inflection point detection of the plotted double logarithmic decay curve is used to identify the transition position from the near-field rapid decay region to the mid-field stable decay region and the position where the vibration velocity decays to the preset safety control threshold. The abscissa values ​​are defined as the near-mid-field boundary distance and the mid-far-field boundary, respectively. For each propagation direction, the propagation path is divided into near zone, middle zone, and far zone by combining the maximum effective propagation distance in that direction, the near-middle zone boundary distance, and the middle-far zone boundary distance; Monitoring points are deployed at predetermined intervals in the near zone of each propagation direction, at multiples of the near zone interval in the middle zone, and at multiples of the middle zone interval in the far zone.

4. The method for predicting the attenuation law of blasting vibration velocity based on regression analysis as described in claim 1, characterized in that: The geological parameters are obtained as described in the following data acquisition process: At each selected monitoring point, a geological drilling rig was used to perform core drilling, and rock samples were obtained from different depths. The rock samples were tested for hardness using a hardness tester. The hardness values ​​measured at different depths at the same monitoring point were then arithmetically averaged to obtain the rock hardness of that monitoring point. Rock samples were taken from the cores drilled at the monitoring point, their natural mass was measured using an electronic balance, and the rock density was measured using the displacement method. Rock samples were collected at the monitoring point, and the water content was obtained by crushing the rocks and drying them.

5. The method for predicting the attenuation law of blasting vibration velocity based on regression analysis as described in claim 1, characterized in that: The peak vibration velocity of the mass point was acquired as follows: Three-axis velocity sensors are deployed at each monitoring point, with their sensitive axes aligned with the vertical, radial, and tangential directions, respectively. When the blasting is triggered, the three-dimensional vibration time history of each monitoring point is automatically collected, and after filtering, baseline correction and vector synthesis, the maximum value in the synthesized velocity time history is extracted as the peak vibration velocity of the corresponding monitoring point.

6. The method for predicting the attenuation law of blasting vibration velocity based on regression analysis as described in claim 3, characterized in that: The process of identifying a single dominant propagation segment from the associated data set is implemented as follows: For each propagation segment, extract each geological parameter measured at the starting and ending points and calculate its relative rate of change within the path; The relative change rate of each geological parameter in each propagation segment is compared with the preset allowable change rate. If only one geological parameter in a propagation segment has a relative change rate greater than the allowable change rate, while the relative change rates of other geological parameters are all less than or equal to the allowable change rate, then the propagation segment is classified as a single dominant propagation segment. The geological parameters with a relative change rate greater than the allowable change rate are marked as dominant parameters, and the other geological parameters are marked as stable parameters.

7. The method for predicting the attenuation law of blasting vibration velocity based on regression analysis as described in claim 1, characterized in that: The further identification of dual-dominant propagation segments from the associated data set includes the following: After excluding those already classified as single dominant propagation segments, the relative rate of change of each geological parameter in all remaining propagation segments is compared with the preset allowable rate of change. If a propagation segment meets the following conditions, it is determined to be a dual dominant propagation segment. a) There are exactly two geological parameters whose relative rate of change is greater than the allowable rate of change; b) One of the geological parameters is a major variable parameter that was previously identified in a single dominant propagation segment; c) The relative rate of change of the remaining geological parameters is less than or equal to the allowable rate of change; For the identified dual dominant propagation segments, the two geological parameters with relative change rates greater than the allowable change rate are marked as dominant parameters, and the other geological parameters are marked as stable parameters.

8. The method for predicting the attenuation law of blasting vibration velocity based on regression analysis as described in claim 7, characterized in that: The process of separating the effect of another geological parameter on the attenuation of blasting vibration velocity also includes the following operations: After completing the regression modeling of the residual decay rate and another principal variable parameter, plot the relationship between the residual term and the other principal variable parameter. If a systematic trend is observed in the relational graph of the residuals with respect to another principal variable parameter, a multiple regression model with an interaction term is constructed. The multiple regression model was refitted and residual diagnosis was performed. After confirming that the model residuals were randomized, the least squares method was used to complete parameter estimation and determine the complete regression equation including the main effect and interaction effect, so as to obtain the influence of another main variable parameter on the attenuation of blasting vibration velocity.

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