A rapid construction method for island and reef underground engineering
By collecting and inverting the rock mass spectral attenuation model, constructing an energy functional, and optimizing the charge parameters, the heterogeneity problem of reef limestone construction in island and reef underground engineering was solved, achieving rapid and accurate construction results.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- INST OF ROCK & SOIL MECHANICS CHINESE ACAD OF SCI
- Filing Date
- 2026-06-09
- Publication Date
- 2026-07-10
AI Technical Summary
Blasting operations for underground engineering on islands and reefs face challenges due to the strong heterogeneity and complex pore structure of reef limestone, which existing technologies struggle to adapt to. This results in significant discrepancies between design schemes and actual working conditions, as well as a lack of effective utilization of the rock mass's spectral characteristics, impacting construction safety and progress.
By collecting blasting construction data, inverting the rock mass spectral attenuation model, constructing an energy functional with spectral attenuation as the weight, determining the charge parameters, and achieving dynamic closed-loop adjustment through spectral feedback to optimize the blasting design.
It achieves precise adaptation to porous reef limestone, enabling rapid and accurate underground space construction, and reducing construction cycle and cost.
Smart Images
Figure CN122365019A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of blasting construction technology, specifically to a rapid construction method for underground engineering on islands and reefs. Background Technology
[0002] The development of underground space on coastal islands and reefs is receiving increasing attention. Vertical or inclined shafts, as key access channels for underground engineering, face severe challenges in blasting operations due to unique geological conditions. On the one hand, islands and reefs typically have small reef platforms and lack large infrastructure and hoisting equipment, making drill-and-blast the primary construction method. On the other hand, the unique geological conditions of porous reef limestone are characterized by strong heterogeneity, complex pore structure, and a tendency to collapse upon blasting, easily leading to surrounding rock instability and affecting construction safety and progress. Therefore, blasting operations for underground engineering on islands and reefs must meet three requirements: first, possessing localized intelligent construction capabilities, achieving complete independence from cloud computing power and local construction plan decision-making to adapt to the limited communication conditions on islands and reefs; second, achieving rapid construction and precise collapse prevention, fully adapting to the characteristics of porous reef limestone; and third, significantly reducing the construction cycle, minimizing operating time and costs.
[0003] However, existing technologies and research findings have significant shortcomings. First, there is a serious disconnect between offline blasting design and real-time control. Current technologies rely on offline design based on preliminary surveys, making it difficult to adapt to changes in the scheme caused by the heterogeneity of reef limestone, resulting in significant deviations between the design scheme and actual working conditions. Second, existing schemes lack effective utilization of the rock mass's spectral characteristics. Current intelligent blasting designs primarily focus on excavation efficiency and forming quality, failing to consider the rock mass's own acoustic spectral response as a design input. This is precisely a key characteristic that distinguishes reef limestone from conventional rock masses. The porous structure of reef limestone exhibits selective and strong absorption or diffusion effects on specific frequency bands of energy. Ignoring this characteristic can easily lead to energy dissipation, insufficient fragmentation, or damage to the surrounding rock. Furthermore, mainstream intelligent blasting design and control platforms often rely on cloud-based big data and public network communication, while network conditions on islands and reefs are often unstable, and engineering data requires confidentiality. Some offline design methods rely on simple empirical formulas and lack machine learning capabilities, making them difficult to adapt to the complex working conditions of highly heterogeneous reef limestone formations. The measured data after each blasting is not effectively fed back into the design of the next cycle, resulting in the accumulation of errors.
[0004] Therefore, there is an urgent need to develop a rapid construction method for underground engineering on islands and reefs to solve the above problems. Summary of the Invention
[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:
[0006] A rapid construction method for underground engineering on islands and reefs includes:
[0007] S1. Collect blasting construction data and invert to obtain the rock mass spectrum attenuation model;
[0008] S2. Using the rock mass spectral attenuation model obtained in step S1 as the physical constraint for energy propagation, construct an energy functional with spectral attenuation as the weight, and solve for the charge energy density distribution that precisely matches the heterogeneous absorption characteristics of the rock mass, thereby determining the charge parameters of each borehole during blasting.
[0009] S3. Calculate the theoretical predicted spectrum at each monitoring point, and collect the measured spectrum data after blasting construction. Compare the theoretical predicted spectrum with the measured spectrum data, and update the rock mass spectrum attenuation model based on the comparison results.
[0010] Furthermore, in step S1, when collecting blasting construction data, specifically:
[0011] A triaxial accelerometer was installed at the drill bit to record the vibration waveform during the drilling process, and the spectral features at different depths were extracted by short-time Fourier transform.
[0012] Furthermore, by placing a transmitter and a receiver array in two adjacent boreholes respectively, broadband acoustic pulses are emitted to obtain the travel time and amplitude attenuation on multiple ray paths.
[0013] Furthermore, in step S1, the collected blasting construction data is represented as d∈R M The rock mass parameter field to be reconstructed is represented as m∈R N The observation process can then be represented as:
[0014] ;
[0015] Where G is the observation matrix, For noise, a Bayesian compressed sensing framework is used to solve the problem, and the posterior probability distribution is:
[0016] ;
[0017] Let be the likelihood function, and treat the noise as a Gaussian distribution, then Represented as:
[0018] ;
[0019] in, Let be the variance of the Gaussian distribution;
[0020] As the prior distribution, using total variational regularization, it is expressed as:
[0021] ;
[0022] in, Used to control the weight of prior information Let be the total variation, and we have:
[0023] ;
[0024] in, Represents the rock mass parameter field The i-th term in , , gradients at , , Component of direction;
[0025] Sampling was performed using the Markov chain Monte Carlo method to obtain the maximum a posteriori estimate of the rock mass parameter field and its uncertainty interval. Simultaneously, a rock mass spectral attenuation model was established based on acoustic attenuation data.
[0026] ;
[0027] in, Indicates frequency, Indicates spatial location, The attenuation coefficient at the reference frequency, This is the frequency index related to the pore structure.
[0028] Furthermore, in step S2, when constructing the energy functional with spectral attenuation as the weight, specifically:
[0029] Let the blasting area be The boundary is Let the energy density distribution of the charge be E(x), then the constructed energy functional is expressed as:
[0030] ;
[0031] Where J(E) is a functional of E(x), For the target energy density, Let E(x) be the gradient. It is a volume infinitesimal element. Let g(E) be a infinitesimal area element, and let E be the area element. 2 Or |E|, where γ is the penalty weight. The spectral diffusion coefficient is... This is the spectrum demand coefficient;
[0032] Spectral diffusion coefficient Represented as:
[0033] ;
[0034] Among them, f maxf min The maximum and minimum values of the effective blasting frequency band, For weighted functions, Obtained from the rock mass spectral attenuation model in step S1;
[0035] Spectrum Demand Coefficient Represented as:
[0036] ;
[0037] in, The main frequency of the explosive;
[0038] Target energy density Represented as:
[0039] ;
[0040] Where K IC For the fracture toughness of reef limestone, d 50 The median particle size is the target size of the fragmented material.
[0041] Furthermore, in step S2, after constructing the energy functional with spectral attenuation as the weight, the first variation of the functional J(E) is set to 0, resulting in the Euler-Lagrange equation:
[0042] in ;
[0043] The boundary conditions are:
[0044] on ;
[0045] The finite element method is used for discretization. The region Ω is divided into tetrahedral meshes, with each node corresponding to an energy density value. The optimal energy density E is obtained by solving the linear equations. * (x);
[0046] According to E * (x) Determine the charging parameters for each borehole, assuming the borehole position is x. i E in a localized area around the hole * Integrate (x) to obtain the total energy that the orifice should bear:
[0047] ;
[0048] Where V i The area of influence of this borehole is determined by the borehole mesh parameters and the explosive heat e. v It is possible to obtain the charge volume V exp,i =Q i / ev This allows us to determine the diameter of the cartridge and the length of the charge.
[0049] Furthermore, in step S3, when calculating the theoretical predicted spectrum at each monitoring point, the optimal energy density obtained in step S2 is used. And the rock mass spectral attenuation model obtained in step S1 Calculate the theoretical predicted spectrum at each monitoring point. :
[0050] ;
[0051] in, For the location of the j-th monitoring point, select exploration boreholes or specially deployed monitoring boreholes around the blasting area as monitoring points. According to The source spectrum derived from the spectral characteristics of the explosive, The term represents the cumulative attenuation along the propagation path, and the integration path l is from the source location to the j-th monitoring point. .
[0052] Furthermore, in step S3, when collecting the measured spectrum data after the blasting operation, broadband vibration sensors are pre-installed at the monitoring points to collect the post-blast spectrum, completely recording the vibration waveform within at least 2 seconds after detonation. The recorded signal is then subjected to a short-time Fourier transform to extract the actual post-blast vibration spectrum. .
[0053] Furthermore, in step S3, when comparing the theoretically predicted spectrum with the measured spectrum data, the spectrum residual function is defined as follows:
[0054] ;
[0055] When the residual exceeds the threshold, an inverse problem is established using the parameters of the rock mass spectral attenuation model as optimization variables:
[0056] ;
[0057] Solving the above equation yields the correction amount for the attenuation coefficient. Correction amount for frequency index The updated rock mass spectral attenuation model is as follows:
[0058] ;
[0059] Updated rock mass spectral attenuation model Replace the original model in step S1 and re-execute step S2 to obtain the corrected charge parameters for the blasting design of the next cycle.
[0060] Compared with existing technologies, the rapid construction method for underground engineering on islands and reefs provided by this invention directly drives the blasting energy design by utilizing the spectral attenuation characteristics of rock mass, and achieves dynamic closed-loop adjustment through spectral feedback. This method is applicable to coastal island and reef environments, adapts to the geological characteristics of porous reef limestone, and can achieve precise adaptation to porous reef limestone, thereby achieving rapid and precise construction of underground spaces in reef limestone. Attached Figure Description
[0061] Figure 1 A flowchart illustrating a rapid construction method for underground engineering on islands and reefs provided by the present invention;
[0062] Figure 2 This is a schematic diagram of the layout of the blasting hole network in a specific case. Detailed Implementation
[0063] To make the technical means, creative features, objectives and effects of this invention easier to understand, the following description, in conjunction with the accompanying drawings and specific embodiments, further explains how this invention is implemented.
[0064] Reference Figure 1 As shown, the present invention provides a rapid construction method for underground engineering on islands and reefs, comprising the following steps:
[0065] S1. Collect blasting construction data and invert to obtain the rock mass spectrum attenuation model.
[0066] S2. Using the rock mass spectral attenuation model obtained in step S1 as the physical constraint for energy propagation, construct an energy functional with spectral attenuation as the weight, and solve for the charge energy density distribution that precisely matches the heterogeneous absorption characteristics of the rock mass, thereby determining the charge parameters of each borehole during blasting.
[0067] S3. Calculate the theoretical predicted spectrum at each monitoring point, and collect the measured spectrum data after blasting construction. Compare the theoretical predicted spectrum with the measured spectrum data, and update the rock mass spectrum attenuation model based on the comparison results.
[0068] In one specific embodiment, in step S1:
[0069] When collecting blasting operation data, a triaxial accelerometer is installed at the drill bit with a sampling rate ≥10kHz to record the vibration waveforms during drilling. Short-time Fourier transform is used to extract the spectral characteristics at different depths, obtaining the amplitude spectrum as a function of depth. Furthermore, a transmitter and receiver array are placed in two adjacent boreholes to emit broadband acoustic pulses (10Hz-10kHz), obtaining the travel time and amplitude attenuation along multiple ray paths. All data acquisition and subsequent processing can be completed on a local edge node without uploading to the cloud.
[0070] Next, the collected blasting construction data will be represented as d∈R M The rock mass parameter field to be reconstructed is represented as m∈R N (Including P-wave velocity, S-wave velocity, density, quality factor, etc.), the observation process can be expressed as:
[0071] ;
[0072] Where G is the observation matrix, For noise, a Bayesian compressed sensing framework is used to solve the problem, and the posterior probability distribution is:
[0073] ;
[0074] Let be the likelihood function, and treat the noise as a Gaussian distribution, then Represented as:
[0075] ;
[0076] in, Let be the variance of the Gaussian distribution;
[0077] For the prior distribution, total variational regularization is used to preserve the boundary characteristics of the geological body, and it is expressed as:
[0078] ;
[0079] in, Used to control the weight of prior information Let be the total variation, and we have:
[0080] ;
[0081] in, Represents the rock mass parameter field The i-th term in , , gradients at , , The directional component. When taking a larger value, the total variation The penalty for probability is stronger, the inversion results are smoother and more uniform, and the boundaries of the inverted geological bodies may be smoothed and blurred. When taking a smaller value, the total variation The penalty is weaker, and the inversion results rely more on actual observation data, thus better preserving the true boundaries of geological bodies.
[0082] Sampling was performed using the Markov chain Monte Carlo method to obtain the maximum a posteriori estimate of the rock mass parameter field and its uncertainty interval. Simultaneously, a rock mass spectral attenuation model was established based on acoustic attenuation data.
[0083] ;
[0084] in, Indicates frequency, Indicates spatial location, The attenuation coefficient at the reference frequency, The frequency index is related to the pore structure. This model quantitatively characterizes the rock mass's ability to absorb and attenuate energy of any frequency, and will be directly used as the energy design input condition in the subsequent step S2.
[0085] As can be seen, in step S1, in view of the practical constraints that make it impossible to conduct intensive borehole exploration in island and reef construction, the present invention adopts a Bayesian compressed sensing framework to jointly invert the drilling vibration signal and cross-hole acoustic data. Through total variational regularization processing, the rock mass spectrum attenuation model can be obtained even with only a small number of boreholes, providing reliable geological input for subsequent blasting design.
[0086] In step S2, specifically:
[0087] When constructing the energy functional with spectral attenuation as the weight, let the blasting region be... The boundary is (Corresponding to the wellbore profile), the goal of blasting is to fully fracture the rock mass within the target area while controlling wellbore damage; defining the charge energy density distribution as E(x), the constructed energy functional is expressed as:
[0088] ;
[0089] Where J(E) is a functional of E(x), For the target energy density, Let E(x) be the gradient. It is a volume infinitesimal element. Let g(E) be a infinitesimal area element, and let E be the area element. 2 Alternatively, |E|, where γ is the penalty weight, used to ensure controllable wellbore damage and prevent gravity-coupled instability in vertical or inclined shafts. The spectral diffusion coefficient is... This is the spectrum demand coefficient.
[0090] Spectral diffusion coefficient Represented as:
[0091] ;
[0092] Among them, f max fmin The maximum and minimum values of the effective blasting frequency band, For weighted functions, It is obtained from the rock mass spectral attenuation model in step S1. When the value is small, a large energy gradient is allowed; conversely, when the value is large, a gentler energy distribution is promoted.
[0093] Spectrum Demand Coefficient Represented as:
[0094] ;
[0095] in, The frequency of the explosive is the dominant frequency. The greater the frequency attenuation, the... The larger the value, the stronger the approach to the target energy, ensuring that the high absorption zone receives sufficient energy.
[0096] Target energy density Represented as:
[0097] ;
[0098] Where K IC For the fracture toughness of reef limestone, d 50 The median particle size is the target fragment size. This is determined by setting d... 50 It can precisely control the size of the blasted pieces, thereby regulating the crushing effect and signal characteristics.
[0099] After constructing an energy functional with spectral attenuation as the weight, setting the first variation of the functional J(E) to 0, we obtain the Euler-Lagrange equation:
[0100] in ;
[0101] The boundary conditions are:
[0102] on ;
[0103] The finite element method is used for discretization. The region Ω is divided into tetrahedral meshes, with each node corresponding to an energy density value. The stiffness matrix is assembled, and the optimal energy density E is obtained by solving the linear equations. * (x).
[0104] According to E * (x) Determine the charging parameters for each borehole, assuming the borehole position is x. i E in a localized area around the hole * Integrate (x) to obtain the total energy that the orifice should bear:
[0105] ;
[0106] Where V i The area of influence of this borehole is determined by the borehole mesh parameters and the explosive heat e. v It is possible to obtain the charge volume V exp,i =Q i / e v This allows us to determine the diameter of the cartridge and the length of the charge.
[0107] As can be seen, this invention establishes a technical path of "spectral attenuation-guided energy design". Through mathematical transformation, the rock mass spectral attenuation model obtained from geological inversion is directly mapped to the spectral diffusion coefficient and spectral demand coefficient in the energy functional, making the blasting energy distribution not only a function of spatial location, but also a function of the rock mass spectral response. Energy is precisely concentrated in the high attenuation zone, and energy is automatically smoothed in the low attenuation zone, fundamentally solving the energy mismatch problem caused by the heterogeneous absorption characteristics of reef limestone.
[0108] In step S3, specifically:
[0109] When calculating the theoretical predicted spectrum at each monitoring point, the optimal energy density obtained in step S2 is used. And the rock mass spectral attenuation model obtained in step S1 Calculate the theoretical predicted spectrum at each monitoring point. :
[0110] ;
[0111] in, For the location of the j-th monitoring point, select exploration boreholes or specially deployed monitoring boreholes around the blasting area as monitoring points. According to The source spectrum derived from the spectral characteristics of the explosive, The term represents the cumulative attenuation along the propagation path, and the integration path l is from the source location to the j-th monitoring point. .
[0112] When collecting the measured spectrum data after blasting, broadband vibration sensors are pre-installed at the monitoring points to collect the post-blast spectrum data. The sampling rate is no less than 20kHz, and the vibration waveform within at least 2 seconds after detonation is recorded completely. The recorded signal is then subjected to a short-time Fourier transform to extract the actual post-blast vibration spectrum. .
[0113] When comparing the theoretically predicted spectrum with the measured spectrum data, the spectral residual function is defined as follows:
[0114] ;
[0115] When the residual exceeds the threshold, an inverse problem is established using the parameters of the rock mass spectral attenuation model as optimization variables:
[0116] ;
[0117] Solving the above equation yields the correction amount for the attenuation coefficient. Correction amount for frequency index The updated rock mass spectral attenuation model is as follows:
[0118] ;
[0119] Updated rock mass spectral attenuation model Replace the original model in step S1 and re-execute step S2 to obtain the corrected charge parameters for the blasting design of the next cycle.
[0120] In a specific case, the layout of the shaft blasting hole mesh is as follows: Figure 2 As shown:
[0121] (1) Stress conditions and boundary settings
[0122] Figure 2 middle, This represents the initial stress state of the rock mass at the depth of the shaft. In step S2, the penalty weight... The value needs to be based on The magnitude is determined comprehensively; the higher the stress level, the greater the stress. The value is increased accordingly to ensure the reliability of the wellbore energy density constraint. Figure 2 The "non-reflective boundary" refers to the artificial boundary condition used in the numerical simulation, which is used to absorb outwardly propagating stress waves, eliminate the interference of boundary reflections on the solution results, and ensure the optimal energy density obtained by solving the Euler-Lagrange equation using the finite element method in step S2. The accuracy.
[0123] (2) Basis for the classification and layout of blast holes
[0124] The boreholes on the vertical shaft cross-section are divided into three categories according to their functions. The spacing and charge amount of each type of borehole are determined by solving the optimal energy density in step S2. The total energy borne by a single hole obtained after integration Sure:
[0125] The cut-out holes are located in the central region of the cross-section and are detonated first, creating a free surface for subsequent boreholes. Their arrangement corresponds to the aforementioned attenuation coefficient. Larger, spectrum demand coefficient A higher position. According to the formula in step S2. Integral calculations show that a single aperture in this region carries a large amount of energy, while the aperture spacing is small, reflecting the design principle of energy enhancement in the high attenuation region.
[0126] Auxiliary holes are distributed in the annular transition area between the cut-out holes and the surrounding holes. Their spacing and charge amount are determined according to... The spatial gradient change from high-value regions to low-value regions is determined by the spectral diffusion coefficient. Smooth constraints and row-by-row adjustments ensure that the energy borne by a single hole falls between that of the slotted hole and the surrounding holes, achieving a smooth transition in energy distribution.
[0127] The peripheral holes are arranged along the inner side of the vertical shaft design outline, and their parameters are determined by the boundary penalty term in step S2. Constraints. Boundary conditions according to the Euler-Lagrange equations. After solving, the energy density of the boundary nodes is limited to a set threshold, which determines that the energy borne by a single hole is relatively small, so as to control over-excavation and under-excavation and protect the integrity of the surrounding rock.
[0128] (3) Monitoring point layout and feedback parameter adjustment
[0129] Figure 2 Monitoring points were set up in exploration holes at a certain distance from the blasting zone around the shaft, and broadband vibration sensors were installed. After blasting, the vibration waveform was recorded completely according to the requirements of step S3, and the measured spectrum was extracted by short-time Fourier transform. At the same time, using the results obtained in step S2 And the rock mass spectral attenuation model in step S1 Calculate the theoretical predicted spectrum for each monitoring point according to the formula in step S3. The residuals are obtained by comparing the two spectra. If the threshold is exceeded, the attenuation model correction procedure will be triggered, and the updated... Feedback is sent to step S1, and step S2 is executed again to design the blasting for the next cycle.
[0130] As can be seen, this invention establishes a closed-loop optimization mechanism of "spectral feedback dynamic parameter adjustment". By inverting the residual between the measured spectrum and the predicted spectrum after blasting, the rock mass spectrum attenuation model is iteratively corrected, so that the model can autonomously approach the real state with the construction cycle. This overcomes the inherent error of the static model in traditional blasting design, realizes self-learning blasting with successive optimization, and forms a closed-loop iteration of "inversion → design → construction → monitoring → feedback → correction".
[0131] In summary, the rapid construction method for underground engineering on islands and reefs provided by this invention directly drives the blasting energy design by utilizing the spectral attenuation characteristics of rock mass and achieves dynamic closed-loop adjustment through spectral feedback. This method is applicable to coastal island and reef environments, adapts to the geological characteristics of porous reef limestone, and can achieve precise adaptation to porous reef limestone, thereby enabling rapid and precise construction of underground spaces in reef limestone.
[0132] Finally, it should be noted that the above description is only an embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.
Claims
1. A rapid construction method for underground engineering on islands and reefs, characterized in that, Includes the following steps: S1. Collect blasting construction data and invert the rock mass spectrum attenuation model; S2. Using the rock mass spectral attenuation model obtained in step S1 as the physical constraint for energy propagation, construct an energy functional with spectral attenuation as the weight, and solve for the charge energy density distribution that precisely matches the heterogeneous absorption characteristics of the rock mass, thereby determining the charge parameters of each borehole during blasting. S3. Calculate the theoretical predicted spectrum at each monitoring point, and collect the measured spectrum data after blasting construction. Compare the theoretical predicted spectrum with the measured spectrum data, and update the rock mass spectrum attenuation model based on the comparison results.
2. The rapid construction method for underground engineering on islands and reefs according to claim 1, characterized in that, In step S1, when collecting blasting construction data, specifically: A triaxial accelerometer was installed at the drill bit to record the vibration waveform during the drilling process, and the spectral features at different depths were extracted by short-time Fourier transform. Furthermore, by placing a transmitter and a receiver array in two adjacent boreholes respectively, broadband acoustic pulses are emitted to obtain the travel time and amplitude attenuation on multiple ray paths.
3. The rapid construction method for underground engineering on islands and reefs according to claim 2, characterized in that, In step S1, the collected blasting construction data is represented as d∈R M The rock mass parameter field to be reconstructed is represented as m∈R N The observation process can then be represented as: ； Where G is the observation matrix, For noise, a Bayesian compressed sensing framework is used to solve the problem, and the posterior probability distribution is: ； Let be the likelihood function, and treat the noise as a Gaussian distribution, then Represented as: ； in, Let be the variance of the Gaussian distribution; As the prior distribution, using total variational regularization, it is expressed as: ； in, Used to control the weight of prior information Let be the total variation, and we have: ； in, Represents the rock mass parameter field The i-th term in , , gradients at , , Component of direction; Sampling was performed using the Markov chain Monte Carlo method to obtain the maximum a posteriori estimate of the rock mass parameter field and its uncertainty interval. Simultaneously, a rock mass spectral attenuation model was established based on acoustic attenuation data. ； in, Indicates frequency, Indicates spatial location, The attenuation coefficient at the reference frequency, This is the frequency index related to the pore structure.
4. The rapid construction method for underground engineering on islands and reefs according to claim 3, characterized in that, In step S2, when constructing the energy functional with spectral attenuation as the weight, specifically: Let the blasting area be The boundary is Let the energy density distribution of the charge be E(x), then the constructed energy functional is expressed as: ； Where J(E) is a functional of E(x), For the target energy density, Let E(x) be the gradient. It is a volume infinitesimal element. Let g(E) be a infinitesimal area element, and let E be the area element. 2 Or |E|, where γ is the penalty weight. The spectral diffusion coefficient is... This is the spectrum demand coefficient; Spectral diffusion coefficient Represented as: ； Among them, f max f min The maximum and minimum values of the effective blasting frequency band, For weighted functions, Obtained from the rock mass spectral attenuation model in step S1; Spectrum Demand Coefficient Represented as: ； in, The main frequency of the explosive; Target energy density Represented as: ； Where K IC For the fracture toughness of reef limestone, d 50 The median particle size is the target fragmentation size.
5. The rapid construction method for underground engineering on islands and reefs according to claim 4, characterized in that, In step S2, after constructing the energy functional with spectral attenuation as the weight, the first variation of the functional J(E) is set to 0, resulting in the Euler-Lagrange equation: in ; The boundary conditions are: on ; The finite element method is used for discretization. The region Ω is divided into tetrahedral meshes, with each node corresponding to an energy density value. The optimal energy density E is obtained by solving the linear equations. * (x); According to E * (x) Determine the charging parameters for each borehole, assuming the borehole position is x. i E in a localized area around the hole * Integrate (x) to obtain the total energy that the orifice should bear: ； Where V i The area of influence of this borehole is determined by the borehole mesh parameters and the explosive heat e. v It is possible to obtain the charge volume V exp,i =Q i / e v This allows us to determine the diameter of the cartridge and the length of the charge.
6. The rapid construction method for underground engineering on islands and reefs according to claim 5, characterized in that, In step S3, when calculating the theoretical predicted spectrum at each monitoring point, the optimal energy density obtained in step S2 is used. And the rock mass spectral attenuation model obtained in step S1 Calculate the theoretical predicted spectrum at each monitoring point. : ； in, For the location of the j-th monitoring point, select exploration boreholes or specially deployed monitoring boreholes around the blasting area as monitoring points. According to The source spectrum derived from the spectral characteristics of the explosive, The term represents the cumulative attenuation along the propagation path, and the integration path l is from the source location to the j-th monitoring point. .
7. The rapid construction method for underground engineering on islands and reefs according to claim 6, characterized in that, In step S3, when collecting the measured spectrum data after blasting, broadband vibration sensors are pre-installed at the monitoring points to collect the post-blast spectrum, completely recording the vibration waveform within at least 2 seconds after detonation. The recorded signal is then subjected to a short-time Fourier transform to extract the actual post-blast vibration spectrum. .
8. The rapid construction method for underground engineering on islands and reefs according to claim 7, characterized in that, In step S3, when comparing the theoretically predicted spectrum with the measured spectrum data, the spectral residual function is defined: ； When the residual exceeds the threshold, an inverse problem is established using the parameters of the rock mass spectral attenuation model as optimization variables: ； Solving the above equation yields the correction amount for the attenuation coefficient. Correction amount for frequency index The updated rock mass spectral attenuation model is as follows: ； Updated rock mass spectral attenuation model Replace the original model in step S1 and re-execute step S2 to obtain the corrected charge parameters for the blasting design of the next cycle.