Method and system for detecting seepage of earth-rock dam based on spectral induced polarization three-dimensional modeling

Abstract

The present application belongs to the technical field of earth-rock dam leakage detection, in order to solve the problem of inaccurate earth-rock dam leakage detection, a method and system for detecting earth-rock dam leakage based on spectral induced polarization three-dimensional modeling are proposed, a three-dimensional gridded electrode array is laid out, and full-dam complex impedance spectrum data is obtained through multi-frequency induced polarization measurement; a three-dimensional finite element model of the earth-rock dam is established, three-dimensional joint inversion and anisotropic spatial interpolation are performed on the complex impedance spectrum data, and a three-dimensional voxel model containing conductivity and three-dimensional normalized polarization rate is obtained; based on the rock physics conversion model of dynamic double electric layer theory, the three-dimensional spatial distribution of water content, cation exchange capacity and permeability is obtained voxel by voxel; a multi-dimensional leakage comprehensive index is constructed based on resistivity, polarization rate, water content, permeability and cation exchange capacity, candidate leakage voxels are marked according to the multi-dimensional leakage comprehensive index, and then three-dimensional connectivity analysis is performed to obtain the earth-rock dam leakage detection result, thereby improving the leakage detection accuracy.

Description

Technical Field

[0001] This invention belongs to the technical field of seepage detection for earth-rock dams, and particularly relates to a method and system for seepage detection of earth-rock dams based on spectral excitation polarization three-dimensional modeling. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] Earth-rock dams, as an economical and adaptable dam type, account for a large proportion of water conservancy projects. However, due to the heterogeneity of materials, the difficulty in controlling construction quality, long-term aging during operation, and the influence of environmental factors (earthquakes, rainstorms, freeze-thaw cycles, etc.), seepage hazards in the dam body or foundation are a common problem. The formation and development of seepage channels is one of the most dangerous hidden dangers of earth-rock dams. It not only leads to the loss of reservoir water resources, but also causes internal erosion, piping, contact scouring, and even dam failure, posing a serious threat to the safety of people and property downstream and the ecological environment.

[0004] Currently, geophysical exploration methods are mainly used to detect potential seepage hazards in earth-rock dams. However, while high-density electrical resistivity tomography (ERT) and induced polarization methods detect seepage through resistivity or polarizability anomalies, non-seepage factors such as high-humidity clay lenses and localized metallic debris can also create similar low-resistivity anomalies, leading to a high false alarm rate. Furthermore, existing resistivity tomography (ERT) methods mostly employ two-dimensional profile measurements, assuming that the underground medium is uniform and constant in the direction perpendicular to the measurement line. When the seepage channel is biased to one side of the measurement line, the inversion results will incorrectly drag it into the profile, resulting in distorted localization. Summary of the Invention

[0005] To overcome the shortcomings of the prior art, this invention provides a method and system for detecting seepage in earth-rock dams based on spectral excitation polarization three-dimensional modeling, which enables three-dimensional quantitative analysis of seepage in earth-rock dams and improves the accuracy of seepage detection.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: In a first aspect, the present invention provides a method for detecting seepage in earth-rock dams based on spectral excitation polarization three-dimensional modeling, comprising: Three-dimensional topographic data of earth-rock dams were acquired and a three-dimensional gridded electrode array was deployed. Complex impedance spectrum data of the entire dam area were obtained through multi-frequency excitation polarization measurement. A three-dimensional finite element model of an earth-rock dam was established based on three-dimensional topographic data of the earth-rock dam. Three-dimensional joint inversion and anisotropic spatial interpolation were performed on the complex impedance spectrum data to obtain a three-dimensional voxel model containing conductivity and three-dimensional normalized polarizability. Based on the dynamic double-layer theory, a rock physical transformation model was used to obtain the three-dimensional spatial distribution of water content, cation exchange capacity and permeability on a voxel-by-voxel basis. A multidimensional leakage comprehensive index was constructed based on resistivity, polarizability, water content, permeability and cation exchange capacity. Candidate leakage voxels were labeled according to the multidimensional leakage comprehensive index, and three-dimensional connectivity analysis was performed on the candidate voxels to obtain the leakage detection results of earth-rock dam.

[0007] Secondly, the present invention provides a seepage detection system for earth-rock dams based on spectral excitation polarization three-dimensional modeling, characterized in that it includes: The acquisition module is configured to: acquire three-dimensional topographic data of the earth-rock dam and deploy a three-dimensional gridded electrode array, and acquire complex impedance spectrum data of the entire dam area through multi-frequency excitation polarization measurement; The modeling module is configured to: establish a three-dimensional finite element model of the earth-rock dam based on the three-dimensional topographic data of the earth-rock dam, perform three-dimensional joint inversion and anisotropic spatial interpolation on the complex impedance spectrum data, and obtain a three-dimensional voxel model containing conductivity and three-dimensional normalized polarizability. The calculation module is configured to: use a rock physical transformation model based on the dynamic double-layer theory to obtain the three-dimensional spatial distribution of water content, cation exchange capacity and permeability on a voxel-by-voxel basis; The permeability detection module is configured to: construct a multidimensional permeability comprehensive index based on resistivity, polarizability, water content, permeability and cation exchange capacity; label candidate permeable voxels according to the multidimensional permeability comprehensive index; and perform three-dimensional connectivity analysis on the candidate voxels to obtain the permeability detection results of the earth-rock dam.

[0008] Thirdly, the present invention provides an electronic device including a memory and a processor, and computer instructions stored in the memory and running on the processor, wherein the computer instructions, when executed by the processor, perform the method described in the first aspect.

[0009] Fourthly, the present invention provides a computer-readable storage medium for storing computer instructions, which, when executed by a processor, perform the method described in the first aspect.

[0010] Fifthly, the present invention provides a computer program product, including a computer program that, when executed by a processor, implements the method described in the first aspect.

[0011] The above one or more technical solutions have the following beneficial effects: In this invention, a three-dimensional finite element model of an earth-rock dam is established. Three-dimensional joint inversion and anisotropic spatial interpolation are performed on complex impedance spectral data to obtain a three-dimensional voxel model including conductivity and three-dimensional normalized polarizability. Based on a rock physical transformation model using dynamic double-layer theory, water content, cation exchange capacity, and permeability are calculated voxel by voxel. A multi-dimensional leakage comprehensive index is constructed based on resistivity, polarizability, water content, permeability, and cation exchange capacity to achieve leakage detection of the earth-rock dam. This invention enables three-dimensional quantitative analysis of leakage in earth-rock dams, improving the accuracy of leakage detection.

[0012] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0013] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0014] Figure 1 This is a flowchart of the seepage detection method for earth-rock dams based on spectral excitation polarization three-dimensional modeling in this embodiment of the present disclosure; Figure 2 This is a schematic diagram of oblique photogrammetry modeling, point cloud, and 3D meshed electrode array layout in an embodiment of this disclosure; wherein, (a) is an oblique photogrammetry modeling diagram; (b) is a point cloud diagram; and (c) is a 3D meshed electrode array layout diagram. Figure 3 The diagram below shows the true three-dimensional joint inversion results in the embodiments of this disclosure; wherein, (a) is a diagram of the true three-dimensional inversion results of conductivity; and (b) is a diagram of the true three-dimensional inversion results of imaginary conductivity. Figure 4 The following are schematic diagrams of the three-dimensional volume of electrical conductivity after physical transformation of rock and the two-dimensional cross-section of electrical conductivity along the parallel dam axis in the embodiments of this disclosure, wherein (a) is a schematic diagram of the three-dimensional volume of electrical conductivity and (b) is a schematic diagram of the two-dimensional cross-section of electrical conductivity along the parallel dam axis. Figure 5 The following are schematic diagrams of the three-dimensional volume of the imaginary part conductivity of the rock physical transformation parameter and the two-dimensional cross-section along the parallel dam axis in the embodiments of this disclosure, wherein (a) is a schematic diagram of the three-dimensional volume of the imaginary part conductivity, and (b) is a schematic diagram of the two-dimensional cross-section of the imaginary part conductivity along the parallel dam axis. Figure 6 The following are schematic diagrams of the three-dimensional volume of water content after physical transformation of rock and the two-dimensional cross-section of water content along the parallel dam axis in the embodiments of this disclosure, wherein (a) is a schematic diagram of the three-dimensional volume of water content and (b) is a schematic diagram of the two-dimensional cross-section of water content along the parallel dam axis. Figure 7The following are schematic diagrams of the three-dimensional volume of permeability and the two-dimensional cross-section of permeability along the parallel dam axis in the embodiments of this disclosure, wherein (a) is a schematic diagram of the three-dimensional volume of permeability and (b) is a schematic diagram of the two-dimensional cross-section of permeability along the parallel dam axis. Figure 8 The following are schematic diagrams of the three-dimensional volume and two-dimensional cross-section of the cation exchange capacity parameter after physical transformation of rocks in the embodiments of this disclosure, wherein (a) is a schematic diagram of the three-dimensional volume of cation exchange capacity, and (b) is a schematic diagram of the two-dimensional cross-section of cation exchange capacity along the parallel dam axis. Figure 9 The following are schematic diagrams of the three-dimensional volume of polarizability after rock physical transformation and the two-dimensional cross-section of the parallel dam axis in the embodiments of this disclosure, wherein (a) is a schematic diagram of the three-dimensional volume of polarizability and (b) is a schematic diagram of the two-dimensional cross-section of polarizability along the parallel dam axis. Figure 10 The following are schematic diagrams of the three-dimensional volume of the normalized polarizability parameter after rock physical transformation and the two-dimensional cross-section along the parallel dam axis in the embodiments of this disclosure, wherein (a) is a schematic diagram of the three-dimensional volume of normalized polarizability, and (b) is a schematic diagram of the two-dimensional cross-section of normalized polarizability along the parallel dam axis. Figure 11 This is a schematic diagram illustrating the verification results of the natural potential method in the embodiments of this disclosure; Figure 12 This is a schematic diagram showing the three-dimensional shape and volume output of the dam seepage channel in an embodiment of this disclosure. Detailed Implementation

[0015] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0016] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations of the present invention.

[0017] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0018] Example 1 like Figure 1 As shown, this embodiment discloses a method for detecting seepage in earth-rock dams based on spectral excitation polarization three-dimensional modeling, including: Three-dimensional topographic data of earth-rock dams were acquired and a three-dimensional gridded electrode array was deployed. Complex impedance spectrum data of the entire dam area were obtained through multi-frequency excitation polarization measurement. A three-dimensional finite element model of an earth-rock dam was established based on three-dimensional topographic data of the earth-rock dam. Three-dimensional joint inversion and anisotropic spatial interpolation were performed on the complex impedance spectrum data to obtain a three-dimensional voxel model containing conductivity and three-dimensional normalized polarizability. Based on the dynamic double-layer theory, a rock physical transformation model was used to obtain the three-dimensional spatial distribution of water content, cation exchange capacity and permeability on a voxel-by-voxel basis. A multidimensional leakage comprehensive index was constructed based on resistivity, polarizability, water content, permeability and cation exchange capacity. Candidate leakage voxels were labeled according to the multidimensional leakage comprehensive index, and three-dimensional connectivity analysis was performed on the candidate voxels to obtain the leakage detection results of earth-rock dam.

[0019] This embodiment establishes a high-precision terrain model by fusing UAV aerial surveying with RTK, ensuring the accuracy of electrode placement and terrain constraints inversion. It employs a three-dimensional mesh array and full three-dimensional voxel inversion, distinct from traditional 2.5D interpolation methods, to achieve true three-dimensional imaging of parameters such as real conductivity, imaginary conductivity, normalized polarizability, sensitivity index, water content, cation exchange capacity, and permeability, significantly improving spatial continuity and positioning accuracy. Based on a rock physical transformation model using dynamic double-layer theory, it originally developed a multi-frequency fusion CEC estimation formula, a partitioned weighted correction field, and a permeability formula with correction terms. Geophysical parameters are directly converted into key engineering parameters, resulting in clear physical meanings and strong cross-regional applicability. A six-dimensional multidimensional leakage comprehensive index is constructed, including resistivity, normalized polarizability, imaginary conductivity, water content, permeability, and cation exchange capacity, to distinguish leakage channels from clay lenses from a physical mechanism perspective, significantly reducing the misjudgment rate. A sensitivity index is introduced to assess the reliability of polarization signals, and leakage channels are automatically extracted by combining three-dimensional connectivity analysis. The channel volume, spatial boundary, geometric shape, main seepage direction, importance index, and fuzzy confidence level are quantitatively output, providing a direct basis for grouting volume calculation and risk level classification.

[0020] The following is a detailed description of the seepage detection method for earth-rock dams based on spectral excitation polarization three-dimensional modeling proposed in this embodiment: Step 1: Acquire three-dimensional topographic data of the earth-rock dam and deploy a three-dimensional gridded electrode array. Obtain complex impedance spectrum data of the entire dam area through multi-frequency excitation polarization measurement.

[0021] Step 1 of this embodiment specifically includes: Step 11: Drone aerial photography 3D terrain modeling and measurement point coordinate extraction.

[0022] A drone equipped with a high-resolution camera was used to conduct oblique photogrammetry of the earth-rock dam body and surrounding area, collecting multi-angle image data (heading overlap ≥80%, lateral overlap ≥70%). A high-precision 3D reality model of the dam body was generated using 3D reconstruction software. This 3D reality model includes a digital surface model (DSM) and a reality texture model, with a planar resolution better than 5 cm.

[0023] The electrode survey lines are planned along the dam crest, upstream dam slope, and downstream dam slope on the 3D reality model, and the theoretical 3D coordinates of each electrode point are generated. The electrode deployment plan is pre-set in the UAV RTK system. Electrodes are then deployed in the field according to the survey lines. The actual planar coordinates of each electrode are automatically recorded by the ABEM instrument. Only one elevation measurement is needed at each electrode using GPS, with the elevation of the top survey line - the dam crest survey line set as the 0m Z-axis coordinate. The coordinates of the remaining measurement points are set as negative numbers of the elevation difference, thus obtaining the final accurate three-dimensional spatial coordinates of each electrode. Through least-squares fitting optimization, the final accurate three-dimensional spatial coordinates of each electrode are obtained: ; In the formula, The final optimized coordinates for the i-th electrode; Theoretical coordinates generated for UAV aerial survey models; These are the coordinates measured on-site using RTK. To fit the residuals, the root mean square error must be less than 5 cm.

[0024] Step 12: Acquisition of true three-dimensional multi-frequency excitation polarization data.

[0025] A three-dimensional gridded electrode array is deployed on the downstream slope (behind the dam) of the earth-rock dam: several measuring lines are laid out at equal intervals along the direction parallel to the dam axis. The spacing between the measuring lines is determined according to the width of the dam body and the detection accuracy requirements, usually 2~5 m; at the suspected seepage point location, several equidistant measuring lines are laid out on the left and right sides along the direction perpendicular to the dam axis to obtain information on the distribution of seepage channels in the direction perpendicular to the dam axis.

[0026] Since the upstream dam slope (front of the dam) is mostly composed of dry-laid stone or concrete revetment, making electrode insertion difficult, electrodes can be selectively installed or not installed on the upstream dam slope depending on the actual situation. All measuring line electrodes are aligned to form a grid, and the coordinates of each electrode are obtained in step S11. Let E be the number of electrodes in a single measurement profile, and a be the electrode spacing (unit: m). The number of measuring lines should be no less than 3. The dam height h and the electrode spacing should satisfy h < 0.2Ea (measuring lines parallel to the dam axis) to ensure that the detection depth covers the entire dam body.

[0027] A multi-frequency current transmitter is used to input pseudo-random waveform current with a frequency range of 0.01 Hz to 100 Hz to the power supply electrode. The frequency points are logarithmically uniformly distributed, and the number of... ≥5, effective value of supply current I0 = 2 A 5 A. The potential difference time series of each measuring electrode pair is synchronously acquired using a multi-channel receiver. Sampling rate ≥2400 Hz, with each power supply-measurement combination's acquisition time window containing at least 10 complete low-frequency cycles.

[0028] Time series of potential differences for each measurement electrode pair Perform a discrete Fourier transform to obtain each frequency. The complex potential difference below as follows: ; In the formula, For frequency The complex potential difference below; The amplitude; is the phase; i is the complex unit.

[0029] Complex impedance spectral data were extracted for each measuring point, and the apparent resistivity was calculated. and apparent polarization Calculated using the conventional excitation polarization formula, while retaining the real part. and the virtual part : ; ; ; In the formula, For frequency Lower complex impedance; is the effective value of the supply current; K is the device coefficient, determined by the geometric arrangement of the electrodes. It is the real part conductivity; It is the imaginary part of conductivity; It is apparent resistivity; It is the apparent polarizability.

[0030] Step 2: Based on the three-dimensional topographic data of the earth-rock dam, establish a three-dimensional finite element model of the earth-rock dam, perform three-dimensional joint inversion and anisotropic spatial interpolation on the complex impedance spectrum data, and obtain a three-dimensional voxel model including conductivity and three-dimensional normalized polarizability.

[0031] First, a three-dimensional finite element mesh corresponding to the actual dimensions of the dam body is established: the mesh is divided into N parts in the x-direction (dam axis). x Each unit is divided into N units in the y-direction (perpendicular to the dam axis). yEach unit is divided into N units in the z-direction (depth). z Each element has a thickness less than the minimum detection depth. The thickness of each subsequent layer increases by 10% with increasing depth, and the deepest layer contains the effective detection depth. The 3D real-world model obtained in step 1 is used as a terrain constraint to adjust the elevation of the surface grid nodes. Under the quasi-static approximation, the steady current field satisfies the Poisson equation as follows, which is discretized using the finite element method: ; In the formula, Here is the conductivity at position r, in units of S / m; Potential distribution, unit: V; It is the Dirac function; The location of the power supply point is discretized using the finite element method. This is the effective value of the supply current.

[0032] The Gauss-Newton method is used to solve the three-dimensional joint inversion problem. The inversion is iterated until the root mean square of the data fitting residuals is less than 1.0. The objective function is shown in the following equation: ; In the formula, The objective function is... This is the parameter vector of the three-dimensional finite element model; The observation data vector, obtained from the measurements in step S1, is the input data for the inversion, containing the real and imaginary parts of the complex impedance at all frequency points; F is the input quantity for the inversion. Theoretical observation data obtained through forward modeling using the three-dimensional finite element method, and They have the same data format; Here, is the data weight matrix, and is a diagonal matrix whose diagonal elements are the reciprocals of the standard deviations of each observation. ,in The noise level estimated from the measured data is used to assign different weights to data of different qualities, thereby suppressing the impact of noise data on the inversion. The smoothness matrix is ​​constructed using first- or second-order difference operators. It is used to apply spatial smoothness constraints to the parameters of adjacent grid elements to prevent non-physical oscillations in the inversion results. This matrix is ​​uniquely determined by the grid partitioning scheme and does not require external calculation. For regularization parameters, The horizontal axis is... Using the vertical axis as the ordinate, calculate different... The inversion results corresponding to the values ​​are plotted as curves, and the value corresponding to the corner of the curve is taken as the optimal value, which is called the L-curve method.

[0033] After the inversion converges, the parameter values ​​of each node on the irregular three-dimensional finite element mesh are obtained. In order to generate a regular three-dimensional voxel model, the Kriging interpolation method is used to map the parameter values ​​of the inversion results, i.e., the irregular mesh nodes, onto the nodes of the regular mesh (i.e., the GRID model).

[0034] interpolation point The estimated value is obtained by the following formula: ; In the formula, Points to be interpolated The estimated value, obtained by weighted summation of the parameter values ​​of the surrounding known inversion grid nodes, is the predicted value at the interpolation point, which is used to fill the irregular inversion result into a regular three-dimensional voxel model; Let the parameter value be the real part of the known value at the i-th point, such as the conductivity. The conductivity reflects the electrical conductivity of a medium under an alternating electric field, and is mainly contributed by the conductivity of pore water, porosity, and the surface conductivity of clay. The imaginary part of conductivity... Normalized polarizability reflects the polarizability of the medium and is sensitive to the polarization of clay minerals, metal ions, and pore water-particle interfaces. It is a key parameter for distinguishing leakage channels from clay lenses. The polarization contribution per unit conductivity eliminates the influence of resistivity background and is directly related to cation exchange capacity and water content. is the Kriging weight coefficient; N is the number of known points.

[0035] Among them, the Kriging weight coefficient The following Kriging equations were obtained by solving them: ; In the formula, The semivariogram values ​​between known point i and known point j; Given point i and the point to be interpolated The semivariogram values ​​between; For Lagrange multipliers; , , Let be the spatial coordinates of the i-th known point, the j-th known point, and the point to be interpolated.

[0036] The semivariogram value between any two points is calculated using the three-dimensional anisotropic semivariogram model proposed in this embodiment: ; In the formula, The value is the semi-variogram value; For anisotropic distances; The nugget constant is the difference (measurement error or microscale variability) that still exists between two points when the spatial distance approaches zero. The sill value is the limiting value at which the semivariogram tends to stabilize as the distance increases, reflecting the total spatial variability. The range is the spatial distance required for the semivariogram to reach the sill value; beyond this distance, the two points are no longer correlated.

[0037] ; In the formula, , , Let be the coordinate difference between any two three-dimensional finite element mesh nodes in three directions; , , These are the anisotropy scaling factors along the dam axis, perpendicular to the dam axis, and in the depth direction, respectively. The dam's length is determined by the ratio of its length to its height; the dam length is usually much greater than its height. A value greater than 1 indicates the continuity of the seepage channel along the dam axis, which is a priority area of ​​concern. The ratio of the average width of the dam body (the average width of the dam crest and dam base) to the dam height determines the lateral distribution scale of seepage channels on the dam's cross-section, and is typically smaller than... ; The baseline value is fixed at 1, and the depth direction is the core direction of detection. The original resolution is maintained based on this, and the anisotropy coefficients of other directions are normalized relative to the depth direction.

[0038] After interpolation, a regular three-dimensional voxel mesh is generated, and the three-dimensional real part conductivity volume is output. (Unit: S / m), Three-dimensional imaginary part conductivity volume (Unit: S / m), Three-dimensional normalized polarizability volume Defined as: ; In the formula, coordinates The imaginary part of the conductivity at the point; coordinates The real conductivity of the body; coordinates The normalized polarization body at that location.

[0039] Step 3: Based on the dynamic double-layer theory, the three-dimensional spatial distribution of water content, cation exchange capacity and permeability is obtained voxel by voxel using the rock physical transformation model.

[0040] Define the following parameter: volumetric water content 0~1, dimensionless; cation exchange capacity CEC, unit: C / kg; cementation index m, value: 1.5~2.5; pore water conductivity Unit: S / m, measured from on-site water samples; particle density Values ​​range from 2650 to 2700 kg / m³, and the surface mobility of counterions, B, is 3.1 × 10⁻⁶. -9 m -2 ·s -1 ·V -1 counterion polarization mobility =3.0×10 -10 m -2 ·s -1 ·V -1 dimensionless constant .

[0041] Rock physical transformation model based on dynamic double-layer theory, real part conductivity polarizability Moisture content The quantitative relationship between cation exchange capacity (CEC) and cation exchange capacity (CEC) is given by two basic equations as follows: ; ; In the formula, The real part conductivity; This is the normalized polarizability; the other parameters are the same as above.

[0042] Using the three-dimensional clustering analysis algorithm (3D K-means) to and Voxel-level stratigraphic zoning was conducted, with the number of zoning K determined based on known geological profiles. Soil samples were collected in each zoning, and the cation exchange capacity (CEC) and cementation index (m) of that zoning were measured.

[0043] Current methods for calculating cation exchange capacity (CEC) only utilize polarization information at a single frequency (or time-domain equivalent), which fails to distinguish the differentiated contributions of different clay mineral types to polarization and ignores the additional information contained in the frequency response characteristics.

[0044] This embodiment proposes a multi-frequency fusion CEC estimation formula as follows: ; In the formula, This refers to the cation exchange capacity. This represents the number of frequency points. The coefficients represent clay mineral type coefficients (kaolinite ≈ 2.1, illite ≈ 3.4, montmorillonite ≈ 5.2). Different clay minerals have different cation exchange capacities, resulting in variations in their polarization relaxation time constants and frequency response characteristics. Montmorillonite exhibits the highest CEC and the strongest low-frequency polarization effect, followed by illite, with kaolinite showing the lowest. The frequency polarization difference factor is defined for a single grid node. For the kth frequency; The frequency attenuation index ranges from 0.2 to 0.6. is the moisture content; m is the cementation index; The sensitivity index reflects the overall reliability of the polarization signal as it changes with frequency. As an auxiliary correction term, it can improve the estimation stability in high-noise regions. The sensitivity index weight ranges from 0.1 to 0.3. , which is the frequency polarization difference factor, reflects the rate of change of polarizability with frequency. This rate of change is directly related to the type and content of clay minerals. The imaginary conductivity volume at the (k+1)th frequency, with a single grid node as the research object; For a single grid node, consider the real conductivity volume at the (k+1)th frequency. The imaginary conductivity volume at the k-th frequency is studied with a single grid node as the research object; Let be the real conductivity volume at the k-th frequency, with a single grid node as the object of study; Let k be the k-th frequency. By weighted fusion of polarization differences across multiple frequency points, clay polarization features richer than those obtained from single-frequency analysis can be extracted.

[0045] To assess the reliability of polarization anomalies, a sensitivity index is defined. The multi-frequency weighted average is calculated using the following formula: ; In the formula, As a sensitivity index, when A value greater than 0.1 indicates high polarization confidence. <0.05 indicates low reliability; The imaginary conductivity volume at the k-th frequency is studied with a single grid node as the research object; The imaginary conductivity volume at the (k+1)th frequency, with a single grid node as the research object; For the kth frequency; ; This represents the number of frequency points.

[0046] To eliminate the effects of heterogeneity, this embodiment proposes a partitioned weighted correction field as shown in the following two equations: ; In the formula, This is the corrected cation exchange capacity; For zoned correction fields; This is the initial calculated value for cation exchange capacity.

[0047] ; In the formula, Let be the systematic bias coefficient for the p-th partition. It is calculated as the arithmetic mean of the ratios of the measured CEC to the initial estimated CEC at all sampling points within the partition. This reflects the systematic bias of the rock physical transformation model within that partition. If... A value greater than 1 indicates that the initial estimates are generally low, and the model systematically underestimates this partition. If the value is less than 1, it indicates that the initial estimates are generally too high and there is a systematic overestimation. This value is reduced by eliminating the systematic differences between different partitions, such as the CEC of the core wall being generally higher than that of the sand shell to reduce the influence of heterogeneity. For the first The local residual weight of each sampling point is calculated as the ratio of the measured CEC to the estimated CEC, minus the systematic bias coefficient of that region. If the data quality of the sampling point is unreliable or located near the partition boundary, it can be multiplied by a reduction factor, with a value of 0.5 to 0.8. Otherwise, the residual value can be taken directly. This value reduces the impact of heterogeneity by eliminating the systematic differences between different partitions, such as the CEC of the core wall being generally higher than that of the sand shell. The coordinates of the point to be corrected; Let J be the spatial coordinates of the j-th sampling point; The spatially relevant length, with a value of 5~10m; This represents the number of sampling points within the partition.

[0048] Then calculate the three-dimensional permeability volume. Unit m 2 Classical penetration formula This method is suitable for sandy soils with low clay content. When the dam body contains high clay areas (such as clay lenses or near the core wall), the permeability of high CEC areas is severely underestimated, with predicted values ​​much lower than measured values. When the clay content exceeds a certain threshold, the structure of the clay particles themselves (such as aggregates and microcracks) can form local water-conducting channels, slowing down the decreasing trend of permeability with CEC. This embodiment proposes a permeability with a correction term, as shown in the following formula: ; In the formula, For penetration rate; It is an empirical constant, and =10 4.30 C 2 m -4 ; Moisture content; Particle density; For the corrected cation exchange capacity, when > The correction term lowers the estimated penetration rate, avoiding overestimation in the original formula when clay content is high, thus bringing the predicted value closer to the measured value. < The formula degenerates into its classical form, retaining its original precision. , These are empirical parameters, calibrated through on-site pressure water tests; among which, CEC is the critical threshold for clay content. The calibration method involves selecting several representative areas with different clay contents in the dam fill material, conducting indoor CEC tests and actual permeability measurements, plotting a CEC-permeability scatter plot, and observing the location of the obvious inflection point in permeability change with CEC. The CEC value corresponding to this inflection point is CEC0. For gravelly sandy soils, CEC0 is typically between 5 and 8 meq / 100g. Based on CEC0, the decreasing trend of permeability with increasing CEC is observed. The exponential decay part of the correction term is fitted, and the CEC increment corresponding to the permeability decreasing to the "fully corrected" state (approximately 1 / e times the permeability without correction) is taken as CEC1. This is the hyperbolic tangent correction function.

[0049] Step 4: Construct a multidimensional leakage comprehensive index based on resistivity, polarizability, water content, permeability and cation exchange capacity. Label candidate leakage voxels according to the multidimensional leakage comprehensive index and perform three-dimensional connectivity analysis on the candidate voxels to obtain the leakage detection results of the earth-rock dam.

[0050] This embodiment analyzes the different response mechanisms of various geophysical and geotechnical parameters in seepage channels and clay lenses. Seepage channels typically exhibit low resistivity, high normalized polarizability, high imaginary conductivity, high water content, high permeability, and moderately low cation exchange capacity. While clay lenses also exhibit low resistivity, high normalized polarizability, high imaginary conductivity, and high water content, their permeability is extremely low, and their cation exchange capacity is very high. Therefore, by introducing cation exchange capacity (CEC) as an additional discriminant, it is possible to effectively distinguish between clay lenses with high water content but low permeability and channels that truly pose a seepage risk.

[0051] First, the threshold values ​​for each parameter are determined through indoor geotechnical tests or field calibration: resistivity threshold. (e.g., 60 Ω·m), normalized polarizability threshold (e.g., 0.001 S / m), imaginary part conductivity threshold (e.g., 0.0005 S / m), moisture content threshold (e.g., 0.35), penetration threshold (e.g., 10) 12 m2), cation exchange capacity threshold (For example, 5 meq / 100g). This embodiment proposes the following multidimensional leakage comprehensive index L: ; In the formula, A multidimensional leakage comprehensive index; Resistivity; Normalized polarizability; The imaginary part of the conductivity; Moisture content; For penetration rate; This represents the cation exchange capacity; the subscript th indicates the threshold, and min and max represent the minimum and maximum values ​​of this parameter within the detection region, respectively. , , , , , These are the weighting coefficients for the corresponding parameters. Based on practical engineering experience, the values ​​for each weight are shown in Table 1 below.

[0052] Table 1: Weight Values

[0053] Voxels with a multidimensional leakage comprehensive index L>0 were designated as candidate leakage voxels. Three-dimensional connectivity analysis was performed on these candidate voxels, employing a 26-neighborhood connectivity labeling algorithm to determine the volume of connected components. Greater than the preset minimum volume threshold (e.g., 1m) 3 The objects are preserved, and each connected component is identified as a leakage channel. For each channel, the 3D spatial boundary is output. , , The geometric shapes are classified according to the ratio of the principal axis lengths (>5 bands, 2~5 dendritic, <2 clumps). Channel volume. ,in For a single voxel volume. The principal permeation direction is analyzed using a weighted principal axis as follows: ; In the formula, The main seepage direction vector; For the first Water content of individual elements; For the first Spatial coordinates of individual elements; The coordinates of the centroid of the channel; The unit direction vector from the voxel to the centroid; Let be the unit direction vector to be solved.

[0054] Define importance index as follows: ; In the formula, The channel importance index is a three-dimensional composite evaluation index used to rank the risks of all identified leakage channels. A higher value indicates a greater hazard and a higher priority for remediation of the channel. This represents the volume of the leakage channel; The average permeability within the leakage channel; This is the average sensitivity index within the leakage channel, used for risk ranking.

[0055] The confidence level is expressed using the fuzzy membership function as follows: ; In the formula, Confidence level, used to assess the reliability of identification results from geophysical methods; The average sensitivity index within the channel is defined as follows: a value > 0.8 indicates high confidence, 0.5 to 0.8 indicates medium confidence, and < 0.5 indicates low confidence. The three-dimensional sensitivity index volume obtained through statistical step S2 serves as the baseline value for the sensitivity index. The calculation method is to calculate all data within the entire detection area. The values ​​are statistically analyzed and the median is taken. This is the steepness coefficient, used to control the confidence level. The smooth transition range is an empirical parameter, ranging from 5 to 15. This parameter value is chosen to ensure... Exceeding the background median At a confidence level of 10%-20%, the confidence level can smoothly jump from 0.5 to above 0.8, which can achieve clear classification and avoid the truncation error caused by hard threshold.

[0056] All three-dimensional parameter volumes, i.e., real part conductivity volumes Imaginary part conductivity Normalized polarizability M n Moisture content Corrected cation exchange capacity The three-dimensional permeability volume K and the identified seepage channels are displayed using regular Kriging interpolation and volume rendering technology, supporting slicing in any direction. At the same time, the potential difference distribution map of the dam surface generated by the natural potential method is superimposed as a verification layer. The above content can be used to perform dam seepage analysis and write test reports.

[0057] This embodiment also includes auxiliary verification using the natural potential method, specifically: At each electrode location measured by the induced polarization method, a spontaneous potential (SPTD) measurement is performed. A fixed zero-potential reference electrode is set up (usually placed at a stable location far from the seepage influence zone), and the potential difference between each electrode point and this reference point is measured to obtain two-dimensional potential difference distribution data. The physical principle behind this data is that groundwater carries excess charge from the electric double layer during seepage, forming a flowing current, which in turn generates a flowing potential, with the water flow direction from high potential to low potential. The potential difference of all measuring points is interpolated using plotting software to generate a potential difference distribution map of the entire dam surface. Due to the rapid flow of groundwater, active seepage areas typically exhibit negative potential anomalies (generally with an amplitude of 10~100 mV). The two-dimensional dam surface potential difference distribution map obtained by the SPTD method is spatially superimposed and compared with the three-dimensional inversion results and seepage channel identification results obtained above. If the negative potential anomaly area highly overlaps with the seepage channel location identified by multi-dimensional joint discrimination, the reliability of the seepage channel is verified. This method is only used in the verification stage and is not used as the core basis for seepage determination.

[0058] Example 1: Taking a small reservoir—Reservoir Z—as an example, the following detailed explanation of the seepage detection method for earth-rock dams based on spectral excitation polarization three-dimensional modeling proposed in this embodiment will be provided: Reservoir Z controls a drainage area of ​​0.22 km², with a total storage capacity of 125,700 m³. It is a small (Class II) reservoir primarily used for farmland irrigation and flood control. The dam is a clay-core dam, 80 m long, with a maximum height of 11.5 m and a crest elevation of 303.39–303.55 m. The upstream slope ratio is 1:3.08, and the downstream slope ratio is 1:2.10. The dam foundation is composed of medium-grained granodiorite from the Proterozoic Lüliang period. After many years of operation, localized humid areas have appeared on the downstream dam slope, and seepage has occurred at the dam toe. The location and extent of the seepage channels need to be investigated.

[0059] S0: 3D terrain modeling and measurement point coordinate extraction by UAV aerial photography.

[0060] A drone equipped with lidar and a high-resolution camera was used to conduct oblique photogrammetry of the dam and surrounding area. The planned flight path covered the entire reservoir area (85% forward overlap and 75% lateral overlap), with a flight altitude of 80 m. A total of 420 images were collected, including point cloud data. Figure 2 As shown in (b), a high-precision 3D model of the dam (planar resolution 4.8 cm) was generated using modeling software, as shown in (b). Figure 2 As shown in (a).

[0061] The electrode survey lines were planned on the 3D reality model: 5 survey lines (P1~P5, 4 m spacing) were laid out along the downstream dam slope parallel to the dam axis, with 64 electrodes on each of P1~P4 and 32 electrodes on P5; 7 survey lines (P6~P12) were laid out perpendicular to the dam axis, with an electrode spacing of 0.3 m and 32 electrodes on each line; auxiliary survey lines were laid out at the dam crest and downstream slope toe, generating theoretical coordinates for a total of 1024 electrodes, as shown below. Figure 2 As shown in (c), the electrode layout plan was imported into the RTK handheld device, and the electrodes were laid out on-site. The altitude of each electrode was measured using GPS, with the altitude of the dam crest survey line as the zero point of the Z-axis (Z=0 m). The coordinates of the remaining survey points were set as negative numbers of the altitude difference to obtain the actual coordinates. The root mean square error of the fitting residual between the theoretical and actual coordinates was 3.2 cm, which meets the accuracy requirements.

[0062] S1: True three-dimensional multi-frequency excitation polarization data acquisition.

[0063] A multi-channel resistivity / excitation polarimeter was used, with 1024 electrodes forming a three-dimensional grid according to step S0. The electrode spacing was 1 m (P1~P5 along the dam axis) and 0.3 m (P6~P12 perpendicular to the dam axis) depending on the different survey lines. The number of electrodes per measurement profile was E=64, and the dam height was h=11.5 m, satisfying h<0.2Ea. The effective value of the emission current was I0=2 A, and five logarithmically uniform frequency points (N) were selected: 0.01 Hz, 0.1 Hz, 1 Hz, 10 Hz, and 100 Hz. f =5). The power supply waveform is a trapezoidal wave with a turn-off time of 20 μs and a sampling rate of 2400 Hz. Ten complete cycles are acquired for each power supply-measurement combination. A multi-channel receiver synchronously acquires the potential difference time series V(t) of each measurement electrode pair. A discrete Fourier transform is performed on V(t) to extract each frequency. The complex potential difference below, according to Calculate complex impedance A total of approximately 1.84 million complex impedance observation data points were obtained (approximately 1024 × 5 × 360 ≈ 1.84 million). Simultaneously, groundwater samples were collected from boreholes in the reservoir area and downstream, and the conductivity of these samples was measured multiple times using a multi-parameter analyzer to obtain an average value. =0.085 S / m.

[0064] S2: True 3D complex resistivity joint inversion and multi-parameter body construction.

[0065] A three-dimensional finite element mesh corresponding to the actual dimensions of the dam was established, with a total of 176,540 data points measured and 88,270 triangular meshes constructed. The three-dimensional real-scene model obtained in step S0 was used as terrain constraints to adjust the elevation of the surface mesh nodes. The Gauss-Newton method was used to solve the three-dimensional joint inversion problem, and the objective function and regularization parameter were calculated. The value was determined to be 6.5 using the L-curve method. After 14 iterations, the root mean square (RMS) of the data fitting residuals was 0.92. The real conductivity on the irregular grid was then obtained through inversion. Imaginary part conductivity Normalized polarizability M n Kriging interpolation is used to map the results onto a regular GRID grid, where the anisotropic semivariogram is adopted using the method proposed in this invention. and Parameters C0=0.01, C1=0.1, range a=5 m. The geometric parameters of the reservoir dam in this embodiment are: dam length 80 m, dam crest width 4 m, dam base width 30 m, dam height H=11.5 m, anisotropy coefficient α=80 / 11.5=6.96, simplified to 1.2 (dam axis direction), β=(30+4) / (2*11.5)=34 / 23=1.48, simplified to 1.0 (perpendicular to dam axis direction), γ=1, simplified to 0.8 (depth direction). After interpolation, according to a regular 3D voxel mesh of 1 m×0.5 m×0.5 m, σ', σ″, and M are output. n Three-dimensional objects, such as Figure 3 As shown in (a)-(b), the sensitivity index Γ was calculated according to the formula proposed in this invention. The results showed that Γ = 0.08~0.12 in the core wall region and reached 0.13~0.18 in the downstream sand shell.

[0066] S3: Three-dimensional rock physical transformation—water content Calculation of cation exchange capacity (CEC) and permeability (K).

[0067] On-site water samples were measured =0.085 S / m, particle density =2650 kg / m³, counterion surface mobility B=3.1×10 -9 m -2 ·s -1 ·V -1 The counterion polarization mobility λ = 3.0 × 10⁻⁶ - ¹ 0 m²·s - ¹·V - ¹. The dam body was divided into four stratigraphic zones using the 3D K-means clustering algorithm: upstream sand crust, clay core, downstream sand crust, and granite bedrock. Uncirculated soil samples were collected from each zone, and the measured cation exchange capacities (CECs) were: upstream sand crust 2.8 meq / 100g, core 8.2 meq / 100g, downstream sand crust 3.1 meq / 100g, and bedrock 1.5 meq / 100g; the cementation indices (m) were 1.55, 1.92, 1.58, and 1.48, respectively. σ' and M were established according to the formula proposed in this invention. n Relationship with θ and CEC.

[0068] Using the multi-frequency fusion CEC estimation formula proposed in this embodiment, the clay mineral type coefficient is taken. =3.4 (mainly illite), frequency attenuation index α=0.4, sensitivity index weight ε=0.2, calculate initial CEC, then perform partitioned weighted correction, spatial correlation length =6 m, thus obtaining Finally, the penetration rate K is calculated, where... =10 4.30 C 2 m -4 Five representative boreholes were selected in the downstream sand crust and core wall junction area of ​​the dam. Water pressure tests were conducted on each borehole at 4-m intervals within a depth range of 6–18 m, directly measuring the permeability K of the filling material in each section. All initial CEC data were plotted on a logarithmic coordinate graph, with CEC on the horizontal axis and permeability K on the vertical axis, to observe the decreasing trend of permeability with increasing CEC. The critical inflection point was determined through piecewise fitting; the CEC value corresponding to this inflection point is CEC0, representing the upper limit of the classical permeability formula applicable in low-clay regions. When CEC exceeds this value, the classical formula exhibits a systematic underestimation, requiring correction. The CEC increment corresponding to a decrease in permeability to 1 / e times the uncorrected permeability is defined as CEC1. The fitting results show that, under the dam material conditions of this embodiment, when CEC0 is 5 meq / 100g and CEC1 is 3 meq / 100g, the fitting effect between the corrected permeability and the measured permeability is optimal, with a correlation coefficient R² reaching 0.94. These values ​​are used as the unified input parameters for subsequent voxel-by-voxel calculations of three-dimensional voxel permeability. Calculations of θ and K show that for the core wall region, θ = 0.32~0.41, and K = 2.5 × 10⁻⁶. - ¹ 4 ~8.3×10 - ¹ 4 m²; downstream sand crust with locally high water content θ = 0.38~0.52, K = 1.2×10⁻⁶ m²; - ¹²~3.6×10 - ¹² m², exceeding the Darcy threshold of 1.

[0069] S4: Multidimensional joint discriminant analysis and three-dimensional connectivity analysis.

[0070] Based on indoor geotechnical tests and field experience, a discrimination threshold was set: resistivity threshold. =60 Ω·m, corresponding to a moisture content of approximately 35% in the dam body fill material. A value below this indicates that the medium has reached saturation, leading to significant seepage and water accumulation; Normalized polarizability threshold. =0.001 S / m, excluding pure sand and gravel layers without clay (Mn<0.0005), screening for media with polarizable particles (clay / metal ions); imaginary part conductivity threshold. =0.0005 S / m, requiring the medium to have significant interfacial polarization capability, eliminate background polarization interference, and ensure that the polarization anomaly is real and reliable; moisture content threshold. =0.35, the critical value for near-saturation of earth-rock dam fill material; below this value, there are no hydrological conditions for seepage channels; permeability threshold. =1×10 - ¹² m², approximately equal to 1 Darcy, is a commonly used engineering boundary line distinguishing between "permeable" and "impermeable" media; below this value, there is no fluid transport capacity for leakage channels; cation exchange capacity threshold. =5 meq / 100g, to distinguish between sandy soil (<5) and clay lens body (>5), and exclude non-permeable interference bodies with high clay content if the value is lower than this.

[0071] In this embodiment, the dam shape is a mixed sand-clay fill (moderately heterogeneous), and the weighting coefficient is taken as... =0.20, =0.15, =0.15, =0.20, =0.20, =0.10. Calculate the multidimensional leakage comprehensive index L, and mark voxels with L>0 as candidate leakage voxels. Perform three-dimensional connectivity analysis on the candidate voxels, using the 26-neighborhood connectivity labeling algorithm, and set the minimum connectivity volume. =2 m³, two main connected seepage channels were identified, located near the left and right sides of the dam respectively. The identified seepage channels L1 and L2 are plotted as follows: Figure 12 As shown: Left Bank Channel L1: Located at chainage 0+020~0+050 (left side of the dam), depth 7~17 m, volume 1452 m³, main seepage direction NE42°, trend is that small-scale seepage in the west is concentrated at the seepage outlet on the west side, importance index =1.38×10 -9 Confidence level =0.91 (high confidence level).

[0072] Right Bank Channel L2: Located at chainage 0+055~0+078 (right side of the dam), depth 2~18 m, volume 5092 m³, main seepage direction NE58°, trend is that large-scale seepage in the central and eastern parts is concentrated at the seepage outlet on the east side, importance index =1.96×10 -9 Confidence level =0.93 (high confidence level).

[0073] Both channels are located near the contact zone between the downstream sand crust and bedrock, with CEC less than 4.5 meq / 100g, ruling out interference from clay lenses. No leakage channels were found in the core wall area, indicating that the core wall's seepage prevention function is basically intact, and leakage mainly occurs on both sides of the contact zone between the core wall and bedrock.

[0074] S5: Verification aided by the natural potential method.

[0075] A zero-potential reference point was set up 10m from the easternmost end of the road on the dam axis. Cu / CuSO4 non-polarized electrodes were laid out along the IP survey line, using the stable zone at the dam crest as the reference electrode. A high-input-impedance multimeter was used to measure the potential difference relative to the reference point at 1024 measuring points (actually the electrode points). After data processing, a potential difference distribution map of the dam surface was obtained, as shown below. Figure 11 As shown in the figure. The results show that there is a negative potential anomaly of -10 to -8 mV in the range of chainage 0+025 to 0+045 on the left bank, which highly coincides with the location of channel L1; there is a negative potential anomaly of -10 to -4 mV in the range of chainage 0+055 to 0+075 on the right bank, which highly coincides with the location of channel L2; and the SP anomaly in the middle area of ​​chainage 0+045 to 0+055 is close to the background value (-14 to -24 mV), further confirming that the leakage is mainly concentrated on the left and right sides of the dam. The spontaneous potential verification results are consistent with the channel location identified by multi-dimensional joint discrimination, which improves the reliability of leakage determination.

[0076] S6: True 3D visualization and result generation.

[0077] All three-dimensional parameter volumes σ', σ″, Mn, θ K performs volume rendering and isosurface extraction on a regular GRID (1 m × 0.5 m × 0.5 m voxel) mesh, supporting arbitrary slicing along the dam axis, perpendicular to the dam axis, and horizontally. Simultaneously, a dam surface potential difference distribution map generated by the natural potential method is overlaid as a verification layer. Figure 4 (a) to (b) Figure 10 As shown in (a)-(b). Output the test results to prepare a test report. The test report includes, but is not limited to: three-dimensional resistivity, polarizability, water content, and permeability distribution maps of the dam body; a list of seepage channels (including location, volume of 1452 m³ and 5092 m³, orientation NE42° and NE58°, confidence level of 0.91 and 0.93, and importance index); a comparison map of spontaneous potential verification; the recommended treatment plan is high-pressure jet grouting for areas L1 and L2, with the estimated grouting volume based on volume. Later, core sampling was performed at location L2 for verification. The measured CEC was 7.6 meq / 100g, water content θ = 40%, and permeability K = 3.4 × 10⁻⁶. -The relative error between the ¹² m² and the inversion results is less than 13%, proving the accuracy of this method.

[0078] Example 2 The purpose of this embodiment is to provide a seepage detection system for earth-rock dams based on spectral excitation polarization three-dimensional modeling, including: The acquisition module is configured to: acquire three-dimensional topographic data of the earth-rock dam and deploy a three-dimensional gridded electrode array, and acquire complex impedance spectrum data of the entire dam area through multi-frequency excitation polarization measurement; The modeling module is configured to: establish a three-dimensional finite element model of the earth-rock dam based on the three-dimensional topographic data of the earth-rock dam, perform three-dimensional joint inversion and anisotropic spatial interpolation on the complex impedance spectrum data, and obtain a three-dimensional voxel model containing conductivity and three-dimensional normalized polarizability. The calculation module is configured to: use a rock physical transformation model based on the dynamic double-layer theory to obtain the three-dimensional spatial distribution of water content, cation exchange capacity and permeability on a voxel-by-voxel basis; The permeability detection module is configured to: construct a multidimensional permeability comprehensive index based on resistivity, polarizability, water content, permeability and cation exchange capacity; label candidate permeable voxels according to the multidimensional permeability comprehensive index; and perform three-dimensional connectivity analysis on the candidate voxels to obtain the permeability detection results of the earth-rock dam.

[0079] In further embodiments, the following is also provided: An electronic device includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor. When executed by the processor, the computer instructions perform the method described in Embodiment 1. For brevity, further details are omitted here.

[0080] It should be understood that in this embodiment, the processor can be a central processing unit (CPU), or it can be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor, etc.

[0081] Memory may include read-only memory and random access memory, and provides instructions and data to the processor. A portion of memory may also include non-volatile random access memory. For example, memory may also store information about the device type.

[0082] A computer-readable storage medium for storing computer instructions, which, when executed by a processor, perform the method described in Embodiment 1.

[0083] The method in Embodiment 1 can be directly implemented by a hardware processor, or implemented by a combination of hardware and software modules within the processor. The software modules can reside in readily available storage media in the art, such as random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, or registers. This storage medium is located in memory; the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method. To avoid repetition, a detailed description is not provided here.

[0084] A computer program product includes a computer program that, when executed by a processor, implements the method described in Embodiment 1.

[0085] The present invention also provides at least one computer program product tangibly stored on a non-transitory computer-readable storage medium. The computer program product includes computer-executable instructions, such as instructions included in program modules, which execute in a device on a target real or virtual processor to perform the processes / methods described above. Typically, program modules include routines, programs, libraries, objects, classes, components, data structures, etc., that perform specific tasks or implement specific abstract data types. In various embodiments, the functionality of program modules can be combined or divided among program modules as needed. The machine-executable instructions for the program modules can execute within a local or distributed device. In a distributed device, the program modules can reside in both local and remote storage media.

[0086] The computer program code used to implement the methods of the present invention may be written in one or more programming languages. This computer program code may be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device, such that when executed by the computer or other programmable data processing device, the program code causes the functions / operations specified in the flowcharts and / or block diagrams to be implemented. The program code may be executed entirely on a computer, partially on a computer, as a stand-alone software package, partially on a computer and partially on a remote computer, or entirely on a remote computer or server.

[0087] In the context of this invention, computer program code or related data may be carried by any suitable carrier to enable a device, apparatus, or processor to perform the various processes and operations described above. Examples of carriers include signals, computer-readable media, and the like. Examples of signals may include electrical, optical, radio, sound, or other forms of propagation signals, such as carrier waves, infrared signals, etc.

[0088] Those skilled in the art will recognize that the units and algorithm steps described in conjunction with the embodiments 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.

[0089] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for detecting seepage in earth-rock dams based on spectral excitation polarization three-dimensional modeling, characterized in that, include: Three-dimensional topographic data of earth-rock dams were acquired and a three-dimensional gridded electrode array was deployed. Complex impedance spectrum data of the entire dam area were obtained through multi-frequency excitation polarization measurement. A three-dimensional finite element model of an earth-rock dam was established based on three-dimensional topographic data of the earth-rock dam. Three-dimensional joint inversion and anisotropic spatial interpolation were performed on the complex impedance spectrum data to obtain a three-dimensional voxel model containing conductivity and three-dimensional normalized polarizability. Based on the dynamic double-layer theory, a rock physical transformation model was used to obtain the three-dimensional spatial distribution of water content, cation exchange capacity and permeability on a voxel-by-voxel basis. The multi-frequency fusion CEC estimation formula is as follows: ； In the formula, This refers to the cation exchange capacity. This represents the number of frequency points. The coefficients for clay mineral types are: kaolinite ≈ 2.1, illite ≈ 3.4, and montmorillonite ≈ 5.

2. The frequency attenuation index ranges from 0.2 to 0.

6. is the moisture content; m is the cementation index; , is the frequency polarization difference factor. The imaginary conductivity volume at the (k+1)th frequency, with a single grid node as the research object; For a single grid node, consider the real conductivity volume at the (k+1)th frequency. The imaginary conductivity volume at the k-th frequency is studied with a single grid node as the research object; Let be the real conductivity volume at the k-th frequency, with a single grid node as the object of study; Sensitivity Index The multi-frequency weighted average is calculated using the following formula: ； In the formula, A value greater than 0.1 indicates high polarization confidence. <0.05 indicates low reliability; A multidimensional leakage index was constructed based on resistivity, polarizability, water content, permeability, and cation exchange capacity. Candidate leakage voxels were labeled according to the multidimensional leakage index, and three-dimensional connectivity analysis was performed on the candidate voxels to obtain the leakage detection results of the earth-rock dam. Specifically: First, the threshold values ​​for each parameter are determined through indoor geotechnical tests or field calibration: resistivity threshold. Normalized polarizability threshold Imaginary part conductivity threshold Moisture content threshold Penetration threshold Cation exchange capacity threshold ; The multidimensional leakage comprehensive index L is as follows: ； In the formula, A multidimensional leakage comprehensive index; Resistivity; Normalized polarizability; The imaginary part of the conductivity; For penetration rate; This represents the cation exchange capacity; the subscript th indicates the threshold, and min and max represent the minimum and maximum values ​​of this parameter within the detection region, respectively. , , , , , These are the weighting coefficients for the corresponding parameters; Voxels with a multidimensional leakage comprehensive index greater than zero are marked as candidate leakage voxels. Three-dimensional connectivity analysis is performed on the candidate leakage voxels to identify connected leakage channels.

2. The method for detecting seepage in earth-rock dams based on spectral excitation polarization three-dimensional modeling as described in claim 1, characterized in that, A three-dimensional finite element model of the earth-rock dam was established based on three-dimensional topographic data. Three-dimensional joint inversion and anisotropic spatial interpolation were performed on the complex impedance spectrum data to obtain a three-dimensional voxel model including conductivity and three-dimensional normalized polarizability. Specifically: The Gauss-Newton method is used to solve the three-dimensional joint inversion. After the inversion converges, the parameter values ​​at each node of the irregular mesh are obtained. The parameter values ​​at each node of the irregular mesh are mapped to the nodes of the regular mesh using the Kriging interpolation method. After interpolation, a regular three-dimensional voxel mesh is generated, resulting in a three-dimensional real part conductivity volume, a three-dimensional imaginary part conductivity volume, and a three-dimensional normalized polarizability volume. The semivariogram value between any two meshes is calculated by a three-dimensional anisotropic semivariogram model. In the three-dimensional anisotropic semivariogram model, the anisotropic distance is determined by the coordinate difference between the two mesh nodes in different directions and the corresponding anisotropic scaling coefficients along the dam axis, perpendicular to the dam axis, and in the depth direction.

3. The method for detecting seepage in earth-rock dams based on spectral excitation polarization three-dimensional modeling as described in claim 1, characterized in that, A partition correction field is introduced to revise the estimated cation exchange capacity, resulting in a corrected cation exchange capacity; wherein the partition correction field is determined based on the systematic deviation of the rock physical transformation model within the partition.

4. The method for detecting seepage in earth-rock dams based on spectral excitation polarization three-dimensional modeling as described in claim 1, characterized in that, The permeability is calculated by introducing a correction term based on the classical permeability calculation. When the corrected cation exchange capacity is greater than the empirical parameter, the permeability estimate is reduced.

5. The method for detecting seepage in earth-rock dams based on spectral excitation polarization three-dimensional modeling as described in claim 1, characterized in that, Also includes: The importance index is determined based on the volume of the leakage channel, the average permeability within the leakage channel, and the average sensitivity index within the leakage channel. The higher the importance index value, the higher the priority of treatment. The confidence level is determined using a fuzzy membership function based on the baseline value of the sensitivity index and the average sensitivity index within the leakage channel; whereby the sensitivity index reflects the confidence level of the polarization anomaly.

6. A seepage detection system for earth-rock dams based on spectral excitation polarization three-dimensional modeling, employing the seepage detection method for earth-rock dams based on spectral excitation polarization three-dimensional modeling as described in any one of claims 1-5, characterized in that, include: The acquisition module is configured to: acquire three-dimensional topographic data of the earth-rock dam and deploy a three-dimensional gridded electrode array, and acquire complex impedance spectrum data of the entire dam area through multi-frequency excitation polarization measurement; The modeling module is configured to: establish a three-dimensional finite element model of the earth-rock dam based on the three-dimensional topographic data of the earth-rock dam, perform three-dimensional joint inversion and anisotropic spatial interpolation on the complex impedance spectrum data, and obtain a three-dimensional voxel model containing conductivity and three-dimensional normalized polarizability. The calculation module is configured to: use a rock physical transformation model based on the dynamic double-layer theory to obtain the three-dimensional spatial distribution of water content, cation exchange capacity and permeability on a voxel-by-voxel basis; The permeability detection module is configured to: construct a multidimensional permeability comprehensive index based on resistivity, polarizability, water content, permeability and cation exchange capacity; label candidate permeable voxels according to the multidimensional permeability comprehensive index; and perform three-dimensional connectivity analysis on the candidate voxels to obtain the permeability detection results of the earth-rock dam.

7. An electronic device, characterized in that, It includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, which, when executed by the processor, perform the method according to any one of claims 1-5.

8. A computer-readable storage medium, characterized in that, Used to store computer instructions, which, when executed by a processor, perform the method described in any one of claims 1-5.

9. A computer program product, characterized in that, Includes a computer program, which, when executed by a processor, implements the method described in any one of claims 1-5.

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