Rock mass anisotropy hierarchical characterization method and system based on multi-scale tensor positive definite mapping

Abstract

This invention discloses a method and system for hierarchical characterization of rock mass anisotropy using multi-scale tensor positive definite mapping, relating to the field of rock mass mechanical parameter characterization. The method includes: determining the microstructure tensor based on rock sample scanning identification; determining the mesoscopic equivalent stiffness tensor based on structural plane surveys; aligning the direction of the mesoscopic equivalent stiffness tensor according to the microstructure tensor; constructing a lower triangular mapping matrix with positive diagonal elements, mapping the direction-registered mesoscopic equivalent stiffness tensor to a macroscopic stiffness tensor through congruence transformation, and ensuring its positive definiteness with a minimum singularity lower bound; updating the macroscopic stiffness tensor based on a Bayesian framework inversion and performing symmetry type identification and order reduction; establishing a spectrum library based on tensor distance and matching it with a model, outputting the final parameters for surrounding rock stability and support design. This invention overcomes the computational anomalies easily caused by traditional empirical reduction, achieving positive definite mapping and dynamic updating of anisotropic parameters from mesoscopic to macroscopic levels.

Description

Technical Field

[0001] This invention relates to the field of rock mass mechanical parameter characterization, and in particular to a method and system for hierarchical characterization of rock mass anisotropy using multi-scale tensor positive definite mapping. Background Technology

[0002] As water conservancy and hydropower projects, transportation tunnels, mining, and deep-earth space development extend into deeper and more complex geological environments, the design and construction of deep rock engineering places increasingly higher demands on the accuracy of rock mass mechanical parameters. In particular, for layered rock masses, gneiss, slate, and other rock formations with significant anisotropy, the directional variation of their mechanical properties has a decisive impact on the evaluation of engineering stability and the design of support parameters.

[0003] Current methods for obtaining rock mass parameters rely solely on empirical reductions without a fixed pattern to convert indoor samples to field rock masses. This conversion process lacks physical constraints, easily disrupting the positive definite properties of the stiffness matrix and leading to anomalies in numerical simulation calculations. Furthermore, existing methods typically presuppose a single, simplified symmetric model, failing to recreate the multi-directional mechanical coupling characteristics of the rock mass, resulting in significant deviations in the actual stress direction parameters. In addition, traditional parameter inversion is only a single static solution, lacking quantitative means to assess parameter reliability in advance, and unable to continuously correct parameters based on newly revealed geological information and monitoring data during excavation. Consequently, the reliability of numerical simulation results is insufficient, and in engineering practice, risks can only be mitigated by increasing safety margins, easily leading to wasted funds or potential geological safety hazards. Summary of the Invention

[0004] The primary technical problem that this invention aims to solve is that traditional methods rely solely on empirical reduction coefficients for scale transformation, which can destroy the positive definiteness of the stiffness tensor matrix, leading to non-convergence in numerical calculations and the appearance of non-physical negative stiffness or negative energy results.

[0005] This invention addresses the shortcomings of existing technologies by providing a method and system for hierarchical characterization of rock mass anisotropy using multi-scale tensor positive definite mapping. In a first aspect, a method for hierarchical characterization of rock mass anisotropy using multi-scale tensor positive definite mapping is provided, comprising the following steps: Based on the results of rock sample scanning and image recognition, the microstructure tensor of the rock sample was determined; Based on the rock mass structural plane survey results and the theory of continuous damage mechanics, the microscopic equivalent stiffness tensor is determined. Based on the microstructure tensor, the mesoscopic equivalent stiffness tensor is anisotropically aligned with the principal directions to obtain the direction-registered mesoscopic equivalent stiffness tensor. Based on the microscopic equivalent stiffness tensor after orientation registration, a lower triangular non-singular mapping matrix with all diagonal elements positive is constructed. Congruence transformation is used to map the microscopic equivalent stiffness tensor after orientation registration to a macroscopic stiffness tensor. The lower bound of the minimum singular value of the mapping matrix ensures that the macroscopic stiffness tensor is positive definite. Based on on-site surrounding rock displacement monitoring data and a Bayesian inversion framework, the macroscopic stiffness tensor is updated through inversion to obtain the updated macroscopic stiffness tensor. This method can provide a quantitative basis for anisotropy determination in rock mass quality classification at different exploration and design stages, effectively improving the accuracy of rock mass classification.

[0006] As one possible implementation, a congruence transformation is used to map the microscopic equivalent stiffness tensor after orientation registration to a macroscopic stiffness tensor, and the lower bound of the minimum singular value of the mapping matrix guarantees that the macroscopic stiffness tensor is positive definite. Specifically, this includes: The positive definite mapping relationship using congruential transformation is as follows:

[0007] in Let L be the macroscopic stiffness tensor matrix. sg It is a lower triangular non-singular mapping matrix. Let LT sg be the microscopic equivalent stiffness tensor matrix after orientation registration. sg The transpose of the matrix; The lower bound of the minimum singular value of the mapping matrix guarantees that the macroscopic stiffness tensor is strictly positive definite:

[0008] in for The smallest eigenvalue, for The smallest eigenvalue, For L sg The minimum singular value. This implementation method eliminates non-physical results such as negative stiffness and positive semidefinite matrix in the cross-scale tensor conversion process, and does not require forced truncation correction of the abnormal stiffness matrix afterward, thus fully preserving the inherent anisotropic tensor structure of the microscopic rock mass.

[0009] As one possible implementation, the rock mass anisotropy classification characterization method based on multi-scale tensor positive definite mapping further includes the following steps: Based on the updated macroscopic stiffness tensor, automatic symmetry type identification is performed. When the deviation between the updated macroscopic stiffness tensor and a certain standard symmetry type is within a set error range, the updated macroscopic stiffness tensor is reduced to the parameterized representation of that symmetry type to obtain the reduced macroscopic stiffness tensor. Based on the tensor distance metric of the reduced macroscopic stiffness tensor, a rock mass anisotropic fabrication map library is established, and a numerical calculation model with corresponding accuracy is matched to the reduced macroscopic stiffness tensor according to the anisotropy degree to obtain the matched engineering calculation parameters. Based on the matched engineering calculation parameters, the final engineering-scale rock mass anisotropy parameters are output through closed-loop iterative updates for surrounding rock stability analysis and support design. This implementation provides a unified, quantitative, and reusable set of mechanical parameters for rock mass classification, surrounding rock stability evaluation, and support optimization design at different design stages.

[0010] As one possible implementation method, determining the microstructure tensor of a rock sample based on rock sample scanning and image recognition results specifically includes: Representative rock samples were scanned using CT scans, and mineral grain boundaries and macroscopic cracks were automatically identified using a rock image segmentation network. Statistical analysis of the distribution function of the long axis of mineral grains and the distribution function of the macroscopic crack orientation; Based on the average value of the cross product of the unit direction vectors of the long axis of mineral grains, the second-order anisotropic tensor of the microstructure that simultaneously characterizes the orientation features of mineral grains and internal cracks is calculated. The second-order tensor is the microstructure tensor. The second-order tensor of the microstructure anisotropy is decomposed into eigenvalues ​​to obtain three principal values ​​of the microanisotropy and three corresponding orthogonal principal directions. This provides a precise and quantitative microscopic orientation reference for subsequent registration of the principal directions of the microstiffness tensor, ensuring that the anisotropic characteristics of the rock mass are not lost or distorted during multi-scale parameter transfer.

[0011] As one possible implementation method, based on the results of rock mass structural plane surveys and the theory of continuous damage mechanics, the determination of the mesoscopic equivalent stiffness tensor specifically includes: By using borehole photography, UAV photogrammetry, or manual geological mapping, the attitude, density, and connectivity of structural surfaces are identified and statistically analyzed; the attitude determines the direction vector of the structural surfaces, the connectivity determines the damage variables of each group of structural surfaces, and the density determines the area proportion weight of each group of structural surfaces. For each set of structural surfaces, construct a direction vector, and construct the damage influence tensor by the cross product of the direction vectors; The damage influence tensor is weighted and superimposed using the damage variables and area proportion weights of each group of structural surfaces to obtain a positive semidefinite fourth-order damage tensor. The fourth-order damage tensor is subjected to spectral truncation to raise the eigenvalues ​​below the first threshold to the first threshold. Based on the initial stiffness tensor of the intact rock block, the fourth-order damage tensor is superimposed onto the initial flexibility matrix in the form of flexibility increments using the flexibility increment method. After inversion, the mesoscopic equivalent stiffness tensor is determined. This accurately restores the weakening effect of joints, bedding, and other structural surfaces on the anisotropy of rock mass mechanics at the mesoscopic level.

[0012] As one possible implementation, based on the microstructure tensor, the anisotropic principal directions of the mesoscopic equivalent stiffness tensor are aligned to obtain the direction-registered mesoscopic equivalent stiffness tensor, specifically including: The three orthogonal principal directions obtained from the eigenvalue decomposition of the microstructure tensor are extracted and used as the reference frame for the anisotropic principal directions. Using the anisotropic principal direction reference frame as the registration target, the six-dimensional contracted matrix form of the mesoscopic equivalent stiffness tensor is rotated to align the anisotropic principal axes of the mesoscopic equivalent stiffness tensor with the principal directions of the microstructure tensor, thus obtaining the directionally registered mesoscopic equivalent stiffness tensor. This eliminates the need for additional compensation for directional deviations, significantly simplifies the constraints of cross-scale tensor mapping, and improves the accuracy of the anisotropic characterization of the macroscopic stiffness tensor.

[0013] As one possible implementation method, automatic symmetry type identification based on the updated macroscopic stiffness tensor specifically includes: The updated macroscopic stiffness tensor is optimized using Euler angle coordinate rotation. The minimum Frobenius distances to five types of standard symmetric tensors—isotropic, transversely isotropic, orthotropic, orthorhombic, and tri-oblique—are calculated. Each minimum Frobenius distance is then divided by the Frobenius norm of the updated macroscopic stiffness tensor to obtain the normalized relative distance. The formula for calculating the normalized relative distance is as follows:

[0014] Where R(θ1, θ2, θ3) is a three-dimensional orthogonal rotation matrix, R T (θ1, θ2, θ3) is the transpose matrix of R(θ1, θ2, θ3), E sym Let E be any one of the five classes of standard symmetric stiffness tensors. g For the updated macroscopic stiffness tensor, d sym This is the normalized relative distance; When the normalized relative distance corresponding to a certain type of standard symmetric tensor does not exceed a second threshold, the updated macroscopic stiffness tensor is reduced to a parameterized representation of that symmetry type. This significantly reduces the number of independent parameters required for inversion and numerical simulation while meeting characterization accuracy requirements, preventing distortion of the anisotropic mechanical characteristics of the rock mass caused by forcibly applying a simplified symmetric model.

[0015] As one possible implementation, a rock mass anisotropic fabrication map library is established based on the tensor distance metric of the reduced macroscopic stiffness tensor, and a numerical calculation model with corresponding accuracy is matched according to the anisotropy degree, specifically including: Based on the Riemann distance of the positive definite tensor manifold, the similarity between the reduced macroscopic stiffness tensor and each reference tensor in the configuration graph library is calculated. The similarity calculation formula is as follows:

[0016] E1 and E2 are two stiffness tensors to be compared. Let Riemann distance be the positive definite tensor space. For reference distance, the average Riemann distance of similar rock masses is used; The anisotropy is calculated based on the ratio of the difference between the maximum and minimum eigenvalues ​​of the reduced macroscopic stiffness tensor to the maximum eigenvalue. Based on the anisotropy degree, the engineering area is divided into strong anisotropy, medium anisotropy, and weak anisotropy regions, and a numerical calculation model with corresponding complexity is matched for each region. After constructing a standardized composition map library, new projects can directly retrieve mature parameters of similar rock masses in the library as initial values ​​for inversion, significantly shortening the parameter calibration and inversion iteration cycle.

[0017] As one possible implementation, the closed-loop iterative update step includes: As the tunnel excavation progresses, newly added on-site surrounding rock displacement monitoring data and newly revealed structural geological information are automatically integrated. Using the current posterior distribution of parameters as the prior, a Bayesian update is performed to refresh the posterior distribution and verifiability index of the macroscopic stiffness tensor. The verifiability index is calculated based on the posterior distribution of the inverted parameters. The standardized residuals between the monitored displacement values ​​and the current parameter prediction values ​​are calculated in real time, and the spatial distribution pattern of the residuals is analyzed through the spatial autocorrelation index. When the spatial autocorrelation index shows that the residuals exhibit a systematic distribution, the recalibration of the mapping matrix is ​​triggered; when the residuals show local high values, a local geological anomaly detection alert is triggered. When the verifiability index reaches the sufficient verification threshold, the iteration stops and the final engineering-scale rock mass anisotropy parameters are output.

[0018] Secondly, a multi-scale tensor positive definite mapping system for classifying rock mass anisotropy is provided, including: The microstructure interpretation module is used to determine the microstructure tensor of a rock sample based on the results of rock sample scanning and image recognition. The micro-damage calculation module is used to determine the micro-equivalent stiffness tensor based on the rock mass structural plane survey results and the continuous damage mechanics theory. The orientation registration module is used to align the microstructure tensor with the micro-equivalent stiffness tensor in anisotropic principal directions based on the microstructure tensor, so as to obtain the orientation-registered micro-equivalent stiffness tensor. The cross-scale mapping module is used to construct a lower triangular non-singular mapping matrix with all diagonal elements positive based on the microscopic equivalent stiffness tensor after orientation registration, and to map the microscopic equivalent stiffness tensor after orientation registration to a macroscopic stiffness tensor using a congruence transformation, and to ensure that the macroscopic stiffness tensor is strictly positive definite with the lower bound of the minimum singular value of the mapping matrix. The Bayesian inversion module is used to invert and update the macroscopic stiffness tensor based on the on-site surrounding rock displacement monitoring data and the Bayesian inversion framework, so as to obtain the updated macroscopic stiffness tensor.

[0019] This invention, by adopting the above technical solutions, has significant technical effects: This invention relies on rock sample scanning to identify and construct a microstructure tensor. It combines on-site structural surface survey and continuous damage mechanics to solve the mesoscopic equivalent stiffness tensor. Then, using the microstructure tensor as a reference, it completes the anisotropic principal direction registration of the mesoscopic stiffness tensor. It achieves cross-scale transformation from mesoscopic to macroscopic stiffness tensor by performing congruent transformation through a diagonally positive lower triangular nonsingular mapping matrix. It uses the lower bound constraint of the minimum singular value of the mapping matrix to ensure that the macroscopic stiffness tensor is positive definite. Finally, it combines surrounding rock monitoring data and a Bayesian framework to complete the inversion of the macroscopic stiffness tensor and quantify the parameter verifiability index. Compared to traditional methods that rely solely on empirical reduction for scale conversion, this invention abandons empirical reduction methods without mathematical constraints. It ensures the strict positive definiteness of the macroscopic stiffness tensor from the perspective of tensor mapping mechanism, effectively overcoming the shortcomings of empirical reduction that easily destroys the positive definiteness of the stiffness matrix and causes anomalies in numerical simulation calculations. At the same time, it unifies the internal orientation benchmark of the rock mass by aligning the principal axes of the microstructure tensor to the mesoscopic equivalent stiffness tensor. It achieves dynamic correction of the macroscopic stiffness tensor to fit the actual field engineering situation by relying on Bayesian inversion, and uses a verifiability index to quantitatively evaluate the reliability of the inversion parameters, thereby improving the physical rationality and engineering credibility of the macroscopic stiffness parameters of the rock mass. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is a flowchart illustrating a method for classifying rock mass anisotropy using multi-scale tensor positive definite mapping according to the present invention. Figure 2 This is a schematic diagram of the multi-scale tensor mapping and positive definiteness preservation principle of the present invention; Figure 3 The mapping matrix L of this invention sg General construction and calibration flowchart; Figure 4 This is the logic block diagram of the adaptive symmetric type recognition and parameter reduction of the present invention. Detailed Implementation

[0022] The present invention will be further described in detail below with reference to the embodiments. The following embodiments are explanations of the present invention, but the present invention is not limited to the following embodiments.

[0023] This invention discloses a method for hierarchical characterization of rock mass anisotropy using multi-scale tensor positive definite mapping, such as... Figure 1 As shown, it includes the following steps: S100, based on the results of rock sample scanning and image recognition, determines the microstructure tensor of the rock sample.

[0024] In this embodiment, representative rock samples are scanned using CT scans, and mineral grain boundaries and macroscopic cracks are automatically identified using a rock image segmentation network.

[0025] Statistical distribution function of mineral grains along their long axis and distribution function of macroscopic crack orientation.

[0026] Based on the average value of the cross product of the unit direction vectors of the long axis of mineral grains, the second-order anisotropic tensor of the microstructure, which simultaneously characterizes the orientation features of mineral grains and internal cracks, is calculated. The second-order tensor is the microstructure tensor.

[0027] The formula for calculating the second-order anisotropic tensor of mesostructure is as follows:

[0028] Where F m To observe the anisotropic second-order tensor of the microstructure, N represents the total number of statistically significant particles / cracks, n i Let be the unit vector of the major axis / crack normal of the i-th particle, and ⊗ be the tensor outer product operation.

[0029] The eigenvalue decomposition of the second-order anisotropic tensor of the microstructure is performed to obtain the three principal values ​​of the microanisotropy and the corresponding three orthogonal principal directions.

[0030] The three principal values ​​of microanisotropy are f1, f2, and f3, satisfying f1 ≥ f2 ≥ f3, and the degree of microanisotropy is defined as follows:

[0031] Where A m The closer to 1, the stronger the anisotropy; the closer to 0, the closer to isotropy.

[0032] By accurately capturing the intrinsic directional properties of rock samples from the microscopic material composition and the origin of fracture development, a unified directional benchmark that fits the actual internal structure of the rock mass is provided for the subsequent registration of the principal axes of the microscopic stiffness tensor. This can completely restore the spatial distribution characteristics of the original anisotropy of the rock mass, avoid the loss of rock mass directional information caused by relying solely on macroscopic geological surveys, and improve the physical fit of the subsequent multi-scale stiffness tensor mapping process.

[0033] S200, based on the results of rock mass structural plane survey and the theory of continuous damage mechanics, determines the microscopic equivalent stiffness tensor.

[0034] In this embodiment, the attitude, density, and connectivity of structural surfaces are identified and statistically analyzed through borehole photography, UAV photogrammetry, or manual geological mapping. The attitude forms the direction vector of the structural surface, the connectivity determines the damage variables of each group of structural surfaces, and the density determines the area proportion weight of each group of structural surfaces. For engineering-scale rock masses, 2 to 4 groups of dominant structural surfaces are usually statistically obtained.

[0035] For each set of structural surfaces, construct a direction vector, and construct the damage influence tensor by the cross product of the direction vectors.

[0036] Specifically, for each set of structural surfaces, a Kelvin-type six-dimensional direction vector b(n) is constructed, whose direction components b(n) are:

[0037] Where n1, n2, and n3 are the three directional cosine components of the unit vector n in a three-dimensional rectangular coordinate system.

[0038] Damage is constructed by constructing the outer product of the direction vector b(n) to affect the tensor M(n):

[0039] The damage influence tensor is weighted and summed using the damage variables and area proportions of each group of structural surfaces to obtain a positive semi-definite fourth-order damage tensor. The formula is as follows:

[0040] Where D s Here, K is the fourth-order damage tensor, and K is the number of structural surface groups. Let λ be the damage variable for the k-th group. k ρ is an empirical coefficient related to connectivity. k This represents the number of structural surfaces per unit area.

[0041] The area proportion weight of the k-th group is... ΣA represents the total exposed area of ​​this group of structural surfaces. j This represents the total area of ​​all structural surfaces within the statistical scope.

[0042] The fourth-order damage tensor D s Mathematical proof of positive semidefiniteness: For any six-dimensional non-zero vector x,

[0043] Due to ω k ≥0, d k ≥0, the squared terms are non-negative, therefore D s Naturally positive semidefinite.

[0044] To ensure numerical stability, the fourth-order damage tensor is spectrally truncated, raising eigenvalues ​​below a first threshold to the level of 10. -6 .

[0045] Based on the initial stiffness tensor of the intact rock block, the fourth-order damage tensor is superimposed onto the initial flexibility matrix in the form of flexibility increments using the flexibility increment method. After inversion, the mesoscopic equivalent stiffness tensor is determined.

[0046] The standard isotropic six-dimensional contracted matrix form of the initial stiffness tensor of the intact rock block is as follows:

[0047] in The first Lamé constant, This is the shear modulus.

[0048] The mesoscopic equivalent stiffness tensor is calculated using the flexibility increment form:

[0049] Where S0 represents the inherent flexibility of the intact rock matrix, A is the damage-flexibility coupling matrix, and S f Add a flexibility term to the joint surface, D s This is a fourth-order damage tensor. Because S... eff It is the sum of a symmetric positive definite matrix and a positive semi-definite matrix, therefore the microscopic equivalent stiffness tensor It naturally maintains symmetry and orthogonality.

[0050] This embodiment can fully integrate real geological survey data from the field, objectively restore the comprehensive weakening effect of the spatial distribution, development scale, and degree of penetration of structural planes on the anisotropy of rock mass stiffness, and ensure the symmetric positive definite property of the final micro-stiffness tensor through the inherent mathematical properties of tensors throughout the process. A complete physical logic chain is formed from geological survey to mechanical parameter conversion, and the obtained micro-stiffness parameters are consistent with the real damage state of the rock mass at the field.

[0051] S300, based on the microstructure tensor, the microscopic equivalent stiffness tensor is anisotropically aligned with the principal directions to obtain the oriented registered microscopic equivalent stiffness tensor.

[0052] In this embodiment, three orthogonal principal directions obtained from the eigenvalue decomposition of the microstructure tensor are extracted and used as anisotropic principal direction reference frames. Using these anisotropic principal direction reference frames as registration targets, the six-dimensional reduced matrix form of the mesoscopic equivalent stiffness tensor is subjected to coordinate rotation, aligning the anisotropic principal axes of the mesoscopic equivalent stiffness tensor with the principal directions of the microstructure tensor, thus obtaining the directionally registered mesoscopic equivalent stiffness tensor. This eliminates the deviation problem of inconsistent orientation references between the two data systems of micromaterial structure and macroscopic structural surfaces, ensuring that the anisotropic variation law of the mesoscopic stiffness tensor fully conforms to the spatial orientation of the original internal structure of the rock mass. It unifies the orientation reference of multi-scale tensors, eliminating scale mapping deviations caused by misalignment of the two sets of tensor orientation references, and providing consistent orientation matching input conditions for subsequent cross-scale stiffness tensor mapping.

[0053] S400, based on the microscopic equivalent stiffness tensor after orientation registration, construct a lower triangular non-singular mapping matrix with all diagonal elements positive, and use congruence transformation to map the microscopic equivalent stiffness tensor after orientation registration into a macroscopic stiffness tensor, and use the lower bound of the minimum singular value of the mapping matrix to ensure that the macroscopic stiffness tensor is positive definite.

[0054] like Figure 2 As shown, a three-level cross-scale characterization system for rock masses is established, ranging from microscopic to mesoscopic to macroscopic. At the microscopic scale, CT scans of cylindrical rock samples are used to identify the internal mineral composition, microfractures, and pores. At the mesoscopic scale, the model reflects the cutting characteristics of numerous joints and fracture surfaces within the rock mass, reflecting its discontinuous structure. Further extending to the macroscopic engineering scale, a rock mass calculation model containing a circular tunnel cross-section is constructed, corresponding to actual underground excavation projects. This achieves cross-scale information transfer and parameter mapping from microscopic information of indoor rock samples to the macroscopic rock mass of tunnel engineering.

[0055] In this embodiment, the microscopic equivalent stiffness tensor after orientation registration is converted into a 6×6 symmetric matrix in six-dimensional contracted matrix representation, and the positive definite mapping relationship preserved by congruence transformation is as follows:

[0056] in Let L be the macroscopic stiffness tensor matrix. sg It is a 6×6 lower triangular nonsingular mapping matrix, with all diagonal elements being positive, therefore L sg Non-singular. det(L) is the determinant of matrix L. A determinant greater than 0 is the core criterion for positive definiteness of the elastic stiffness matrix. ii Let be the main diagonal component of matrix L. Let LT sg be the microscopic equivalent stiffness tensor matrix after orientation registration. sg The transpose of .

[0057] Mathematical proof of positive definiteness preservation: Because L sg Full rank, for any non-zero vector X:

[0058] because The lower bound of the minimum singular value of the mapping matrix guarantees that the macroscopic stiffness tensor is strictly positive definite:

[0059] in for The smallest eigenvalue, for The smallest eigenvalue, For L sg The smallest singular value.

[0060] Abandoning the traditional approach of relying on human experience coefficients for scale reduction, this method avoids disrupting the inherent positive definiteness of the stiffness tensor due to the arbitrariness of manual value selection. By ensuring that the final macroscopic stiffness tensor always meets the positive definiteness requirement from the underlying mathematical mechanism of tensor operations, it effectively reduces anomalies such as iterative divergence and calculation errors caused by the non-positive definiteness of the stiffness matrix during subsequent numerical simulation calculations. At the same time, it fully inherits the anisotropic mechanical characteristics brought about by the internal structure and structural planes of the rock mass in the mesoscopic stage, ensuring that the anisotropic mechanical laws of the rock mass will not be distorted during cross-scale conversion, and the obtained macroscopic stiffness parameters match the real mechanical properties of the rock mass.

[0061] In this embodiment, as Figure 3 As shown, the mapping matrix L sg It features a universal construction and calibration method applicable to any lithology and engineering type, and is not an empirical fit for a specific project. The complete process is as follows: S401, Input data list. Specifically, mapping matrix L sg The calibration requires the following 5 types of input data: fourth-order damage tensor D s and its corresponding mesoscopic equivalent stiffness tensor Macroscopic reference stiffness tensor obtained from field tests or reliable inversion Geological structural features such as the dominant direction of structural planes, number of groups, and connectivity rate, as well as on-site monitoring displacement data. mon and the corresponding numerical simulation displacement field u num Rock mass type and engineering scale parameters include burial depth, tunnel diameter, and lithology classification code.

[0062] S402, L sg The parameterization form is as follows. Specifically, a lower triangular matrix is ​​used for parameterization, and the diagonal elements are in exponential form to ensure positive values:

[0063] Where a i For unconstrained optimization variables, the value range is typically [-1.2, 0.4], corresponding to L. ii ∈[0.3,1.5], which is within the physically reasonable range for rock mass parameter reduction.

[0064] Off-diagonal lower triangular element L ij Linear parameterization is used, where i>j, L ij The value range is [-0.3, 0.3], reflecting the coupling correction between different stiffness components. There are a total of 21 independent optimization variables in the entire matrix.

[0065] S403, Construct the objective function. Specifically, the objective function is an optimization function with multiple weight constraints. The two error terms are normalized using the Frobenius norm to address the issue of dimensional differences.

[0066] The recommended values ​​for each weight term are: W1:W2:W3:W4 = 2:1:0.05:0.02. These values ​​can be adjusted appropriately based on data reliability. For example, W1 can be increased when reference tensor data is sufficient, and W2 can be increased when monitoring data is abundant. The first physical term is the tensor mapping fidelity term, which, after Frobenius norm normalization, ensures that the relative Frobenius distance between the mapped macroscopic tensor and the reference tensor is minimized. The second physical term is the displacement fitting term, which, after Frobenius norm normalization, ensures that the mapped parameters can accurately fit the field-monitored displacement. In the third physical term... Regularization of the identity matrix to avoid L sg The deviation from the identity matrix is ​​too large, the fourth physical term For conditional penalty terms, avoid L sg The inherent pathological condition leads to amplified numerical errors.

[0067] S404, constraint-based optimization solution. Specifically, the constraints include a positive definite engineering constraint that specifies the minimum eigenvalue λ of the mapped tensor. min (LC s L T )≥0.5GPa, parameter range constraint is L ii ∈[0.3,1.5],|L ij |≤0.3 (i>j), the condition number constraint is cond(L)≤10 to ensure numerical stability, and the engineering rationality constraint is that the reduction coefficient in each direction is within the range of [0.3,0.9], which conforms to the engineering experience of the scale effect of rock mass parameters.

[0068] S405, Solution Algorithm and Convergence Criterion. Specifically, the bounded constraint quasi-Newton method L-BFGS-B is used for the solution, with the following settings: Initial values: For new projects, use the L values ​​of the three projects with the highest similarity in the graph library. sg The matrix mean is used as the initial value; when there is no reference, L0 = 0.7 × I is used as the initial estimate.

[0069] Convergence tolerance: The relative change in the objective function is less than 10. -8 And the gradient norm is less than 10 -6 .

[0070] The maximum number of iterations is 200, and convergence is usually achieved in 30 to 50 steps.

[0071] Multiple initial value verification: Three sets of different initial values ​​are used for parallel optimization, and the solution with the smallest objective function is taken as the final solution to avoid local optima.

[0072] S406, Post-calibration verification and cross-validation. Specifically, after calibration, the following three tests must be passed: the positive definiteness test is λ. min (LC s L T If the condition value is greater than 0.5 GPa, the condition number test result is cond(LC). s L T If the error is less than or equal to 20, cross-validation is performed using 3-fold cross-validation. The calibration project is divided into a training set and a validation set. A pass is achieved if the displacement prediction error on the validation set is less than or equal to 20%. If the test fails, recalibration is performed by increasing the regularization weight W3 or by supplementing more calibration project data.

[0073] S407 outputs a calibration mapping matrix based on parameter adjustment rules for different lithologies. Specifically, the empirical initial value range for typical lithologies is as follows: Intact massive granite / basalt: L ii ∈[0.8,1.0], and the off-diagonal terms are close to 0.

[0074] Layered sandstone / limestone: L 11 ,L 22 ∈[0.6,0.8],L 33 ∈[0.4,0.6], the plane direction coupling term is non-zero.

[0075] Gneiss / Slate: L 11 ,L 22 ∈[0.5,0.7],L 33 ∈[0.3,0.5], the schistosity direction coupling term is significant.

[0076] S500, based on the on-site surrounding rock displacement monitoring data and the Bayesian inversion framework, performs inversion and updates on the macroscopic stiffness tensor to obtain the updated macroscopic stiffness tensor, and calculates the overall parameter verifiability index based on the posterior distribution of the inversion parameters.

[0077] Specifically, the macroscopic stiffness tensor matrix is ​​parameterized using Cholesky decomposition, and the inversion parameters are the 21 independent elements of the lower triangular matrix. The prior distribution adopts a multivariate normal distribution.

[0078] Where x0 is the initial value obtained from the cross-scale mapping, Σ0 is the prior covariance matrix, the diagonal elements are set as the square of the standard deviation of the initial value, and the prior upper and lower bounds are taken as the physically reasonable range corresponding to the engineering lithology, for example, an elastic modulus of 180 GPa and a Poisson's ratio range of 0.1-0.45. The likelihood function is as follows:

[0079] Where σ is the standard deviation of the monitoring error, typically ranging from 0.5 to 1.0 mm, determined based on the accuracy of the on-site monitoring equipment. I is the identity matrix, u num To predict displacement, u obs denoted as , where x is the measured displacement in the engineering project, and x is the variable to be inverted.

[0080] The delayed rejection adaptive algorithm is used for MCMC sampling to obtain the posterior distribution and covariance matrix Σ of the inversion parameters; The coefficient of variation (CV) of each inversion parameter is calculated based on the ratio of the diagonal elements of the covariance matrix to the posterior mean of the corresponding parameter. i :

[0081] Where, Σ ii For the diagonal elements of the posterior covariance matrix, μ i Let be the posterior mean of the i-th inversion parameter; Based on the mean coefficient of variation of all inversion parameters, the overall parameter verifiability index is defined as follows:

[0082] Wherein, P is the total number of inversion parameters, and V is the verifiability index, with a value range of 0 to 1. When the verifiability index is below 0.3, it is determined that the monitoring data is insufficient to uniquely determine the parameters and a prompt to supplement monitoring points is issued. When the verifiability index reaches 0.7, it is determined that the parameters have been fully verified.

[0083] Monitoring deployment optimization is performed based on Fisher information gain. For each potential new monitoring point j, the expected Fisher information matrix F after the addition of that point is calculated. j :

[0084] J j Let F be the sensitivity matrix of the displacement at point j to the parameters. old Let σ be the old Fisher information matrix accumulated and saved from the previous iteration, and let σ be the standard deviation of the monitoring error. The information gain is defined as the expected reduction in the trace of the covariance matrix IG(j), calculated using the finite difference method.

[0085] Based on the information gain sorted from largest to smallest, the monitoring points with the largest information gain are recommended first.

[0086] This embodiment relies on the posterior distribution of the parameters obtained through inversion to quantify the overall reliability of the entire set of mechanical parameters. It can intuitively determine the constraint effect of existing monitoring data on mechanical parameters and promptly prompt improvements to the monitoring deployment when data support is insufficient. Furthermore, it can select the optimal new monitoring points by quantifying information gain, specifically strengthening the monitoring system and improving parameter identification effectiveness with minimal deployment cost.

[0087] S600, such as Figure 4 As shown, based on the updated macroscopic stiffness tensor, symmetry type is automatically identified. When the deviation between the updated macroscopic stiffness tensor and a certain standard symmetry type is within a set error range, the updated macroscopic stiffness tensor is reduced to the parameterized representation of that symmetry type to obtain the reduced macroscopic stiffness tensor.

[0088] In this embodiment, the updated macroscopic stiffness tensor is optimized using Euler angle coordinate rotation, and its minimum Frobenius distance with five types of standard symmetric tensors—isotropic, transversely isotropic, orthotropic, orthorhombic, and triclinic—is calculated. Each minimum Frobenius distance is then divided by the Frobenius norm of the updated macroscopic stiffness tensor to obtain the normalized relative distance. The formula for calculating the normalized relative distance is as follows:

[0089] Where R(θ1, θ2, θ3) is a three-dimensional orthogonal rotation matrix, R T (θ1, θ2, θ3) is the transpose matrix of R(θ1, θ2, θ3), E sym Let E be any one of the five classes of standard symmetric stiffness tensors. g For the updated macroscopic stiffness tensor, d sym This is the normalized relative distance.

[0090] When the normalized relative distance corresponding to a certain type of standard symmetric tensor does not exceed a second threshold, the updated macroscopic stiffness tensor is reduced to a parameterized representation of that symmetry type. The second threshold is that the relative error with a certain type of symmetric tensor does not exceed 12%, and it is automatically reduced to a parameterized representation of the corresponding symmetry type: isotropic, transversely isotropic, orthotropic, orthogonal symmetric; otherwise, the complete tri-oblique symmetric form with 21 independent parameters is retained. This achieves adaptive representation from simple to complex, minimizing parameter dimensionality while ensuring accuracy.

[0091] S700, based on the tensor distance metric of the reduced macroscopic stiffness tensor, establish a rock mass anisotropic fabrication map library, and according to the anisotropy degree, match the numerical calculation model with the corresponding accuracy of the reduced macroscopic stiffness tensor to obtain the matched engineering calculation parameters.

[0092] In this embodiment, based on the Riemann distance of the positive definite tensor manifold, the similarity between the reduced macroscopic stiffness tensor and each reference tensor in the configuration graph library is calculated. The similarity calculation formula is as follows:

[0093] E1 and E2 are two stiffness tensors to be compared. Let Riemann distance be the positive definite tensor space. For reference distance, the average Riemann distance of similar rock masses is used. A matrix diagram library is established. When the similarity between a new project and a project in the library is greater than or equal to 0.85, the parameter experience of that project can be directly referenced, and the initial parameter error can usually be controlled within 20%.

[0094] Anisotropy is calculated based on the ratio of the difference between the largest and smallest eigenvalues ​​of the reduced macroscopic stiffness tensor to the largest eigenvalue. The engineering area is then divided into strong anisotropy, moderate anisotropy, and weak anisotropy regions according to this anisotropy. Numerical calculation models of corresponding complexity are matched to each region. The strong anisotropy region uses full parameter calculation, the moderate anisotropy region uses an orthogonal anisotropy model, and the weak anisotropy region uses a simplified isotropic model.

[0095] A three-tiered standardized implementation process is established for different design stages and project scales. The entire process is divided into tiered levels according to the entire lifecycle from the project's early stages to construction implementation. Based on the project's survey and design stages, the importance of the project, and the required control precision, survey and monitoring methods, data analysis methods, and output standards are progressively deployed at each level, gradually transitioning from extensive and rapid qualitative grading to refined parameter closed-loop optimization. Level 1 relies on lightweight remote sensing and indoor scanning methods to quickly define basic parameter ranges, serving the project's early assessment. Level 2 overlays in-situ monitoring and conventional numerical simulation to determine the parameters required for the formal design and supporting engineering schemes. Level 3 integrates comprehensive refined geological exploration, a high-density monitoring system, and Bayesian dynamic inversion closed-loop calibration, continuously correcting rock mechanics parameters based on measured data throughout the construction process, and outputting optimized construction and support design schemes adapted to the actual geological conditions on site. The three levels progressively improve in terms of human and material resources, implementation cycle, and technical precision, accurately matching the work objectives of different stages: pre-feasibility study, preliminary feasibility study design, and construction implementation. An example is provided below.

[0096] The rapid assessment of Level 1 requires only 35 rock sample CT scans and surface UAV structural surface surveys. It directly provides initial parameter values ​​and uncertainty ranges through cross-scale mapping, making it suitable for the pre-feasibility study stage. The cycle is about 1 week, and the cost is about 10.2 million yuan.

[0097] The conventional design is at level two, with the addition of multi-point displacement gauges monitoring 35 key sections. The first Bayesian update is completed after excavating 12 sections. It is suitable for feasibility study and preliminary design stages, with a cycle of approximately 46 weeks and a cost of approximately 50.8 million yuan.

[0098] The system features a refined three-level inversion method, enhanced with borehole photography and detailed geological logging, 58 monitoring sections, and closed-loop updates throughout the entire excavation process. It is suitable for both the bidding and construction phases, with a cycle of approximately 23 months and a cost of approximately 1 million to 1.5 million yuan.

[0099] With the development of supporting automated calculation software, ordinary geological engineers can master the basic operation after one week of training, without needing a deep theoretical foundation in anisotropic mechanics.

[0100] This embodiment constructs a rock mass anisotropic composition library based on tensor spatial distances. Engineering parameters are efficiently referenced through library comparison. Work areas are divided according to the degree of anisotropy, and numerical models of corresponding precision are adapted. It is equipped with a tiered implementation mode suitable for different design stages of the project, and automated processing tools lower the professional operation threshold, ensuring the reliability of the analysis while considering the efficiency and economy of engineering implementation.

[0101] S800, based on the matched engineering calculation parameters, outputs the final engineering-scale rock mass anisotropy parameters through closed-loop iterative updates, which are used for surrounding rock stability analysis and support design.

[0102] In this embodiment, as the tunnel excavation progresses, newly added on-site surrounding rock displacement monitoring data and newly revealed structural geological information are automatically integrated. Using the current posterior distribution of parameters as the prior, a Bayesian update is performed to refresh the posterior distribution of the macroscopic stiffness tensor and the verifiability index, which is calculated based on the posterior distribution of the inverted parameters. The standardized residuals between the monitored displacement values ​​and the predicted values ​​of the current parameters are calculated in real time, and the spatial distribution pattern of the residuals is analyzed through the spatial autocorrelation index. When the spatial autocorrelation index shows that the residuals exhibit a systematic distribution, the recalibration of the mapping matrix is ​​triggered. When the residuals exhibit local high values, a local geological anomaly detection alert is triggered. When the verifiability index reaches the sufficient verification threshold, the iteration stops and the final engineering-scale rock mass anisotropy parameters are output. The entire mechanism continuously optimizes rock mass mechanical parameters in accordance with the dynamic construction scenario of the project, promptly identifies anomalies at the geological and computational levels, and ultimately obtains rock mass anisotropy parameters that conform to the actual on-site working conditions.

[0103] As an example, taking the left bank water diversion tunnel project of a hydropower station in Southwest China as an example, the water diversion tunnel is approximately 2.3 km long, 380-520 m deep, and 9.2 m in diameter, and was excavated in stages using the drill-and-blast method. The surrounding rock is mainly biotite plagioclase gneiss with well-developed foliation, trending N35°E, dipping northwest at an angle of 68°, and exhibiting obvious anisotropic characteristics. The elastic modulus of the intact rock block in the laboratory test was E=52 GPa, and the Poisson's ratio was 0.24. The anisotropic parameters of the tunnel section from K0+850 to K1+150, a total length of 300 m, were characterized using the method of this invention.

[0104] The first step involved CT scanning of rock samples and calculation of the microstructure tensor. Five representative rock samples, each 100 mm in diameter and 200 mm in height, were scanned using a standard medical CT scanner with a slice thickness of 0.625 mm and a voltage of 120 kV. The distribution of mineral grains along their long axes showed a dominant strike of N30°–50°E, dipping northwest, which was generally consistent with the foliation direction. The eigenvalues ​​of the microstructure tensor were: f1 = 0.58, f2 = 0.29, f3 = 0.13, and the microanisotropy A... m =0.78.

[0105] The second step involved structural plane investigation and microscopic damage tensor calculation. Aerial surveys of the tunnel entrance and exit outcrops, combined with borehole photography, identified 217 effective structural planes, which were divided into 3 groups of dominant joints and 1 group of foliation. The first group of foliation had an attitude of 135°∠70° and a surface density of 0.28 planes / m². 2 The connectivity rate is 0.65; the joint orientation of the second group is 45°∠85°, and the surface density is 0.12 joints / m². 2 The connectivity is 0.42; the joint orientation of the third group is 270°∠65°, and the areal density is 0.09 joints / m². 2 The connectivity rate is 0.35.

[0106] Damage variables are calculated as follows: d1 = 1 - exp(-1.5 × 0.28) = 0.34; d2 = 1 - exp(-1.0 × 0.12) = 0.11; d3 = 1 - exp(-0.8 × 0.09) = 0.07. Area proportion weights are: ω1 = 0.58, ω2 = 0.25, ω3 = 0.17.

[0107] The six-dimensional contracted matrix form of the mesoscopic damage tensor constructed based on the outer product is as follows:

[0108] The damage tensor is positive semidefinite, and the minimum eigenvalue λ is obtained through eigenvalue decomposition. min (D s The equation 0.026 ≥ 0 satisfies the positive semidefinite requirement. The elastic modulus E is 52 GPa, and the Poisson's ratio is... The shear modulus is 0.24. GPa, first Lamé constant GPa.

[0109]

[0110] The microscopic equivalent stiffness tensor is calculated using the flexibility increment method:

[0111] Microscopic verification of the positive definiteness of the stiffness matrix, minimum eigenvalue λ min (C s =7.2GPa>0, condition number cond(C) s =6.8, which satisfies the positive definiteness requirement.

[0112] The third step is cross-scale congruential mapping. This involves using the mapping matrix L. sg A general construction and calibration method was used, employing measured data from three other completed tunnel sections of the power station. The weights were set to w1:w2:w3:w4=2:1:0.05:0.02, and the L-BFGS-B algorithm was used for 42 iterative steps to converge. The resulting lower triangular mapping matrix was:

[0113] Post-calibration verification: λ min (LC s L T =4.3 GPa > 0.5 GPa engineering threshold, positive definiteness test passed; due to cond(LC) s L T =14.7 < 20, the condition number test is passed; the average displacement prediction error of the validation set is 13.8% < 20%, the 3-fold cross-validation is passed.

[0114] Lsg Matrix positive definiteness verification: min(L) of the diagonal elements ii ) = 0.68 > 0, minimum singular value σ min (L) = 0.66. The initial value of the macroscopic stiffness tensor is obtained through congruence mapping:

[0115] Positive definiteness verification after mapping: minimum eigenvalue λ min (E g,0 = 4.3 GPa > 0, satisfying the minimum singular value lower bound σ min (L) 2 ·λ min (C s )=0.66 2 ×7.2 = 3.14 GPa, the actual value 4.3 > 3.14, so the theory holds true. The mapping yields a modulus of approximately 26.4 GPa in the foliation direction and approximately 14.8 GPa in the perpendicular foliation direction, showing clear transverse isotropic characteristics.

[0116] The fourth step is Bayesian inversion and convergence. Five monitoring sections were set up on site, and five multi-point displacement gauges were installed at each section, with depths of 3m, 6m, 9m, 12m, and 15m, respectively. Displacement data were collected continuously for six months during the excavation process, with a monitoring error standard deviation σ=0.8mm.

[0117] Before excavation, there was no initial inversion with monitoring data. It was based solely on cross-scale mapping priors, with a parameter verifiability index of V0=0.21, resulting in high uncertainty. The typical parameter 95% confidence interval width was 17.8 GPa.

[0118] In the first update, 15 displacement monitoring data points from the first cross-section were accessed after excavation to 20m. The parameter verifiability index V1=0.38, and the average width of the 95% confidence interval narrowed by 35%.

[0119] In the second update, 45 displacement monitoring data points from 3 cross sections were collected after excavation to 60m. The parameter verifiability index V2=0.62, and the average width of the 95% confidence interval narrowed by 68%.

[0120] Finally, the excavation reached 120m, and displacement monitoring data from all 5 cross-sections, totaling 75 data points, were collected. The coefficients of variation for the 9 orthogonal anisotropy parameters were: CV(E1)=0.056, CV(E2)=0.074, CV(E3)=0.070, CV(G23)=0.103, CV(G13)=0.083, CV(G12)=0.084, CV(ν12)=0.115, CV(ν13)=0.095, CV(ν23)=0.105. The average coefficient of variation... The verifiability index V = 1 - 0.087 = 0.913, which meets the sufficient verification standard.

[0121] The final inversion parameters of the orthogonal anisotropy model are: parallel to the foliation direction, E1 = 25.8 ± 1.4 GPa, E2 = 23.4 ± 1.7 GPa; perpendicular to the foliation direction, E3 = 14.7 ± 1.0 GPa; shear modulus G... 23 =6.4±0.6GPa, G 13 =6.8±0.5GPa, G 12 =9.1±0.7GPa; Poisson's ratio , , The final stiffness matrix has a minimum eigenvalue λ. min (E g ) = 4.0 GPa > 0, positive definiteness remains true.

[0122] Step 5: Verification and Engineering Application. Compared with the results of 5 sets of field deformation tests, the modulus error range in each direction was 8%-15%, with an average error of 11.2%. Compared with traditional methods: traditional isotropic inversion yielded a single elastic modulus E=20.8GPa, and the maximum error between the numerically calculated tunnel perimeter deformation and the monitored value was 38%. The maximum error in the tunnel perimeter deformation obtained by the anisotropic inversion of this invention was 12%. Fabrication map verification: the deviation between the anisotropic principal axis and the foliation strike obtained by the inversion was less than 7°, consistent with geological understanding.

[0123] The project adopted a two-level process, with a total implementation period of 5 weeks and a total cost of approximately 650,000 yuan. After the parameters were fully verified, they were directly used for support parameter optimization, saving approximately 12% of the support engineering work compared to traditional experience-based design.

[0124] To demonstrate the universality of the method of this invention, the verification results of a layered sandstone tunnel on a highway in Southwest China are supplemented. The surrounding rock of this tunnel is mainly medium-thick sandstone, with a bedding angle of 15°∠35°. The rock block test showed an elastic modulus E=48GPa and a Poisson's ratio of... =0.22, burial depth is 260~320m, and tunnel diameter is 11.6m.

[0125] Using monitoring data from two completed traffic tunnels in the same area, plus the initial excavation monitoring data, as the third set of calibration data, L was calibrated. sg The matrix yields:

[0126] Comparison of core verification metrics: The minimum eigenvalue of micro-stiffness is 6.1 GPa > 0, and the minimum eigenvalue of macro-stiffness after mapping is λ. min =3.2GPa > 0.5GPa engineering threshold, positive definiteness holds. Theoretical lower bound verification: σ min (L)2 ·λ min (C s )=0.57 2 ×6.1 = 1.98 GPa, the actual value 3.2 > 1.98, so the theory holds true. Condition number cond(E) g The value is 12.7, indicating a good state. The average displacement prediction error is 10.5%, with a maximum of 14.2%, far superior to the 41% of the empirical reduction method and the 27% of the linear mapping method. The verifiability index V=0.87, meeting the sufficient verification standard, with the anisotropic principal axis deviating from the bedding plane strike by less than 5°, and the physical structure remaining intact. The positive definite congruent mapping method of this invention is applicable not only to gneiss but also to other anisotropic rock masses such as layered sandstone, possessing engineering universality.

[0127] As a comparative example, Comparative Example 1 uses the conventional empirical reduction method, employing a reduction factor of 0.5 commonly used for gneiss in Southwest China, to directly reduce the indoor test modulus to a scalar value:

[0128] While the empirical reduction method avoids negative stiffness, it suffers from four core drawbacks: ① Complete loss of anisotropic information; for layered and foliated rock masses, isotropic assumptions lead to principal axis deviations exceeding 30°; ② Distortion of the stiffness tensor's physical structure, failing to reflect modulus differences and coupling relationships in different directions; ③ Large displacement prediction error; the predicted crown displacement is 12.8 mm, while the measured value is 8.3 mm, a relative error of 54%; ④ Lack of uncertainty quantification capability; it cannot provide parameter confidence intervals or verifiability indices, requiring multiplication by a safety factor of 1.5 to 2.0 in engineering applications, resulting in overly conservative approaches. Furthermore, due to its overly simplified calculations, it cannot perform refined evaluations of surrounding rock stability.

[0129] Compared with Example 2, which uses unconstrained linear tensor mapping and eigenvalue truncation correction, this example employs a conventional least-squares unconstrained linear mapping E lin =A·C s +b, without applying positive definiteness constraints, if negative eigenvalues ​​appear after mapping, a forced truncation correction is performed, that is, eigenvalues ​​less than 0 are forcibly set to 0.1GPa.

[0130] The original minimum eigenvalue λ after mapping min,raw = -0.82GPa, indicating a non-physical negative stiffness, suggesting that the unconstrained linear mapping itself carries an inherent risk of violating positive definiteness; the minimum eigenvalue λ after truncation correction. min,fix=0.10GPa, the minimum eigenvalue is close to zero, below the 0.5GPa engineering threshold; the condition number after correction is 187, much larger than the 14.7 of this invention, indicating poor numerical stability; the numerical simulation of the tunnel surrounding rock barely converged, but the number of iterations increased by 3 times, and local stress anomalies appeared, with the maximum principal stress reaching 87MPa, far exceeding the compressive strength of gneiss; the predicted value of the arch displacement was 10.6mm, and the measured value was 8.3mm, with a relative error of 28%; the verifiability index V=0.57, only meeting the partial verification standard; the average coefficient of variation... =0.186, which is 114% higher than the 0.087 of the present invention; the anisotropic principal axis of the original microscopic tensor and the foliation angle are 7°, and the angle after correction becomes 23°, resulting in serious distortion of the physical structure.

[0131] This comparative example fully illustrates that without a positive definite preservation design during the cross-scale mapping stage, although subsequent truncation corrections can be calculated with difficulty, they will severely damage the physical meaning and numerical stability of the parameters.

[0132] This application also proposes a multi-scale tensor positive definite mapping system for classifying rock mass anisotropy, including: The microstructure interpretation module is used to determine the microstructure tensor of a rock sample based on the results of rock sample scanning and image recognition. The micro-damage calculation module is used to determine the micro-equivalent stiffness tensor based on the rock mass structural plane survey results and the continuous damage mechanics theory. The orientation registration module is used to align the microstructure tensor with the micro-equivalent stiffness tensor in anisotropic principal directions based on the microstructure tensor, so as to obtain the orientation-registered micro-equivalent stiffness tensor. The cross-scale mapping module is used to construct a lower triangular non-singular mapping matrix with all diagonal elements positive based on the microscopic equivalent stiffness tensor after orientation registration, and to map the microscopic equivalent stiffness tensor after orientation registration to a macroscopic stiffness tensor using a congruence transformation, and to ensure that the macroscopic stiffness tensor is strictly positive definite with the lower bound of the minimum singular value of the mapping matrix. The Bayesian inversion module is used to invert and update the macroscopic stiffness tensor based on the on-site surrounding rock displacement monitoring data and the Bayesian inversion framework, so as to obtain the updated macroscopic stiffness tensor.

[0133] As the device embodiment is basically similar to the method embodiment, the description is relatively simple, and relevant parts can be found in the description of the method embodiment.

[0134] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0135] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, apparatus, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0136] This invention is described with reference to flowchart illustrations and / or block diagrams of the method, terminal device (system), and computer program product according to the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing terminal device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing terminal device, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0137] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing terminal device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0138] These computer program instructions can also be loaded onto a computer or other programmable data processing terminal equipment, causing a series of operational steps to be performed on the computer or other programmable terminal equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable terminal equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0139] It should be noted that: The phrase "an embodiment" or "an embodiment" used in this specification means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the invention. Therefore, the phrase "an embodiment" or "an embodiment" appearing in various places throughout the specification does not necessarily refer to the same embodiment.

[0140] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the invention.

[0141] Furthermore, it should be noted that the shapes and names of the components in the specific embodiments described in this specification may differ. All equivalent or simple variations made to the structure, features, and principles described in this patent concept are included within the protection scope of this patent. Those skilled in the art to which this invention pertains may make various modifications or additions to the described specific embodiments or use similar methods to substitute them, as long as they do not depart from the structure of this invention or exceed the scope defined in these claims, they should all fall within the protection scope of this invention.

Claims

1. A method for hierarchical characterization of rock mass anisotropy using multi-scale tensor positive definite mapping, characterized in that, Includes the following steps: S1, Based on the results of rock sample scanning and image recognition, determine the microstructure tensor of the rock sample; S2, based on the rock mass structure plane survey results and the continuous damage mechanics theory, the microscopic equivalent stiffness tensor is determined; S3. Based on the microstructure tensor, the microscopic equivalent stiffness tensor is anisotropically aligned with the principal directions to obtain the microscopic equivalent stiffness tensor after orientation registration. S4. Based on the microscopic equivalent stiffness tensor after orientation registration, construct a lower triangular non-singular mapping matrix with all diagonal elements positive. Use congruence transformation to map the microscopic equivalent stiffness tensor after orientation registration into a macroscopic stiffness tensor. The lower bound of the minimum singular value of the mapping matrix ensures that the macroscopic stiffness tensor is positive definite. S5. Based on the on-site surrounding rock displacement monitoring data and the Bayesian inversion framework, the macroscopic stiffness tensor is inverted and updated to obtain the updated macroscopic stiffness tensor.

2. The method for hierarchical characterization of rock mass anisotropy using multi-scale tensor positive definite mapping according to claim 1, characterized in that, Step S4 includes: The positive definite mapping relationship using congruential transformation is as follows: in Let L be the macroscopic stiffness tensor matrix. sg It is a lower triangular non-singular mapping matrix. Let LT sg be the microscopic equivalent stiffness tensor matrix after orientation registration. sg The transpose of the matrix; The lower bound of the minimum singular value of the mapping matrix guarantees that the macroscopic stiffness tensor is strictly positive definite: in for The smallest eigenvalue, for The smallest eigenvalue, For L sg The smallest singular value.

3. The method for hierarchical characterization of rock mass anisotropy using multi-scale tensor positive definite mapping according to claim 1, characterized in that, It also includes the following steps: S6. Based on the updated macroscopic stiffness tensor, perform automatic symmetry type identification. When the deviation between the updated macroscopic stiffness tensor and a certain standard symmetry type is within a set error range, reduce the updated macroscopic stiffness tensor to the parameterized representation of the symmetry type to obtain the reduced macroscopic stiffness tensor. S7. Based on the tensor distance metric of the reduced macroscopic stiffness tensor, establish a rock mass anisotropic fabrication map library, and obtain the matched engineering calculation parameters by matching the numerical calculation model with the corresponding accuracy for the reduced macroscopic stiffness tensor according to the anisotropy. S8. Based on the matched engineering calculation parameters, the final engineering-scale rock mass anisotropy parameters are updated and output through closed-loop iteration, which are used for surrounding rock stability analysis and support design.

4. The method for hierarchical characterization of rock mass anisotropy using multi-scale tensor positive definite mapping according to claim 1, characterized in that, Step S1 specifically includes: Representative rock samples were scanned using CT scans, and mineral grain boundaries and macroscopic cracks were automatically identified using a rock image segmentation network. Statistical analysis of the distribution function of the long axis of mineral grains and the distribution function of the macroscopic crack orientation; Based on the average value of the cross product of the unit direction vectors of the long axis of mineral grains, the second-order anisotropic tensor of the microstructure that simultaneously characterizes the orientation features of mineral grains and internal cracks is calculated. The second-order tensor is the microstructure tensor. The eigenvalue decomposition of the second-order anisotropic tensor of the microstructure is performed to obtain the three principal values ​​of the microanisotropy and the corresponding three orthogonal principal directions.

5. The method for hierarchical characterization of rock mass anisotropy using multi-scale tensor positive definite mapping according to claim 4, characterized in that, Step S2 specifically includes: By using borehole photography, UAV photogrammetry, or manual geological mapping, the attitude, density, and connectivity of structural surfaces are identified and statistically analyzed; the attitude determines the direction vector of the structural surfaces, the connectivity determines the damage variables of each group of structural surfaces, and the density determines the area proportion weight of each group of structural surfaces. For each set of structural surfaces, construct a direction vector, and construct the damage influence tensor by the cross product of the direction vectors; The damage influence tensor is weighted and superimposed using the damage variables and area proportion weights of each group of structural surfaces to obtain a positive semidefinite fourth-order damage tensor. The fourth-order damage tensor is subjected to spectral truncation to raise the eigenvalues ​​below the first threshold to the first threshold. Based on the initial stiffness tensor of the intact rock block, the fourth-order damage tensor is superimposed onto the initial flexibility matrix in the form of flexibility increments using the flexibility increment method. After inversion, the mesoscopic equivalent stiffness tensor is determined.

6. The method for hierarchical characterization of rock mass anisotropy using multi-scale tensor positive definite mapping according to any one of claims 4 or 5, characterized in that, Step S3 specifically includes: The three orthogonal principal directions obtained from the eigenvalue decomposition of the microstructure tensor are extracted and used as the reference frame for the anisotropic principal directions. Using the anisotropic principal direction reference frame as the registration target, the six-dimensional contracted matrix form of the mesoscopic equivalent stiffness tensor is rotated in coordinates to align the anisotropic principal axis of the mesoscopic equivalent stiffness tensor with the principal direction of the microstructure tensor, thereby obtaining the directionally registered mesoscopic equivalent stiffness tensor.

7. The method for hierarchical characterization of rock mass anisotropy using multi-scale tensor positive definite mapping according to claim 3, characterized in that, Step S6 specifically includes: The updated macroscopic stiffness tensor is optimized using Euler angle coordinate rotation. The minimum Frobenius distances to five types of standard symmetric tensors—isotropic, transversely isotropic, orthotropic, orthorhombic, and tri-oblique—are calculated. Each minimum Frobenius distance is then divided by the Frobenius norm of the updated macroscopic stiffness tensor to obtain the normalized relative distance. The formula for calculating the normalized relative distance is as follows: Where R(θ1, θ2, θ3) is a three-dimensional orthogonal rotation matrix, R T (θ1, θ2, θ3) is the transpose matrix of R(θ1, θ2, θ3), E sym Let E be any one of the five classes of standard symmetric stiffness tensors. g For the updated macroscopic stiffness tensor, d sym This is the normalized relative distance; When the normalized relative distance corresponding to a certain type of standard symmetric tensor does not exceed the second threshold, the updated macroscopic stiffness tensor is reduced to the parameterized representation of that symmetry type.

8. The method for hierarchical characterization of rock mass anisotropy using multi-scale tensor positive definite mapping according to claim 7, characterized in that, Step S7 specifically includes: Based on the Riemann distance of the positive definite tensor manifold, the similarity between the reduced macroscopic stiffness tensor and each reference tensor in the configuration graph library is calculated. The similarity calculation formula is as follows: E1 and E2 are two stiffness tensors to be compared. Let Riemann distance be the positive definite tensor space. For reference distance, the average Riemann distance of similar rock masses is used; The anisotropy is calculated based on the ratio of the difference between the maximum and minimum eigenvalues ​​of the reduced macroscopic stiffness tensor to the maximum eigenvalue. Based on the anisotropy degree, the engineering area is divided into a strong anisotropy region, a medium anisotropy region, and a weak anisotropy region, and a numerical calculation model with corresponding complexity is matched for each region.

9. The method for hierarchical characterization of rock mass anisotropy using multi-scale tensor positive definite mapping according to claim 8, characterized in that, The closed-loop iterative update steps include: As the tunnel excavation progresses, newly added on-site surrounding rock displacement monitoring data and newly revealed structural geological information are automatically integrated. Using the current posterior distribution of parameters as the prior, a Bayesian update is performed to refresh the posterior distribution and verifiability index of the macroscopic stiffness tensor. The verifiability index is calculated based on the posterior distribution of the inverted parameters. The standardized residuals between the monitored displacement values ​​and the current parameter prediction values ​​are calculated in real time, and the spatial distribution pattern of the residuals is analyzed through the spatial autocorrelation index. When the spatial autocorrelation index shows that the residuals exhibit a systematic distribution, the recalibration of the mapping matrix is ​​triggered; when the residuals show local high values, a local geological anomaly detection alert is triggered. When the verifiability index reaches the sufficient verification threshold, the iteration stops and the final engineering-scale rock mass anisotropy parameters are output.

10. A multi-scale tensor positive definite mapping system for classifying rock mass anisotropy, characterized in that, include: The microstructure interpretation module is used to determine the microstructure tensor of a rock sample based on the results of rock sample scanning and image recognition. The micro-damage calculation module is used to determine the micro-equivalent stiffness tensor based on the rock mass structural plane survey results and the theory of continuous damage mechanics. The orientation registration module is used to align the microstructure tensor with the micro-equivalent stiffness tensor in anisotropic principal directions based on the microstructure tensor, so as to obtain the orientation-registered micro-equivalent stiffness tensor. The cross-scale mapping module is used to construct a lower triangular non-singular mapping matrix with all diagonal elements positive based on the microscopic equivalent stiffness tensor after orientation registration, and to map the microscopic equivalent stiffness tensor after orientation registration to a macroscopic stiffness tensor using a congruence transformation, and to ensure that the macroscopic stiffness tensor is strictly positive definite with the lower bound of the minimum singular value of the mapping matrix. The Bayesian inversion module is used to invert and update the macroscopic stiffness tensor based on the on-site surrounding rock displacement monitoring data and the Bayesian inversion framework to obtain the updated macroscopic stiffness tensor. At the same time, it calculates the overall parameter verifiability index based on the posterior distribution of the inversion parameters.

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