A method and system for rock-soil mass stability analysis based on strain energy density

Abstract

The application provides a rock-soil body stability analysis method and system based on strain energy density, relates to the technical field of rock-soil body stability analysis, and comprises the following steps: obtaining rock-soil body parameters through field investigation and indoor test; combining the rock-soil body parameters, generalized Hooke's law and Mohr-Coulomb yield criterion to obtain a strain tensor expression, and performing stress tensor calculation to obtain the elastic stress tensor, strain tensor and plastic strain tensor of the rock-soil body; then performing integral calculation respectively to obtain the total strain energy density increment of the rock-soil body under different stress states; and performing stability analysis based on the total strain energy density increment of the rock-soil body under different stress states to obtain the stability abnormal area of the rock-soil body. The application comprehensively considers the elastic and plastic deformation characteristics of the rock-soil body, and improves the accuracy of stability evaluation.

Description

Technical Field

[0001] This invention relates to the field of rock and soil stability analysis technology, and more specifically, to a method and system for rock and soil stability analysis based on strain energy density. Background Technology

[0002] With the continuous development of geotechnical engineering in areas such as slope protection, foundation reinforcement, and underground tunnels, the stability analysis of soil and rock masses under complex stress environments has become a key issue in ensuring engineering safety and economy. Currently, the stability assessment methods commonly used in engineering practice mainly include the limit equilibrium method and numerical analysis. The limit equilibrium method, based on mechanical equilibrium, is computationally simple and suitable for macroscopic overall stability analysis. However, this method does not consider the stress-strain relationship and deformation evolution process of the soil and rock mass, making it difficult to reflect local instability mechanisms, especially failing to accurately identify potential sliding surfaces or local failure zones. In contrast, numerical methods such as the finite element method can simulate the stress and deformation distribution within the soil and rock mass, compensating for the shortcomings of the limit equilibrium method. However, these methods have extremely high requirements for model establishment, constitutive parameter selection, computational accuracy, and resource allocation. Furthermore, the identification of plastic zones relies on complex constitutive models and nonlinear solution strategies, resulting in high application difficulty and low computational efficiency in engineering practice, failing to meet the needs for fast, accurate, and engineering-applicable stability analysis.

[0003] There is an urgent need for a method and system for analyzing the stability of soil and rock masses based on strain energy density to solve the above problems. Summary of the Invention

[0004] The purpose of this invention is to provide a method and system for analyzing the stability of soil and rock masses based on strain energy density, in order to improve the aforementioned problems. To achieve the above objective, the technical solution adopted by this invention is as follows:

[0005] Firstly, this application provides a method for analyzing the stability of soil and rock masses based on thermodynamic-tensor invariant coupling, including:

[0006] Obtain geotechnical parameters from field investigations and laboratory tests;

[0007] The strain tensor expression is obtained by combining the parameters of the soil and rock mass, the generalized Hooke's law and the Mohr-Coulomb yield criterion, and the stress tensor is calculated to obtain the elastic stress tensor, strain tensor and plastic strain tensor of the soil and rock mass.

[0008] The total strain energy density increment of the rock and soil mass under different stress states is obtained by integrating the elastic stress tensor, elastic strain tensor, and plastic strain tensor of the rock and soil mass respectively.

[0009] Stability analysis was performed on the soil and rock mass under different stress states to identify areas of instability in the soil and rock mass.

[0010] Secondly, this application also provides a rock and soil stability analysis system based on thermodynamic-tensor invariant coupling, comprising:

[0011] The acquisition unit is used to acquire soil and rock parameters from field investigations and laboratory tests.

[0012] The first calculation unit is used to combine the soil and rock parameters, the generalized Hooke's law and the Mohr-Coulomb yield criterion to obtain the strain tensor expression, and to perform stress tensor calculation to obtain the elastic stress tensor, strain tensor and plastic strain tensor of the soil and rock.

[0013] The second calculation unit is used to perform integral calculations based on the elastic stress tensor, elastic strain tensor and plastic strain tensor of the rock and soil mass respectively, to obtain the total strain energy density increment of the rock and soil mass under different stress states.

[0014] The analysis unit is used to perform stability analysis based on the total strain energy density increment of the soil and rock mass under different stress states, and to obtain the stability anomaly region of the soil and rock mass.

[0015] The beneficial effects of this invention are as follows:

[0016] This invention introduces precise derivations of elastic and plastic strain energy densities, combines the Mohr-Coulomb yield criterion with the correlated flow rule, and constructs a strain energy density expression under the stress-strain relationship, thereby forming a stability assessment index. This method fully utilizes field-obtained mechanical parameters to establish a continuous calculation chain from soil and rock parameters → stress and strain → energy distribution → stability judgment, achieving a unified description of the entire elastic-plastic process of soil and rock.

[0017] This invention comprehensively considers the elastic and plastic deformation characteristics of soil and rock, and compared with the traditional limit equilibrium method, it can more accurately reflect the mechanical behavior of soil and rock under complex stress conditions, thus improving the accuracy of stability assessment.

[0018] Compared with numerical analysis methods, the calculation process of this invention is relatively simple, requires less computing resources and technical personnel, reduces computing costs, and is easy to promote and apply in practical engineering.

[0019] By using strain energy density analysis to identify potential unstable regions and sliding surfaces, we can provide clear guidance for geotechnical engineering design and reinforcement, which helps to improve the safety and reliability of projects.

[0020] Other features and advantages of the invention will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing embodiments of the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description, claims, and drawings. Attached Figure Description

[0021] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 This is a schematic diagram of the process for analyzing the stability of soil and rock masses based on thermodynamic-tensor invariant coupling, as described in an embodiment of the present invention.

[0023] Figure 2 This is a schematic diagram of the structure of the rock and soil stability analysis system based on thermodynamic-tensor invariant coupling as described in an embodiment of the present invention.

[0024] In the diagram: 701, acquisition unit; 702, first calculation unit; 703, second calculation unit; 704, analysis unit. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0026] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, in the description of this invention, terms such as "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0027] Example 1:

[0028] This embodiment provides a method for analyzing the stability of soil and rock masses based on thermodynamic-tensor invariant coupling.

[0029] See Figure 1 The figure shows that the method includes steps S1, S2, S3 and S4.

[0030] Step S1: Obtain soil and rock parameters from field investigation and laboratory tests;

[0031] Understandably, this step integrates both field investigation and laboratory testing, ensuring completeness and representativeness. During field investigation, methods such as drilling, standard penetration testing (SPT), and static cone penetration testing (CPT) are used to obtain the distribution characteristics, burial structure, and preliminary physical properties of the soil and rock layers, providing spatial foundation information for sample selection and subsequent modeling. Laboratory testing is a crucial step in parameter quantification, including triaxial compression testing to determine shear strength parameters (cohesion and internal friction angle), static compression and shear modulus testing to determine Poisson's ratio and shear modulus, and, if necessary, the pressure density method to calculate the elastic modulus. Compared to traditional methods relying on empirical values ​​or literature searches, this invention emphasizes the acquisition of in-situ parameters, ensuring the authenticity and engineering applicability of the model input. Furthermore, after parameter acquisition, normalization is used to form a unified parameter matrix format, facilitating efficient use in subsequent constitutive equations and tensor expressions. This step provides accurate, systematic, and representative initial physical and mechanical data for subsequent energy density-based stability analysis, ensuring model reliability and analytical accuracy from the outset.

[0032] Step S2: Combine the soil and rock parameters, generalized Hooke's law and Mohr-Coulomb yield criterion to obtain the strain tensor expression, and perform stress tensor calculation to obtain the elastic stress tensor, strain tensor and plastic strain tensor of the soil and rock.

[0033] It is understandable that the unified establishment of the elastic strain tensor, stress tensor, and plastic strain tensor in this step enables a continuous expression of the transition process from elastic to plastic in soil and rock. This not only provides an accurate tensor basis for piecewise integration of energy density but also possesses strong engineering applicability, effectively addressing complex situations such as non-uniform loads, structural abrupt changes, or geologically heterogeneous zones. Through stress-strain modeling within a unified tensor framework, the completeness and accuracy of the mechanical analysis are improved, laying a solid foundation for the construction of stability indices. In this step, step S2 includes steps S21, S22, and S23.

[0034] Step S21: Based on the elastic modulus and Poisson's ratio in the soil and rock parameters, process them and construct the elastic stress-strain tensor relationship through the generalized Hooke's law to obtain the elastic stress tensor and elastic strain tensor of the soil and rock.

[0035] It is understood that this step assumes the slope soil and rock mass is a linearly elastic, homogeneous, and isotropic material in the elastic state, conforming to the generalized Hooke's law. It also assumes compliance with the Mohr-Coulomb plastic yield criterion and satisfies the correlated flow law during plastic deformation.

[0036] In the elastic state: strain energy density refers to the strain energy per unit volume, which can be derived from the stress-strain relationship in the elastic state.

[0037] For a three-dimensional stress state, according to the generalized Huke's law, the relationship between stress and strain can be expressed as:

[0038] σ ij =C ijkl ε kl (1)

[0039] Where, σ ij Let ε be the stress tensor. kl For the strain tensor, C ijkl Let be the elastic constant tensor.

[0040] The strain energy density can be obtained by integrating the stress-strain relationship per unit volume:

[0041]

[0042] Where, σ ij Let ε be the stress tensor. ij Let u be the strain tensor and u be the strain energy density.

[0043] Substituting the generalized Hooke's law into formula (2), we get:

[0044]

[0045] Where u is the strain energy density, C ijkl Let ε be the elastic constant tensor. ij ,ε kl Let be the strain tensor, where and are common notations in tensor operations, indicating that they are different components of the same second-order strain tensor. In Cartesian coordinates, for isotropic materials, the elastic constant tensor can be expressed as:

[0046] C ijkl =λδ ij δ kl +μ(δ ik δ jl +δ il δ jk (4)

[0047] Where, δ kl δ ik δ jl δ il δ jk The symbol for Croneck is 1 when the base and index are the same, and 0 otherwise. ijkl Let λ be the elastic constant tensor, μ be Lamé constants, and δ be the elastic constant tensor. ijIt is the Kronecker symbol.

[0048] C ijkl Substituting into the expression for strain energy density, we get:

[0049]

[0050] Where λ is Lamé's constant, ε ii ε is the principal diagonal component of the strain tensor. jj With ε ii Consistency, in the summation convention, indicates summation with repeated subscripts, ε ij It represents all components of the strain tensor (including normal strain and shear strain).

[0051] Further expansion and simplification yields:

[0052]

[0053] Where E is the elastic modulus, v is Poisson's ratio, G is the shear modulus, and σ is the elastic modulus. x σ y σ z It is normal stress, γ xy γ yz γ xz It is shear stress.

[0054] In this scenario, the data in this step is engineering-specific: the elastic modulus and Poisson's ratio are in-situ measured values ​​obtained from field and laboratory tests for specific soil and rock layers, ensuring that the constructed tensor relationship is not only theoretically complete but also physically consistent with the actual geological body. Through this process, not only is a stress-strain tensor expression used to describe the elastic response behavior of the soil and rock mass obtained, but also a clear and quantifiable input variable structure is provided for subsequent energy density calculations.

[0055] Step S22: Based on the cohesion and internal friction angle in the soil and rock parameters, establish the yield function, construct the yield function expression through the Mohr-Coulomb yield criterion, and obtain the yield boundary function of the soil and rock in the plastic state.

[0056] It is understandable that in this step, under the plastic state, the strain energy density includes two parts: the elastic strain energy density and the plastic strain energy density, that is:

[0057] u = u e +u p (7)

[0058] Where u is the strain energy density, u e It is the elastic strain energy density, u p It is the plastic strain energy density.

[0059] Elastic strain energy density u e The calculation can still be performed using the formula for the elastic state:

[0060]

[0061] Among them, u e It is the elastic strain energy density, σ ij It is the stress tensor. It is the elastic strain tensor.

[0062] In the field of plastic deformation research of soil and rock masses, the correlation flow rule is widely used due to its many significant advantages. From a physical perspective, it aligns with the energy dissipation principle of the second law of thermodynamics, ensuring that plastic work is always positive and accurately mapping the energy dissipation phenomenon when soil and rock masses are subjected to stress. Furthermore, it corresponds to the deformation mechanisms such as slippage and rotation of microscopic particles in soil and rock masses. In describing the properties of soil and rock masses, the correlation flow rule, combined with yield criteria such as the Mohr-Coulomb method, can effectively characterize the dilatational properties of soil and rock masses during shearing. Simultaneously, by utilizing the concept of plastic multipliers, it powerfully interprets the nonlinear characteristics of the stress-strain relationship in soil and rock masses. In terms of experimental verification, whether it is conventional indoor triaxial and direct shear tests, or in-situ pressure sidewall and dilatation tests, the predicted results of the plastic constitutive model constructed based on the correlation flow rule are in high agreement with the measured data. Moreover, the correlation flow rule provides a simple and efficient theoretical foundation for building plastic constitutive models, and the derived constitutive equations are easily integrated into numerical algorithms such as the finite element method. Numerous successful application cases have been accumulated in various geotechnical engineering practices, including slope, foundation, and tunnel engineering. Therefore, this paper adopts the correlation flow rule to describe the stress-strain relationship during the plastic deformation of soil and rock masses, and its formula is shown below:

[0063]

[0064] Where dλ is the plasticity multiplier, a nonnegative scalar; F is the yield function, and σ ij It is the stress tensor

[0065] As mentioned in the assumptions, the Mohr-Coulomb yield criterion is chosen, therefore the expression for the yield function F in the three-dimensional principal stress space is:

[0066]

[0067] Where σ1 and σ3 are the maximum and minimum principal stresses (σ1>σ2>σ3), respectively, and c is the cohesion. Let F be the internal friction angle, and F be the yield function.

[0068] The relationship between principal stresses and stress tensors can be determined using stress invariants:

[0069] I1=σ xx +σ yy +σzz (11)

[0070]

[0071] σ 3 -I1σ 2 -3J2σ-J3=0 (14)

[0072] Where I1 is the first invariant of stress, J2 is the second invariant of stress deviatoric tensor, J3 is the third invariant of stress deviatoric tensor, and σ xx σ yy σ zz It is normal stress, τ xy τ yz τ xz It is shear stress, and σ is the principal stress value.

[0073] Substitute into formula (14) to solve for the principal stresses. After simplification, it can be expressed as:

[0074]

[0075] Where θ is the Rhodes angle, F is the yield function, I1 is the first stress invariant, J2 is the second stress deviator tensor invariant, J3 is the third stress deviator tensor invariant, and σ x σ y σ z It is normal stress, γ xy γ yz γ xz It is shear stress.

[0076] This step transforms the experimentally obtained parameters into mathematical criteria, constructing a yield surface expression applicable to three-dimensional stress fields. This allows subsequent plasticity analysis to no longer rely on empirical judgments, but possesses the rigor of being theoretically deriveable and numerically feasible, laying a key criterion foundation for the calculation of plastic strain tensor and plasticity properties.

[0077] Step S23: Calculate the plastic strain increment based on the yield boundary function, and obtain the plastic strain tensor increment by combining the associated flow rule with the iterative algorithm of the plastic multiplier.

[0078] It is understandable that the derivative of the yield function in this step yields:

[0079]

[0080] Where F is the yield function, σ ij It is the stress tensor. It is the plastic strain tensor.

[0081] Combining equations (9) and (22), we can obtain:

[0082]

[0083] Where F is the yield function, σ ij It is the stress tensor. dλ is the plastic strain tensor, and dλ is the plastic multiplier, which is a non-negative scalar.

[0084] After simplification, we get:

[0085]

[0086] Where dλ is the plasticity multiplier, a nonnegative scalar; F is the yield function, and σ ij It is the stress tensor. It is the plastic strain tensor.

[0087] For hardened materials, we assume an isotropic hardening model, i.e.:

[0088]

[0089] Where H is the hardening parameter, F is the yield function, and σ ij It is the stress tensor. It is the plastic strain tensor.

[0090] Substituting into formula (25), we get:

[0091]

[0092] Where dλ is the plasticity multiplier, a nonnegative scalar; F is the yield function, and σ ij It is the stress tensor, and H is the hardening parameter.

[0093] Of course, for an ideal elastic-plastic material, the following must be met:

[0094]

[0095] Where F is the service function, It is the plastic strain tensor.

[0096] Therefore, when the yield condition F = 0 and the loading criterion is met... In such cases, the plastic multiplier can be determined by additional supplementary conditions, such as the iterative calculation method often used in finite element calculations to solve for the plastic multiplier.

[0097] After solving the plastic multiplier using different methods, we substitute it into formula (9). Thus, we obtain the complete formula for calculating the plastic strain increment under three-dimensional stress state based on the Mohr-Coulomb yield criterion.

[0098] Understandably, this step achieves quantitative modeling of plastic deformation of soil and rock during the yielding stage. It not only precisely controls the deformation direction and amplitude, but also considers the influence of material hardening characteristics on the deformation process, making the strain energy density calculation results more consistent with the actual soil response characteristics, and significantly improving the physical authenticity of subsequent stability analysis and the reliability of engineering predictions.

[0099] Step S3: Based on the elastic stress tensor, elastic strain tensor and plastic strain tensor of the rock and soil, perform integral calculations to obtain the total strain energy density increment of the rock and soil under different stress states.

[0100] It is understandable that this step, by separately calculating elastic and plastic strain energies, clearly distinguishes between structural energy storage and energy dissipation processes, providing a physical basis for stability analysis from an energy perspective. Simultaneously, the unified tensor integral framework improves the computational consistency and scalability of the analysis, giving it good compatibility and allowing direct embedding into various numerical simulations and stability assessment algorithms, thus enhancing the model's application efficiency and interpretability in engineering environments. In this step, step S3 includes steps S31, S32, and S33.

[0101] Step S31: Calculate the elastic strain energy density increment based on the elastic stress tensor and elastic strain tensor of the soil and rock mass to obtain the elastic strain energy density increment of the soil and rock mass.

[0102] It is understandable that the increase in elastic strain energy density in this step can be expressed as:

[0103]

[0104] Among them, u e For elastic strain energy density, σ ij For stress tensor, It is the elastic strain tensor.

[0105] Step S32: Calculate the plastic strain energy density increment based on the plastic strain tensor increment to obtain the plastic strain energy density increment of the soil and rock mass.

[0106] It is understandable that the increase in plastic strain energy density in this step can be expressed as:

[0107]

[0108] Among them, u p For plastic strain energy density, σ ij For stress tensor, It is the plastic strain tensor.

[0109] Step S33: The elastic strain energy density increment and the plastic strain energy density increment of the rock and soil are superimposed to obtain the total strain energy density increment of the rock and soil under different stress states.

[0110] It is understandable that in this step, the increase in total strain energy density can be expressed as:

[0111] du = du p +du e (31)

[0112] Among them, u p For plastic strain energy density, u e Let u be the elastic strain energy density, and u be the strain energy density. Integrating u over the domain yields the total strain energy density.

[0113] u=∫ Ω du (32)

[0114] Where u is the strain energy density and Ω is the integration domain.

[0115] It is understandable that this step involves superimposing the strain energy density components of the soil and rock under different stress states to obtain the total strain energy density increment of the soil and rock under different stress states. This energy superposition model can effectively identify high energy density regions caused by stress concentration, structural weakness, or uneven loading, thereby predicting potential failure locations.

[0116] Step S4: Based on the total strain energy density increment of the soil and rock mass under different stress states, perform stability analysis to obtain the stability anomaly region of the soil and rock mass.

[0117] It is understandable that this step, through a stability analysis mechanism driven by an energy field rather than a force field, overcomes the limitations of traditional limit equilibrium methods that neglect material deformation history and energy dissipation processes, enabling a more refined revelation of the potential instability evolution mechanisms within the soil and rock mass. Furthermore, this method is applicable to safety analysis under irregular boundaries, heterogeneous structures, and complex loading paths, and is particularly suitable for engineering scenarios such as slope deformation, weakening of surrounding rock in tunnels, and foundation settlement, significantly improving the physical rationality of stability assessment and the spatial resolution of risk identification in geotechnical engineering. In this step, step S4 includes steps S41, S42, S43, and S44.

[0118] Step S41: The total strain energy density increment of the rock and soil mass under different stress states is reconstructed in space. The three-dimensional spatial strain energy density distribution model of the rock and soil mass is obtained by finite element mesh interpolation.

[0119] Understandably, this step employs mesh interpolation techniques from the finite element method for field reconstruction. Specifically, the study area of ​​the soil and rock mass is divided into three-dimensional finite element units (such as tetrahedrons or hexahedrons). The known strain energy density increments at each element node are treated as discrete data, and numerical interpolation (e.g., linear interpolation, bilinear interpolation, or higher-order Lagrange interpolation) is used to fit and continuousize the function across the entire mesh. During the interpolation process, Gaussian integral point weights and deformation gradient tensors can be incorporated to improve the accuracy of the energy density field reconstruction.

[0120] Step S42: Perform local extremum search processing on the three-dimensional spatial strain energy density distribution model of the rock and soil mass, calculate the strain energy gradient and Laplace operator at each point, and identify the strain energy region where the strain energy gradient and Laplace operator are greater than a preset threshold.

[0121] Understandably, this step first calculates the spatial gradient of strain energy density for each grid node or Gaussian integral point in the reconstructed energy density field to measure the directionality and severity of energy change at that point. Then, its second derivative, the Laplace operator, is calculated to capture potential local "well" or "peak" structures in the energy field, i.e., centers of energy concentration or dissipation. By comparing these calculation results with preset thresholds, regions exhibiting both high energy density and significant spatial abrupt changes can be effectively identified, typically corresponding to locations of plasticity concentration, severe stress redistribution, or abrupt changes in material properties.

[0122] Step S43: Cluster the strain energy gradient and strain energy regions where the Laplace operator is greater than a preset threshold, and perform cluster analysis using the K-means algorithm to obtain strain energy anomaly regions.

[0123] It is understandable that in this step, the K-means algorithm, as a commonly used clustering method based on distance metrics, treats all points that meet the anomaly conditions as a sample set and divides them into several cluster centers based on Euclidean distance, so that the energy change characteristics between points within a cluster are most consistent and the differences between clusters are the greatest, thus forming functionally relatively independent "strain energy anomaly blocks".

[0124] In practical implementation, the cluster number K can be selected by combining physical scale information of geotechnical engineering (such as the width of the sliding surface and the distance of the fracture zone extension), or the optimal K value can be automatically determined by data-driven methods such as the profile coefficient and the elbow method. Each energy anomaly region obtained after clustering not only has spatial clustering but also retains its inherent similarity in mechanical response, thus better reflecting the true zoning of local material failure or structural instability. At the application level, these anomaly regions can be used to mark potential sliding surfaces, fracture paths, or stress redistribution core areas, serving as an important foundation for guiding refined reinforcement design and risk control strategy deployment.

[0125] Step S44: The strain energy abnormal region is regarded as the stability abnormal region of the soil and rock mass.

[0126] Understandably, this step systematically and data-drivenly completes the clear mapping from energy anomalies to stability risks, enabling the stability assessment of soil and rock masses to move from traditional mechanical analysis to an energy criterion system that combines field theory and intelligent analysis. This significantly improves the physical accuracy and engineering effectiveness of risk identification and lays an operational decision-making foundation for the subsequent promotion and application of the model.

[0127] It is understandable that step S4 is followed by steps S5 and S6.

[0128] Step S5: Analyze the stability anomaly area of ​​the rock and soil mass to determine the predicted orientation and depth of the potential sliding surface of the rock and soil mass;

[0129] Understandably, this step utilizes Principal Component Analysis (PCA) to extract the principal axis direction of point cloud data within clustered regions, determining the dip and tilt angle of the slip surface. Simultaneously, it analyzes the depth variation trend using an energy isosurface extraction algorithm (isosurface reconstruction), thereby providing predictions of the slip surface's projection path and burial depth on different profiles. Unlike traditional slip surface identification based on experience or simple displacement field fitting, this method utilizes the physical mechanism of energy response to identify real structurally weak zones and fracture development surfaces, exhibiting stronger causal correlation and predictive capabilities.

[0130] Step S6: Perform stability grading on the predicted orientation and depth of the potential sliding surface of the soil and rock mass to obtain the stability anomaly level of the unstable area of ​​the soil and rock mass.

[0131] Understandably, the specific grading method used in this step is a rule-based grading method. In this method, grading thresholds are set based on engineering specifications or empirical indicators. For example, shallow high-energy areas may be marked as first-level warning slip surfaces, while deep low-dipping areas may be rated as substable areas. By grading stability, the model results are transformed into identifiable, comparable, and operable engineering level information, providing direct basis for on-site monitoring and early warning, reinforcement design prioritization, and resource allocation. This is particularly valuable in scenarios such as slope mobilization and proactive prevention and control of geological disasters.

[0132] Example 2:

[0133] like Figure 2 As shown, this embodiment provides a rock and soil stability analysis system based on thermodynamic-tensor invariant coupling. See [link to documentation]. Figure 2 The system includes an acquisition unit 701, a first calculation unit 702, a second calculation unit 703, and an analysis unit 704.

[0134] Acquisition unit 701 is used to acquire soil and rock parameters from field investigations and laboratory tests;

[0135] The first calculation unit 702 is used to combine the soil and rock parameters, the generalized Hooke's law and the Mohr-Coulomb yield criterion to obtain the strain tensor expression, and to perform stress tensor calculation to obtain the elastic stress tensor, strain tensor and plastic strain tensor of the soil and rock.

[0136] The second calculation unit 703 is used to perform integral calculations based on the elastic stress tensor, elastic strain tensor and plastic strain tensor of the rock and soil mass respectively, to obtain the total strain energy density increment of the rock and soil mass under different stress states.

[0137] Analysis unit 704 is used to perform stability analysis based on the total strain energy density increment of the rock and soil mass under different stress states, and to obtain the stability anomaly region of the rock and soil mass.

[0138] It should be noted that the specific methods by which each module performs operations in the system described in the above embodiments have been described in detail in the embodiments related to the method, and will not be elaborated here.

[0139] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0140] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A geotechnical stability analysis method based on thermodynamic-tensor invariant coupling, characterized by, include: Obtain geotechnical parameters from field investigations and laboratory tests; Based on the elastic modulus and Poisson's ratio in the soil and rock parameters, the elastic stress-elastic strain tensor relationship is constructed through the generalized Hooke's law to obtain the elastic stress tensor and elastic strain tensor of the soil and rock. Based on the cohesion and internal friction angle in the soil and rock parameters, the yield function is established, and the yield function expression is constructed through the Mohr-Coulomb yield criterion to obtain the yield boundary function of the soil and rock in the plastic state. The plastic strain increment is calculated based on the yield boundary function, and the plastic strain tensor increment is obtained by combining the associated flow rule with the iterative algorithm of the plastic multiplier. The correlation flow rule is used to describe the stress-strain relationship during the plastic deformation of soil and rock, and its formula is shown below: ； wherein, is the plastic strain tensor, is the plastic multiplier, a non-negative scalar; is the yield function, is the stress tensor; The elastic strain energy density increment of the rock and soil mass is calculated by processing the elastic stress tensor and elastic strain tensor of the rock and soil mass. The plastic strain energy density increment of the soil and rock mass is obtained by calculating the plastic strain tensor increment. The elastic strain energy density increment and the plastic strain energy density increment of the rock and soil mass are superimposed to obtain the total strain energy density increment of the rock and soil mass under different stress states. The total strain energy density increment of the soil and rock mass under different stress states is reconstructed in space, and the three-dimensional spatial strain energy density distribution model of the soil and rock mass is obtained by finite element mesh interpolation. The three-dimensional spatial strain energy density distribution model of the soil and rock mass is subjected to local extremum search processing. By calculating the strain energy gradient and Laplace operator at each point, strain energy regions where the strain energy gradient and Laplace operator are greater than a preset threshold are identified. The strain energy gradient and strain energy regions where the Laplace operator exceeds a preset threshold are clustered, and cluster analysis is performed using the K-means algorithm to obtain strain energy anomaly regions. The strain energy anomaly region is considered as the stability anomaly region of the soil and rock mass.

2. The method for analyzing the stability of soil and rock masses based on thermodynamic-tensor invariant coupling according to claim 1, characterized in that... After identifying the areas of abnormal stability in the soil and rock mass, the following steps are also included: Based on the analysis of the stability anomaly area of ​​the rock and soil mass, the predicted orientation and depth of the potential sliding surface of the rock and soil mass are determined. The predicted orientation and depth of the potential sliding surface of the soil and rock mass are subjected to stability classification to obtain the stability anomaly level of the unstable area of ​​the soil and rock mass.

3. A system for analyzing the stability of soil and rock masses based on thermodynamic-tensor invariant coupling, using the method for analyzing the stability of soil and rock masses based on thermodynamic-tensor invariant coupling as described in any one of claims 1-2, characterized in that, include: The acquisition unit is used to acquire soil and rock parameters from field investigations and laboratory tests. The first calculation unit is used to combine the parameters of the soil and rock mass, the generalized Hooke's law and the Mohr-Coulomb yield criterion to obtain the expression of the elastic strain tensor, and to calculate the elastic stress tensor to obtain the elastic stress tensor, elastic strain tensor and plastic strain tensor of the soil and rock mass. The second calculation unit is used to perform integral calculations based on the elastic stress tensor, elastic strain tensor and plastic strain tensor of the rock and soil mass respectively, to obtain the total strain energy density increment of the rock and soil mass under different stress states. The analysis unit is used to perform stability analysis based on the total strain energy density increment of the soil and rock mass under different stress states, and to obtain the stability anomaly region of the soil and rock mass.

4. The rock and soil stability analysis system based on thermodynamic-tensor invariant coupling according to claim 3, characterized in that, The first computing unit includes: The first processing subunit is used to process the elastic modulus and Poisson's ratio in the soil and rock mass parameters, and to construct the elastic stress-elastic strain tensor relationship through the generalized Hooke's law to obtain the elastic stress tensor and elastic strain tensor of the soil and rock mass. The second processing subunit is used to establish the yield function based on the cohesion and internal friction angle in the soil and rock parameters, and to construct the yield function expression through the Mohr-Coulomb yield criterion to obtain the yield boundary function of the soil and rock in the plastic state. The first calculation subunit is used to perform plastic strain increment calculation based on the yield boundary function, and obtain the plastic strain tensor increment by combining the associated flow rule with the iterative algorithm of the plastic multiplier.

5. The rock and soil stability analysis system based on thermodynamic-tensor invariant coupling according to claim 4, characterized in that, The second computing unit includes: The second calculation subunit is used to calculate the elastic strain energy density increment based on the elastic stress tensor and elastic strain tensor of the soil and rock mass, and to obtain the elastic strain energy density increment of the soil and rock mass. The third calculation subunit is used to calculate the plastic strain energy density increment based on the plastic strain tensor increment, so as to obtain the plastic strain energy density increment of the soil and rock mass. The third processing subunit is used to superimpose the elastic strain energy density increment and the plastic strain energy density increment of the soil and rock mass to obtain the total strain energy density increment of the soil and rock mass under different stress states.

6. The rock and soil stability analysis system based on thermodynamic-tensor invariant coupling according to claim 4, characterized in that, The analysis unit includes: The fourth processing subunit is used to reconstruct the spatial field of the total strain energy density increment of the soil and rock mass under different stress states. Through finite element mesh interpolation, a three-dimensional spatial strain energy density distribution model of the soil and rock mass is obtained. The fifth processing subunit is used to perform local extremum search processing on the three-dimensional spatial strain energy density distribution model of the rock and soil mass, by calculating the strain energy gradient and Laplace operator at each point, and identifying strain energy regions where the strain energy gradient and Laplace operator are greater than a preset threshold. The sixth processing subunit is used to cluster the strain energy gradient and strain energy regions where the Laplace operator is greater than a preset threshold, and to perform cluster analysis using the K-means algorithm to obtain strain energy anomaly regions. The seventh processing subunit is used to treat the strain energy anomaly region as the stability anomaly region of the soil and rock mass.

7. The rock and soil stability analysis system based on thermodynamic-tensor invariant coupling according to claim 4, characterized in that, Also includes: The third processing unit is used to analyze the stability anomaly area of ​​the rock and soil mass and determine the predicted value of the potential sliding surface orientation and depth of the rock and soil mass. The fourth processing unit is used to perform stability grading on the predicted orientation and depth of the potential sliding surface of the soil and rock mass to obtain the stability anomaly level of the unstable area of ​​the soil and rock mass.

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