Rock-soil body stability analysis method and system based on strain energy density

Abstract

The invention provides a rock-soil body stability analysis method and system based on strain energy density, and relates to the technical field of rock-soil body stability analys.The rock-soil body stability analysis method comprises the steps that rock-soil body parameters of field investigation and indoor tests are obtained; combining the rock-soil body parameters, the generalized Hooke law and the Mohr-Coulomb yield criterion to obtain a strain tensor expression, and performing stress tensor calculation to obtain an elastic stress tensor, a strain tensor and a plastic strain tensor of the rock-soil body; respectively carrying out integral calculation to obtain the total strain energy density increment of the rock-soil body in different stress states; and performing stability analysis based on the total strain energy density increment of the rock-soil body in different stress states to obtain a stability abnormal area of the rock-soil body. According to the method, the elasticity and plastic deformation characteristics of the rock-soil body are comprehensively considered, and the accuracy of stability evaluation is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of rock and soil stability analysis, and in particular to a rock and soil stability analysis method and system based on strain energy density. Background Art

[0002] With the continuous development of geotechnical engineering construction in areas such as slope support, foundation reinforcement, and underground tunnels, the stability analysis of geotechnical masses under complex stress environments has become a key issue in ensuring engineering safety and economic efficiency. 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 of the geotechnical mass, making it difficult to reflect local instability mechanisms, especially the accurate identification of potential sliding surfaces or localized failure zones. In contrast, numerical methods such as finite element method can simulate the stress and deformation distribution within the geotechnical mass, thus compensating for the shortcomings of the limit equilibrium method. However, these methods place extremely high demands on 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 difficulty in application and low computational efficiency in engineering practice. Consequently, they cannot meet the requirements for fast, accurate, and engineering-applicable stability analysis.

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

[0004] The purpose of the present invention is to provide a rock and soil stability analysis method and system based on strain energy density to improve the above-mentioned problems. To achieve the above-mentioned purpose, the technical solutions adopted by the present invention are as follows:

[0005] In a first aspect, the present application provides a method for analyzing rock and soil stability based on thermodynamics-tensor invariant coupling, comprising:

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

[0007] Combining the rock and soil parameters, the generalized Hooke's law, and the Moore-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 and soil;

[0008] Based on the elastic stress tensor, elastic strain tensor and plastic strain tensor of the rock and soil body, integral calculations are performed respectively to obtain the total strain energy density increment of the rock and soil body under different stress states;

[0009] Based on the total strain energy density increment of the rock and soil body under different stress states, stability analysis is performed to obtain the stability abnormal area of ​​the rock and soil body.

[0010] In a second aspect, the present application also provides a rock and soil stability analysis system based on thermodynamics-tensor invariant coupling, comprising:

[0011] Acquisition unit, used to obtain rock and soil parameters from field investigation and indoor tests;

[0012] a first calculation unit, configured to combine the rock and soil parameters, the generalized Hooke's law, and the Moore-Coulomb yield criterion to obtain a strain tensor expression, and perform stress tensor calculation to obtain an elastic stress tensor, a strain tensor, and a plastic strain tensor of the rock and soil;

[0013] a second calculation unit, configured 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 a 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 rock and soil body under different stress states to obtain the stability abnormal area of ​​the rock and soil body.

[0015] The beneficial effects of the present invention are:

[0016] This method utilizes precise derivations of elastic and plastic strain energy densities, combines the Mohr-Coulomb yield criterion with associated flow laws, and constructs an expression for strain energy density in the context of stress-strain relationships, thereby forming a stability assessment index. This method fully utilizes mechanical parameters acquired on-site, establishing a continuous computational chain from geotechnical parameters to stress and strain, energy distribution, and finally stability assessment, achieving a unified description of the entire elastic-plastic process of geotechnical structures.

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

[0018] Compared with the numerical analysis method, the present invention has a relatively simple calculation process, has lower requirements on computing resources and technical personnel, reduces computing costs, and is easy to promote and apply in actual engineering.

[0019] Identifying potential unstable areas and sliding surfaces through strain energy density analysis provides clear guidance for geotechnical engineering design and reinforcement, helping to improve the safety and reliability of projects.

[0020] Other features and advantages of the present invention will be described in the following description, and in part will become apparent from the description, or understood by practicing the embodiments of the present invention. The purposes and other advantages of the present invention can be realized and obtained by the structures particularly pointed out in the written description, claims, and drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without paying any creative work.

[0022] Figure 1 Schematic diagram of the flow of a rock and soil stability analysis method based on thermodynamics-tensor invariant coupling according to an embodiment of the present invention;

[0023] Figure 2 Schematic diagram of the structure of the rock and soil stability analysis system based on thermodynamics-tensor invariant coupling described in an embodiment of the present invention.

[0024] In the figure: 701, acquisition unit; 702, first calculation unit; 703, second calculation unit; 704, analysis unit. DETAILED DESCRIPTION

[0025] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. The components of the embodiments of the present invention generally described and shown in the drawings herein can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0026] It should be noted that similar reference numerals and letters represent similar items in the following drawings. Therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings. At the same time, in the description of the present invention, the terms "first", "second", etc. are used only to distinguish the description and should not be understood as indicating or implying relative importance.

[0027] Example 1:

[0028] This embodiment provides a rock and soil stability analysis method based on thermodynamics-tensor invariant coupling.

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

[0030] Step S1: obtaining rock and soil parameters from on-site investigation and indoor testing;

[0031] It is understandable that this step combines two means of on-site investigation and indoor test, with integrity and representativeness. During the on-site investigation process, by drilling, standard penetration test (SPT), static cone penetration test (CPT) and other methods, the distribution characteristics of rock and soil layers, buried depth structure and preliminary physical indicators are obtained, and spatial basic information is provided for sample selection and subsequent modeling. Indoor test is the key link of parameter quantification, including triaxial compression test for measuring shear strength index (cohesion and internal friction angle), static compression and shear modulus test for determining Poisson's ratio and shear modulus, and elastic modulus can also be calculated in combination with pressure density method when necessary. Compared with the traditional method of relying on experience selection or literature value search, the present invention emphasizes the acquisition of in-situ parameters, ensures the authenticity and engineering applicability of model input. In addition, after the parameters are obtained, a unified parameter matrix format is formed by normalization, which is convenient for subsequent efficient calling in constitutive equations and tensor expressions. This step can provide accurate, systematic and representative initial physical and mechanical data for subsequent stability analysis based on energy density, and guarantees model reliability and analysis accuracy from the source.

[0032] Step S2: combining the rock and soil parameters, generalized Hooke's law, and the Moore-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 and soil;

[0033] It can be understood that the unified establishment of the elastic strain tensor, stress tensor, and plastic strain tensor in this step achieves a continuous expression of the transition process from elasticity to plasticity in the rock and soil. This not only provides a precise tensor basis for the piecewise integration of energy density, but also has strong engineering applicability, effectively addressing complex situations such as uneven loads, structural mutations, or geological heterogeneity. Through stress-strain modeling within a unified tensor framework, the completeness and accuracy of mechanical analysis are improved, laying a solid foundation for the construction of stability indicators. In this step, step S2 includes steps S21, S22, and S23.

[0034] Step S21: processing the elastic modulus and Poisson's ratio among the rock and soil parameters, constructing an elastic stress-strain tensor relationship through generalized Hooke's law, and obtaining the elastic stress tensor and elastic strain tensor of the rock and soil;

[0035] It is understood that this step assumes that the slope rock mass is a linear elastic, homogeneous, isotropic material in the elastic state, conforms to the generalized Hooke's law, obeys the Mohr-Coulomb plastic yield criterion, and satisfies the associated flow law during the plastic deformation process.

[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 Hooke's law, the relationship between stress and strain can be expressed as:

[0038] σ ij =C ijkl ε kl (1)

[0039] Among them, σ ij is the stress tensor, ε kl is the strain tensor, C ijkl is the elastic constant tensor.

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

[0041]

[0042] Among them, σ ij is the stress tensor, ε ij is the strain tensor, and u is the strain energy density.

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

[0044]

[0045] Where u is the strain energy density, C ijkl is the elastic constant tensor, ε ij ,ε kl is the strain tensor, where the two are common notations in tensor operations, indicating that they are different components of the same second-order strain tensor. In the Cartesian coordinate system, 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] Among them, δ kl , δ ik , δ jl , δ il , δ jk is the Kronecker symbol, which is 1 when the bases are consistent, otherwise it is 0. ijkl is the elastic constant tensor, λ and μ are the Lame constants, δ ijis the Kronecker symbol.

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

[0049]

[0050] Where λ is the Lame constant, ε ii is the principal diagonal component of the strain tensor, ε jj With ε ii Consistent, in the summation convention, it means repeated subscript summation, ε ij are 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, σ x , σ y , σ z is the normal stress, γ xy , γ yz , γ xz is the shear stress.

[0054] In this scenario, the data in this step is project-specific: the elastic modulus and Poisson's ratio are in-situ measurements of specific geotechnical layers obtained through field and laboratory testing. This ensures that the tensor relationship constructed is both theoretically sound and physically consistent with the actual geological structure. This process not only yields a stress-strain tensor expression describing the elastic response of the geotechnical structure, but also provides a clear and quantifiable input variable structure for subsequent energy density calculations.

[0055] Step S22: performing yield function establishment processing based on the cohesion and internal friction angle among the rock and soil parameters, constructing a yield function expression by the Mohr-Coulomb yield criterion, and obtaining a yield boundary function of the rock and soil in a plastic state;

[0056] It can be understood that in this step, in the plastic state, the strain energy density includes two parts: elastic strain energy density and plastic strain energy density, namely:

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

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

[0059] Elastic strain energy density u e It can still be calculated according to the formula in the elastic state:

[0060]

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

[0062] In the study of plastic deformation of geotechnical materials, the associated flow rule has been widely adopted due to its 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 of geotechnical materials under stress. It also corresponds to deformation mechanisms such as slip and rotation of microscopic particles in geotechnical materials. In describing geotechnical properties, the associated flow rule, combined with yield criteria such as Mohr-Coulomb, effectively characterizes the dilatancy of geotechnical materials during shear. Furthermore, leveraging the concept of plastic multipliers, it powerfully explains the nonlinear characteristics of the stress-strain relationship in geotechnical materials. Experimental validation demonstrates that plastic constitutive models constructed based on the associated flow rule have highly consistent predictions with measured data, whether in conventional tests such as indoor triaxial and direct shear tests, or in-situ lateral pressure and flat shovel dilation tests. Furthermore, the associated flow rule provides a concise and efficient theoretical foundation for the construction of plastic constitutive models. The derived constitutive equations are easily integrated into numerical algorithms such as finite element methods, resulting in numerous successful applications in various geotechnical engineering applications, including slopes, foundations, and tunnels. Therefore, this paper adopts the associated flow law to describe the stress-strain relationship during the plastic deformation of rock and soil. The formula is as follows:

[0063]

[0064] Where dλ is the plastic multiplier, which is a non-negative scalar; F is the yield function, σ ij is the stress tensor

[0065] As mentioned in the assumption, the Mohr-Coulomb yield criterion is selected, so the expression of the yield function F in the three-dimensional principal stress space is:

[0066]

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

[0068] The relationship between the principal stress and the stress tensor can be determined by the stress invariant:

[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 deviator, J3 is the third invariant of stress deviator, σ xx , σ yy , σ zz is the normal stress, τ xy , τ yz , τ xz is the shear stress and σ is the principal stress value.

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

[0074]

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

[0076] This step converts the experimentally obtained parameters into mathematical criteria to construct a yield surface expression applicable to three-dimensional stress fields. This allows subsequent plastic analysis to no longer rely on empirical judgment, but instead possesses the rigor of theoretical derivation and numerical achievability, laying a key criterion foundation for the calculation of plastic strain tensors and plastic properties.

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

[0078] It can be understood that the derivative of the yield function in this step can be obtained:

[0079]

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

[0081] Combining formula (9) and formula (22), we can get:

[0082]

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

[0084] After simplification, we can get:

[0085]

[0086] Where dλ is the plastic multiplier, which is a non-negative scalar; F is the yield function, σ ij is the stress tensor, is the plastic strain tensor.

[0087] For hardening materials, an isotropic hardening model is assumed, that is:

[0088]

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

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

[0091]

[0092] Where dλ is the plastic multiplier, which is a non-negative scalar; F is the yield function, σ ij is the stress tensor and H is the hardening parameter.

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

[0094]

[0095] Among them, F is the service function, is the plastic strain tensor.

[0096] Therefore, when the yield condition F = 0 and the loading criterion When the plastic multiplier is , it can be determined by additional supplementary conditions. For example, in finite element calculation, iterative calculation method is often used to solve the plastic multiplier.

[0097] After solving the plastic multiplier according to different methods and substituting it into formula (9), we have obtained the calculation formula for the plastic strain increment based on the Mohr-Coulomb yield criterion under the complete three-dimensional stress state.

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

[0099] Step S3, performing integral calculations based on the elastic stress tensor, elastic strain tensor, and plastic strain tensor of the rock and soil mass, respectively, to obtain a total strain energy density increment of the rock and soil mass under different stress states;

[0100] It can be understood that this step clearly distinguishes between the structural energy storage and energy dissipation processes by separately calculating elastic and plastic strain energy, providing a physical basis for stability analysis from an energy perspective. At the same time, the unified tensor integration framework improves the computational consistency and scalability of the analysis, making it highly compatible and directly embeddable in various numerical simulation and stability determination algorithms, enhancing the model's application efficiency and explanatory power in engineering environments. In this step, step S3 includes steps S31, S32, and S33.

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

[0102] It can be understood that the elastic strain energy density increment in this step can be expressed as:

[0103]

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

[0105] Step S32: performing calculation processing on the plastic strain energy density increment based on the plastic strain tensor increment to obtain the plastic strain energy density increment of the rock and soil mass;

[0106] It can be understood that the plastic strain energy density increment in this step can be expressed as:

[0107]

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

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

[0110] It can be understood that in this step, the total strain energy density increment can be expressed as:

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

[0112] Among them, u p is the plastic strain energy density, u e is the elastic strain energy density, u is the strain energy density, and the total strain energy density can be obtained by integrating it within the definition domain:

[0113] u=∫ Ω du (32)

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

[0115] It can be understood that this step obtains the total strain energy density increment of the rock and soil under different stress states by superimposing the strain energy density components of the rock and soil under different stress states. This energy superposition model can effectively identify high-energy density areas caused by stress concentration, weak structure or uneven loading, thereby predicting potential damage locations.

[0116] Step S4: performing stability analysis based on the total strain energy density increment of the rock and soil mass under different stress states to obtain stability abnormality areas of the rock and soil mass.

[0117] It can be understood that this step breaks through the limitations of the traditional limit equilibrium method that ignores the material deformation history and energy dissipation process through a stability analysis mechanism driven by an energy field rather than a force field, and can more accurately reveal the potential unstable evolution mechanism within the rock and soil. In addition, this method is suitable for safety analysis under irregular boundaries, heterogeneous structures and complex loading paths, and is particularly suitable for engineering scenarios such as slope deformation, weakening of tunnel surrounding rock, and foundation settlement. It significantly improves the physical rationality of stability judgment and the spatial resolution of risk identification in geotechnical engineering. In this step, step S4 includes step S41, step S42, step S43 and step S44.

[0118] Step S41: performing spatial field reconstruction processing on the total strain energy density increments of the rock and soil mass under different stress states, and obtaining a three-dimensional spatial strain energy density distribution model of the rock and soil mass through finite element mesh interpolation processing;

[0119] It is understandable that this step uses the grid interpolation technology in the finite element method to reconstruct the field. Specifically, the study area of ​​the geotechnical body is divided into three-dimensional finite element units (such as tetrahedrons or hexahedrons), and the known strain energy density increments at each unit node are used as discrete data. Function fitting and continuity processing are performed in the entire grid through numerical interpolation (such as linear interpolation, bilinear interpolation, or high-order Lagrangian interpolation). The interpolation process can be combined with Gaussian integral point weights, deformation gradient tensors, etc. to improve the reconstruction accuracy of the energy density field.

[0120] Step S42: performing a local extreme value search process on the three-dimensional spatial strain energy density distribution model of the rock and soil mass, calculating the strain energy gradient and the Laplace operator at each point, and identifying strain energy regions where the strain energy gradient and the Laplace operator are greater than a preset threshold;

[0121] It can be understood that this step first calculates the spatial gradient of the strain energy density at each grid node or Gaussian integration point in the reconstructed energy density field to measure the directionality and intensity of energy changes at that point. Its second-order derivative, the Laplace operator, is then calculated to capture possible local "wells" or "peaks" in the energy field, representing centers of energy concentration or dissipation. By comparing these calculated results with a preset threshold, regions with both high energy density and significant spatial mutation characteristics can be effectively identified. These typically correspond to locations with concentrated plastic zones, severe stress redistribution, or sudden changes in material properties.

[0122] Step S43: clustering the strain energy regions where the strain energy gradient and the Laplace operator are greater than a preset threshold, performing cluster analysis using a K-means algorithm to obtain strain energy abnormal regions;

[0123] It can be understood that in this step, the K-means algorithm, as a commonly used clustering method based on distance measurement, regards all points that meet the abnormal conditions as sample sets and divides them into several cluster centers based on Euclidean distance, so that the energy change characteristics between points within the class are the most consistent and the differences between classes are the largest, thus forming a relatively independent "strain energy abnormality block" in function.

[0124] In actual implementation, the number of clusters K can be selected in combination with the physical scale information of geotechnical engineering (such as the width of the sliding surface and the extension distance of the fracture zone), or the optimal K value can be automatically determined by data-driven methods such as the silhouette coefficient and the elbow method. Each energy anomaly region obtained after clustering not only has spatial aggregation, but also retains its inherent similarity in mechanical response, so it can better reflect the true partitioning of local material damage or structural response instability. At the application level, these abnormal areas can be used to mark potential sliding surfaces, fracture paths or stress redistribution core areas, which are an important basis for guiding refined reinforcement design and risk control strategy deployment.

[0125] Step S44: taking the abnormal strain energy region as an abnormal stability region of the rock and soil mass.

[0126] It can be understood that this step completes the clear mapping from energy anomalies to stability risks in a systematic and data-driven manner, enabling the stability assessment of geotechnical masses to move from traditional mechanical analysis to an energy criterion system that combines field theory and intelligent analysis, significantly improving the physical accuracy and engineering effectiveness of risk identification, and laying an operational decision-making foundation for the subsequent promotion and application of the model.

[0127] It can be understood that step S4 is followed by step S5 and step S6.

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

[0129] This step, understandably, uses principal component analysis (PCA) to extract the principal axis directions of the point cloud data within the clustered area, determining the inclination and dip angle of the sliding surface. Simultaneously, an energy isosurface extraction algorithm (isosurface reconstruction) analyzes its depth variation trends, providing projection paths and depth predictions for the sliding surface on different sections. Unlike traditional sliding surface identification methods based on empirical evidence or simple displacement field fitting, this method leverages the physical mechanism of energy response to identify true structural weaknesses and fracture development surfaces, offering stronger causal relationships and predictive capabilities.

[0130] Step S6: performing stability classification processing on the potential sliding surface orientation and depth prediction value of the rock and soil mass to obtain the stability abnormality grade of the stability abnormality area of ​​the rock and soil mass.

[0131] It's understood that the specific classification method used in this step is rule-based. In this rule-based classification method, classification thresholds are set based on engineering specifications or empirical indicators. For example, shallow, high-energy areas might be marked as Level 1 warning slip surfaces, while deep, low-angle areas might be classified as substable areas. Stability classification transforms model results into recognizable, comparable, and actionable engineering-grade information, providing a direct basis for on-site monitoring and early warning, reinforcement design prioritization, and resource allocation. This approach is particularly valuable in scenarios such as slope management and proactive geological disaster prevention and control.

[0132] Example 2:

[0133] like Figure 2 As shown, this embodiment provides a rock and soil stability analysis system based on thermodynamics-tensor invariant coupling, see 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] An acquisition unit 701 is used to acquire rock and soil parameters from field investigations and indoor tests;

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

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

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

[0138] It should be noted that, regarding the system in the above embodiment, the specific manner in which each module performs operations has been described in detail in the embodiment of the method, and will not be elaborated on here.

[0139] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be 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 modifications or substitutions that can be easily conceived by a person 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 based on the scope of protection of the claims.

Claims

1. A method for analyzing rock and soil stability based on thermodynamics-tensor invariant coupling, characterized in that: include: Obtain geotechnical parameters from field investigations and laboratory tests; Combining the rock and soil parameters, the generalized Hooke's law, and the Moore-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 and soil; Based on the elastic stress tensor, elastic strain tensor and plastic strain tensor of the rock and soil body, integral calculations are performed respectively to obtain the total strain energy density increment of the rock and soil body under different stress states; Based on the total strain energy density increment of the rock and soil body under different stress states, stability analysis is performed to obtain the stability abnormal area of ​​the rock and soil body.

2. The method for analyzing rock and soil stability based on thermodynamics-tensor invariant coupling according to claim 1 is characterized in that , combining the rock mass parameters, generalized Hooke's law and Moore-Coulomb yield criterion to obtain the strain tensor expression and perform stress tensor calculation, including: Based on the elastic modulus and Poisson's ratio of the rock and soil parameters, the elastic stress-strain tensor relationship is constructed through the generalized Hooke's law to obtain the elastic stress tensor and elastic strain tensor of the rock and soil; A yield function is established based on the cohesion and internal friction angle among the rock and soil parameters, and a yield function expression is constructed using the Mohr-Coulomb yield criterion to obtain a yield boundary function of the rock and soil in a plastic state; The plastic strain increment calculation process is performed based on the yield boundary function, and the plastic strain tensor increment is obtained through an iterative algorithm combining an associated flow rule with a plastic multiplier.

3. The method for analyzing rock and soil stability based on thermodynamics-tensor invariant coupling according to claim 2 is characterized in that , based on the elastic strain tensor and the plastic strain tensor of the rock and soil body, integral calculation is performed respectively, including: The elastic strain energy density increment is calculated based on the elastic stress tensor and elastic strain tensor of the rock and soil mass to obtain the elastic strain energy density increment of the rock and soil mass; The plastic strain energy density increment is calculated based on the plastic strain tensor increment to obtain the plastic strain energy density increment of the rock and soil mass. The elastic strain energy density increment and the plastic strain energy density increment of the rock and soil body are superimposed to obtain the total strain energy density increment of the rock and soil body under different stress states.

4. The method for analyzing rock and soil stability based on thermodynamics-tensor invariant coupling according to claim 1, characterized in that , based on the total strain energy density increment of the rock and soil mass under different stress states, stability analysis is performed, including: The total strain energy density increment of the rock and soil mass under different stress states is processed by spatial field reconstruction, and a three-dimensional spatial strain energy density distribution model of the rock and soil mass is obtained through finite element mesh interpolation. A local extreme value search process is performed on the three-dimensional spatial strain energy density distribution model of the rock and soil mass, by calculating the strain energy gradient and the Laplace operator at each point, and identifying the strain energy region where the strain energy gradient and the Laplace operator are greater than a preset threshold; Clustering the strain energy regions where the strain energy gradient and the Laplace operator are greater than a preset threshold, performing cluster analysis using a K-means algorithm to obtain strain energy anomaly regions; The abnormal strain energy area is regarded as the abnormal stability area of ​​the rock and soil mass.

5. The method for analyzing rock and soil stability based on thermodynamics-tensor invariant coupling according to claim 1 is characterized in that ,After obtaining the abnormal stability area of ​​the rock and soil mass, it also includes: Analyzing the abnormal stability area of ​​the rock and soil mass to determine the predicted value of the potential sliding surface orientation and depth of the rock and soil mass; The potential sliding surface orientation and depth prediction values ​​of the rock and soil body are subjected to stability classification processing to obtain the stability anomaly grade of the stability anomaly area of ​​the rock and soil body.

6. A rock and soil stability analysis system based on thermodynamics-tensor invariant coupling, characterized in that: include: Acquisition unit, used to obtain rock and soil parameters from field investigation and indoor tests; a first calculation unit, configured to combine the rock and soil parameters, the generalized Hooke's law, and the Mohr-Coulomb yield criterion to obtain a strain tensor expression, and perform stress tensor calculation to obtain an elastic stress tensor, a strain tensor, and a plastic strain tensor of the rock and soil; a second calculation unit, configured 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 a 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 rock and soil body under different stress states to obtain the stability abnormal area of ​​the rock and soil body.

7. The geotechnical stability analysis system based on thermodynamics-tensor invariant coupling according to claim 6, characterized in that: The first computing unit includes: A first processing subunit is configured to perform processing based on the elastic modulus and Poisson's ratio among the rock and soil mass parameters, construct an elastic stress-strain tensor relationship through the generalized Hooke's law, and obtain an elastic stress tensor and an elastic strain tensor of the rock and soil mass; The second processing subunit is used to establish a yield function based on the cohesion and internal friction angle among the rock and soil parameters, construct a yield function expression through the Mohr-Coulomb yield criterion, and obtain the yield boundary function of the rock and soil 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 through an iterative algorithm combining an associated flow rule and a plastic multiplier.

8. The geotechnical stability analysis system based on thermodynamics-tensor invariant coupling according to claim 7, characterized in that: The second computing unit includes: The second calculation subunit is used to calculate and process the elastic strain energy density increment based on the elastic stress tensor and elastic strain tensor of the rock and soil body to obtain the elastic strain energy density increment of the rock and soil body; The third calculation subunit is used to calculate and process the plastic strain energy density increment based on the plastic strain tensor increment to obtain the plastic strain energy density increment of the rock and soil mass; The third processing subunit is used to superimpose the elastic strain energy density increment and the plastic strain energy density increment of the rock and soil body to obtain the total strain energy density increment of the rock and soil body under different stress states.

9. The geotechnical stability analysis system based on thermodynamics-tensor invariant coupling according to claim 6, characterized in that: The analysis unit comprises: The fourth processing subunit is used to perform spatial field reconstruction processing on the total strain energy density increment of the rock and soil mass under different stress states, and obtain a three-dimensional spatial strain energy density distribution model of the rock and soil mass through finite element grid interpolation processing; a fifth processing subunit, configured to perform a local extreme value search process on the three-dimensional spatial strain energy density distribution model of the rock mass, calculate the strain energy gradient and the Laplace operator at each point, and identify strain energy regions where the strain energy gradient and the Laplace operator are greater than a preset threshold; a sixth processing subunit, configured to cluster the strain energy regions where the strain energy gradient and the Laplace operator are greater than a preset threshold, and perform cluster analysis using a K-means algorithm to obtain strain energy abnormal regions; The seventh processing subunit is configured to treat the abnormal strain energy region as an abnormal stability region of the rock and soil mass.

10. The geotechnical stability analysis system based on thermodynamics-tensor invariant coupling according to claim 6, characterized in that: After the analysis unit, it also includes: a third processing unit, configured to analyze the abnormal stability region of the rock and soil mass and determine a 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 classification processing on the potential sliding surface orientation and depth prediction value of the rock and soil body to obtain the stability abnormality level of the stability abnormal area of ​​the rock and soil body.

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