Method for determining equivalent GSI parameters of rock mass based on three-dimensional strength and strain softening

Abstract

The application belongs to the technical field of geotechnical engineering, and discloses a rock mass equivalent GSI parameter value determination method based on three-dimensional strength and strain softening, which comprises the following steps: determining rock mass mechanical parameters and tunnel excavation parameters; calculating model plastic zone radius by using peak GSI p and ideal elastic-plastic model R p,epp ; calculating an attenuation factor according to the determined parameters k ; determining a proportional coefficient based on the attenuation factor k and the model plastic zone radius R p,epp ; determining a proportional coefficient by an exponential attenuation relationship β , and obtaining equivalent parameter GSI eq ; finally, calculating the mechanical response of surrounding rock by using equivalent parameter GSI eq and ideal elastic-plastic model. The application converts the complex strain softening problem into an efficient ideal elastic-plastic problem by introducing the equivalent GSI parameter, significantly improves the calculation efficiency while ensuring the calculation accuracy, and fully considers the influence of the three-dimensional stress state, thereby providing a practical and reliable technical means for tunnel engineering stability analysis.

Description

Technical Field

[0001] This invention belongs to the field of surrounding rock analysis technology for underground engineering, and specifically relates to a method for determining the equivalent GSI parameters of rock mass based on three-dimensional strength and strain softening. It is applicable to the stability analysis and support design of surrounding rock in underground engineering such as tunnels and roadways, and can improve the efficiency of engineering design and analysis while ensuring calculation accuracy. Background Technology

[0002] In the design and construction of underground engineering projects such as tunnels and mine roadways, surrounding rock stability analysis is a core aspect of ensuring project safety, and numerical simulation is an important means of achieving this analysis. Its accuracy and efficiency directly depend on the rock mass constitutive model used. Currently, the rock mass constitutive models widely used in engineering are mainly divided into two categories: ideal perfect plastic model (EPP) and elastic strain softening model (ESS). However, both have significant limitations in application.

[0003] The ideal elastoplastic model is favored by engineers for its simplicity, readily available parameters, and stable and efficient numerical calculations. However, this model has a critical flaw—it assumes that the bearing capacity of the rock mass remains constant after reaching its peak strength. This is significantly inconsistent with the strain softening behavior (i.e., strength gradually decreases with increasing deformation) exhibited by most rock masses (especially weak rock masses) after reaching their peak strength. Therefore, using the ideal elastoplastic model will overestimate the residual strength of the surrounding rock, resulting in an overestimation of the self-supporting capacity and an underestimation of the required support force, thus posing a potential risk to engineering safety.

[0004] To more accurately describe the post-peak behavior of rock masses, strain softening models have been proposed and developed. These models can simulate the process of rock mass strength decaying from its peak value to its residual value, which is theoretically more consistent with reality. However, strain softening models are complex in structure and computationally intensive, and the softening parameters involved (such as softening modulus and critical plastic strain) are difficult to accurately determine through field tests. This makes them difficult to promote in engineering practice, especially failing to meet the needs of rapid design and multi-scheme comparison.

[0005] In summary, the existing technology suffers from a prominent contradiction between being "efficient but inaccurate" and "accurate but inefficient." Therefore, the engineering community urgently needs a method for determining rock mechanics parameters that can balance computational accuracy and efficiency, consider both the three-dimensional strength and strain softening characteristics of rock masses, and possess simplicity and practicality. Summary of the Invention

[0006] The purpose of this invention is to overcome the limitations of existing rock mass constitutive models in engineering applications and to provide a method for determining the equivalent GSI parameters of rock mass based on three-dimensional strength and strain softening. By introducing attenuation factors and scaling factors related to the plastic zone range, the complex rock mass strain softening problem is equivalently transformed into an ideal elastoplastic problem using "equivalent GSI parameters (GSIeq)". While retaining the computational efficiency of the ideal elastoplastic model, this method fully reflects the three-dimensional strength characteristics and strain softening behavior of the rock mass, achieving a balance between computational accuracy and efficiency, and providing reliable technical support for the rapid and safe design of underground engineering projects such as tunnels.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] A method for determining the equivalent GSI parameters of rock mass based on three-dimensional strength and strain softening includes the following steps:

[0009] S1. Determine the mechanical parameters of strain-softened rock mass and tunnel excavation parameters;

[0010] S2, using the peak value of the geological strength index GSI p Using an ideal elastic-plastic (EPP) model, the mechanical response of the surrounding rock after excavation is calculated, and the radius R of the plastic zone of the model is obtained. p,epp ;

[0011] S3. Calculate the attenuation factor k based on the parameters determined in step S1;

[0012] S4. Based on the attenuation factor k and the radius of the model's plastic zone R p,epp Calculate the scaling factor β, and obtain the equivalent parameter GSI based on the definition of the scaling factor β. eq ;

[0013] S5. Using equivalent parameter GSI eq Using an ideal elastoplastic model, the mechanical response of the surrounding rock is calculated.

[0014] As a further description of the above technical solution: the mechanical parameters of the strain-softened rock mass in step S1 include the uniaxial compressive strength σ c Elastic modulus E, Poisson's ratio ν, peak geological strength index GSI p Geological strength index residual value (GSI) r Rock mass characteristic parameters m i The disturbance coefficient D, the dilatation angle ψ, and the critical plastic deviatoric strain γ p* ;

[0015] The tunnel excavation parameters include the excavation radius R0, the hydrostatic stress of the original rock p, the axial stress of the original rock q, and the support stress after excavation p. s ;

[0016] The post-peak strain softening behavior of the rock mass is characterized by the geological strength index (GSI). The GSI increases with plastic deviatoric strain γ during the softening stage. p The increase of γ decreases linearly, reaching the critical plastic deviatoric strain γ p* Residual value of geological strength index (GSI) is maintained. r constant.

[0017] As a further description of the above technical solution, the calculation of the mechanical response of the surrounding rock after excavation in step S2 includes the calculation of stress and strain in the elastic zone, the calculation of stress and radius in the plastic zone, and the calculation of strain and displacement in the plastic zone.

[0018] As a further description of the above technical solution, the calculation of the mechanical response of the surrounding rock after excavation in step S2 uses a thick-walled cylindrical model to simulate the excavation scenario. The material is an ideal elastic-plastic model, and the three-dimensional Hoek–Brown strength criterion (GZZ strength criterion) is used to determine whether the surrounding rock has entered the plastic zone.

[0019] The expression for the three-dimensional Hoek–Brown intensity criterion is:

[0020] ;

[0021] Where, σ m,2 =(σ1+σ3) / 2 is the mean of the maximum and minimum principal stresses; τ oct For octahedral shear stress; m b s and a are rock mass material parameters, determined by the geological strength index GSI and the rock mass characteristic parameter m. i The disturbance coefficient D is converted to obtain:

[0022] .

[0023] As a further description of the above technical solution, the stress and strain in the elastic region are calculated using elastic mechanics, and the expression is:

[0024] ,

[0025] Where: σ r σ θ σ z These represent radial, tangential, and axial stresses, respectively, ε r ε θ u r These represent radial strain, tangential strain, and radial displacement, respectively; G = E / (1+ν) / 2 is the shear modulus; and r is the radial distance.

[0026] When the support stress p after excavation s Less than the critical stress p in the plastic zone c When a plastic zone appears in the surrounding rock, the radius R of the plastic zone is used.p and the critical stress p in the plastic zone c Replace R0 and p in the formula respectively s We obtain the stress-strain expression for the elastic region when the plastic region exists.

[0027] As a further description of the above technical solution, the stress in the plastic zone is calculated using the finite difference method: the plastic zone is calculated according to the constant radial stress difference Δσ. r = –(p c – p s The stress is divided into n rings, and the stress components of each ring are calculated step by step from the plastic zone boundary i = 0 to the cavity wall i = n. The expression is:

[0028] ;

[0029] By using the finite difference scheme of the equilibrium equations to solve for the radii of each annulus, the radius R of the plastic zone can be obtained. p .

[0030] As a further description of the above technical solution, the strain in the plastic region is calculated using the elastoplastic separation method, decomposing the total strain into elastic strain and plastic strain. The elastic strain is calculated using Hooke's theorem; the plastic strain is calculated based on the non-associated flow rule considering the shear dilatation angle and the plastic strain compatibility equation, and the expression is:

[0031] ,

[0032] Where: λ=(1+sinψ) / (1-sinψ) is the dilatation coefficient, and ψ is the dilatation angle;

[0033] Radial displacement u at each point r Based on the strain in the plastic zone combined with geometric equations The calculation yielded the result.

[0034] As a further description of the above technical solution, the attenuation factor k in step S3 satisfies the empirical formula for the rock mass and tunnel parameters:

[0035] ,

[0036] Among them, S i For each input calculation parameter, c i This is the corresponding empirical coefficient.

[0037] As a further description of the above technical solution, the scaling factor β in step S4 is defined as:

[0038] ,

[0039] The scaling factor β and the radius R of the plastic zone of the model p,epp The excavation radius R0 follows an exponential decay relationship:

[0040] ,

[0041] By obtaining R in step S2 p,epp Substituting the attenuation factor k obtained in step S3 into the above formula, we obtain β, and then calculate GSI using the definition of the proportionality coefficient β. eq .

[0042] As a further description of the above technical solution, when R p,epp When R = 0, the surrounding rock is in an elastic state, and the peak strength is used directly for calculation. Taking β = 1, i.e., GSI eq = GSI p When R p,epp When ≥3R0, the softening region is ignored, and β=0 is taken, i.e., GSI eq = GSI r .

[0043] As a further description of the above technical solution, step S5 uses the equivalent parameter GSI. eq The mechanical responses of the surrounding rock (such as stress, strain, displacement, etc.) calculated by the ideal elastic-plastic model (EPP) are within the acceptable range of error compared with the results obtained by directly using the strain softening model (ESS), and the calculation efficiency is improved.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] 1. Balancing accuracy and efficiency: By using "equivalent GSI parameters," the complex strain softening problem is transformed into an ideal elastoplastic problem. This retains the advantages of the ideal elastoplastic model, such as fast calculation speed and high stability, while indirectly reflecting the strain softening characteristics of the rock mass through equivalent parameters. This solves the contradiction between the traditional model's "high efficiency but inaccuracy" or "accuracy but low efficiency," and significantly improves the efficiency of engineering design and analysis.

[0046] 2. Closely reflects actual stress state: The plastic zone of the surrounding rock is determined based on the three-dimensional Hoek-Brown strength criterion, which fully considers the influence of the three-dimensional stress state of the rock mass. This makes the determination of equivalent parameters more consistent with the actual stress conditions of the surrounding rock in tunnel engineering, and significantly improves the accuracy and reliability of plastic zone prediction and mechanical response results.

[0047] 3. High practicality: Most of the required parameters can be obtained through conventional field tests or engineering surveys. The coefficients of the empirical formula for the attenuation factor have been verified by a large number of calculation examples, and the values ​​are clear. They are easy for engineering technicians to master and apply, and can be widely used for the stability analysis and support design of surrounding rock in underground engineering such as tunnels and roadways. Attached Figure Description

[0048] Figure 1 This is a flowchart of the method of the present invention.

[0049] Figure 2 This is a schematic diagram of the post-peak strain softening path.

[0050] Figure 3 This is a schematic diagram of the excavation model.

[0051] Figure 4 Is β and R p,epp The exponential decay relationship between / R0.

[0052] Figure 5 It is a comparison between the corresponding calculation results of the surrounding rock and the results of the strain softening model.

[0053] Figure 6 This is a comparison between the GRC calculation results and the strain softening model results. Detailed Implementation

[0054] The claims of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments, but this does not constitute any limitation on the present invention. Any limited modifications made by any person within the scope of protection of the claims of the present invention shall still be within the scope of protection of the claims of the present invention.

[0055] The method for determining the equivalent GSI parameters of rock mass based on three-dimensional strength and strain softening is as follows: Figure 1 As shown, it includes the following steps:

[0056] S1. Determine the mechanical parameters of strain-softened rock mass and tunnel excavation parameters:

[0057] The mechanical parameters of the strain-softened rock mass include: uniaxial compressive strength σ c = 40 MPa, elastic modulus E = 5 GPa, Poisson's ratio ν = 0.25, peak geological strength index GSI p = 50. Geological Strength Index Residual Value (GSI) r = 25.6, Rock mass characteristic parameter m i = 10, perturbation coefficient D = 0, shear dilatation angle ψ = 10°, critical plastic deviatoric strain γ p* = 0.02;

[0058] The tunnel excavation parameters include: excavation radius R0 = 8 m, original rock hydrostatic stress p = 30 MPa, original rock axial stress q = 30 MPa, and post-excavation support stress p. s = 1 MPa;

[0059] Among them, the post-peak strain softening behavior of the rock mass is characterized by the geological strength index GSI. The GSI changes from the peak GSI during the strain softening stage. p With plastic deviatoric strain γp The increase of γ decreases linearly, reaching the critical plastic deviatoric strain γ p* Residual value GSI is retained afterward. r Unchanged, such as Figure 2 As shown.

[0060] S2, using the peak value of the geological strength index GSI p Using parameters and an ideal elastic-plastic (EPP) model, the mechanical response of the surrounding rock after excavation is calculated, and the radius R of the plastic zone of the model is obtained. p,epp ;

[0061] The mechanical response calculation of the surrounding rock after excavation includes: stress and strain calculation in the elastic zone, stress and radius calculation in the plastic zone, and strain and displacement calculation in the plastic zone.

[0062] The mechanical response of the surrounding rock after excavation is calculated using the following method: Figure 3 The thick-walled cylindrical model shown is made of an ideal elastoplastic material. The three-dimensional Hoek–Brown strength criterion (i.e., the GZZ strength criterion) is used to determine whether the surrounding rock has entered the plastic zone. The expression for the three-dimensional Hoek–Brown strength criterion is as follows:

[0063] ,

[0064] Where, σ m,2 =(σ1+σ3) / 2 is the mean of the maximum and minimum principal stresses, τ oct For octahedral shear stress, m b s and a are rock mass material parameters, determined by the geological strength index GSI and the rock mass characteristic parameter m. i The disturbance coefficient D is converted to obtain:

[0065] ;

[0066] The stress and strain in the elastic region are calculated using elasticity mechanics.

[0067] ,

[0068] Where: σ r σ θ σ z These represent radial, tangential, and axial stresses, respectively, ε r ε θ u r These represent radial strain, tangential strain, and radial displacement, respectively. G = E / (1+ν) / 2 is the shear modulus, and r is the radial distance.

[0069] When the support stress p s Less than the critical stress p in the plastic zone c When a plastic zone appears in the surrounding rock, the radius R of the plastic zone is used. pand the critical stress p in the plastic zone c Replace R0 and p in the above formula s The formula for calculating the elastic response when the plastic region exists is as follows:

[0070] .

[0071] The stress in the plastic region described above is solved using the finite difference method. The plastic region is then calculated using a constant radial stress difference Δσ. r = –(p c – p s The area is divided into n = 1000 rings, and the stress components are calculated progressively from the plastic zone boundary i = 0 to the cavity wall i = n. Based on the plastic flow characteristics of the ideal elastoplastic model, the expressions for the stress components of each ring are obtained as follows:

[0072]

[0073] Based on the obtained stress components of each ring, and using the difference scheme of the equilibrium equation, the radius of each ring is solved to obtain the radius R of the plastic zone of the model. p,epp = 12.48 m = 1.56 R0.

[0074] The strain in the plastic region described above is solved using the elastoplastic separation method, decomposing the total strain into elastic strain and plastic strain. The elastic strain is obtained using Hooke's theorem; the plastic strain, based on the non-associated flow rule considering the shear dilatation angle and the plastic strain compatibility equation, yields the explicit expression as follows:

[0075]

[0076] Where: λ=(1+sinψ) / (1-sinψ) is the dilatation coefficient, and ψ is the dilatation angle.

[0077] The radial displacement of each point is obtained by calculating the strain in the plastic zone using geometric equations. Find the answer.

[0078] S3. Calculate the attenuation factor k based on the parameters determined in step S1:

[0079] The attenuation factor k satisfies the following empirical formula with respect to the basic parameters of the rock mass and tunnel:

[0080]

[0081] Among them, S i For each input calculation parameter, c i This is the corresponding empirical coefficient.

[0082] Based on extensive numerical analysis, the empirical coefficient c i The recommended values ​​are shown in Table 1.

[0083] Table 1 Empirical coefficient c i Recommended value table

[0084]

[0085] Where η = (GSI) p – GSI r ) / γ p* This represents the GSI softening rate.

[0086] Based on the empirical formula and the values ​​in Table 1, k = –2.129 is obtained.

[0087] S4. Based on the above attenuation factor k and the radius of the model's plastic zone R... p,epp Calculate the proportionality coefficient β, and then obtain the equivalent parameter GSI. eq ;

[0088] The proportionality constant β is defined as:

[0089]

[0090] The results of 4 sets of randomized examples show that β and R p,epp The relationship between / R0 and R0 approximately follows an exponential decay relationship, such as Figure 4 As shown, β and R p,epp The relationship between / R0 can be represented as:

[0091]

[0092] By R p,epp Substituting 12.48 m = 1.56 R0 and k = –2.129 into the above formula, we get β = 0.30, and then calculate GSI. eq = 33.0.

[0093] When R p,epp When R = 0, the surrounding rock is in an elastic state, and the peak strength is used directly for calculation. Taking β = 1, i.e., GSI eq = GSI p When R p,epp ≥3R0 indicates a large plastic region. Ignoring the small amount of softening region, we take β=0, i.e., GSI. eq =GSI r The calculation results are conservative and have a small error.

[0094] S5. Using the above equivalent parameter GSI eq The ideal elastic-plastic (EPP) model was used to calculate the mechanical response of the surrounding rock. The results were then compared with those obtained using the strain softening (ESS) model directly. Figure 5As shown in the figure, the comparison shows that the radial displacement u at the tunnel wall varies between the two methods. r and radial stress σ r The results are basically consistent with those above, with small errors; tangential stress σ θ There is a certain deviation, and the plastic zone radius R estimated by the method of this invention... p The values ​​are too high. In engineering practice, radial displacement and stress distribution are key indicators, and the calculation results of the method of this invention in this regard are in good agreement with the strain softening method.

[0095] Furthermore, by calculating the tunnel wall displacement under different support stresses, the surrounding rock characteristic curve (GRC) is plotted, such as... Figure 6 As shown, the GRC curves obtained by the two models (EPP and ESS) have an error of less than 10%, which is within the acceptable range for engineering applications.

[0096] Implementation examples demonstrate that the equivalent GSI parameters and ideal elastoplastic model of this invention can effectively replace complex strain softening analysis methods while ensuring computational accuracy. This method can reasonably reflect the influence of geostress conditions, rock mass properties, and engineering excavation factors on the surrounding rock excavation response, while significantly improving computational efficiency, making it suitable for rapid evaluation and design optimization in engineering projects.

[0097] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them; those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions will not cause the essence of the corresponding technical solutions to deviate from the protection scope of the present invention.

Claims

1. A method for determining the equivalent GSI parameters of rock mass based on three-dimensional strength and strain softening, characterized in that, Includes the following steps: S1. Determine the mechanical parameters of strain-softened rock mass and tunnel excavation parameters; The mechanical parameters of the strain-softened rock mass include uniaxial compressive strength σ. c Elastic modulus E, Poisson's ratio ν, peak value of geological strength index GSI p Geological strength index residual value (GSI) r Rock mass characteristic parameters m i The disturbance coefficient D, the dilatation angle ψ, and the critical plastic deviatoric strain γ p* ; The tunnel excavation parameters include the excavation radius R0, the hydrostatic stress of the original rock p, the axial stress of the original rock q, and the support stress after excavation p. s ; The post-peak strain softening behavior of the rock mass is characterized by the geological strength index (GSI). The GSI increases with plastic deviatoric strain γ during the strain softening stage. p The increase of γ decreases linearly, reaching the critical plastic deviatoric strain γ p* Residual value of geological strength index (GSI) is maintained. r constant; S2, using the peak value of the geological strength index GSI p Using an ideal elastoplastic model, the mechanical response of the surrounding rock after excavation is calculated, and the radius R of the plastic zone of the model is obtained. p,epp ; The calculation of the mechanical response of the surrounding rock after excavation uses a thick-walled cylindrical model to simulate the excavation scenario, and the three-dimensional Hoek-Brown strength criterion is used to determine whether the surrounding rock has entered the plastic zone. The expression for the three-dimensional Hoek–Brown intensity criterion is: ； Where, σ m,2 =(σ1+σ3) / 2 is the mean of the maximum and minimum principal stresses; τ oct For octahedral shear stress; m b s and a are rock mass material parameters, determined by the geological strength index GSI and the rock mass characteristic parameter m. i The disturbance coefficient D is converted to obtain: ； S3. Calculate the attenuation factor k based on the parameters determined in step S1; S4. Based on the proportionality coefficient β and the radius R of the plastic zone of the model p,epp The excavation radius R0 follows an exponential decay relationship; calculate the proportionality coefficient β: ； The equivalent parameter GSI is obtained by combining the definition of the scaling factor β. eq The proportionality coefficient β is defined as: ； Among them, GSI r This represents the residual value of the geological strength index. S5. Using equivalent parameter GSI eq Using an ideal elastoplastic model, the mechanical response of the surrounding rock is calculated.

2. The method for determining the equivalent GSI parameters of rock mass based on three-dimensional strength and strain softening according to claim 1, characterized in that: The calculation of the mechanical response of the surrounding rock after excavation in step S2 includes the calculation of stress and strain in the elastic zone, the calculation of stress and radius in the plastic zone, and the calculation of strain and displacement in the plastic zone.

3. The method for determining the equivalent GSI parameters of rock mass based on three-dimensional strength and strain softening according to claim 2, characterized in that: The stress and strain in the elastic region are calculated using elasticity mechanics, and the expression is: ， Where: σ r σ θ σ z These represent radial, tangential, and axial stresses, respectively, ε r ε θ u r These represent radial strain, tangential strain, and radial displacement, respectively; G = E / (1+ν) / 2 is the shear modulus; and r is the radial distance. When the support stress p after excavation s Less than the critical stress p in the plastic zone c When a plastic zone appears in the surrounding rock, the radius R of the plastic zone is used. p and the critical stress p in the plastic zone c Replace R0 and p in the formula respectively s We obtain the stress-strain expression for the elastic region when the plastic region exists.

4. The method for determining the equivalent GSI parameters of rock mass based on three-dimensional strength and strain softening according to claim 2, characterized in that: The stress in the plastic zone is calculated using the finite difference method: the plastic zone is divided according to the constant radial stress difference Δσ. r = –(p c -p s The area is divided into n rings. The stress components of each ring are calculated step by step from the boundary of the plastic zone i = 0 to the cavity wall i = n. The expression is: ； By using the finite difference scheme of the equilibrium equations to solve for the radii of each annulus, the radius R of the plastic zone can be obtained. p .

5. The method for determining the equivalent GSI parameters of rock mass based on three-dimensional strength and strain softening according to claim 2, characterized in that: The strain in the plastic region is calculated using the elastoplastic separation method, decomposing the total strain into elastic strain and plastic strain. The elastic strain is calculated using Hooke's theorem; the plastic strain is calculated based on the non-associated flow rule considering the shear dilatation angle and the plastic strain compatibility equation, expressed as: ， Where: λ=(1+sinψ) / (1-sinψ) is the dilatation coefficient, and ψ is the dilatation angle; Radial displacement u at each point r Based on the strain in the plastic zone combined with geometric equations The calculation yielded the result.

6. The method for determining the equivalent GSI parameters of rock mass based on three-dimensional strength and strain softening according to claim 1, characterized in that: The attenuation factor k mentioned in step S3 satisfies the empirical formula for the rock mass and tunnel parameters: ， Among them, S i For each input calculation parameter, c i This is the corresponding empirical coefficient.

7. The method for determining the equivalent GSI parameters of rock mass based on three-dimensional strength and strain softening according to claim 1, characterized in that: When R p,epp When = R0, take β=1, i.e., GSI eq = GSI p When R p,epp When ≥3R0, we take β=0, i.e., GSI eq = GSI r .

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