A stress balance-based analytical prediction method for plastic failure zone of surrounding rock

Abstract

The application discloses a kind of based on stress balance's surrounding rock plastic damage zone analytical prediction method, belong to tunnel engineering technical field, including the following steps: obtaining initial plastic zone boundary;Based on plastic zone area correction model and lower than plastic stress part elastic stress distribution is invariable, obtain the elastic load summation of surrounding rock stress before adjustment lower than yield stress part and the elastic load summation of elastic zone after stress adjustment is equal when radius tends to infinity, and the elastic load summation of surrounding rock stress before adjustment higher than yield stress part and the summation of load of plastic zone after stress adjustment is equal;Based on stress balance principle, obtain the radius of surrounding rock plastic zone;Based on the radius of surrounding rock plastic zone and polar coordinate plotting, obtain the range and form distribution characteristics of tunnel surrounding rock plastic zone;The application solves the problem of insufficient accuracy of tunnel engineering surrounding rock plastic zone solution in stress prominent area.

Description

Technical Field

[0001] This invention belongs to the field of tunnel engineering technology, and in particular relates to an analytical prediction method for the plastic failure zone of surrounding rock based on stress balance. Background Technology

[0002] The plastic zone of the surrounding rock is an important basis for evaluating the stability of tunnel surrounding rock and the theoretical foundation for tunnel support design. In actual engineering, the original rock environment is mostly a non-uniform stress field, especially in tectonically active areas with strong tectonic stress. Due to the stress asymmetry of the non-uniform stress field, elastoplastic analysis is more complex and difficult than that of the uniform stress field. Usually, appropriate assumptions are made, and some approximate algorithms or mathematical analysis methods are used to solve the problem. Existing technology one refers to the existing elastic stress solution of the surrounding rock in a non-uniform stress field and the plastic solution in a uniform stress field to construct the expression of the stress components of the surrounding rock and derive an approximate solution for the boundary of the plastic zone. Existing technology two equates the mechanical model of the plastic zone of the surrounding rock of a circular cavern in a non-uniform stress field to an axisymmetric plane strain problem, and then combines the classical elastic Kiel's solution to approximately obtain the elastoplastic boundary of the surrounding rock. In recent years, some studies have derived the analytical expression of the boundary of the plastic zone of the surrounding rock in a non-uniform stress field through the method of tectonic stress. This kind of classical analytical method is summarized as the "stress-tectonic method". The stress-tectonic method has a simple solution process and the results have a certain degree of accuracy, but it also has the following drawbacks:

[0003] (1) The radial stress at the elastic-plastic interface is zero;

[0004] (2) Use the equilibrium differential equations in the case of axis symmetry;

[0005] (3) It is assumed that the maximum and minimum principal stresses of the surrounding rock in the plastic zone are respectively the tangential stress σ θ and radial force σ r Theoretical shortcomings, etc.

[0006] The approximate implicit method is one of the mainstream methods for analyzing the plastic zone of the surrounding rock in a non-uniform stress field circular tunnel. Since its proposal in 1971, a large number of scholars have used the approximate implicit method to develop the theoretical research on the analysis of the plastic zone of the surrounding rock in a non-uniform stress field. First, the range of the plastic zone was analyzed based on different strength criteria, and then the influence of the intermediate principal stress, rock dilatation characteristics and seepage in the rock mass occurrence environment on the range of the plastic zone was considered in turn.

[0007] In addition to the stress structure method and the approximate implicit method, existing technologies have also introduced mathematical analysis methods into the analytical study of the plastic zone of the surrounding rock in non-uniform stress fields. Analytical methods such as the complex variable function method, the perturbation method, and the logarithmic strain method have been explored. These methods have also provided ideas for the analysis of the plastic zone of the surrounding rock in non-circular caverns and enriched the theory of elastic-plastic analysis of the surrounding rock in non-uniform stress fields. However, the theoretical analysis based on these methods is relatively complex and has limited engineering application. Summary of the Invention

[0008] To address the aforementioned shortcomings in existing technologies, this invention provides an analytical prediction method for the plastic failure zone of surrounding rock based on stress balance. Based on an approximate implicit method, it attempts to correct the range of the plastic zone of surrounding rock in the non-uniform stress field obtained by the traditional point criterion method using the stress balance principle, thus solving the problem of insufficient accuracy in solving the plastic zone of surrounding rock in tunnel engineering with prominent stress areas.

[0009] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows:

[0010] This invention provides an analytical prediction method for the plastic failure zone of surrounding rock based on stress balance, comprising the following steps:

[0011] S1. Obtain the initial plastic zone boundary R p ;

[0012] S2. Based on the static equilibrium condition, the initial plastic zone boundary is extended to obtain the plastic zone area correction model;

[0013] S3. Based on the plastic zone area correction model and the unchanged elastic stress distribution in the part below the plastic stress, the total elastic load S2 in the part below the yield stress before the surrounding rock stress adjustment is equal to the total elastic load S4 borne by the elastic zone after the stress adjustment when the radius r approaches infinity.

[0014] S4. Based on the fact that the total elastic load S2 of the portion below the yield stress before the surrounding rock stress adjustment is equal to the total elastic load S4 borne by the elastic zone after stress adjustment when the radius r approaches infinity, we obtain that the total elastic load S1 of the portion above the yield stress before the surrounding rock stress adjustment is equal to the total load S3 borne by the plastic zone after stress adjustment.

[0015] S5. Based on the fact that the total elastic load S1 of the portion exceeding the yield stress before stress adjustment is equal to the total load S3 borne by the plastic zone after stress adjustment, and the principle of stress balance, the radius R of the plastic zone of the surrounding rock is obtained. p0 ;

[0016] S6, based on the radius R of the plastic zone of the surrounding rock p0 By plotting in polar coordinates, the extent and morphological distribution characteristics of the plastic zone in the surrounding rock of the tunnel can be obtained.

[0017] The beneficial effects of this invention are as follows: This invention provides an analytical prediction method for the plastic failure zone of surrounding rock based on stress balance. It analyzes the analytical solution of the radius of the plastic zone of surrounding rock based on the point criterion, derives the analytical solution of the radius of the plastic zone of tunnel surrounding rock in non-uniform stress field, corrects the boundary and range of the plastic zone, and introduces the concept of stress balance into the analysis of the radius of the plastic zone of tunnel surrounding rock. From the perspective of force balance, it realizes a relatively more reasonable derivation of the radius of the plastic zone, and achieves a more accurate solution for the plastic zone of surrounding rock in tunnel engineering with prominent stress areas.

[0018] Further, step S1 includes the following steps:

[0019] S11. Based on the Mohr-Coulomb criterion, the Mohr-Coulomb criterion model for elastic boundary surrounding rocks is obtained:

[0020]

[0021]

[0022] Where σ1 represents the maximum principal stress of the surrounding rock at the boundary of the elastic zone, σ3 represents the minimum principal stress of the surrounding rock at the boundary of the elastic zone, m represents the internal friction angle coefficient of the rock mass, and c represents the cohesion of the rock mass. Indicates the friction angle within the rock mass;

[0023] S12. Based on the Mohr-Coulomb criterion model and the shear stress of the surrounding rock in a non-uniform stress field, the principal stress model is obtained:

[0024]

[0025] Where, σ r σ represents the radial stress of the surrounding rock. θ τ represents the tangential stress in the surrounding rock. rθ Indicates the shear stress of the surrounding rock;

[0026] S13. Substituting the yield criterion into the principal stress model, we obtain the yield model expressed by stress components:

[0027]

[0028] S14. Based on the yield model and the elastic zone stress model, the boundary model of the plastic region is obtained:

[0029] f(ρ)=k4ρ 4 +k3ρ 3 +k2ρ 2 +k1ρ+k0=0

[0030]

[0031]

[0032] Where f(ρ) represents the boundary of the plastic region, k4, k3, k2, k1, and k0 are constant coefficients, ρ represents the radius square ratio, R0 represents the tunnel radius, r represents the radius, λ represents the lateral pressure coefficient, and p s p0 represents the initial vertical ground stress, θ represents the angle, and σ represents the reaction force acting on the tunnel wall. c Represents the radius coefficient based on the Mohr-Coulomb method;

[0033] S15. Based on the plastic region boundary model, implicit equations for radius r and angle θ are obtained;

[0034] S16. Based on implicit equations and actual engineering conditions, the initial plastic zone boundary R is calculated. p .

[0035] The beneficial effects of adopting the above-mentioned further scheme are as follows: assuming that the surrounding rock of the tunnel is in an elastic state in the initial state, when the magnitude of its elastic stress satisfies the Mohr-Coulomb criterion, the surrounding rock reaches the condition for plastic initiation and enters the plastic zone. The position of this critical state is obtained as the boundary of the initial plastic zone, which provides a basis for obtaining the plastic zone area correction model.

[0036] Furthermore, the calculation expression for the plastic zone area correction model in step S2 is as follows:

[0037] S1 + S2 = S3 + S4

[0038] Wherein, S1 represents the total elastic load of the portion of the surrounding rock stress exceeding the yield stress before stress adjustment, S2 represents the total elastic load of the portion of the surrounding rock stress below the yield stress before stress adjustment, S3 represents the total load borne by the plastic zone after stress adjustment, and S4 represents the total elastic load borne by the elastic zone after stress adjustment.

[0039] The beneficial effects of adopting the above-mentioned further scheme are as follows: According to the stress balance condition before and after the yielding of the surrounding rock, the area under the modified stress distribution curve should be equal to the area under the curve of the linear elastic stress state. Therefore, a calculation method for the plastic zone area correction model is provided, which provides a basis for the analysis of the radius of the plastic zone of the surrounding rock.

[0040] Further, step S5 includes the following steps:

[0041] S51. Set the stress distribution in the plastic zone of the surrounding rock as linear, and calculate the total elastic load S1 of the portion of the surrounding rock stress exceeding the yield stress before stress adjustment based on the radius r.

[0042] S52. The tangential stress σ at the boundary of the plastic zone is calculated based on the point criterion. θp ;

[0043] S53, the total load S3 borne by the plastic zone after stress adjustment is calculated based on the radius r;

[0044] S54. Based on the sum of the loads borne by the plastic zone after stress adjustment, S3, the radius R of the plastic zone of the surrounding rock is obtained. p0 .

[0045] The beneficial effects of adopting the above-mentioned further scheme are: it provides a specific method for obtaining the radius of the plastic zone of the surrounding rock based on the stress balance principle and the plastic zone area correction model, thus providing a basis for the analysis of the radius of the plastic zone of the surrounding rock.

[0046] Furthermore, the calculation expression for the total elastic load S1 in step S51 is as follows:

[0047]

[0048] The beneficial effects of adopting the above-mentioned further scheme are: assuming that the stress distribution in the plastic zone of the surrounding rock is linear, and calculating the total elastic load based on the stress balance principle, thus providing a basis for the analysis of the radius of the plastic zone of the surrounding rock.

[0049] Furthermore, in step S52, the tangential stress σ at the boundary of the plastic zone... θp The calculation expression is as follows:

[0050]

[0051] The beneficial effects of adopting the above-mentioned further scheme are: it provides a calculation method for solving the tangential stress at the boundary of the plastic zone based on the point criterion, and provides a basis for the analysis of the radius of the plastic zone of the surrounding rock.

[0052] Furthermore, the calculation expression for the total load S3 borne by the plastic zone after stress adjustment in step S53 is as follows:

[0053]

[0054] The beneficial effects of adopting the above-mentioned further scheme are: assuming that the stress distribution in the plastic zone of the surrounding rock is linear, and calculating the total load borne by the plastic zone after adjustment based on the stress balance principle, thus providing a basis for the analysis of the radius of the plastic zone of the surrounding rock.

[0055] Furthermore, in step S54, the radius R of the plastic zone of the surrounding rock... p0 The calculation expression is as follows:

[0056]

[0057] The beneficial effect of adopting the above-mentioned further scheme is: to increase the radius R of the plastic zone of the surrounding rock. p0 The calculation method provides a basis for intuitive analysis and research on the range and morphological distribution characteristics of the plastic zone in the surrounding rock of tunnels. Attached Figure Description

[0058] Figure 1 This is a schematic diagram of the rock mass after yielding in an embodiment of the present invention.

[0059] Figure 2 This is a schematic diagram of stress decomposition of a non-uniform stress field in an embodiment of the present invention.

[0060] Figure 3 This is a schematic diagram of the polar coordinate stress state of a non-uniform stress field in an embodiment of the present invention.

[0061] Figure 4 This is a flowchart illustrating the steps of an analytical prediction method for the plastic failure zone of surrounding rock based on stress balance, as described in an embodiment of the present invention.

[0062] Figure 5 This is a schematic diagram of the stress principle for solving the plastic zone radius based on the point criterion in an embodiment of the present invention.

[0063] Figure 6 This is a schematic diagram illustrating the principle of plastic zone radius correction based on stress balance in an embodiment of the present invention.

[0064] Figure 7 This is a schematic diagram illustrating the correction of the plastic zone radius in an embodiment of the present invention.

[0065] Figure 8 This is a diagram illustrating the morphology of the plastic zone in an engineering case study of this invention.

[0066] Figure 9 This is a comparison chart of the range of the plastic zone and the analytical value obtained from on-site testing and analysis of an existing tunnel project in this embodiment of the invention. Detailed Implementation

[0067] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0068] Example 1

[0069] Based on the basic mechanical properties of a deeply buried circular tunnel after excavation, the following assumptions are made regarding the plastic zone:

[0070] (1) The radius of the circular tunnel is R0, and the tunnel wall is subjected to a uniform support reaction force p. s ;

[0071] (2) The tunnel is under non-uniform stress, with vertical stress p0 and horizontal stress λ·p0 acting at infinite distance of the cross section.

[0072] (3) The tunnel cross section is more than 4R0 away from the tunnel excavation face, that is, the excavation face effect is not considered. The strain in the orthogonal direction of the cross section (i.e. the tunnel axis direction) can be approximately equal to 0, and the surrounding rock is in a plane strain state.

[0073] (4) The surrounding rock is a homogeneous, isotropic elasto-plastic material; before excavation, the surrounding rock at the study section is under triaxial compression, and the surrounding rock is in an elastic state in the initial stage; after excavation, when the support force p sWhen the support force is greater than the critical support force, the surrounding rock will always be in an elastic state; when the support force is less than the critical support force, the surrounding rock gradually develops into a plastic zone.

[0074] After the rock mass yields, it softens. Based on the stress state, the surrounding rock can be divided into two regions: a deeper, elastic region, such as... Figure 1 In Zone II, the rock mass was not affected by the unloading during excavation; the area from the elastic zone to the tunnel wall is the plastic zone, such as... Figure 1 In Zone I of the rock mass, the rock mass is in a yielding state.

[0075] Because the stress environment of a circular tunnel is a non-uniform stress field, the stress solution for the elastic region cannot be directly given using the conventional elastic solution for a uniform stress field. Therefore, the non-uniform stress field can be decomposed into... Figure 2 The situation;

[0076] like Figure 2 As shown, the non-uniform stress field actually located in the tunnel is equal to a magnitude of The result of superimposing a uniform stress field and a non-uniform stress field; by superimposing the stress fields, we obtain a stress field with vertical stress p0 and horizontal stress λ·p0, where λ is the lateral pressure coefficient.

[0077] The initial vertical ground stress outside the elastic zone is p0, the horizontal ground stress is λ·p0, and the support reaction force p from the tunnel wall is... s The tunnel radius is R0, and the radius of the plastic zone is R. p For a size of Given a uniform stress field, the stress in the elastic region can be calculated using the theory of elastic thick-walled cylinders. Combining this with boundary conditions, the expression for calculating the stress in the elastic region is obtained as follows:

[0078]

[0079] For non-uniform stress fields, the classical stress concentration problem of a circular hole in elasticity can be solved in polar coordinates. The specific solution method is as follows:

[0080] like Figure 3 As shown in Figure A1, the stress components in the rectangular coordinate system are transformed to the polar coordinate system. The calculation expression for the coordinate transformation is as follows:

[0081]

[0082] Where, σ θ σ θ and τ rθ Let θ represent the radial stress, tangential stress, and shear stress of the surrounding rock in polar coordinates, respectively, and let θ represent the angle.

[0083] A2. Let the stress function φ be within the elastic zone of the surrounding rock:

[0084] φ=f(r)cos2θ

[0085] Where f(r) represents the radius function;

[0086] A3. Substituting the stress function φ into the compatibility equation in polar coordinates, we obtain a fourth-order equation for the radius function:

[0087]

[0088] A4. Based on the fourth-order equation concerning the radius function, the general solution for the radius function is obtained:

[0089] f(r) = C1r 4 +C2r 2 +C3+C4r -2

[0090] Where C1, C2, C3 and C4 are all integration constants;

[0091] A5. Based on the general solution of the radius function, the stress expression in polar coordinates for the elastic zone of rock in a non-uniform stress field is obtained:

[0092]

[0093] A6. Based on the fact that the surrounding rock mass element at a sufficient distance from the tunnel is not affected by the tunnel excavation and the stress is not adjusted, its stress state is the same as when the tunnel is not excavated. That is, when the radius r approaches ∞, according to the calculation expression of coordinate transformation and the stress in the polar coordinate system of the rock elastic zone, the boundary conditions of the non-uniform stress field are obtained:

[0094]

[0095] A7. Based on the fact that the tunnel wall has no support reaction force and the shear stress is zero, the boundary conditions of the tunnel wall are obtained as follows:

[0096]

[0097] A8. Based on the boundary conditions of the non-uniform stress field, the integral constants are obtained as follows:

[0098]

[0099] A9. Based on the integral constants and the stress expression in the polar coordinate system of the rock elastic zone, the stress model of the surrounding rock elastic zone and the stress model of the circular cavern elastic zone under the non-uniform stress field are obtained:

[0100]

[0101]

[0102] When the lateral pressure coefficient λ≠1, the boundary of the plastic zone of the tunnel surrounding rock is no longer a regular circle, but has various shapes such as sickle and cross. Therefore, it is difficult to obtain its analytical solution based on the plasticity theory. Generally, it is first assumed that the surrounding rock is in an elastic state before and after the excavation of the tunnel. Then, the stress of the surrounding rock after excavation is obtained according to the elasticity theory, and then the plasticity condition is substituted to determine whether the surrounding rock yields.

[0103] When a plastic zone forms in the surrounding rock, according to the stress continuity condition, the surrounding rock at the boundary between the elastic and plastic zones satisfies both the stress condition of the elastic zone and is in a critical plastic yielding state.

[0104] like Figure 1 As shown, in one embodiment of the present invention, the present invention provides an analytical prediction method for the plastic failure zone of surrounding rock based on stress balance, comprising the following steps:

[0105] S1. Obtain the initial plastic zone boundary R p ;

[0106] Step S1 includes the following steps:

[0107] S11. Based on the Mohr-Coulomb criterion, the Mohr-Coulomb criterion model for elastic boundary surrounding rocks is obtained:

[0108]

[0109]

[0110] Where σ1 represents the maximum principal stress of the surrounding rock at the boundary of the elastic zone, σ3 represents the minimum principal stress of the surrounding rock at the boundary of the elastic zone, m represents the internal friction angle coefficient of the rock mass, and c represents the cohesion of the rock mass. Indicates the friction angle within the rock mass;

[0111] S12. Based on the Mohr-Coulomb criterion model and the shear stress of the surrounding rock in a non-uniform stress field, the principal stress model is obtained:

[0112]

[0113] Where, σ r σ represents the radial stress of the surrounding rock. θ τ represents the tangential stress in the surrounding rock. rθ Indicates the shear stress of the surrounding rock;

[0114] S13. Substituting the yield criterion into the principal stress model, we obtain the yield model expressed by stress components:

[0115]

[0116] S14. Based on the yield model and the elastic zone stress model, the boundary model of the plastic region is obtained:

[0117] f(ρ)=k4ρ 4 +k3ρ 3 +k2ρ 2 +k1ρ+k0=0

[0118]

[0119]

[0120] Where f(ρ) represents the boundary of the plastic region, k4, k3, k2, k1, and k0 are all constant coefficients, ρ represents the radius square ratio, R0 represents the tunnel radius, r represents the radius, λ represents the lateral pressure coefficient, and p s p0 represents the initial vertical ground stress, θ represents the angle, and σ represents the reaction force acting on the tunnel wall. c Represents the radius coefficient based on the Mohr-Coulomb method;

[0121] S15. Based on the plastic region boundary model, implicit equations for radius r and angle θ are obtained;

[0122] S16. Based on implicit equations and actual engineering conditions, the initial plastic zone boundary R is calculated. p ;

[0123] Assuming the tunnel surrounding rock is initially in an elastic state, when the magnitude of its elastic stress satisfies the Mohr-Coulomb criterion, the surrounding rock reaches the plastic initiation condition and enters the plastic zone. The location of this critical state is the boundary of the plastic zone. This is equivalent to solving for the stress points satisfying the Mohr-Coulomb criterion on the elastic stress distribution curve of the tunnel surrounding rock, as shown in Figure 5 (using the tangential stress σ in the direction of θ=0°). θ (For example). Therefore, for ease of distinction, this solution process is called the analytical solution of the radius of the plastic zone of the surrounding rock based on the point criterion; the shortcoming of this key assumption is that R0~R p After the surrounding rock within the range enters the plastic state, R p The surrounding rock outside the elastic stress still maintains its original elastic stress magnitude, which is inconsistent with reality; after the rock mass transitions from an elastic state to a plastic state, it relaxes, and the net force it can withstand decreases. This force will be transferred outwards by R. p The surrounding rock mass continues to bear the load, so the elastic zone surrounding rock in the critical state is affected by the increased force and will reach the condition for plasticization and enter the plastic zone. Therefore, the original boundary of the plastic zone will be pushed outward. Thus, the analytical method of plastic zone radius based on the point criterion assumption ignores the stress transfer caused by the plastic deformation of the surrounding rock, and the obtained range of plastic zone is too small.

[0124] When the initial elastic stress in the surrounding rock of a tunnel exceeds the yield strength of the rock, it enters a plastic state, resulting in plastic deformation. This causes a redistribution of stress in the surrounding rock, forming the initial plastic zone boundary R. pWithin this plastic zone, the surrounding rock stress will no longer be the original elastic stress distribution. Considering the softening that occurs after the surrounding rock yields, its plastic stress distribution is as follows: Figure 6 As shown, to satisfy the static equilibrium condition, the elastic stress originally exceeding the yield stress must undergo stress relaxation. This results in an increase in the elastic stress in the original elastic zone immediately adjacent to the plastic zone boundary. This will cause a portion of the elastic region to enter the plastic zone, meaning the original plastic zone boundary expands outwards. The stress in the elastic zone outside the new boundary continues to increase, and so on, until a new equilibrium state is reached. This process is equivalent to the stress in segment AB being readjusted to segment DE, and line BC being pushed outwards to position EF. Therefore, the adjusted plastic zone range is larger than the original R. p The scope has been expanded, and further revisions are needed.

[0125] according to Figure 6 Assuming that the linear elastic solution still applies in the elastic region outside the plastic region, i.e., the BC line is shifted to EF, according to the stress equilibrium condition before and after the surrounding rock yields, the area under the modified stress distribution curve DEF should be equal to the area under the ABC curve of the linear elastic stress state.

[0126] S2. Based on the static equilibrium condition, the initial plastic zone boundary is extended to obtain the plastic zone area correction model;

[0127] The calculation expression for the plastic zone area correction model in step S2 is as follows:

[0128] S1 + S2 = S3 + S4

[0129] Wherein, S1 represents the total elastic load of the portion above the yield stress before the surrounding rock stress is adjusted, S2 represents the total elastic load of the portion below the yield stress before the surrounding rock stress is adjusted, S3 represents the total load borne by the plastic zone after the stress is adjusted, and S4 represents the total elastic load borne by the elastic zone after the stress is adjusted.

[0130] S3. Based on the plastic zone area correction model and the unchanged elastic stress distribution in the part below the plastic stress, the total elastic load S2 in the part below the yield stress before the surrounding rock stress adjustment is equal to the total elastic load S4 borne by the elastic zone after the stress adjustment when the radius r approaches infinity.

[0131] S4. Based on the fact that the total elastic load S2 of the portion below the yield stress before the surrounding rock stress adjustment is equal to the total elastic load S4 borne by the elastic zone after stress adjustment when the radius r approaches infinity, we obtain that the total elastic load S1 of the portion above the yield stress before the surrounding rock stress adjustment is equal to the total load S3 borne by the plastic zone after stress adjustment.

[0132] like Figure 7As shown, scholars both domestically and internationally have conducted extensive hypotheses and research on the stress distribution patterns and laws within the plastic zone of surrounding rock, resulting in various surrounding rock zoning models, such as two-zone, three-zone, and even four-zone models, based on corresponding engineering conditions. These models consider the softening, associated flow, and rheological properties of the rock mass to solve for the stress distribution within the plastic zone, leading to a wealth of research results. These results meticulously consider the complex physical and mechanical properties of different rock masses, providing models that more accurately describe the mechanical behavior of the surrounding rock mass. However, the cumbersome solution process and the complexity of the results make them difficult to widely apply in engineering practice. Therefore, this paper assumes that the stress distribution within the plastic zone of the surrounding rock is linear, such as... Figure 7 As shown by line D′E′, the radius of the plastic zone of the tunnel surrounding rock is solved according to the principle of stress balance;

[0133] S5. Based on the fact that the total elastic load S1 of the portion exceeding the yield stress before stress adjustment is equal to the total load S3 borne by the plastic zone after stress adjustment, and the principle of stress balance, the radius R of the plastic zone of the surrounding rock is obtained. p0 ;

[0134] Step S5 includes the following steps:

[0135] S51. Set the stress distribution in the plastic zone of the surrounding rock as linear, and calculate the total elastic load S1 of the portion of the surrounding rock stress exceeding the yield stress before stress adjustment based on the radius r.

[0136] The calculation expression for the total elastic load S1 in step S51 is as follows:

[0137]

[0138] S52. The tangential stress σ at the boundary of the plastic zone is calculated based on the point criterion. θp ;

[0139] In step S52, the tangential stress σ at the boundary of the plastic zone θp The calculation expression is as follows:

[0140]

[0141] S53, the total load S3 borne by the plastic zone after stress adjustment is calculated based on the radius r;

[0142] The calculation expression for the total load S3 borne by the plastic zone after stress adjustment in step S53 is as follows:

[0143]

[0144] S54. Based on the sum of the loads borne by the plastic zone after stress adjustment, S3, the radius R of the plastic zone of the surrounding rock is obtained. p0 ;

[0145] In step S54, the radius R of the plastic zone of the surrounding rock p0 The calculation expression is as follows:

[0146]

[0147] S6, based on the radius R of the plastic zone of the surrounding rock p0 By plotting in polar coordinates, the extent and morphological distribution characteristics of the plastic zone in the surrounding rock of the tunnel can be obtained.

[0148] Example 2

[0149] In another embodiment of the present invention, in order to verify the rationality and accuracy of the analytical calculation method for the plastic zone in practical engineering applications, this embodiment collected engineering data from 16 sections of 10 completed tunnel projects, as well as data on the range of the plastic zone of the surrounding rock determined by researchers based on on-site testing and analysis using methods such as acoustic wave testing and multi-point displacement meter testing. Based on the surrounding rock parameters and stress parameters at the tunnel section, the analytical solutions for the range of the plastic zone of the surrounding rock at the section were calculated using the point criterion method and the stress balance method, respectively. These solutions were then compared with the range of the plastic zone obtained from the analysis of the section using methods such as on-site acoustic wave testing. Since Class IV and Class V surrounding rocks usually have strong plastic characteristics and are prone to forming plastic zones after tunnel excavation, the following first provides a detailed introduction and analysis using one typical engineering case each for Class IV and Class V surrounding rocks. Finally, the range of the plastic zone obtained from the analysis of the 16 sections using methods such as on-site acoustic wave testing is compared with the two sets of analytical values.

[0150] Using a section of the Shimen Tunnel on the Baohan Railway as a case study for engineering verification in the Class IV surrounding rock plastic zone, the tunnel section has a net width of 16.50m and a net height of 5.50m. Assuming it is a circular cross-section, the calculated equivalent radius is R0 = 8.93m, the burial depth is 375m, the lateral pressure coefficient λ is 1.15, and the unit weight of the surrounding rock is 25.99kN / m³. 3 The calculated vertical stress at the cross-section is p0 = 9.7 MPa, the support reaction force is 0.1 MPa, and c = 1.4 MPa. The range of the plastic zone determined by the on-site acoustic wave test analysis of the cross section is 0.81m to 1.18m for the sidewalls and 1.10m to 1.53m for the arch.

[0151] Substituting the rock mass mechanical parameters and in-situ stress data of the surrounding rock section into the calculation formulas of the point criterion method and the stress balance analytical method in this paper, the morphology diagram of the plastic zone of the surrounding rock section is calculated and plotted as follows. Figure 8As shown, the left side represents Class IV surrounding rock, and the right side represents Class V surrounding rock. The results show that the plastic zone boundary shape analyzed by the point criterion method is nearly circular, with the sidewall range of 0.42–0.57 m and the crown range of 0.58–0.68 m. The plastic zone shape analyzed by the stress balance method is elliptical, with the sidewall plastic zone range of 1.00 m–1.33 m and the crown plastic zone range of 1.36 m–1.69 m. Comparing the two sets of analytical values ​​with the field test analysis results shows that:

[0152] (1) The analytical results obtained by the point criterion method are 0.39 to 0.61m smaller at the sidewall and 0.52 to 0.85m smaller at the arch.

[0153] (2) The stress balance method analysis results are 0.15 to 0.19m larger at the sidewalls and 0.16 to 0.26m larger at the arch crown than the field test analysis results;

[0154] (3) As can be seen from the above results, compared with the point criterion method, the range of the plastic zone of the Class IV surrounding rock section of Shimen Tunnel calculated by the stress balance analytical method derived in this paper has a smaller error than the range of the plastic zone determined by the acoustic wave method, and has higher accuracy.

[0155] This embodiment collected engineering geological data, rock mechanics parameters, and the range of the plastic zone obtained from on-site acoustic testing and other methods for 16 cross-sections of 10 tunnels. Among them, 10 cross-sections were classified as Class IV surrounding rock, and 6 were classified as Class V surrounding rock. Based on the rock mechanics parameters and in-situ stress parameters of each cross-section, the range of the plastic zone was obtained by subtracting the excavation radius from the analytical value of the plastic zone radius. Finally, the maximum value of the plastic zone range was compared with the range determined by on-site testing and analysis, and the error was calculated. Figure 9 As shown, the columnar values ​​of each tunnel, from left to right, are the measured value, the analytical value, and the analytical value of the point criterion;

[0156] Comparative analysis of the plastic zone range obtained from field tests and analysis of 16 cross sections with the two sets of analytical values ​​shows that the analytical values ​​obtained by the point criterion method are on average 50.68% smaller than the values ​​determined by field tests and analysis, while the analytical values ​​obtained by the stress balance method are on average 14% larger. The analytical results obtained by the stress balance method are 19% to 52% smaller than those obtained by the point criterion method, and have higher accuracy in engineering practice.

[0157] A detailed analysis of the plastic zone range and stress balance analytical values ​​obtained from field tests on 16 cross-sections revealed that for Class V surrounding rock sections, the analytical values ​​for the plastic zone range were generally larger than those determined by field tests. This may be because when the surrounding rock quality is poor, under high tectonic stress levels, the plastic zone is more prone to irregular shapes. Analytical calculations can comprehensively calculate the radius of the plastic zone at all angles around the tunnel, while field measurements are always limited by engineering conditions and the number of boreholes, allowing tests to be conducted only in certain directions. It is difficult to accurately measure the location of the maximum value of the plastic zone, resulting in the maximum value of the plastic zone obtained from field tests being generally smaller than the analytical maximum value. This also demonstrates the advantage of using the analytical method presented in this paper to calculate the range of the plastic zone of the surrounding rock. It has good accuracy in terms of quantity and can clearly obtain the range of the plastic zone in all directions of the surrounding rock, thereby enabling targeted support measures to be taken for the surrounding rock.

[0158] By systematically analyzing the influence of rock mass mechanical parameters and in-situ stress data on the plastic zone, the influencing factors of the plastic zone of the surrounding rock can be summarized as follows: the maximum range of the plastic zone is affected by the cohesion c and the internal friction angle of the rock mass. The value and vertical ground stress p0 have a significant impact, while the morphology of the plastic zone is dominated by the lateral pressure coefficient λ.

Claims

1. An analytical prediction method for the plastic failure zone of surrounding rock based on stress equilibrium, characterized in that, Includes the following steps: S1. Obtain the initial plastic zone boundary. ; Step S1 includes the following steps: S11. Based on the Mohr-Coulomb criterion, the Mohr-Coulomb criterion model for elastic boundary surrounding rocks is obtained: in, This represents the maximum principal stress in the surrounding rock at the boundary of the elastic zone. This represents the minimum principal stress in the surrounding rock at the boundary of the elastic zone. Indicates the friction angle coefficient within the rock mass. Indicates the cohesion of the rock mass. Indicates the friction angle within the rock mass; S12. Based on the Mohr-Coulomb criterion model and the shear stress of the surrounding rock in a non-uniform stress field, the principal stress model is obtained: in, Indicates the radial stress of the surrounding rock. Indicates the tangential stress of the surrounding rock. Indicates the shear stress of the surrounding rock; S13. Substituting the yield criterion into the principal stress model, we obtain the yield model expressed by stress components: ； S14. Based on the yield model and the elastic zone stress model, the boundary model of the plastic region is obtained: in, Indicates the boundary of the plastic region. , , , and All are constant coefficients. Represents the ratio of the squares of radii. Indicates the tunnel radius. Indicates radius, Indicates the lateral pressure coefficient. This indicates the supporting reaction force acting on the tunnel wall. Indicates the initial vertical ground stress. Indicates angle, Represents the radius coefficient based on the Mohr-Coulomb method; S15. Based on the plastic region boundary model, obtain information about the radius. r and angle The implicit equation; S16. Based on implicit equations and actual engineering conditions, the initial plastic zone boundary is calculated. ; S2. Based on the static equilibrium condition, the initial plastic zone boundary is extended to obtain the plastic zone area correction model; S3. Based on the plastic zone area correction model and the unchanged elastic stress distribution in the portion below the plastic stress, the total elastic load in the portion below the yield stress of the surrounding rock before stress adjustment is obtained. The sum of the elastic loads borne by the elastic zone after stress adjustment In radius r They are equal as they approach infinity; S4. The sum of elastic loads below the yield stress before adjusting the surrounding rock stress. The sum of the elastic loads borne by the elastic zone after stress adjustment In radius r When the stress approaches infinity, the loads are equal, yielding the sum of elastic loads exceeding the yield stress before the surrounding rock stress is adjusted. The sum of the loads borne by the plastic zone after stress adjustment equal; S5. The sum of elastic loads exceeding the yield stress before adjusting the surrounding rock stress. The sum of the loads borne by the plastic zone after stress adjustment Based on the principles of equality and stress balance, the radius of the plastic zone of the surrounding rock is obtained. ; S6, Based on the radius of the plastic zone of the surrounding rock By plotting in polar coordinates, the extent and morphological distribution characteristics of the plastic zone in the surrounding rock of the tunnel can be obtained.

2. The analytical prediction method for the plastic failure zone of surrounding rock based on stress balance according to claim 1, characterized in that, The calculation expression for the plastic zone area correction model in step S2 is as follows: in, This represents the total elastic load exceeding the yield stress before the surrounding rock stress is adjusted. This represents the total elastic load below the yield stress in the surrounding rock before stress adjustment. This represents the total load borne by the plastic zone after stress adjustment. This represents the total elastic load borne by the elastic zone after stress adjustment.

3. The analytical prediction method for the plastic failure zone of surrounding rock based on stress balance according to claim 2, characterized in that, Step S5 includes the following steps: S51. Set the stress distribution within the plastic zone of the surrounding rock as linear, and based on the radius... r The total elastic load exceeding the yield stress before stress adjustment in the surrounding rock was calculated. ; S52. Calculation of tangential stress at the boundary of the plastic zone based on the point criterion. ; S53, Based on radius r The total load borne by the plastic zone after stress adjustment was calculated. ; S54, Based on the sum of loads borne by the plastic zone after stress adjustment The radius of the plastic zone of the surrounding rock is obtained. .

4. The analytical prediction method for the plastic failure zone of surrounding rock based on stress balance according to claim 3, characterized in that, The total elastic load in step S51 The calculation expression is as follows: 。 5. The analytical prediction method for the plastic failure zone of surrounding rock based on stress balance according to claim 4, characterized in that, The tangential stress at the boundary of the plastic zone in step S52 The calculation expression is as follows: 。 6. The analytical prediction method for the plastic failure zone of surrounding rock based on stress balance according to claim 5, characterized in that, In step S53, the total load borne by the plastic zone after stress adjustment is mentioned. The calculation expression is as follows: 。 7. The analytical prediction method for the plastic failure zone of surrounding rock based on stress balance according to claim 6, characterized in that, The radius of the plastic zone of the surrounding rock in step S54 The calculation expression is as follows: 。

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