Circular tunnel surrounding rock strain softening elastic-plastic analysis method based on H-B strength criterion

Abstract

The invention discloses a circular tunnel surrounding rock strain softening elastic-plastic analysis method based on an H-B strength criterion, the whole tunnel excavation process is regarded as n times of tunnel inner wall rock mass radial stress uniform release process, the whole tunnel excavation process is divided into n calculation steps, and 0 to n calculation steps are respectively equivalent to 1 to n + 1 concentric rings; and assuming that a certain calculation step from 0 to n is the ith calculation step, the change range of i is 0 to n, and in the ith calculation step, sequentially calculating stress, strain and displacement distribution conditions from the (i + 1) th circular ring to the first circular ring. On the basis of an existing method for calculating stress and radial displacement distribution around a circular tunnel in a strain softened rock mass, the maximum calculation ring number n is 500, the number of circular rings participating in calculation is increased along with calculation, the calculation efficiency can be guaranteed in the early stage of calculation, and the calculation accuracy can be guaranteed in the later stage of calculation. Meanwhile, redundant hypothesis and calculation are not needed in the whole calculation process, and the calculation result is simple, convenient, efficient and easy to understand.

Description

Technical Field

[0001] The present invention relates to the technical field of tunnels, and is particularly applicable to a circular tunnel surrounding rock strain softening elastoplastic analysis method based on the HB strength criterion. Background Art

[0002] The mechanical properties of surrounding rock are crucial to the stability and safety of structures. During underground construction, rock mass deforms when subjected to stress. This deformation progresses from elastic to plastic, ultimately leading to softening. Rock softening has a significant impact on underground and geotechnical engineering, potentially leading to post-excavation instability and increasing project risks. Therefore, accurately predicting and analyzing the deformation state of surrounding rock under stress is crucial to ensuring project safety and reliability.

[0003] Currently, the elastic-plastic calculation method for surrounding rock deformation proposed by Zhang Xiangdong in his 2010 book Tunnel Mechanics, published by China University of Mining and Technology Press, is commonly used to analyze the elastic-plastic mechanical behavior of rock masses during tunnel construction and excavation, such as the variations in displacement, stress, and strain. However, this method only describes the elastic-plastic state of the rock mass and cannot effectively describe its softening behavior. Consequently, it cannot address the softening of surrounding rock before support structures are applied during actual underground construction.

[0004] The paper (Lee YK, Pietruszczak SA, New numerical procedure for elasto-plastic analysis of a circular opening excavated in a strain-softening rockmass.) proposes a method for calculating the stress and radial displacement distribution around a circular tunnel in strain-softening rockmass. This method assumes that the initial stress state is hydrostatic pressure and that the rockmass is isotropic. The rockmass is then treated as multiple concentric rings, with the radial stress difference between adjacent rings considered constant. The stress and radial displacement distribution around a circular tunnel in strain-softening rockmass is calculated using a finite difference method, moving from the outermost ring to the innermost ring. However, this method requires a fixed number of rings. In the early stages of the calculation, when the plastic range is small, an excessive number of rings can waste computational resources. In the later stages of the calculation, an insufficient number of rings can also reduce the accuracy of the calculation.

[0005] To this end, the paper (Xu C, Xia C, Han C. Modified ground response curve (GRC) instrain-softening rock mass based on the generalized Zhang-Zhu strength criterion considering over-excavation) improves on Lee YK's method. This method increases the number of rings involved in the calculation as the calculation progresses. However, when a plastic zone appears in the surrounding rock, it requires the separate assumption and calculation of adjacent elastic rings outside the plastic zone, which increases the complexity of the calculation and the difficulty of understanding. Summary of the Invention

[0006] The present invention aims to provide a circular tunnel surrounding rock strain softening elastoplastic analysis method based on the HB strength criterion, aiming to solve the surrounding rock strain softening elastoplastic analysis problem.

[0007] To achieve the above object, the present invention adopts the following technical solutions: The elastoplastic analysis method for circular tunnel surrounding rock strain softening based on the HB strength criterion of the present invention comprises the following steps: Obtain the parameters of the tunnel surrounding rock, including surrounding rock mechanical parameters (such as surrounding rock elastic modulus, Poisson's ratio, etc.) and design parameters (such as tunnel diameter, ground stress, etc.). The entire tunnel excavation process is regarded as a process of uniformly releasing the radial stress of the tunnel inner wall rock mass n times, which is divided into n calculation steps (n times of rock mass stress release). The calculation steps 0 to n are equivalent to 1 to n+1 concentric rings respectively. Assuming that a calculation step from 0 to n is the i-th calculation step, and the range of i is 0 to n, in the i-th calculation step, the distribution of stress, strain, and displacement from the i+1th ring (the outermost ring) to the 1st ring (the innermost tunnel wall ring) is calculated in sequence. The solution process includes: S1, determine the critical support force p of the rock mass based on the parameters of the surrounding rock ic ; S2, calculate the virtual support force p of the tunnel in the i-th calculation step i , when p ic ≤p i When , the rock mass affected by excavation is elastic surrounding rock, and the stress, strain and displacement distributions from the i+1th ring to the 1st ring in the current calculation step are calculated in sequence; S3, when p ic >p i When the rock mass affected by excavation has both elastic surrounding rock and plastic surrounding rock, the stress, strain and displacement distribution of the surrounding rock ring in the elastic zone and the surrounding rock ring in the plastic zone of the current calculation step are calculated respectively.

[0008] Furthermore, in the initial state, i is 0, corresponding to the first ring.

[0009] Furthermore, the calculation formula p in step S1 is ic for Where σ0 is the initial stress of the surrounding rock; σ c is the uniaxial compressive strength of the surrounding rock; β=(m*σ c ) / 4, m and s are the surrounding rock strength parameters in the HB criterion.

[0010] Furthermore, in step S2 It represents the radial stress of the first ring in the i-th calculation step, s1 represents the difference in radial stress between adjacent rings, and the difference in radial stress between all adjacent rings is s1.

[0011] Furthermore, step S2 is specifically to calculate from the i+1th ring to the first ring one by one until the calculation result of the first ring is solved. The specific calculation formula is: i represents the i-th calculation step, 0≤i≤n, j represents the j-th ring in the i-th calculation step, 1≤j≤i+1; σ r , σ θ , ε r , ε θ They represent the radial and tangential stresses, radial and tangential strains of the ring respectively; u represents the displacement of the ring; R a is the excavation radius of the tunnel, G represents the shear modulus of the surrounding rock, ρ is the normalized radius of the ring, is 1.

[0012] Furthermore, the calculation of the elastic zone of the surrounding rock in step S3 requires first determining that the radial stress in the i-th calculation step is equal to p ic The corresponding ring number is recorded as the kth ring. Then the calculation is performed one by one from the i+1th ring to the kth ring until the calculation result of the kth ring is solved. The specific calculation formula is: in is 1. i represents the i-th calculation step, j represents the j-th ring in the i-th calculation step, and the range of the elastic zone ring j that needs to be calculated in this step is k≤j≤i+1; σ r , σ θ , ε r , ε θrepresent the radial and tangential stresses, and radial and tangential strains of the ring, respectively; G represents the shear modulus of the surrounding rock, and ρ is the normalized radius of the ring.

[0013] Furthermore, the calculation of the plastic zone of the surrounding rock in step S3 needs to be calculated from the kth ring to the inner rings in sequence, and the results of the outer rings are obtained first (such as ), and then combined with the calculation results of the previous calculation step (i-1 calculation step) (such as ), calculate the results of the inner ring one by one (such as ) until the calculation result of the first circle (the circle on the inner wall of the tunnel) is solved. The specific calculation formula is: In the above formula, the range of the plastic zone ring j is 1≤j≤k; and denote the radial and tangential stresses of the jth ring in the i-th calculation step, respectively; and They represent the increments of radial stress and tangential stress of the ring respectively; and denote the increments of radial stress and tangential stress increments, respectively; represents the increment of radial elastic strain increment, represents the increment of tangential elastic strain increment, G represents the shear modulus of the surrounding rock, and v represents the Poisson's ratio of the surrounding rock; and denote radial elastic strain increment and tangential elastic strain increment respectively; and denote the radial plastic strain increment and the tangential plastic strain increment, k (i) =(1+sinψ (i) ) / (1-sinψ (i) ) represents the volume expansion coefficient, ψ (i) represents the dilatancy angle; represents the increment of radial plastic strain increment, represents the increment of tangential plastic strain increment; and represent radial strain increment and tangential strain increment respectively; ε r and ε θ They represent the radial and tangential strains of the ring respectively; ρ represents the normalized radius of the ring, r represents the actual radius of the ring, and R a is the excavation radius of the tunnel.

[0014] Furthermore, in step S3, for the rock mass with both elastic and plastic zones, the radial displacement of any ring in the elastic and plastic zones is The calculation formula is The range of j is 1≤j≤i+1; Elastic surrounding rock k represents the elastic-plastic boundary ring, and the plastic surrounding rock Utilize plastic surrounding rock Formula calculation.

[0015] The advantage of this method is that, based on existing methods for calculating stress and radial displacement distribution around a circular tunnel in strain-softening rock, the maximum number of calculation rings is 500. The number of rings involved in the calculation increases as the calculation progresses, ensuring high efficiency in the early stages and high accuracy in the later stages. Furthermore, the entire calculation process does not require redundant assumptions or calculations, resulting in simple, efficient, and easy-to-understand results. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 This is the distribution map of the surrounding rock elastic-plastic area.

[0017] Figure 2 This is the evolution diagram of the strength parameters of the surrounding rock under the plastic state.

[0018] Figure 3 This is a schematic diagram of the step-by-step solution of the rock mass strain softening elastoplastic analysis method described in the present invention.

[0019] Figure 4 Schematic diagram of surrounding rock solution in the method of the present invention: (a) purely elastic rock mass, (b) elastic-plastic rock mass.

[0020] Figure 5 This is a comparison diagram of the surrounding rock characteristic curves in the method of the present invention and the theoretical solution in the existing paper.

[0021] Figure 6 The comparison diagram between the method of the present invention and the theoretical solution of the existing paper: (a) surrounding rock characteristic curve, (b) surrounding rock plastic zone radius (R p ) and the radius of the surrounding rock residual area (R s ). DETAILED DESCRIPTION

[0022] The following is a clear and complete description of the technical solutions in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of them. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts are within the scope of protection of the present invention.

[0023] The elastoplastic analysis method for circular tunnel surrounding rock strain softening based on the HB strength criterion of the present invention comprises the following steps: Obtain tunnel surrounding rock parameters, including surrounding rock mechanical parameters (such as the surrounding rock elastic modulus and Poisson's ratio) and design parameters (such as tunnel diameter and in-situ stress). The entire tunnel excavation process is considered to be a process of uniformly releasing radial stress in the tunnel inner wall rock mass n times, divided into n calculation steps (n rock mass stress releases), with calculation steps 0 to n being equivalent to 1 to n+1 concentric rings, respectively. Assuming that a calculation step from 0 to n is the i-th calculation step, where i ranges from 0 to n, in the i-th calculation step, the stress, strain, and displacement distributions are calculated sequentially from the i+1th ring (the outermost ring) to the 1st ring (the innermost tunnel wall ring).

[0024] S1, determine the critical support force p of the rock mass based on the parameters of the surrounding rock ic .

[0025] p ic The calculation formula is: Where σ0 is the initial stress of the surrounding rock; σ c is the uniaxial compressive strength of the surrounding rock.

[0026] β=(m*σ c ) / 4 (2) m and s are the surrounding rock strength parameters in the HB criterion.

[0027] S2, calculate the virtual support force p of the tunnel in the i-th calculation step i , when p ic ≤p i When , the rock mass affected by excavation is all elastic surrounding rock, and the distribution of stress, strain and displacement from the i+1th ring to the 1st ring in the current calculation step is calculated in sequence.

[0028] p i The calculation formula is: represents the radial stress of the first ring in the i-th calculation step.

[0029] s1 represents the difference in radial stress between adjacent rings. The difference in radial stress between all adjacent rings is s1. The calculation formula for s1 is: When p ic ≤p i When , the rock mass affected by excavation is elastic surrounding rock. The stress, strain and displacement distribution from the i+1th ring to the 1st ring in the current calculation step are calculated in sequence. The specific calculation formula is: Where i represents the i-th calculation step, 0≤i≤n, j represents the j-th ring in the i-th calculation step, 1≤j≤i+1; σ r , σ θ , ε r , ε θ They represent the radial and tangential stresses, radial and tangential strains of the ring respectively; u represents the displacement of the ring; R a is the excavation radius of the tunnel, G represents the shear modulus of the surrounding rock, and ρ is the normalized radius of the ring.

[0030] is 1.

[0031] S3, when p ic >p i When the rock mass affected by excavation has both elastic surrounding rock and plastic surrounding rock, the stress, strain and displacement distribution of the surrounding rock ring in the elastic zone and the surrounding rock ring in the plastic zone of the current calculation step are calculated respectively.

[0032] When there are both elastic and plastic zones in the rock mass affected by excavation, it is first necessary to determine whether the radial stress in the i-th calculation step is equal to p ic The corresponding ring is numbered as the kth ring, which is also the ring at the elastic-plastic boundary.

[0033] Then, the calculation of the surrounding rock in the elastic zone is carried out, and based on the elastic-plastic theory, the kth ring at the elastic-plastic boundary is calculated. The specific calculation formula is: Then, the calculation is performed from the i+1th ring to the kth ring one by one until the calculation result of the kth ring is solved. The specific calculation formula is: =1, i represents the i-th calculation step, j represents the j-th ring in the i-th calculation step, and the range of the elastic zone ring j to be calculated in this step is k≤j≤i+1; r , σ θ , ε r , ε θ Represent the radial and tangential stresses, radial and tangential strains of the ring respectively; G represents the shear modulus of the surrounding rock, ρ is the normalized radius of the ring, and u represents the radial displacement of the ring. It should be noted that in the elastic-plastic surrounding rock, the displacement of the jth ring in the i-th calculation step is Need to wait until the normalized radius of the ring on the inner wall of the tunnel Since the first circle in the ith calculation step of the elastic-plastic surrounding rock is located in the plastic zone, the calculation formula for the normalized radius of the circle in the plastic zone of the elastic-plastic surrounding rock needs to be used.

[0034] The calculation of the surrounding rock in the plastic zone is carried out from the kth ring to the inner rings in sequence until the calculation result of the first ring is solved, that is, 1≤j≤k. The specific calculation formula is: The calculation formula for the normalized radius of the circular ring of the plastic zone surrounding rock in the elastic-plastic surrounding rock is as follows: In the above formulas, the range of the plastic zone ring j is 1≤j≤k; and denote the radial and tangential stresses of the jth ring in the i-th calculation step, respectively; and They represent the increments of radial stress and tangential stress of the ring respectively; and denote the increments of radial stress and tangential stress increments, respectively; represents the increment of radial elastic strain increment, represents the increment of tangential elastic strain increment, G represents the shear modulus of the surrounding rock, and v represents the Poisson's ratio of the surrounding rock; and denote radial elastic strain increment and tangential elastic strain increment respectively; and denote the radial plastic strain increment and the tangential plastic strain increment, k (i) =(1+sinψ (i) ) / (1-sinψ (i) ) represents the volume expansion coefficient, ψ (i) represents the dilatancy angle; represents the increment of radial plastic strain increment, represents the increment of tangential plastic strain increment; and represent radial strain increment and tangential strain increment respectively; ε r and ε θ They represent the radial and tangential strains of the ring respectively; ρ represents the normalized radius of the ring, r represents the actual radius of the ring, and R a is the excavation radius of the tunnel, and u represents the displacement of the ring.

[0035] It should be noted that in this step, the normalized radius of the inner wall ring of the plastic zone surrounding rock tunnel in the elastic-plastic surrounding rock can be obtained. The radial displacement of all rings in the i-th calculation step can be obtained Radial displacement of surrounding rock in elastic zone Calculations are also performed in this step.

[0036] The principle of the circular tunnel surrounding rock strain softening elastoplastic analysis method based on the HB strength criterion of the present invention is as follows: This paper considers the circular tunnel as an axisymmetric problem, assumes the initial stress state is hydrostatic, and assumes the rock mass is isotropic. The entire tunnel excavation process is considered as a process of multiple uniform releases of radial stress in the rock mass.

[0037] First, the strain softening elastoplastic problem of the surrounding rock of a circular tunnel is described as follows: like Figure 1 As shown, the excavation radius of the circular tunnel is R a Before tunnel excavation, a hydrostatic stress field σ0 is applied to the entire area. i Below the critical support force p ic When the radius R is formed around the tunnel p In the case of elastic-brittle-plastic or elastic-ideally plastic behavior, the plastic radius R can be derived. p In some cases, in addition to the plastic zone R p In addition, there is another s The residual area is a zone in which the mechanical properties of the surrounding rock are reduced. In the invention, it is stipulated that the compressive stress is positive and the shrinkage displacement is positive.

[0038] Assume that the yield criterion of the rock mass is as follows: F(σθ,σ r ,γ p )=σθ-σ r -H(σ r ,γ p ) (36) In the above formula: σ θ and σ r Represent the principal stress and secondary stress respectively, here they represent the tangential stress and radial stress of the surrounding rock. p represents the strain softening coefficient.

[0039] Alonso et al. (2003) pointed out that the above formula is the most widely accepted method for calculating the strain softening coefficient. Reference: Alonso, E., Alejano, L. International journal for numerical and analytical methods in geomechanics.

[0040] For Hoek-Brown rock mass, H can be expressed as: In the above formula: σ c is the uniaxial compressive strength of the surrounding rock, m, s, and a are the surrounding rock strength parameters in the criterion.

[0041] The plastic potential function of the HB strength criterion can be written as: G(σθ,σ r ,γ p )=σθ-k(γ p )σ r (38) Among them, k(γ p ) is called the volume expansion coefficient and is defined as: ψ represents the dilatancy angle. The relationship between radial and tangential plastic strain increments is shown as follows: It should be noted that in the plastic zone surrounding rock, the surrounding rock mechanical parameters are all γ p The present invention assumes that γ p is a piecewise linear function, as shown below: Where η is the strength parameter (σ c , m, s, a). Figure 2 As shown, is the critical plastic shear strain of the residual state of the rock mass, which can be determined by indoor tests. p and η r are the peak and residual values ​​of η, respectively.

[0042] When the tunnel internal support force p i Below the critical support force p ic When the plastic zone is formed around the tunnel, the plastic zone will be formed around the tunnel. For Hoek-Brown rock mass, p ic It can be obtained by solving the following nonlinear equation: Only when a p = 0.5, we can get p ic The analytical expression of is as follows: Where β=(m*σ c ) / 4. If a p >0.5, then p can be numerically solved by using a suitable root-finding algorithmic .

[0043] It should be noted that when the plastic zone is formed, the radial stress σ acting on the elastic-plastic interface r Equal to p ic .

[0044] σ r (R p )=p ic (43) Based on the above problem description, the solution process of the circular tunnel surrounding rock strain softening elastoplastic analysis method based on the HB strength criterion described in the present invention is described as follows: A notable characteristic of the tunnel excavation process is the gradual release of rock mass stress. During this process, the rock mass gradually transitions from an elastic state to an elastoplastic state. In this case, the concept of "load release" can be applied to solve the rock mass problem.

[0045] The entire excavation process is regarded as a process of uniformly releasing the radial stress of the rock mass on the inner wall of the tunnel n times (i.e., it is divided into n calculation steps in total), as follows: Figure 3 As shown. The value of n can be set by yourself. The larger n is, the more accurate the calculation result is, and vice versa. In the calculation process, (i, j) is used to represent the information of the ring, i represents the current calculation step, and j represents the ring number in the current calculation step, such as represents the radial stress of the surrounding rock at the jth ring in the i-th calculation step. The i numbers start at 0 and are 0, 1, 2, ..., n. The j numbers increase from the inner ring to the outer ring, with the innermost ring being numbered 1 and the outermost ring being numbered i+1. From the inside out, the numbers are 1, 2, ..., i+1.

[0046] In the initial calculation step (i=0), there is no stress release yet and there is only one initial ring. The number of this ring is j=1 and it is located on the inner wall of the tunnel. Figure 3 (a) shows the radial stress of the ring. is equal to the original rock stress σ0, and the distance from the tunnel center Equal to R a At the same time, the radial strain Tangential strain and radial displacement represent the radial strain, tangential strain and radial displacement of the ring respectively.

[0047] In the first calculation step, the inner wall of the tunnel will release radial stress s1, which is calculated as shown below. At the same time, a new ring will be generated outside the initial calculation step ring. Figure 3As shown in (b), it includes two rings: one is the ring (0, 1) when i = 0, which becomes the ring (1, 1) when i = 1, and the other is the ring (1, 2) newly generated outside the ring (1, 1). In these two rings, their radial stresses are and Equal to σ0, the difference between them is s1. By calculation, the tangential stress σ of each ring can be obtained θ , radial strain ε r , tangential strain ε θ and displacement u, etc.

[0048] The rock mass continuously releases stress. In each new calculation step, the inner wall of the tunnel releases radial stress of s1. The ring in the previous calculation step gradually shrinks inward, so the rock mass gradually shrinks and deforms toward the inside of the tunnel. A new ring is also generated outside the ring in the previous calculation step. The radial stress of this ring is equal to σ0. Therefore, the range affected by excavation gradually expands to the deep part of the rock mass. Figure 3 (c) The radial stress difference between adjacent rings is a constant value s1, as shown in Figure 3 (b) Figure 3 (c) In the i-th calculation step, the radial stress of any ring is and radial stress on the tunnel wall As shown in the following formula: Through calculation, the distribution and evolution of the radial stress of the rock mass during the entire construction process can be obtained. Subsequently, the dynamic evolution law of parameters such as the tangential stress, strain and displacement of the rock mass can be gradually derived until the construction is completed, that is, when i=n, ​​as shown in Figure 3 (d) shown.

[0049] The stress distribution and evolution of rock mass in elastic zone can be divided into two cases: the stress distribution and evolution of rock mass in pure elastic state, such as Figure 4 (a) shows the stress distribution and evolution of the rock mass in the elastic zone under the elastic-plastic state, as shown in Figure 4 (b) shown.

[0050] The calculation process for both cases is essentially the same, starting from the outermost ring and working your way toward the inner rings. That is, the results for the outermost ring are obtained first, followed by the results for the next outermost ring, and so on, until the results for the ring at the tunnel wall or the elastic-plastic interface are obtained.

[0051] The stress distribution and evolution of rock mass under pure elastic state are analyzed and explained as an example. Figure 4In (a), the schematic diagram of the solution of the i-th calculation step is shown. Since the results of the outermost ring are known, such as the radial stress =Equal to the initial rock stress σ0, and the radial stress difference s1 between adjacent rings remains unchanged, so the radial stress of each ring can be easily calculated. Using the normalized radius for calculation, the normalized radius of the outermost ring is Here, for the convenience of calculation, In the calculation, since only the ratio between the normalized radii is used, the calculation result is consistent with that using the original radius. Through the elastic theory, the ring of the inner wall of the tunnel can be easily calculated. The normalized radius of : In the calculation process, the calculation is performed from the outermost ring to the inner ring one by one. When solving a certain ring, first of all, the normalized radius of the ring needs to be calculated. As shown in the following formula: Then, the tangential stress of the ring is calculated radial strain Tangential strain and displacement The actual radius r of each ring is given by the following formula: By repeating the above process, the stress, strain, radius and displacement of all rings in the i-th calculation step can be obtained.

[0052] When a plastic zone is generated, the method for solving the stress distribution and evolution of the elastic zone rock mass under the elastic-plastic state is basically the same as the above solution method, which is to start from the outermost ring and calculate one by one to the inner ring until the elastic-plastic boundary is reached. Less than critical support force p ic When , the plastic zone ring is calculated.

[0053] When a plastic zone is generated, it is assumed that the circular ring at the elastic-plastic boundary is the kth ring. Based on the elastic-plastic theory, the stress and strain of the kth ring can be easily calculated: By balancing the differential equations, we can obtain the following: Since in the current calculation step, and The result of is unknown, so use the same numbered ring in the i-1th calculation step replace Although some errors may occur during the calculation process, as long as s1 is small enough, that is, the number of rings involved in the calculation is large enough, the error caused by each ring will be very small and can be ignored.

[0054] Tangential stress of the jth ring Radial stress can be used and To express it, as shown below: In the i-th calculation step, the strain of the current rock mass is The strain in the i-1th calculation step can be used and the strain increment of the i-th calculation step The sum of: and They represent the radial strain increment and tangential strain increment of the jth ring in the i-th calculation step. For the ring located at the elastic-plastic boundary (the kth ring), its radial strain and tangential strain For the remaining rings (1≤j≤k), the strain increment is and The strain increment can be calculated using the results of the outer and adjacent rings. It consists of the following components: the strain increment of the j+1th ring The increment of radial strain increment of the jth ring and the increment of the tangential strain increment As shown in the following formula: In the above formula, the subscripts r and θ represent the radial and tangential directions respectively. and It represents the increment of the strain increment of the jth ring in the i-th calculation step, and represents the difference between the strain increment and the strain increment in the i-1-th calculation step. represents the increment of radial elastic strain increment, represents the increment of radial plastic strain increment, represents the increment of the tangential elastic strain increment, Increment representing the increment of tangential plastic strain. and Hooke's law is used for calculation, as shown below: represents the increment of radial stress increment of the jth ring, and represents the increment of the tangential stress increment of the jth ring, as shown in the following formula: and It represents the increment of radial stress and tangential stress of the jth ring, as shown in the following formula: Total strain increment and The following deformation coordination equation needs to be satisfied, as shown in the following equation: The total strain increment Rewritten as plastic strain increment and elastic strain increment The radial and tangential components of the plastic strain increment are expressed as follows: in, and They represent radial elastic strain increment and tangential elastic strain increment respectively, and the calculation formula is The difference in plastic strain increment between the inner and outer sides of the jth ring As shown in the following formula: By calculation, the radial strain of the jth ring in the i-th calculation step can be obtained and tangential strain

[0055] From the yield function, we can get The formula is as follows: Normalized radius The calculation is as follows: The actual radius of the jth ring in the i-th calculation step As shown in the following formula: R a is the excavation radius of the tunnel, the displacement of the jth ring in the i-th calculation step is As shown in the following formula: Specific calculation example 1 like Figure 5As shown in the figure, a set of data in the paper is used to verify the accuracy of the new method. The dimensionless displacement is 2Gu / [R a (σ0-p ic )]=12.738. 2Gu / [R a (σ0-p ic )] = 12.313, with a relative error of 3.34%. Obviously, the method proposed in this paper is very consistent with the results of the method in the paper. (Zhang, Q., Quan, XwAnumerical solution of a circular tunnel in a confining pressure-dependent strain-softening rock mass.) Specific calculation example 2 Figure 6 The surrounding rock characteristic curve (GRC) obtained by the method of the present invention is shown, as Figure 6 As shown in a, the surrounding rock shaping radius (R p ) and the residual radius of the surrounding rock (R a ),like Figure 6 b is compared with the paper (Zhang, Q., Zhang, ChElastoplasticcoupling solution of circular openings in strain-softening rock massconsidering pressure-dependent effect.). In the method of the present invention, 2Gu / [R a (σ0-p ic )]=15.95,R p / R a =2.88, R s / R a =2.20, in the method of the paper, 2Gu / [R a (σ0-p ic )]=15.78,R p / R a =2.84, R s / R a =2.14, and the errors are 1.07%, 1.39%, and 2.73% respectively. The results show that the results of the method proposed in this paper are very consistent with those of the method in this paper.

[0056] Theoretically, if a sufficient number of rings are involved in the calculation, the calculation accuracy is high; if a relatively small number of rings are involved, the calculation accuracy is low. Therefore, it is necessary to study the relationship between the number of rings involved in the calculation, n, and the calculation accuracy. After extensive research and testing, the researchers of this invention found that when n is greater than 50, the ultimate displacement deformation of the surrounding rock no longer changes significantly, indicating that n of 50 can meet the calculation accuracy requirements. When n is set to 500, the calculation error is negligible. In the above examples, n is always 500.

[0057] The method can be implemented using Matlab programming. When executed on a desktop computer with an i7-6700 CPU at 3.4GHz, the code instantly outputs relevant results after each calculation step, including cloud maps of the elastic and plastic regions of the surrounding rock mass, as well as cloud maps of the radial stress distribution, the tangential stress distribution, and the radial displacement. The specific running times are as follows: 14 seconds for an n value of 50; 33 seconds for an n value of 100; 212 seconds for an n value of 500; 493 seconds for an n value of 1000; and 3661 seconds for an n value of 5000.

[0058] When the maximum number of rings is n, the number of rings involved in the calculation in the method of the present invention gradually changes from 1 to n. In the early stage of calculation, smaller n can ensure the high efficiency of calculation, and in the later stage of calculation, larger n can ensure the accuracy of calculation. In the method of prior art Lee (Lee YK, Pietruszczak S.Anew numerical procedure for elasto-plastic analysis of a circular opening excavated in astrain-softening rockmass.), after the plastic zone of surrounding rock is generated, the number of rings involved in the calculation in the plastic zone is a fixed value. In the process of calculation, n will not change. Therefore, in the early stage of calculation, when the plastic range is smaller, too many number of rings may cause the waste of computing resources. In the later stage of calculation, the shortage of number of rings may also cause the reduction of computing accuracy. Because Lee's paper adopts Frotran 90 language programming to realize, and there is the difference between CPU and GHz, it is impossible to intuitively compare the calculation time difference. From the perspective of the total number of rings involved in calculation, the computing time of this algorithm has saved about 50%. Therefore, the calculation concept proposed by the method of the present invention is more conducive to the rational use of computing resources, which can not only ensure the accuracy of the calculation results, but also ensure high computing efficiency.

[0059] In the calculation process, since only the ratio between the normalized radii is used, the invention proposes to use the normalized radius of the secondary outer ring This avoids the normalized radius of the outermost ring. Set to 1, the innermost ring The calculation result is 0, thus ensuring the smooth progress of subsequent calculation steps.

[0060] In the paper (Xu C, Xia C. Modified ground response curve (GRC) in strain-softening rockmass based on the generalized Zhang-Zhu strength criterion considering over-excavation.), the actual radius of the ring obtained in the i-1th calculation is used in the i-th calculation after the plastic zone is generated. But in the i-1th calculation, only the actual radius exists to No actual radius Therefore, certain assumptions need to be made to obtain the actual radius This increases the complexity of the calculation and the difficulty of understanding. In the method of the present invention, the actual radius obtained in the previous calculation step can be conveniently used. No unnecessary assumptions and calculations are required, and the calculation results are simple, efficient and easy to understand.

Claims

1. A circular tunnel surrounding rock strain softening elastoplastic analysis method based on HB strength criterion, characterized in that: The following steps are involved: Obtain the parameters of the tunnel surrounding rock, including surrounding rock mechanical parameters and design parameters; The entire tunnel excavation process is regarded as a process of uniformly releasing the radial stress of the rock mass on the inner wall of the tunnel for n times, which is divided into n calculation steps. The calculation steps 0 to n are equivalent to 1 to n+1 concentric rings respectively. Assuming that a certain calculation step from 0 to n is the i-th calculation step, the range of i is 0 to n. In the i-th calculation step, the stress, strain and displacement distribution from the i+1th ring to the 1st ring are calculated in sequence. The solution process includes: S1, determine the critical support force p of the rock mass according to the parameters of the surrounding rock ic ; S2, calculate the virtual support force p of the tunnel in the i-th calculation step i , when p ic ≤p i When , the rock mass affected by excavation is elastic surrounding rock, and the stress, strain and displacement distribution of the i+1th ring to the 1st ring in the current calculation step are calculated in sequence; S3, when p ic >p i When the rock mass affected by excavation has both elastic surrounding rock and plastic surrounding rock, the stress, strain and displacement distribution of the surrounding rock ring in the elastic zone and the surrounding rock ring in the plastic zone of the current calculation step are calculated respectively.

2. The method for analyzing the strain softening elastic-plasticity of the surrounding rock of a circular tunnel based on the HB strength criterion according to claim 1 is characterized by: In the initial state, i is 0, corresponding to the first ring.

3. The method for analyzing the strain softening elastic-plasticity of the surrounding rock of a circular tunnel based on the HB strength criterion according to claim 1 is characterized by: In step S1, the formula p is calculated ic for Where σ0 is the initial stress of the surrounding rock; σ c is the uniaxial compressive strength of the surrounding rock; β=(m*σ c ) / 4, m and s are the surrounding rock strength parameters in the HB criterion.

4. The method for analyzing the strain softening elastic-plasticity of the surrounding rock of a circular tunnel based on the HB strength criterion according to claim 1 is characterized by: In step S2 represents the radial stress of the first ring in the i-th calculation step, s1 represents the difference in radial stress between adjacent rings, and the difference in radial stress between all adjacent rings is s1.

5. The method for analyzing the strain softening elastic-plasticity of the surrounding rock of a circular tunnel based on the HB strength criterion according to claim 1, characterized in that: Step S2 specifically calculates from the i+1th ring to the 1st ring one by one until the calculation result of the 1st ring is solved. The specific calculation formula is: i represents the i-th calculation step, 0≤i≤n, j represents the j-th ring in the i-th calculation step, 1≤j≤i+1; σ r , σ θ , ε r , ε θ They represent the radial and tangential stresses, radial and tangential strains of the ring, respectively; u represents the displacement of the ring; R a is the excavation radius of the tunnel, G represents the shear modulus of the surrounding rock, ρ is the normalized radius of the ring, is 1.

6. The circular tunnel surrounding rock strain softening elastoplastic analysis method based on HB strength criterion according to claim 1, characterized in that: The calculation of the elastic zone of the surrounding rock in step S3 requires first determining that the radial stress in the i-th calculation step is equal to p ic The corresponding ring number is recorded as the kth ring; then the calculation is performed from the i+1th ring to the kth ring one by one until the calculation result of the kth ring is solved. The specific calculation formula is: in is 1; i represents the i-th calculation step, j represents the j-th ring in the i-th calculation step, and the range of j is k≤j≤i+1; σ r , σ θ , ε r , ε θ represent the radial and tangential stresses, radial and tangential strains of the ring respectively; G represents the shear modulus of the surrounding rock, and ρ is the normalized radius of the ring.

7. The method for analyzing the strain softening elastic-plasticity of the surrounding rock of a circular tunnel based on the HB strength criterion according to claim 6, characterized in that: The calculation of the surrounding rock plastic zone in step S3 needs to be calculated from the kth ring to the inner rings in sequence. The results of the outer rings are obtained first, and then combined with the calculation results of the previous calculation step, the results of the inner rings are calculated one by one until the calculation results of the first ring are solved. The specific calculation formula is: In the above formula, the range of j is 1≤j≤k; and denote the radial and tangential stresses of the jth ring in the i-th calculation step, respectively; and They represent the increments of radial stress and tangential stress of the ring respectively; and denote the increments of radial stress and tangential stress increments, respectively; represents the increment of radial elastic strain increment, represents the increment of the tangential elastic strain increment, G represents the shear modulus of the surrounding rock, and v represents the Poisson's ratio of the surrounding rock; and denote radial elastic strain increment and tangential elastic strain increment respectively; and denote the radial plastic strain increment and the tangential plastic strain increment, respectively, k (i) =(1+sinψ (i) ) / (1-sinψ (i) ) represents the volume expansion coefficient, ψ (i) represents the dilatancy angle; represents the increment of radial plastic strain increment, represents the increment of tangential plastic strain increment; and denote radial strain increment and tangential strain increment respectively; ε r and ε θ They represent the radial and tangential strains of the ring, respectively; ρ represents the normalized radius of the ring, r represents the actual radius of the ring, and R a is the excavation radius of the tunnel.

8. The method for analyzing the strain softening elastic-plasticity of the surrounding rock of a circular tunnel based on the HB strength criterion according to claim 7 is characterized by: In step S3, for a rock mass with both elastic and plastic zones, the radial displacement of any ring in the elastic and plastic zones is The calculation formula is The range of j is 1≤j≤i+1; Elastic surrounding rock k represents the elastic-plastic boundary ring, and the plastic surrounding rock Using plastic surrounding rock Formula calculation.

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