Rock mass self-weight-considered circular tunnel surrounding rock plastic zone model and construction method thereof

Abstract

The invention discloses a round tunnel surrounding rock plastic zone model considering rock mass self weight and a construction method thereof. A round tunnel surrounding rock plastic zone theoretical model considering rock mass self weight, middle principal stress and surrounding rock-support structure interaction at the same time is established. The rule of influence of initial crustal stress, rock mass shear modulus, rock mass dead weight, rock cohesive force, support structure rigidity and intermediate principal stress coefficient on the calculation result of the plastic zone of the surrounding rock is analyzed and researched through parameter sensitivity. As the initial crustal stress, the rock mass shear modulus and the rock mass weight are increased, the plastic zone of the surrounding rock is gradually increased, and as the rock mass cohesive force, the supporting structure rigidity and the middle principal stress coefficient are increased, the plastic zone of the surrounding rock is gradually decreased, but the increasing or decreasing amplitude of the plastic zone of the surrounding rock is different.

Description

Technical Field

[0001] The invention belongs to the technical field of tunnel engineering surrounding rock stability control, and in particular relates to a circular tunnel surrounding rock plastic zone model taking into account the deadweight of the rock mass and a construction method thereof. Background Art

[0002] Tunnel excavation will inevitably produce a certain range of plastic zone in the surrounding rock, and the size of the plastic zone of the surrounding rock will directly affect the safety and economy of tunnel construction. Therefore, it has attracted the attention of many scholars, and they have conducted in-depth research on it using model tests and field tests, theoretical analysis and numerical simulation. However, since the theoretical method has stronger universality, the results obtained are also easy to promote and apply. For this reason, Kastner proposed a theoretical model for calculating the plastic zone of the surrounding rock of a circular tunnel under hydrostatic pressure earlier, which has been widely recognized and has become the basis for theoretical research on the plastic zone of the surrounding rock of the tunnel. However, this method follows the following basic assumptions, namely: the dead weight of the rock mass is not considered, the rock is an isotropic homogeneous body and obeys the Mohr-Coulomb (MC) strength criterion and the ideal elastic-plastic model, and the support force is regarded as a constant. As the research gradually deepens, many scholars believe that the above assumptions are not in line with the actual situation. For example, in terms of rock strength criteria and constitutive models, many scholars believe that the MC criterion does not consider the influence of intermediate principal stress, and the ideal elastic-plastic model cannot reflect the dilatancy and softening characteristics of rock. Therefore, many theoretical models of surrounding rock plastic zone based on other strength criteria such as Drucker-Prager (DP) criterion, unified strength theory and rock dilatancy-softening model have been proposed. At the same time, in terms of the value of support force, Hou Gongyu et al. believe that the support force is not a constant, but is closely related to the deformation of the surrounding rock. Liu et al. also conducted in-depth research on this.

[0003] However, although many improvements have been made to the Kastner theory, there are few reports on the improvement of the first assumption of this method, that is, not considering the deadweight of the rock mass. On the one hand, when the tunnel is buried deep, ignoring the deadweight of the rock mass will not cause large errors in the calculation results. On the other hand, when the deadweight of the rock mass is considered, the problem cannot be simplified to an axisymmetric problem, so it is difficult to solve the problem theoretically, or even there is no theoretical solution. However, relevant studies have shown that when the tunnel is buried shallow, the probability and severity of roof collapse are much higher than the corresponding bottom drum and sidewalls, which means that the damage range and degree of the tunnel top are much higher than the bottom plate and the two sides, that is, the plastic zone of the surrounding rock is no longer circularly symmetrical. Therefore, how to establish a theoretical model of the plastic zone of the tunnel surrounding rock considering the deadweight of the rock mass is an important issue that needs to be solved urgently. Some scholars have also carried out useful explorations on this. For example, Zhi Xizhe studied the calculation method of polar coordinate stress components under constant body force conditions earlier, and gave the expressions of three stress components in plane polar coordinates under constant body force conditions, but he did not further explore the calculation method of the plastic zone of the tunnel surrounding rock under constant body force conditions. Song Haoran et al. obtained the analytical solution of the stress field of the surrounding rock of a shallow buried tunnel under the condition of ground load and surrounding rock self-weight based on the theory of complex variables. They believed that when the tunnel is shallow, the surrounding rock is mainly subjected to a composite failure of tension and shear, while when the tunnel is deep, the main failure mode of the surrounding rock is shear failure of the side wall. Zhou Wei derived the calculation formula of the plastic zone at the arch crown, arch waist and arch bottom of the tunnel under the condition of rock mass self-weight based on the unified strength theory. They believed that when the rock mass self-weight is considered, the size of the plastic zone at the three locations is the arch crown, arch waist and arch bottom. This study provides a good research idea for the calculation of the plastic zone of the tunnel surrounding rock under the condition of rock mass self-weight, but it assumes that the tunnel support force is constant, and fails to consider the change of support force caused by the interaction between surrounding rock and support structure.

[0004] In conclusion, the current research status shows that for shallow buried tunnels, the influence of rock mass deadweight on the plastic zone of tunnel surrounding rock cannot be ignored and should be considered. However, there is little theoretical research in this area. Therefore, based on the previous research, this paper proposes a theoretical model of the plastic zone of circular tunnel surrounding rock considering the deadweight of rock mass based on the ideal elastic-plastic theory, and at the same time considers the influence of intermediate principal stress and the interaction between surrounding rock and supporting structure on the plastic zone of surrounding rock. Summary of the invention

[0005] In order to solve the above problems, the present invention proposes a plastic zone model of the surrounding rock of a circular tunnel considering the deadweight of the rock mass and a construction method thereof. First, the unified strength theory considering the intermediate principal stress is introduced. Secondly, the theoretical model of the plastic zone of the surrounding rock at three locations of the circular tunnel arch, arch waist and arch bottom is established based on the ideal elastic-plastic theory. Then, the above theoretical model is modified by introducing the theory of interaction between the surrounding rock and the supporting structure. Finally, a theoretical model of the plastic zone of the surrounding rock of a circular tunnel considering the deadweight of the rock mass, the intermediate principal stress and the interaction between the surrounding rock and the supporting structure is proposed. Finally, parameter sensitivity analysis is used to study the influence of parameters such as initial geostress, rock mass shear modulus, gravity, rock cohesion, support structure stiffness and intermediate principal stress coefficient on the plastic zone of the surrounding rock.

[0006] The circular tunnel surrounding rock plastic zone model considering the deadweight of the rock mass of the present invention is a tunnel surrounding rock plastic zone model considering the interaction between the surrounding rock and the supporting structure. The model corresponds the three parts of the tunnel vault, the vault waist and the vault bottom to four points on the circular tunnel surrounding rock. After the plastic zone radius of the above four points is obtained, they are connected by a smooth curve to obtain a closed curve. The curve is the boundary between the elastic and plastic zones of the surrounding rock, and the area between the curve and the tunnel contour line is the range of the plastic zone of the surrounding rock. The calculation formula of the plastic zone radius is:

[0007]

[0008] Formula (12) is about r p The implicit equation cannot be solved directly and needs to be solved by iteration. p is the radius of the surrounding rock plastic zone, r0 is the tunnel radius, k s is the tensile and compressive stiffness of the supporting structure, γ is the weight of the rock mass, p0 is the initial ground stress, G is the rock shear modulus, c and are rock cohesion and internal friction angle respectively, and b (0≤b≤1) is the intermediate principal stress coefficient.

[0009] The method for constructing a plastic zone model of a circular tunnel surrounding rock taking into account the deadweight of the rock mass of the present invention comprises the following steps:

[0010] S1. Establish a unified strength theory considering intermediate principal stresses;

[0011] S2. Based on the ideal elastic-plastic theory, a circular tunnel mechanical model considering the deadweight of rock mass is established;

[0012] S3. The theory of surrounding rock-support structure interaction is introduced to modify the mechanical model of circular tunnel, and a tunnel surrounding rock plastic zone model is obtained which takes into account the deadweight of rock mass, intermediate principal stress and the interaction between surrounding rock and support structure.

[0013] The unified strength theory formula of S1 considering the intermediate principal stress is:

[0014]

[0015] In the formula, c and are rock cohesion and internal friction angle, b (0≤b≤1) is the intermediate principal stress coefficient, σ θ is the hoop stress of rock, σ r is the radial stress of rock.

[0016] The circular tunnel mechanical model of S2 considering the deadweight of the rock mass is a model of the tunnel vault, the haunch and the bottom of the vault. The circular tunnel mechanical model considering the deadweight of the rock mass includes a surrounding rock stress model and a surrounding rock displacement model.

[0017] The radial stress on the elastic-plastic interface and the radius of the plastic zone of the surrounding rock in the surrounding rock stress model are respectively:

[0018] ① Vault:

[0019]

[0020] ② Arch waist:

[0021]

[0022] ③ Arch bottom:

[0023]

[0024] Among them, only equation (5b) is an explicit equation and can be solved directly, while equations (5a) and (5c) are implicit equations and cannot be solved directly. Therefore, an iterative method can be used to first calculate r p , then find p r ;p r is the radial stress, r p is the radius of the plastic zone of the surrounding rock, p s is the tunnel support force, γ is the weight of rock mass, p0 is the initial ground stress, and r0 is the tunnel radius.

[0025] The surrounding rock displacement model is

[0026]

[0027] In the formula, u r0 is the tunnel wall displacement, γ is the weight of the rock mass, p0 is the initial ground stress, G is the rock shear modulus, r p is the radius of the surrounding rock plastic zone, r0 is the radius of the tunnel, c and are rock cohesion and internal friction angle respectively, and b (0≤b≤1) is the intermediate principal stress coefficient.

[0028] The p s The calculation formula is

[0029] p s =k s u r0 (11)

[0030] In the formula, p s is the tunnel support force, k s is the tensile and compressive stiffness of the supporting structure, u r0 is the displacement of the tunnel wall.

[0031] The beneficial effect of the present invention is that the present invention establishes a theoretical model of the plastic zone of the surrounding rock of a circular tunnel that simultaneously considers the deadweight of the rock mass, the intermediate principal stress and the interaction between the surrounding rock and the supporting structure. The influence of the initial geostress, the shear modulus of the rock mass, the deadweight of the rock mass, the rock cohesion, the stiffness of the supporting structure and the intermediate principal stress coefficient on the calculation results of the plastic zone of the surrounding rock is studied through parameter sensitivity analysis. It is found that with the increase of the initial geostress, the shear modulus of the rock mass and the weight of the rock mass, the plastic zone of the surrounding rock gradually increases, while with the increase of the cohesion of the rock mass, the stiffness of the supporting structure and the intermediate principal stress coefficient, the plastic zone of the surrounding rock gradually decreases, but the increase or decrease amplitude is different. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a stress analysis diagram of the plastic zone of the surrounding rock of the circular tunnel and micro-element bodies at different positions of the present invention.

[0033] Figure 2 It is a diagram of the calculation results of the surrounding rock plastic zone of the present invention.

[0034] Figure 3 It is the influence diagram of the initial ground stress on the calculation result of the plastic zone of the surrounding rock according to the present invention.

[0035] Figure 4 It is an influence diagram of the rock mass shear modulus on the calculation results of the surrounding rock plastic zone of the present invention.

[0036] Figure 5 It is an influence diagram of the rock mass on the calculation results of the plastic zone of the surrounding rock according to the present invention.

[0037] Figure 6 It is a diagram showing the influence of cohesion on the calculation results of the plastic zone of the surrounding rock according to the present invention.

[0038] Figure 7 It is an influence diagram of the stiffness of the support structure of the present invention on the calculation results of the plastic zone of the surrounding rock.

[0039] Figure 8 It is an influence diagram of the intermediate principal stress coefficient of the present invention on the calculation results of the plastic zone of the surrounding rock. DETAILED DESCRIPTION

[0040] Embodiments of the present invention are described in detail below, and examples of the embodiments are shown in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are exemplary and intended to be used to explain the present invention, but should not be understood as limiting the present invention.

[0041] The method for constructing a plastic zone model of a circular tunnel surrounding rock taking into account the deadweight of the rock mass of the present invention comprises the following steps:

[0042] S1. Establish a unified strength theory considering intermediate principal stresses;

[0043] When σ2=(σ1+σ3) / 2, the unified strength theory can be written in a form similar to the MC criterion, that is (expressed in polar coordinates):

[0044]

[0045] Where: c and are rock cohesion and internal friction angle, b (0≤b≤1) is the intermediate principal stress coefficient, σ θ is the hoop stress of rock, σ r is the radial stress of rock.

[0046] S2. Based on the ideal elastic-plastic theory, a circular tunnel mechanical model considering the deadweight of rock mass is established;

[0047] S201. Surrounding rock stress

[0048] Since the tunnel's length dimension is much larger than its cross-sectional dimension, it can be considered as a plane strain problem, so a certain cross section can be selected for study. Figure 1 The figure shows the calculation model of a circular tunnel cross section under the action of the far-field uniformly distributed initial ground stress p0. Since the tunnel cross section is circular, polar coordinates are used for the solution here, and the direction perpendicular to the cross section is set as the z direction, so σ θ , σ r , σ z , ε θ , ε r , ε z are the annular, radial and axial stress and strain components of the tunnel calculation model, and satisfy σ θ >σ z >σ r .

[0049] When the deadweight of the rock mass is taken into account, the plastic zone of the surrounding rock will no longer be a circular area symmetrical with the center of the tunnel, but will appear as follows: Figure 1 An asymmetrical area shown with a larger top range, a smaller bottom range, and a centered waist.

[0050] The stress conditions of the micro-element at the tunnel vault, waist and bottom are as follows: Figure 1 As shown in the figure, when the deadweight of the rock mass is considered, the tangential stresses of the above three locations are all zero due to symmetry, while the tangential stresses at other locations are no longer zero, so the problem is not a completely axisymmetric problem. Therefore, for the convenience of research, only the microelement bodies at the above three locations are taken as examples for research.

[0051] The microelement equilibrium equations at the three locations of the tunnel vault, waist and bottom are as follows:

[0052]

[0053] Where: r , σ θ are radial and annular normal stresses respectively, γ is the weight of rock mass, and r is the distance from a certain point A to be determined to the center of the tunnel.

[0054] The subscripts "e" and "p" are used below to represent the physical quantities in the elastic zone and plastic zone of the tunnel surrounding rock. If the unified strength theory is used as the rock strength criterion, then the stress component expressions of the tunnel surrounding rock in the plastic zone at the above three locations can be obtained by combining equations (1) and (2): (r0≤r≤r p , where r p is the radius of the plastic zone, and r0 is the radius of the tunnel.

[0055] ① Vault:

[0056]

[0057] ② Arch waist:

[0058]

[0059] ③ Arch bottom:

[0060]

[0061] Where: p s It is the tunnel support force, acting evenly on the inner wall of the tunnel.

[0062] If the radial stress on the elastic-plastic interface is assumed to be p r Similarly, when considering physical strength, the stress components of the elastic zone at the above three locations are (r≥r p ):

[0063] ① Vault:

[0064] ② Arch waist:

[0065] ③ Arch bottom:

[0066] Since the stress at the elastic-plastic interface is continuous, that is, σ re =σ rp , σ θe =σ θp , so r=r p Substituting into equations (3) to (4), the radial stress p on the elastic-plastic interface at the three locations of the tunnel vault, arch waist and arch bottom can be obtained: r and the radius of the surrounding rock plastic zone r p They are:

[0067] ① Vault:

[0068]

[0069] ② Arch waist:

[0070]

[0071] ③ Arch bottom:

[0072]

[0073] It can be seen that only equation (5b) is an explicit equation and can be solved directly, while equations (5a) and (5c) are implicit equations and cannot be solved directly. Therefore, an iterative method can be used to first solve r p , then find p r .

[0074] S202. Surrounding rock displacement

[0075] Here we only study the displacement of the surrounding rock at the tunnel vault, arch waist and arch bottom. According to the elastic theory, when the radial stress p on the elastic-plastic interface is obtained, r After that, the stress in the elastic zone of the surrounding rock at the above three locations can be obtained as follows:

[0076]

[0077] Yu et al. believed that there was initial geostress in the rock mass before tunnel excavation. Tunnel excavation not only caused stress redistribution, but also led to convergent displacement of the surrounding rock. Therefore, the convergent displacement of the surrounding rock is caused by the stress increment caused by tunnel excavation. Therefore, according to formula (6) and the elastic constitutive relationship, the displacement of the surrounding rock at the above three locations can be obtained as:

[0078]

[0079] Where: E and v are the rock elastic modulus and Poisson's ratio respectively.

[0080] When rock undergoes plastic deformation, its shape mainly changes. Therefore, it is assumed that the volume of the rock in the plastic zone remains unchanged. Combined with the geometric equation, we have:

[0081]

[0082] At the same time, according to the displacement continuity condition on the interface of the surrounding rock elastic-plastic zone, the displacement of the surrounding rock in the plastic zone can be obtained as follows (the direction toward the center of the tunnel is positive):

[0083]

[0084] Where: G is the shear modulus of rock.

[0085] It can be seen that the displacement expressions of the elastic and plastic zones are the same. r Substituting into equation (9), we can obtain the tunnel inner wall displacement u at the above three locations: r0 for:

[0086]

[0087] S3. The theory of surrounding rock-support structure interaction is introduced to modify the mechanical model of circular tunnel, and a tunnel surrounding rock plastic zone model is obtained which takes into account the deadweight of rock mass, intermediate principal stress and the interaction between surrounding rock and support structure.

[0088] At present, the tunnel support structures commonly used in engineering mainly include reinforced concrete lining, steel arch frame, anchor rod and their combination. Therefore, compared with rock, their stiffness is generally larger, so it can be considered that they only produce elastic deformation. At the same time, in order to achieve a good support effect, it is generally required that the support structure should be supported in time and fit closely with the surrounding rock, and the two do not slide relative to each other. Therefore, it can be considered that the radial convergence displacement of the surrounding rock is equal to the elongation of the support structure, from which:

[0089] p s =k s u r0 (11)

[0090] Where: k s It is the tensile and compressive stiffness of the supporting structure.

[0091] Then, by substituting equations (10) and (11) into the second equation of equation (5), the calculation formula for the radius of the surrounding rock plastic zone can be obtained as follows:

[0092]

[0093] It can be seen that formula (12) is about r p The implicit equation cannot be solved directly, so an iterative method is needed to solve it.

[0094] It should be noted that the present invention only proposes a calculation method for the plastic zone of the surrounding rock at three locations, namely, the tunnel vault, the arch waist and the arch bottom. For other locations, since they are not axisymmetric problems, there is usually no theoretical solution. The present invention intends to use an approximate method to process, that is, the above three locations correspond to four points on the surrounding rock of the circular tunnel. After the plastic zone radius of the above four points is obtained, they are connected by a smooth curve to obtain a closed curve. The curve is the boundary between the elastic and plastic zones of the surrounding rock, and the area between the curve and the tunnel contour line is the range of the plastic zone of the surrounding rock.

[0095] Case Analysis

[0096] 1. Computational Model

[0097] Take Figure 1 The circular tunnel shown is a calculation model. The calculation parameters are shown in Table 1. The plastic zone of the tunnel surrounding rock is calculated using the theory of this paper.

[0098] Table 1 Calculation parameters

[0099] Tab.1The calculation parameters

[0100]

[0101] According to the above parameters, the plastic zone of surrounding rock can be obtained as follows Figure 2As shown in the figure, it can be seen that when the deadweight of the rock mass is considered, the plastic zone of the tunnel surrounding rock will no longer be a circle with the tunnel center point O as the center, but will present a shape with a large arch, a small arch bottom, and a central arch waist, which fully illustrates the influence of the deadweight of the rock mass on the plastic zone of the tunnel surrounding rock. For this example, when the deadweight of the rock mass is not considered, the radius of the plastic zone of the surrounding rock is the radius of the plastic zone of the tunnel waist, that is, 4.86m, while when the deadweight of the rock mass is considered, the plastic zone radii of the arch and arch bottom are 5.74m and 4.07m respectively, and the increase or decrease is 18.11% and 16.26% respectively. This is because when the deadweight of the rock mass is considered, the gravity direction of the rock mass on the arch is toward the center of the tunnel, which is a favorable factor for inducing roof collapse and damage to the rock mass, and is therefore beneficial to the formation of the plastic zone of the surrounding rock. Correspondingly, the radius of the plastic zone at the arch is larger. The gravity direction of the rock mass at the bottom of the arch is away from the center of the tunnel, so it has a restraining effect on the bottom drum damage at the bottom of the arch, so it is not conducive to the formation of the plastic zone of the surrounding rock. Correspondingly, the radius of the plastic zone at the bottom of the arch is also small. The deadweight of the rock mass at the waist of the arch is perpendicular to the radius of the tunnel, so it has no effect on the range of the plastic zone. This can also be seen from the second equation of equation (12). In short, it can be considered that when the deadweight of the rock mass is considered, the range of the plastic zone of the surrounding rock is no longer a circular area with the center of the tunnel as the center, but a non-circular area with a large upper part, a small bottom and a central waist. It should also be noted that in this example, p0 = 100 kPa. According to the γ value in Table 1, it can be obtained that when only the deadweight stress is considered, the thickness of the overlying rock mass is only 5 m, and the radius of the tunnel is 3 m. Therefore, it can be considered that the tunnel is shallowly buried or even ultra-shallowly buried. In other words Figure 2 The calculation results of the surrounding rock plastic zone shown are obtained when the tunnel is shallowly buried or even ultra-shallowly buried. As the tunnel depth increases, the directional characteristics of the tunnel surrounding rock plastic zone will gradually weaken, which can be seen from the parameter sensitivity analysis for p0 below. In short, it can be considered that it is very necessary to consider the influence of the rock mass deadweight on the tunnel surrounding rock plastic zone when the tunnel depth is shallow.

[0102] 2. Parameter sensitivity analysis

[0103] From the above calculation example, it can be seen that the deadweight of the rock mass has an important influence on the range of the plastic zone of the surrounding rock at different positions of the tunnel. However, the influence of the above calculation parameters on the calculation results of the plastic zone of the surrounding rock needs further study. To this end, the following parameter sensitivity analysis is proposed to study the initial ground stress p0, rock mass shear modulus G, gravity γ, rock shear strength (here taking cohesion c as an example), support structure stiffness k s , intermediate principal stress coefficient b, etc. on the calculation results of the plastic zone of surrounding rock.

[0104] (1) Influence of initial geostress p0

[0105] Taking p0 as 100 kPa, 1000 kPa, 10000 kPa and 100000 kPa respectively, and keeping other parameters unchanged, the variation law of the surrounding rock plastic zone at the three parts of the tunnel vault, arch waist and arch bottom is as follows: Figure 3 . It can be seen that: ① With the increase of p0, the range of the plastic zone of the surrounding rock gradually increases, but its increasing trend gradually slows down and eventually tends to a certain value. Taking the plastic zone at the arch as an example, when p0 gradually increases from 100kPa to 1000kPa, 10000kPa and 100000kPa, its plastic zone increases from 5.74m to 6.80m, 6.89m and 6.9m respectively, that is, its increase rate gradually decreases, which also shows that tunnel excavation only affects a certain range of rock mass, that is, the stress concentration caused by tunnel excavation is local, so the range of influence on the surrounding rock is also local, and will not increase infinitely. ② With the increase of p0, the range of the plastic zone changes from the overall characteristics of large top, middle waist and smallest bottom to the plastic zone range of each part around the tunnel being equal, that is, the distribution of the plastic zone is more uniform. This is because when p0 is small, the deadweight of the rock mass in the plastic zone accounts for a large proportion of the total stress field. When p0 increases to a certain extent, the range of the plastic zone no longer increases significantly, so the deadweight of the rock mass in the plastic zone will not increase significantly. At this time, the proportion of the deadweight of the rock mass in the plastic zone in the total stress field gradually decreases. Therefore, when p0 is large enough, the influence of the deadweight of the rock mass in the plastic zone on the calculation results of the surrounding rock plastic zone can be ignored, so the range of the plastic zone gradually approaches a circle. This is also the reason why the deadweight of the rock mass is usually not considered when calculating the plastic zone of the surrounding rock of a deep buried tunnel.

[0106] (2) Influence of rock mass shear modulus G

[0107] When G is set to 40MPa, 400MPa, 4000MPa and 40000MPa respectively and other parameters remain unchanged, the variation law of the surrounding rock plastic zone at the three parts of the tunnel vault, arch waist and arch bottom is as follows: Figure 4. It can be seen that: ① With the increase of G, the range of the plastic zone of the surrounding rock gradually increases, but its increasing trend gradually slows down and eventually tends to a certain value. Taking the surrounding rock at the arch as an example, when G gradually increases from 40MPa to 400MPa, 4000MPa and 40000MPa, its plastic zone increases from 5.74m to 5.89m, 5.91m and 5.91m respectively, that is, its increase rate gradually decreases and gradually tends to a certain value. ② With the increase of G, the range of the plastic zone gradually changes from the overall characteristics of large top, middle waist and smallest bottom to the range of the plastic zone in all directions being approximately equal, that is, the distribution of the plastic zone is more uniform. This is because when G is small, the rock mass deformation is large, and the deformation of the support structure will increase accordingly, which will lead to an increase in the support force accordingly. Therefore, under the condition that the shear strength of the rock mass remains unchanged, when the support force increases, the plastic zone of the surrounding rock will decrease accordingly. As G increases, the displacement of the surrounding rock decreases, and the deformation of the supporting structure decreases accordingly, and the supporting force also decreases, so the plastic zone will increase. ③ From the increase of the plastic zone of the surrounding rock at different positions, as G increases, the increase rate of the plastic zone of the surrounding rock at the arch is much smaller than that at the bottom. This is because as G increases, the deformation of the surrounding rock at the arch decreases rapidly and gradually converges to the deformation at other positions, so the range of the plastic zone of the surrounding rock at different positions is also more uniform.

[0108] (3) The influence of rock mass γ

[0109] Take γ as 18kN / m 3 , 19kN / m 3 , 20kN / m 3 and 21kN / m 3 , the other parameters remain unchanged, the change law of the surrounding rock plastic zone at the three parts of the tunnel vault, arch waist and arch bottom is as follows Figure 5 . It can be seen that: ① With the increase of γ, the change law of the plastic zone of the surrounding rock at different parts is inconsistent, among which the crown gradually increases, the waist remains unchanged, and the bottom of the arch gradually decreases. This is because the gravity of the rock mass at the crown is toward the center of the tunnel. Therefore, with the increase of the deadweight of the rock mass, the rock mass at the crown is more likely to be damaged by its own weight, so its plastic zone range increases. As can be seen from formula (12), the plastic zone of the surrounding rock at the waist has nothing to do with the weight of the rock mass, while the plastic zone at the bottom of the arch decreases with the increase of the deadweight of the rock mass. This is because the gravity of the rock mass at the bottom of the arch deviates from the center of the tunnel, which plays a role in curbing the adverse deformation such as the uplift of the bottom of the tunnel. Therefore, it is more difficult to form a plastic zone under the action of gradually increasing deadweight. ② With the increase of γ, the increase in the plastic zone at the crown and bottom of the arch does not change much. Taking the surrounding rock at the crown as an example, when γ increases from 18kN / m 3 Increased to 19kN / m respectively 3 , 20kN / m 3and 21kN / m 3 When γ increases, the plastic zone increases from 5.56m to 5.62m, 5.74m and 5.78m respectively, that is, the increase rate does not change much, which shows that the influence of rock mass deadweight on the plasticity of surrounding rock is approximately linear. ③ With the increase of γ, the range of plastic zone gradually changes from the characteristics of large top, middle waist and smallest bottom to the characteristics of larger top, smaller bottom and unchanged waist, that is, the range of plastic zone gradually migrates from bottom to top.

[0110] (4) Influence law of rock mass shear strength

[0111] The shear strength parameters of rock mass include cohesion c and internal friction angle The influence of the two is basically the same. Therefore, the former is taken as an example for research. Taking c as 10kPa, 20kPa, 30kPa and 40kPa respectively, and keeping other parameters unchanged, the change law of the surrounding rock plastic zone at the three parts of the tunnel arch, arch waist and arch bottom is as follows Figure 6 . It can be seen that: ① With the increase of c, the range of the plastic zone of the surrounding rock gradually decreases, but its decreasing trend gradually slows down and eventually tends to a certain value. Taking the surrounding rock at the arch as an example, when c increases from 10kPa to 20kPa, 30kPa and 40kPa respectively, its plastic zone decreases from 5.74m to 4.32m, 3.76m and 3.43m respectively, that is, its decrease gradually decreases. On the one hand, this is because with the increase of c, the shear strength of the rock mass increases, and the ability to resist shear failure increases, so the range of the plastic zone gradually decreases. On the other hand, it can be seen from formula (12) that the radius of the plastic zone is not a simple linear relationship with c, so with the increase of c, the radius of the plastic zone does not decrease linearly. ② From the perspective of the influence of c on the plastic zone at different parts of the tunnel, as c increases, the plastic zone ranges of the arch crown, arch waist and arch bottom are all reduced, but the reduction ranges are still slightly different. For example, when c increases from 10kPa to 40kPa, the plastic zone reduction ranges at the three parts are 40.24%, 30.65% and 26.29% respectively, that is, the plastic zone radius at the arch crown is the largest. This is because the arch crown is more likely to yield under the combined action of rock mass ground stress and deadweight, so when the shear strength of the rock mass increases, its plastic zone is reduced to the greatest extent.

[0112] (5) Support structure stiffness k s The influence of

[0113] Take k s The plastic zone changes of the surrounding rock at the three locations of the tunnel vault, arch waist and arch bottom are as follows: Figure 7 It can be seen that: ① As k sAs k increases, the plastic zone of the surrounding rock gradually decreases, but the reduction range at different locations is different. The reduction range at the arch top does not change much, while the reduction range at the arch waist and arch bottom gradually decreases. Taking the surrounding rock at the arch bottom as an example, when k s When the pressure increases from 1.5MPa to 3MPa, 6MPa and 9MPa, the radius of the plastic zone decreases from 4.07m to 3.57m, 3.09m and 3m, respectively, that is, the reduction rate gradually decreases. This is because as k s As k increases, the support force provided by the support structure also increases, so the surrounding rock will not easily produce large deformation, and the radius of its plastic zone will also decrease. s With the increase of the plastic zone, the plastic zone range of different parts is characterized by large top, small bottom and middle waist. The shape of the top plastic zone is similar to the collapse arch commonly seen in tunnels. This shows that increasing the stiffness of the support structure can reduce the plastic zone of the surrounding rock and improve the stability of the surrounding rock, but it will increase the support cost accordingly, so the problem of safety and benefit should be balanced comprehensively.

[0114] (6) Influence of the intermediate principal stress coefficient b

[0115] When b is set to 0, 0.33, 0.67 and 1 respectively, and the other parameters remain unchanged, the radius variation of the surrounding rock plastic zone at the three locations of the tunnel vault, arch waist and arch bottom is as follows: Figure 8 . It can be seen that: ① With the increase of b, the radius of the plastic zone of the surrounding rock gradually decreases, but its decreasing trend gradually slows down and eventually tends to a certain value. Taking the surrounding rock at the arch as an example, when b increases from 0 to 0.33, 0.67 and 1 respectively, its plastic zone decreases from 6.5m to 5.74m, 5.29m and 5.05m respectively, that is, its decrease is gradually decreasing. On the one hand, this shows that when the intermediate principal stress is considered, the plastic zone of the surrounding rock is gradually reduced, that is, the intermediate principal stress has a certain influence on the stability of the surrounding rock. On the other hand, it also shows that the influence of the intermediate principal stress on the plastic zone of the surrounding rock is limited. ② With the increase of b, the difference in the range of plastic zones in various parts will gradually decrease. This is because with the increase of b, the influence weight of the intermediate principal stress on the plastic zone of the tunnel surrounding rock gradually increases. That is, when b = 0 and 1, the unified strength theory corresponds to the MC strength theory that completely ignores the intermediate principal stress and the double shear strength theory that completely considers the intermediate principal stress. Therefore, the surrounding rock gradually evolves from a two-way stress state to a three-way stress state, and the damage of the surrounding rock in all directions tends to be more uniform.

[0116] Although the above embodiments have been shown and described, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations on the present invention. Changes, modifications, substitutions and variations of the above embodiments by those of ordinary skill in the art are all within the scope of protection of the present invention.

Claims

1. A plastic zone model of the surrounding rock of a circular tunnel considering the deadweight of the rock mass, characterized in that: The model is a tunnel surrounding rock plastic zone model that takes into account the interaction between surrounding rock and supporting structure. The model corresponds the three parts of the tunnel vault, arch waist and arch bottom to four points on the circular tunnel surrounding rock. After the plastic zone radius of the above four points is obtained, they are connected by a smooth curve to obtain a closed curve. The curve is the boundary between the elastic and plastic zones of the surrounding rock, and the area between the curve and the tunnel contour is the range of the surrounding rock plastic zone. The calculation formula of the plastic zone radius is: Formula (12) is about r p The implicit equation cannot be solved directly and needs to be solved by iteration. p is the radius of the surrounding rock plastic zone, r0 is the tunnel radius, k s is the tensile and compressive stiffness of the supporting structure, γ is the weight of the rock mass, p0 is the initial ground stress, G is the rock shear modulus, c and are rock cohesion and internal friction angle respectively, and b (0≤b≤1) is the intermediate principal stress coefficient.

2. A method for constructing a plastic zone model of a circular tunnel surrounding rock taking into account the deadweight of the rock mass according to claim 1, characterized in that: The following steps are involved: S1. Establish a unified strength theory considering intermediate principal stresses; S2. Based on the ideal elastic-plastic theory, a circular tunnel mechanical model considering the deadweight of rock mass is established; S3. The theory of surrounding rock-support structure interaction is introduced to modify the mechanical model of circular tunnel, and a tunnel surrounding rock plastic zone model is obtained which takes into account the deadweight of rock mass, intermediate principal stress and the interaction between surrounding rock and support structure.

3. The method for constructing a plastic zone model of a circular tunnel surrounding rock considering the deadweight of the rock mass according to claim 2, characterized in that: The unified strength theory formula of S1 considering the intermediate principal stress is: In the formula, c and are rock cohesion and internal friction angle, b (0≤b≤1) is the intermediate principal stress coefficient, σ θ is the hoop stress of rock, σ r is the radial stress of rock.

4. The method for constructing a plastic zone model of a circular tunnel surrounding rock considering the deadweight of the rock mass according to claim 2, characterized in that: The circular tunnel mechanical model of S2 considering the deadweight of the rock mass is a model of the tunnel vault, the haunch and the bottom of the vault. The circular tunnel mechanical model considering the deadweight of the rock mass includes a surrounding rock stress model and a surrounding rock displacement model.

5. The method for constructing a plastic zone model of a circular tunnel surrounding rock considering the deadweight of the rock mass according to claim 4, characterized in that: The radial stress on the elastic-plastic interface and the radius of the plastic zone of the surrounding rock in the surrounding rock stress model are respectively: ① Vault: ② Arch waist: ③ Arch bottom: Among them, only equation (5b) is an explicit equation and can be solved directly, while equations (5a) and (5c) are implicit equations and cannot be solved directly. Therefore, an iterative method can be used to first calculate r p , then find p r ;p r is the radial stress, r p is the radius of the plastic zone of the surrounding rock, p s is the tunnel support force, γ is the weight of rock mass, p0 is the initial ground stress, and r0 is the tunnel radius.

6. The method for constructing a plastic zone model of a circular tunnel surrounding rock considering the deadweight of the rock mass according to claim 4, characterized in that: The surrounding rock displacement model is In the formula, u r0 is the tunnel wall displacement, γ is the weight of the rock mass, p0 is the initial ground stress, G is the rock shear modulus, r p is the radius of the surrounding rock plastic zone, r0 is the radius of the tunnel, c and are rock cohesion and internal friction angle respectively, and b (0≤b≤1) is the intermediate principal stress coefficient.

7. The method for constructing a plastic zone model of a circular tunnel surrounding rock considering the deadweight of the rock mass according to claim 5, characterized in that: The p s The calculation formula is p s =k s u r0 (11) In the formula, p s is the tunnel support force, k s is the tensile and compressive stiffness of the supporting structure, u r0 is the displacement of the tunnel wall.

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