Deep tunnel energy evolution calculation method considering synergistic effect of surrounding rock and anchor rod

Abstract

The invention provides a deep tunnel energy evolution calculation method considering the synergistic effect of surrounding rocks and anchor rods, and belongs to the technical field of tunnel engineering. Comprising the steps that a deep tunnel calculation model considering the synergistic effect of surrounding rock and anchor rods is established, and tunnel model basic parameters, surrounding rock strength parameters and anchor rod material parameters are input; based on the deep tunnel calculation model, solving a stress evolution path of the surrounding rock of the deep tunnel under the synergistic effect of the surrounding rock and the anchor rod after tunnel excavation; solving a stress evolution path of the deep tunnel anchor rod under the synergistic effect of the surrounding rock and the anchor rod after tunnel excavation; calculating the energy density and total energy of the surrounding rock according to the stress evolution path of the surrounding rock; and calculating the energy density and total absorption energy of the anchor rod according to the stress evolution path of the anchor rod. According to the deep tunnel energy evolution calculation method provided by the invention, the problem of solving the strain softening surrounding rock energy field under the elastic-plastic unloading condition is solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of tunnel engineering, and relates to a calculation method for energy evolution of deep tunnels considering the collaborative action of surrounding rock and bolts. Background Technique

[0002] Deep rock masses in high in-situ stress environments store high strain energy and belong to high-energy geological environments. The excavation of deep tunnels results in a free face in the surrounding rock of the tunnel, causing stress redistribution in the surrounding rock and the accumulation of energy on the free face. When the energy accumulated in the surrounding rock near the tunnel perimeter exceeds the energy storage limit, energy dissipation and release will be triggered, thereby inducing deformation, damage, and failure of the surrounding rock. Therefore, the deformation and failure process of the surrounding rock of deep high in-situ stress tunnels is driven by energy, and the evolution law of the energy field during the excavation unloading process of deep high in-situ stress tunnels has always been a research hotspot in the field of rock mechanics at home and abroad, and is of great significance for the stability evaluation and disaster prevention and control of deep high in-situ stress tunnels.

[0003] Existing studies have carried out extensive work on the energy field evolution mechanism of deep tunnel surrounding rock through methods such as theoretical calculation, numerical simulation, model tests, and field monitoring. However, in terms of theoretical calculation, existing studies mainly focus on the calculation of the elastic strain energy of deep tunnel surrounding rock under elastic unloading conditions. There are few studies on the energy calculation and evolution mechanism of surrounding rock under elastoplastic unloading conditions, and most of them assume that the surrounding rock is an elastic body or an ideal elastoplastic body. However, a large number of indoor test studies have shown that the post-peak strain softening of rocks is significant under high confining pressure environments, and the squeezing deformation of the surrounding rock of deep high in-situ stress tunnels is controlled by the strain softening behavior. Existing studies do not involve the energy calculation problem in the post-peak strain softening stage of the surrounding rock, and the energy evolution law of the surrounding rock during the elastoplastic unloading process is not clear. In addition, the load-bearing body of deep high in-situ stress soft rock tunnels includes the surrounding rock and the support structure. The surrounding rock is the main load bearer, and the support structure plays a role in mobilizing and assisting the surrounding rock to bear the load, that is, the surrounding rock and the support structure are a collaborative load-bearing system. Existing studies do not involve the energy evolution calculation problem considering the collaborative action between the surrounding rock and the support structure, and the energy regulation effect of the support structure is also not clear. Summary of the Invention

[0004] The present invention provides a calculation method for energy evolution of deep tunnels considering the collaborative action of surrounding rock and bolts, including the following steps: Step 1: Establish a calculation model of a deep tunnel considering the collaborative action of surrounding rock and bolts, and input the basic parameters of the tunnel model, the strength parameters of the surrounding rock, and the material parameters of the bolts; The basic parameters of the tunnel model include: the excavation radius of the tunnel is , the virtual support reaction force acting on the tunnel wall is , the in-situ stress of the tunnel is , the layout spacing of adjacent bolts along the tunnel axis is , the included angle between adjacent bolts along the circumferential direction of the tunnel is , the length of the bolt is and the radius of the anchorage zone is ; The surrounding rock strength parameters include: elastic modulus , Poisson's ratio , uniaxial compressive strength , peak geological strength index , rock mass characteristic parameter and disturbance coefficient ; The bolt material parameters include: the shear stiffness between the bolt and the grout interface , the bond strength between the bolt and the grout interface or between the surrounding rock and the grout interface , the friction angle of the grout failure surface , the elastic modulus of the bolt , the hardening modulus of the bolt , the yield strength of the bolt , the ultimate tensile strength of the bolt , the yield strain of the bolt and the failure strain of the bolt ; Step 2: Based on the deep tunnel calculation model, solve the stress evolution path of the deep tunnel surrounding rock under the synergy of the surrounding rock and bolts after tunnel excavation; Step 3: Based on the radial deformation of the -th layer of the surrounding rock at the -th unloading, solve the stress evolution path of the deep tunnel bolts under the synergy of the surrounding rock and bolts after tunnel excavation; Step 4: Calculate the energy density and total energy of the surrounding rock according to the stress evolution path of the surrounding rock; Step 5: Calculate the energy density and total absorbed energy of the bolts according to the stress evolution path of the bolts.

[0005] Further, the deep tunnel calculation model established in Step 1 satisfies the following conditions: (I), assume that the tunnel depth is greater than 500m, and the in-situ stress before excavation is a hydrostatic pressure environment with uniform distribution; (II), assume that the surrounding rock is a homogeneous and isotropic elastic material, and the stress state in the plastic stage satisfies the three-dimensional H-B strength criterion and the strain increment conforms to the non-associated flow rule; (III), the mechanical behavior of the interaction between the bolt and the surrounding rock satisfies the bond-slip model, and the relationship between the shear stress per unit length of the bolt and the relative displacement between the bolt and the surrounding rock satisfies the following formula: ; Where, is the shear stress per unit length of the bolt is the relative displacement between a certain point on the bolt and the surrounding rock at this position is the shear stiffness between the bolt and the grout interface or between the surrounding rock and the grout interface is the bond strength between the bolt and the grout interface or between the surrounding rock and the grout interface is the friction angle of the failure surface of the grouting body is the effective diameter of the interface between the bolt and the grouting layer is the confining pressure per unit length of the bolt. For a bolt embedded in the surrounding rock, the confining pressure on the bolt is equal to the radial stress of the surrounding rock ; (IV) The relationship between the axial force and the tensile deformation of the bolt satisfies the linear hardening elastoplastic mechanical model shown in the following formula: ; Among them, is the axial stress of the bolt is the tensile strain of the bolt

[0006] Furthermore, the specific process of solving the radial deformation of the th layer of the surrounding rock during the th unloading is as follows: S2.1. Assume that the stress in the anchored area of the surrounding rock satisfies the following equilibrium equation: ; Among them, is the bolt geometric coefficient ; is the distance from any position of the surrounding rock to the center of the circle is the radial stress of the surrounding rock The stress in the unanchored area of the surrounding rock satisfies the following equilibrium equation: ; The stress in the elastic area of the surrounding rock satisfies the following quantitative relationship; ; The stress in the plastic area of the surrounding rock satisfies the three-dimensional H-B strength criterion; S2.2. Calculate the stress of the surrounding rock; Assume that the virtual support reaction force acting on the tunnel wall is gradually unloaded to 0 from the in-situ stress of the tunnel and requires steps. The serial number of the surrounding rock layer is . Then, the stress of the th layer of the surrounding rock during the th unloading is obtained by the finite difference method as,in, is the number of unloading steps for support reaction unloading, is the number of the surrounding rock layer, ; S2.3. According to the calculation results of surrounding rock stress, solve the surrounding rock Layer relative to Elastic strain increment of the layer ; S2.4. Combine deformation coordination equation and plastic potential function to solve the total strain of surrounding rock ; S2.5. Total strain based on surrounding rock , solve The surrounding rock mass at the first unloading Radial deformation of the layer .

[0007] Furthermore, the specific process of solving the stress evolution path of the anchor bolt in the deep tunnel under the synergistic effect of the surrounding rock and the anchor bolt after tunnel excavation is as follows: S3.1, based on The surrounding rock mass at the first unloading Radial deformation of the layer , solve for any point in the anchor Relative displacement between the surrounding rock and the first unloading and the shear stress of the anchor bolt; S3.2. Based on the shear stress of the anchor rod, calculate The first unloading of the anchor Axial force of each layer ; S3.3 Calculation of the tensile strain of anchor bolts based on the linear strengthening elastoplastic mechanical model of anchor bolts .

[0008] Furthermore, the neutral point position of the anchor rod is determined as follows: The position of the neutral point is determined based on the self-balancing equation of the anchor bolt; The self-balancing equation of the anchor is as follows: ; in, is the distance between the neutral point of the anchor and the anchor head, is the distance between any point on the anchor and the anchor.

[0009] Furthermore, when solving the neutral point position of the anchor rod, the specific process is as follows: (i) Assume the position of the neutral point to be ; (ii) Based on The expression and The expressions are used to calculate the relative displacements and shear stresses of each node of the bolt in turn; the trial calculation results of the shear stresses are substituted into the self - equilibrium equation of the bolt; (iii), judge whether the shear stress satisfies the self - equilibrium equation; (iv), if not satisfied, adjust the position of the neutral point to , and return to (ii); if satisfied, directly determine the position of the neutral point of the bolt as the final position.

[0010] Furthermore, the specific process of calculating the energy density and total energy of the surrounding rock according to the stress path of the surrounding rock is as follows: S4.1. According to the calculation results of the stress path of the surrounding rock, obtain the elastic energy density of the th layer of the surrounding rock after times of unloading, the plastic dissipation energy density and the plastic release energy density ; S4.2. Integrate the energy density components within the plastic zone range to obtain the increment of elastic strain energy , the plastic dissipation energy and the plastic release energy of the plastic zone of the surrounding rock in the plastic deformation stage.

[0011] Furthermore, the specific process of calculating the energy density and absorbed total energy of the bolt according to the stress path of the bolt is as follows: S5.1. According to the calculation results of the stress path of the bolt, the distribution density of the absorbed energy of the bolt along the length direction; S5.2. Integrate the energy density of any point of the bolt along the length direction to solve the absorbed energy of a single bolt at the th unloading; According to the number of bolts contained in the tunnel per unit length in the longitudinal direction, obtain the total absorbed energy of the bolts per unit cross - section of the tunnel under plane - strain conditions .

[0012] Compared with the prior art, the present invention has the following beneficial effects: (1) The deep - tunnel energy evolution calculation method proposed by the present invention solves the problem of solving the energy field of strain - softening surrounding rock under elastoplastic unloading conditions. The existing research mainly focuses on the calculation of the elastic strain energy of the deep - tunnel surrounding rock under elastic unloading conditions, and for the calculation of the energy field of the surrounding rock under elastoplastic unloading conditions, it mainly assumes that the surrounding rock is an elastic body or an ideal elastoplastic body.

[0013] (2) The deep tunnel energy evolution calculation method proposed by the present invention solves the problem of solving the energy field of deep tunnels under the combined action of surrounding rock and anchor bolts. The load-bearing bodies of high in-situ stress soft rock tunnels include the surrounding rock and the support structure. The surrounding rock is the main load bearer, and the support structure plays a role in mobilizing and assisting the surrounding rock to bear the load, that is, the surrounding rock and the support structure are a system of collaborative load-bearing. Existing research has not addressed the issue of energy evolution calculation considering the collaborative action of the surrounding rock and the support. The present invention proposes a deep tunnel energy evolution calculation method considering the collaborative action of the surrounding rock and the anchor bolts, which can quantify and clarify the energy regulation effect of the support structure on the surrounding rock.

[0014] In addition to the purposes, features, and advantages described above, the present invention has other purposes, features, and advantages. The following will refer to the drawings for a more detailed description of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] The drawings forming a part of this application are used to provide a further understanding of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings: Figure 1 is a schematic diagram of the overall process of a deep tunnel energy evolution calculation method considering the collaborative action of surrounding rock and anchor bolts in an embodiment of the present invention; Figure 2 is a schematic diagram of a deep tunnel calculation model in an embodiment of the present invention; Fig. 3(a) is a schematic diagram of the zoning in the elastic deformation stage of the surrounding rock in an embodiment of the present invention; Fig. 3(b) is a schematic diagram of the zoning in the plastic deformation stage of the surrounding rock and the radius of the plastic zone is less than the radius of the anchored zone in an embodiment of the present invention; Fig. 3(c) is a schematic diagram of the zoning in the plastic deformation stage of the surrounding rock and the radius of the plastic zone is greater than the radius of the anchored zone in an embodiment of the present invention; Figure 4 is a schematic diagram of the relative displacement and shear stress between the surrounding rock and the anchor bolt in an embodiment of the present invention.

[0016] Wherein: ① is the elastic zone of the surrounding rock, ② is the plastic zone of the surrounding rock, ③ is the elastic-plastic boundary, ④ is the anchor bolt, ⑤ is the anchored elastic zone, ⑥ is the unanchored elastic zone, ⑦ is the anchored plastic zone, ⑧ is the unanchored plastic zone, ⑨ is the neutral point of the anchor bolt, and ⑩ is the shear stress distribution curve of the anchor bolt. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0017] To make the above objects, features, and advantages of the present invention more clearly understandable, the following provides a detailed description of the specific embodiments of the present invention with reference to the accompanying drawings. It should be noted that the drawings of the present invention are all in simplified forms and use non-precise scales, only for conveniently and clearly assisting in the description of the implementation of the present invention; the several mentioned in the present invention are not limited to the specific quantities in the attached drawing examples; the orientation or positional relationships indicated by 'front','middle', 'back', 'left', 'right', 'up', 'down', 'top', 'bottom','middle', etc. in the present invention are all based on the orientation or positional relationships shown in the drawings of the present invention, and do not indicate or imply that the devices or components referred to must have a specific orientation, nor can it be understood as a limitation to the present invention. Embodiment:

[0018] See Figure 1 As shown, a calculation method for the energy evolution of deep tunnels considering the collaborative effect of surrounding rock and bolts provided by the present invention includes the following steps: Step 1. Establish a calculation model of a deep tunnel considering the collaborative effect of surrounding rock and bolts as shown in Figure 2 and input the basic parameters of the tunnel model, the strength parameters of the surrounding rock, and the material parameters of the bolts; Preferably, the basic parameters of the tunnel model include: the excavation radius of the tunnel is , the virtual support reaction force acting on the tunnel wall is , the initial in-situ stress of the tunnel is , the layout spacing of adjacent bolts along the tunnel axis is , the included angle between adjacent bolts along the circumferential direction of the tunnel is , the length of the bolt is and the radius of the anchorage zone is ;

[0019] Preferably, the strength parameters of the surrounding rock include: elastic modulus , Poisson's ratio , uniaxial compressive strength , peak geological strength index , rock mass characteristic parameter and disturbance coefficient ; where: the elastic modulus , Poisson's ratio and uniaxial compressive strength are obtained through the uniaxial compression test of the rock, and the peak geological strength index , rock mass characteristic parameter and disturbance coefficient are obtained by using the chart prediction method according to the data obtained from the on-site survey of the surrounding rock of the tunnel face. Specifically, the chart prediction method is a prior art.

[0020] Preferably, the bolt material parameters include: the shear stiffness between the bolt and the grout interface , the bond strength between the bolt and the grout interface or between the surrounding rock and the grout interface , the friction angle of the grout failure surface , the elastic modulus of the bolt , the hardening modulus of the bolt , the yield strength of the bolt , the ultimate tensile strength of the bolt , the yield strain of the bolt and the failure strain of the bolt . Among them: the shear stiffness , the bond strength and the bond strength are obtained through the pull-out test of the bolt, while other strength parameters are found according to the "Code for Design of Steel Structures" (GB 50017-2017).

[0021] The calculation model of the deep tunnel needs to meet the following conditions: (I), Assume that the tunnel burial depth is large enough (burial depth greater than 500m), and the in-situ stress before excavation is a hydrostatic pressure environment with uniform distribution; (II), Take the rock at the tunnel burial depth, and the rock is a homogeneous and isotropic elastic material. And the stress state of the rock in the plastic stage satisfies the three-dimensional H-B strength criterion, and the strain increment of the rock in the plastic stage conforms to the non-associated flow rule; (III), The mechanical behavior of the interaction between the bolt and the surrounding rock satisfies the bond-slip model, and the relationship between the shear stress per unit length of the bolt and the relative displacement between the bolt and the surrounding rock satisfies the following formula: ; Among them, is the shear stress per unit length of the bolt; is the relative displacement between a certain point on the bolt and the surrounding rock at this position; is the shear stiffness between the bolt and the grout interface or between the surrounding rock and the grout interface; is the bond strength between the bolt and the grout interface or between the surrounding rock and the grout interface; is the friction angle of the grout failure surface; is the effective diameter of the interface between the bolt and the grout layer; is the confining pressure per unit length of the bolt, and for the bolt embedded in the surrounding rock, the confining pressure on the bolt is equal to the radial stress of the surrounding rock ;

[0022] (IV), The relationship between the axial force and the tensile deformation of the bolt satisfies the linear hardening elastoplastic mechanical model shown in the following formula: ; wherein, is the axial stress of the bolt, is the tensile strain of the bolt.

[0023] Furthermore, the expression of the three-dimensional H-B strength criterion is as follows: ; ; ; ; ; ; wherein, is the octahedral shear stress, is the average value of the first principal stress and the third principal stress in the octahedron, is the uniaxial compressive strength of the octahedron, , , are the strength parameters reflecting the rock characteristics in the three-dimensional H-B strength criterion, and are calculated according to the geological strength index of the rock, the rock mass characteristic parameter and the disturbance coefficient ; is the maximum principal stress of the specimen, is the intermediate principal stress of the specimen, is the minimum principal stress of the specimen, , and are obtained by conducting a true triaxial loading and unloading test on the specimen to simulate the true stress path of the surrounding rock after the excavation of a deep-buried tunnel.

[0024] Furthermore, the strain increment of the rock in the plastic zone conforms to the non-associated flow rule and satisfies the plastic potential function ; The expression of the plastic potential function is as follows: ; wherein, is the plastic radial strain increment, is the plastic circumferential strain increment, is the dilatancy coefficient of the rock.

[0025] Furthermore, due to the strain-softening behavior of the surrounding rock in the plastic stage, the geological strength index of the rock linearly decays with the increase of its plastic deviatoric strain. Therefore, a strain-softening model of the surrounding rock in the plastic stage is established; Strain softening model of surrounding rock in plastic stage The expression is as follows: ; ; in, is the plastic deviatoric strain of the rock, is the plastic hoop strain and plastic radial strain difference; is the critical plastic deviatoric strain of rock; It is an indicator of the geological strength of rock. The peak value of is also its initial value; It is an indicator of the geological strength of rock. The residual value of .

[0026] Step 2: Based on the deep tunnel calculation model, solve the stress evolution path of the surrounding rock of the deep tunnel under the synergistic effect of the surrounding rock and anchor after tunnel excavation (i.e. solve the first The surrounding rock mass at the first unloading Radial deformation of the layer ); The details are as follows: S2.1. The stress in the surrounding rock anchoring area must satisfy the following equilibrium equation: ; in, is the anchor geometry coefficient, ; is the distance from any position of the surrounding rock to the center of the circle, is the radial stress of the surrounding rock.

[0027] The stress in the non-anchored area of ​​the surrounding rock must satisfy the following equilibrium equation: ; The stress in the elastic zone of the surrounding rock must satisfy the following quantitative relationship: ; The stress in the plastic zone of the surrounding rock must meet the three-dimensional HB strength criterion.

[0028] S2.2. Calculate surrounding rock stress; the specific process is as follows: As shown in Figures 3(a) to 3(c), according to the relationship between the radius of the anchoring zone and the radius of the plastic zone, the surrounding rock is divided into an elastic zone with anchor, an elastic zone without anchor, a plastic zone with anchor, and a plastic zone without anchor.

[0029] Among them, the stress in the elastic zone with anchor is calculated by combining the stress balance equation of the surrounding rock anchoring zone and the stress quantitative relationship formula of the elastic zone of the surrounding rock; the stress in the elastic zone without anchor is calculated by combining the stress balance equation of the surrounding rock non-anchoring zone and the stress quantitative relationship formula of the elastic zone of the surrounding rock; the stress in the plastic zone with anchor is calculated by combining the stress balance equation of the rock anchoring zone and the three-dimensional HB strength criterion expression; the stress in the plastic zone without anchor is calculated by combining the stress balance equation of the surrounding rock non-anchoring zone and the three-dimensional HB strength criterion expression.

[0030] Furthermore, when calculating the stresses in the elastic zone with anchor, the elastic zone without anchor, the plastic zone with anchor, and the plastic zone without anchor, the finite difference method is used to obtain the stress evolution path of the surrounding rock during the tunnel excavation unloading process. The specific calculation method is as follows: Assume that the virtual support reaction force acting on the tunnel wall is The original rock stress of the tunnel Gradually uninstall to 0 required The number of the step and surrounding rock layer is , then the finite difference method is used to obtain the The surrounding rock mass at the first unloading The stress of the layer is ,in, is the number of unloading steps for support reaction unloading, is the number of the surrounding rock layer, .

[0031] S2.3. According to the calculation results of surrounding rock stress, solve the surrounding rock Elastic strain of the layer ; The specific process is as follows: According to Hooke's law, the surrounding rock Layer relative to Elastic strain increment of the layer , and then get the surrounding rock Elastic strain of the layer ; Surrounding rock Layer relative to Elastic strain increment of the layer The expression is as follows: ; Surrounding rock Elastic strain of the layer The expression is as follows: ; ; in, For the Layer relative to The stress increment of the layer; S2.4. Simultaneously solve the deformation compatibility equation and the plastic potential function to obtain the total strain of the surrounding rock ; The total strain of the surrounding rock The expression is as follows: ; ; .

[0032] S2.5. From the total strain of the surrounding rock and the elastic strain increment , solve for the plastic strain increment of the -th layer of the surrounding rock relative to the -th layer, and then obtain the plastic strain of the -th layer of the surrounding rock; The plastic strain increment of the -th layer of the surrounding rock relative to the -th layer is expressed as follows: ; The plastic strain of the -th layer of the surrounding rock is expressed as follows: ; From the strain and physical equation of the surrounding rock, the radial deformation of the -th layer of the surrounding rock during the -th unloading can be solved; ; where is the radius of the -th layer of the surrounding rock.

[0033] Step Three. Based on the radial deformation of the -th layer of the surrounding rock during the -th unloading, solve the stress evolution path of the deep tunnel bolt under the combined action of the surrounding rock and the bolt after tunnel excavation; The specific process is as follows: S3.1. Solve for the relative displacement between any point in the bolt and the surrounding rock during the -th unloading, as well as the shear stress of the bolt; The relative displacement between any point in the bolt and the surrounding rock during the -th unloading is expressed as follows: ; Among them, is the node number of the neutral point of the bolt; After the bolt is installed, it is the th layer of the surrounding rock corresponding to the neutral point of the bolt at the th unloading deformation; After the bolt is installed, it is the deformation of the corresponding th layer of the surrounding rock at the th unloading.

[0034] Furthermore, the judgment method of the position of the neutral point of the bolt is as follows: The position of the neutral point is determined according to the self - balance equation of the bolt; The self - balance equation of the bolt is as follows: ; Among them, is the distance between the neutral point of the bolt and the bolt head, is the distance between any point on the bolt and the bolt.

[0035] Furthermore, as shown in Figure 4 , when specifically solving the position of the neutral point of the bolt, the specific process is as follows: (i) Assume that the position of the neutral point is ; (ii) According to the expression of and the expression of , calculate the relative displacement and shear stress of each node of the bolt by trial calculation in turn; (iii) Substitute the trial calculation result of the shear stress into the self - balance equation of the bolt, and judge whether the shear stress satisfies the self - balance equation; (iv) If not satisfied, adjust the position of the neutral point to , and return to step (ii) to recalculate the relative displacement and shear stress of each node of the bolt until the calculation converges to find a suitable position of the neutral point , and confirm this position of the neutral point as the final position.

[0036] If satisfied, directly determine the position of the neutral point of the bolt as the final position.

[0037] S3.2. Calculate the axial force of the th layer of the bolt at the th unloading based on the shear stress of the bolt; The axial force of the th layer of the bolt at the th unloading is expressed as follows: ; S3.3 Calculate the tensile strain of the bolt based on the linear hardening elastoplastic mechanical model of the bolt ; The tensile strain of the bolt is expressed as follows: ; where, is the cross-sectional area of the bolt.

[0038] Step Four: Calculate the energy density and total energy of the surrounding rock according to the stress path of the surrounding rock; The specific process is as follows: S4.1 Obtain the elastic energy density , plastic dissipation energy density and plastic release energy density of the th layer of the surrounding rock after times of unloading according to the calculation results of the stress path of the surrounding rock; The elastic energy density , plastic dissipation energy density and plastic release energy density are expressed as follows: ; ; ; where, is the plastic dissipation strain, is the plastic release strain, is the natural constant; S4.2 Integrate the energy density components within the plastic zone to obtain the elastic strain energy increment , plastic dissipation energy and plastic release energy of the plastic zone of the surrounding rock in the plastic deformation stage; The elastic strain energy increment , plastic dissipation energy and plastic release energy of the plastic zone of the surrounding rock in the plastic deformation stage are expressed as follows: ; ; where, is the initial elastic energy density of the surrounding rock before tunnel excavation, is the Poisson's ratio of the surrounding rock, is the elastic modulus of the surrounding rock.

[0039] Step 5: Calculate the energy density and total absorbed energy of the anchor bolt according to the stress path of the anchor bolt.

[0040] The specific process is as follows: S5.1. According to the calculation results of the stress path of the anchor bolt, the distribution density of the absorbed energy of the anchor bolt along the length direction ; The distribution density of the absorbed energy of the anchor bolt along the length direction has the following expression: ; S5.2. Integrate the energy density of any point of the anchor bolt along the length direction to solve the absorbed energy of a single anchor bolt during the th unloading. Further, according to the number of anchor bolts contained in the unit length of the tunnel along the longitudinal direction, the total absorbed energy of the anchor bolts in the unit cross-section of the tunnel under plane strain conditions can be obtained ; The total absorbed energy of the anchor bolts in the unit cross-section of the tunnel under plane strain conditions has the following expression: .

[0041] Where: is the differential.

[0042] The above are only the preferred embodiments of the present invention and are not used to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for calculating the energy evolution of a deep tunnel considering the synergistic effect of surrounding rock and anchor bolts, characterized in that: The following steps are involved: Step 1: Establish a deep tunnel calculation model that takes into account the synergistic effect of surrounding rock and anchor bolts, and input the basic parameters of the tunnel model, surrounding rock strength parameters, and anchor bolt material parameters; The basic parameters of the tunnel model include: the excavation radius of the tunnel is , the virtual support reaction force acting on the cave wall is , the original rock stress of the tunnel is , the spacing between adjacent anchor bolts along the tunnel axis is , the angle between adjacent anchor bolts along the circumference of the tunnel is The length of the anchor rod is and the radius of the anchoring zone is ; The surrounding rock strength parameters include: elastic modulus , Poisson's ratio , Uniaxial compressive strength , Peak geological intensity index , rock quality characteristic parameters and the disturbance coefficient ; The anchor material parameters include: shear stiffness between the anchor and slurry interface , the bond strength between the anchor and the grout interface or between the surrounding rock and the grout interface , friction angle of the failure surface of the grouting body , elastic modulus of anchor , Hardening modulus of anchor , yield strength of anchor , Ultimate tensile strength of anchor , yield strain of anchor and the failure strain of the anchor ; Step 2: Based on the deep tunnel calculation model, the stress evolution path of the surrounding rock of the deep tunnel under the synergistic effect of the surrounding rock and anchor after tunnel excavation is solved to obtain the first The surrounding rock mass at the first unloading Radial deformation of the layer ; Step 3: Based on The surrounding rock mass at the first unloading Radial deformation of the layer Solve the stress evolution path of deep tunnel anchors under the synergistic effect of surrounding rock and anchors after tunnel excavation; Step 4: Calculate the energy density and total energy of the surrounding rock according to the stress evolution path of the surrounding rock; Step 5: Calculate the energy density and total absorbed energy of the anchor according to the stress evolution path of the anchor.

2. The method for calculating the energy evolution of a deep tunnel considering the synergistic effect of surrounding rock and anchor bolts according to claim 1 is characterized in that: The deep tunnel calculation model established in step 1 satisfies the following conditions: (I) Assuming the tunnel burial depth is greater than 500m, the ground stress before excavation is a uniformly distributed hydrostatic pressure environment; (II) Assume that the surrounding rock is a homogeneous and isotropic elastic material and the stress state in the plastic stage satisfies the three-dimensional HB strength criterion and the strain increment complies with the non-associated flow law; (III) The mechanical behavior of the interaction between the anchor and the surrounding rock satisfies the bond-slip model. The relationship between the shear stress per unit length of the anchor and the relative displacement between the anchor and the surrounding rock satisfies the following formula: ； in, is the shear stress per unit length of the anchor; is the relative displacement between a certain point on the anchor and the surrounding rock at that position; is the shear stiffness between the anchor and grout interface or between the surrounding rock and grout interface; It is the bond strength between the anchor and grout interface or between the surrounding rock and grout interface; is the friction angle of the failure surface of the grouting body; is the effective diameter of the interface between the anchor and the grouting layer; is the confining pressure per unit length of the anchor rod. For an anchor rod embedded in the surrounding rock, the confining pressure on the anchor rod is equal to the radial stress of the surrounding rock. ; (IV) The relationship between the axial force and tensile deformation of the anchor bolt satisfies the linear strengthening elastic-plastic mechanical model shown in the following formula: ； in, is the axial stress of the anchor rod, is the tensile strain of the anchor rod.

3. The method for calculating the energy evolution of a deep tunnel considering the synergistic effect of surrounding rock and anchor bolts according to claim 2 is characterized in that: Solve The surrounding rock mass at the first unloading Radial deformation of the layer The specific process is as follows: S2.

1. Assume that the stress in the surrounding rock anchoring area satisfies the following equilibrium equation: ； in, is the geometric coefficient of the anchor rod, ; is the distance from any position of the surrounding rock to the center of the circle, is the radial stress of the surrounding rock; The stress in the non-anchored area of ​​the surrounding rock satisfies the following equilibrium equation: ； The stress in the elastic zone of the surrounding rock satisfies the following quantitative relationship: ； The stress in the plastic zone of the surrounding rock satisfies the three-dimensional HB strength criterion; S2.2, calculate surrounding rock stress; Assume a virtual support reaction force acting on the cave wall The original rock stress of the tunnel Gradually uninstall to 0 required The number of the step and surrounding rock layer is , then the finite difference method is used to obtain the The surrounding rock mass at the first unloading The stress of the layer is ,in, is the number of unloading steps for support reaction unloading, is the number of the surrounding rock layer, ; S2.

3. According to the calculation results of surrounding rock stress, solve the surrounding rock Layer relative to Elastic strain increment of the layer ; S2.

4. Combine deformation coordination equation and plastic potential function to solve the total strain of surrounding rock ; S2.

5. Total strain based on surrounding rock , solve The surrounding rock mass at the first unloading Radial deformation of the layer .

4. The method for calculating the energy evolution of a deep tunnel considering the synergistic effect of surrounding rock and anchor bolts according to claim 3 is characterized in that: The specific process of solving the stress evolution path of deep tunnel anchors under the synergistic effect of surrounding rock and anchors after tunnel excavation is as follows: S3.1, based on The surrounding rock mass at the first unloading Radial deformation of the layer , solve for any point in the anchor Relative displacement between the surrounding rock and the first unloading and the shear stress of the anchor; S3.

2. Based on the shear stress of the anchor rod, calculate The first unloading of the anchor Axial force of each layer ; S3.3 Calculation of the tensile strain of anchor bolts based on the linear strengthening elastoplastic mechanical model of anchor bolts .

5. The method for calculating the energy evolution of a deep tunnel considering the synergistic effect of surrounding rock and anchor bolts according to claim 4 is characterized in that: The method for determining the neutral point position of the anchor rod is as follows: The position of the neutral point is determined based on the self-balancing equation of the anchor bolt; The self-balancing equation of the anchor is as follows: ； in, is the distance between the neutral point of the anchor and the anchor head, is the distance between any point on the anchor and the anchor.

6. The method for calculating the energy evolution of a deep tunnel considering the synergistic effect of surrounding rock and anchor bolts according to claim 5 is characterized in that: When solving the neutral point position of the anchor rod, the specific process is as follows: (i) Assume the position of the neutral point to be ; (ii) Based on The expression and The relative displacement and shear stress of each node of the anchor bolt are calculated in turn by using the expression of; the calculated results of shear stress are substituted into the self-balance equation of the anchor bolt; (iii) Determine whether the shear stress satisfies the self-equilibrium equation; (iv) If not satisfied, adjust the neutral point to , and return to (ii); if satisfied, directly determine the neutral point position of the anchor rod as the final position.

7. The method for calculating the energy evolution of a deep tunnel considering the synergistic effect of surrounding rock and anchor bolts according to claim 3 is characterized in that: The specific process of calculating the energy density and total energy of the surrounding rock according to the stress path of the surrounding rock is as follows: S4.

1. According to the calculation results of surrounding rock stress path, the surrounding rock stress path is obtained. Layers are experiencing Elastic energy density after unloading , plastic dissipated energy density and plastic release energy density ; S4.

2. Integrate the energy density component within the plastic zone to obtain the elastic strain energy increment of the surrounding rock plastic zone during the plastic deformation stage. , Plastic dissipated energy and plastic release energy .

8. The method for calculating the energy evolution of a deep tunnel considering the synergistic effect of surrounding rock and anchor bolts according to claim 7 is characterized in that: The specific process of calculating the energy density and total absorbed energy of the anchor according to the stress path of the anchor is as follows: S5.

1. Based on the calculation results of the anchor stress path, the distribution density of the anchor absorbed energy along the length direction ; S5.

2. Integrate the energy density at any point of the anchor along its length and solve The absorbed energy of a single anchor during the first unloading; According to the number of anchors contained in the tunnel unit length along the longitudinal direction, the total absorbed energy of the anchors per unit section of the tunnel under plane strain conditions is obtained. .

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