Calculation method for energy evolution of deep tunnels considering the synergy between surrounding rock and bolts

Abstract

The present invention provides a calculation method for the energy evolution of deep tunnels considering the synergistic effect of surrounding rock and bolts, belonging to the technical field of tunnel engineering; it includes: establishing a calculation model of a deep tunnel considering the synergistic effect of surrounding rock and bolts, and inputting the basic parameters of the tunnel model, the strength parameters of the surrounding rock, and the material parameters of the bolts; solving the stress evolution path of the surrounding rock of the deep tunnel under the synergistic effect of the surrounding rock and bolts after tunnel excavation based on the deep tunnel calculation model; solving the stress evolution path of the bolts in the deep tunnel under the synergistic effect of the surrounding rock and bolts after tunnel excavation; calculating the energy density and total energy of the surrounding rock according to the stress evolution path of the surrounding rock; calculating the energy density and absorbed total energy of the bolts according to the stress evolution path of the bolts. The calculation method for the energy evolution of deep tunnels proposed by the present invention solves the problem of solving the energy field of strain-softening surrounding rock under elastoplastic unloading conditions.

Description

Technical Field

[0001] The present invention belongs to the technical field of tunnel engineering and relates to a calculation method for the 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 amounts of strain energy and belong to high-energy geological environments. The excavation of deep tunnels results in a free face in the surrounding rock around 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 in the near-tunnel area exceeds the energy storage limit, energy dissipation and release will be triggered, which will further induce the 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 it has important significance for the stability evaluation and disaster prevention and control of high in-situ stress deep 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 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 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 the energy evolution of deep tunnels considering the collaborative action of surrounding rock and bolts, including the following steps:

[0005] Step 1: Establish a calculation model for deep tunnels 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;

[0006] 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 rock bolts along the tunnel axis is The included angle between adjacent rock bolts along the circumferential direction of the tunnel is The length of the rock bolt is and the radius of the anchorage area is ;

[0007] 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 ;

[0008] The rock bolt material parameters include: shear stiffness between the rock bolt and the grout interface bonding strength between the rock bolt and the grout interface or between the surrounding rock and the grout interface friction angle of the grout failure surface elastic modulus of the rock bolt hardening modulus of the rock bolt yield strength of the rock bolt ultimate tensile strength of the rock bolt yield strain of the rock bolt and failure strain of the rock bolt ;

[0009] Step 2: Based on the deep tunnel calculation model, solve the stress evolution path of the deep tunnel surrounding rock under the combined action of the surrounding rock and the rock bolts after tunnel excavation;

[0010] 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 rock bolts under the combined action of the surrounding rock and the rock bolts after tunnel excavation;

[0011] Step 4: Calculate the energy density and total energy of the surrounding rock according to the stress evolution path of the surrounding rock;

[0012] Step 5: Calculate the energy density and total absorbed energy of the rock bolts according to the stress evolution path of the rock bolts.

[0013] Furthermore, the deep tunnel calculation model established in Step 1 satisfies the following conditions:

[0014] (I). Assume that the tunnel burial depth is greater than 500 m, and the in-situ stress before excavation is a hydrostatic pressure environment with uniform distribution;

[0015] (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;

[0016] (III) The mechanical behavior of the interaction between the bolt and the surrounding rock satisfies the bond-slip model. 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:

[0017] ;

[0018] 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 the bolt embedded in the surrounding rock, the confining pressure on the bolt is equal to the radial stress of the surrounding rock ;

[0019] (IV) The relationship between the axial force of the bolt and the tensile deformation satisfies the linear hardening elastoplastic mechanical model shown in the following formula:

[0020] ;

[0021] Where, is the axial stress of the bolt, is the tensile strain of the bolt.

[0022] Furthermore, the specific process of solving the radial deformation of the th layer of the surrounding rock during the th unloading is as follows:

[0023] S2.1 Assume that the stress in the bolted area of the surrounding rock satisfies the following equilibrium equation:

[0024] ;

[0025] Where, 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;

[0026] The stress in the unbolted area of the surrounding rock satisfies the following equilibrium equation:

[0027] ;

[0028] The stress in the elastic zone of the surrounding rock satisfies the following quantitative relationship:

[0029] ;

[0030] The stress in the plastic zone of the surrounding rock satisfies the three-dimensional HB strength criterion;

[0031] S2.2. Calculate surrounding rock stress;

[0032] 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 time of 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, ;

[0033] S2.3. According to the calculation results of surrounding rock stress, solve the surrounding rock Layer relative to the Elastic strain increment of the layer ;

[0034] S2.4. Combine the deformation coordination equation and the plastic potential function to solve the total strain of the surrounding rock ;

[0035] S2.5. Total strain based on surrounding rock , solve the The surrounding rock mass at the time of first unloading Radial deformation of the layer .

[0036] Furthermore, 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:

[0037] S3.1, based on The surrounding rock mass at the time of first unloading Radial deformation of the layer , solve any point in the anchor Relative displacement between the surrounding rock and the surrounding rock during the first unloading and the shear stress of the anchor;

[0038] S3.2. Based on the shear stress of the anchor rod, calculate When the anchor rod is unloaded for the first time Axial force of each layer ;

[0039] S3.3. Calculate the tensile strain of the bolt based on the linear hardening elastoplastic mechanical model of the bolt .

[0040] Furthermore, the method for judging the position of the neutral point of the bolt is as follows:

[0041] The position of the neutral point is determined according to the self - balance equation of the bolt;

[0042] The self - balance equation of the bolt is as follows:

[0043] ;

[0044] wherein, 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.

[0045] Furthermore, when specifically solving the position of the neutral point of the bolt, the specific process is as follows:

[0046] (i). Assume the position of the neutral point is ;

[0047] (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; substitute the trial calculation result of the shear stress into the self - balance equation of the bolt;

[0048] (iii). Judge whether the shear stress satisfies the self - balance equation;

[0049] (iv). If not, 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.

[0050] 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:

[0051] S4.1. According to the calculation result 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 ;

[0052] S4.2. Integrate the energy density components within the plastic zone range to obtain the increment of elastic strain energy of the plastic zone of the surrounding rock in the plastic deformation stage, the plastic dissipation energy And plastic release energy .

[0053] Furthermore, the specific process of calculating the energy density and total absorbed energy of the anchor bolt according to the stress path of the anchor bolt is as follows:

[0054] S5.1. According to the calculation results of the anchor bolt stress path, the distribution density of the absorbed energy of the anchor bolt along the length direction ;

[0055] S5.2. Integrate the energy density at any point of the anchor bolt along the length direction to solve the absorbed energy of a single anchor bolt during the th unloading;

[0056] According to the number of anchor bolts contained in the tunnel per unit longitudinal length, obtain the total absorbed energy of the anchor bolts in the unit cross-section of the tunnel under plane strain conditions .

[0057] Compared with the prior art, the present invention has the following beneficial effects:

[0058] (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.

[0059] (2) The deep tunnel energy evolution calculation method proposed by the present invention solves the problem of solving the energy field of the deep tunnel under the synergistic action of the surrounding rock and the anchor bolt. The load-bearing body of the high in-situ stress soft rock tunnel 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 synergistic load-bearing system. The existing research does not involve the energy evolution calculation problem considering the synergistic action of the surrounding rock and the support. The present invention proposes a deep tunnel energy evolution calculation method considering the synergistic action of the surrounding rock and the anchor bolt, which can quantify and clarify the energy regulation effect of the support structure on the surrounding rock.

[0060] 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 to further elaborate on the present invention in detail. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] 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 to the present invention. In the drawings:

[0062] Figure 1It is a schematic diagram of the overall process of a deep tunnel energy evolution calculation method considering the collaborative effect of surrounding rock and bolts in an embodiment of the present invention;

[0063] Figure 2 It is a schematic diagram of the deep tunnel calculation model in an embodiment of the present invention;

[0064] Figure 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;

[0065] Figure 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;

[0066] Figure 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;

[0067] Figure 4 It is a schematic diagram of the relative displacement and shear stress between the surrounding rock and the bolt in an embodiment of the present invention.

[0068] Where:

[0069] 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 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 bolt, and ⑩ is the shear stress distribution curve of the bolt. Detailed implementation manner

[0070] To make the above objects, features, and advantages of the present invention more clearly understood, the following detailed description of the specific implementation manners of the present invention will be given in conjunction with the accompanying drawings. It should be noted that the accompanying 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 embodiments of the present invention; the several mentioned in the present invention are not limited to the specific quantities in the accompanying drawing examples; the orientation or positional relationships indicated by 'front','middle', 'back', 'left', 'right', 'top', 'bottom','middle', etc. in the present invention are all based on the orientation or positional relationships shown in the accompanying 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 they be construed as a limitation to the present invention.

[0071] Embodiment:

[0072] See Figure 1 As shown, a deep tunnel energy evolution calculation method considering the collaborative effect of surrounding rock and bolts provided by the present invention includes the following steps:

[0073] Step 1. Establish a deep tunnel calculation model 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;

[0074] 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 in-situ stress of the rock mass where the tunnel is located is , the layout spacing of adjacent rock bolts along the tunnel axis is , the included angle between adjacent rock bolts along the circumferential direction of the tunnel perimeter is , the length of the rock bolt is and the radius of the anchorage zone is ;

[0075] Preferably, the surrounding rock strength parameters include: elastic modulus , Poisson's ratio , uniaxial compressive strength , peak geological strength index , rock mass quality characteristic parameter and disturbance coefficient ; among them: 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 quality characteristic parameter and disturbance coefficient are obtained according to the data from the on-site survey of the surrounding rock at the tunnel face and then by using the chart prediction method. Specifically, the chart prediction method is an existing technology.

[0076] Preferably, the rock bolt material parameters include: the shear stiffness between the rock bolt and the grout interface , the bond strength between the rock 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 rock bolt , the hardening modulus of the rock bolt , the yield strength of the rock bolt , the ultimate tensile strength of the rock bolt , the yield strain of the rock bolt and the failure strain of the rock bolt . Among them: the shear stiffness , the bond strength and the bond strength are obtained through the pull-out test of the rock bolt, and the other strength parameters are found according to the "Code for Design of Steel Structures" (GB 50017-2017).

[0077] The calculation model of the deep tunnel needs to meet the following conditions:

[0078] (I). Assume that the tunnel burial depth is large enough (burial depth greater than 500 m), and the in-situ stress before excavation is a hydrostatic pressure environment with uniform distribution.

[0079] (II). Rock is taken at the tunnel burial depth, and the rock is a homogeneous and isotropic elastic material. 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.

[0080] (III). The mechanical behavior of the interaction between the bolt and the surrounding rock satisfies the bond-slip model. 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:

[0081] ;

[0082] 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 grout 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 ;

[0083] (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:

[0084] ;

[0085] where is the axial stress of the bolt, is the tensile strain of the bolt.

[0086] Further, the expression of the three-dimensional H-B strength criterion is as follows:

[0087] ;

[0088] ;

[0089] ;

[0090] ;

[0091] ;

[0092] ;

[0093] 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 respectively 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 the deep-buried tunnel.

[0094] Furthermore, the strain increment of the rock in the plastic zone conforms to the non-associated flow rule and satisfies the plastic potential function ;

[0095] The plastic potential function has the following expression:

[0096] ;

[0097] wherein, is the plastic radial strain increment, is the plastic circumferential strain increment, is the dilatancy coefficient of the rock.

[0098] 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;

[0099] The strain-softening model of the surrounding rock in the plastic stage has the following expression:

[0100] ;

[0101] ;

[0102] wherein, is the plastic deviatoric strain of the rock, which is the plastic circumferential strain and plastic radial strain difference; is the critical plastic deviatoric strain of rock; The geological strength index of rock The peak value of is also its initial value; The geological strength index of rock The residual value of .

[0103] 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 time of first unloading Radial deformation of the layer );

[0104] The details are as follows:

[0105] S2.1. The stress in the surrounding rock anchorage area must satisfy the following equilibrium equation:

[0106] ;

[0107] 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.

[0108] The stress in the non-anchored area of the surrounding rock must satisfy the following equilibrium equation:

[0109] ;

[0110] The stress in the elastic zone of the surrounding rock must satisfy the following quantitative relationship:

[0111] ;

[0112] The stress in the plastic zone of the surrounding rock must meet the three-dimensional HB strength criterion.

[0113] S2.2. Calculate the surrounding rock stress; the specific process is as follows:

[0114] As shown in Figures 3(a) to 3(c), 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 according to the relationship between the radius of the anchoring zone and the radius of the plastic zone.

[0115] 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.

[0116] Furthermore, when calculating the stresses in the elastic zone with anchors, the elastic zone without anchors, the plastic zone with anchors, and the plastic zone without anchors, the finite difference method is used to solve 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 time of 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, .

[0117] S2.3. According to the calculation results of surrounding rock stress, solve the surrounding rock Elastic strain of the layer ;

[0118] The specific process is as follows:

[0119] According to Hooke's law, the surrounding rock Layer relative to the Elastic strain increment of the layer , and then get the surrounding rock Elastic strain of the layer ;

[0120] Surrounding rock Layer relative to the Elastic strain increment of the layer The expression is as follows:

[0121] ;

[0122] Surrounding rock Elastic strain of the layer The expression is as follows:

[0123] ;

[0124] ;

[0125] Among them, is the stress increment of the th layer relative to the th layer;

[0126] S2.4. Simultaneously solve the deformation coordination equation and the plastic potential function to obtain the total strain of the surrounding rock ;

[0127] The expression of the total strain of the surrounding rock is as follows:

[0128] ;

[0129] ;

[0130] .

[0131] 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;

[0132] The plastic strain increment of the th layer of the surrounding rock relative to the th layer is expressed as follows:

[0133] ;

[0134] The plastic strain of the th layer of the surrounding rock is expressed as follows:

[0135] ;

[0136] 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;

[0137] ;

[0138] Among them, is the radius of the th layer of the surrounding rock.

[0139] Step Three. Based on the Radial deformation of the th layer of surrounding rock during the second unloading; solve the stress evolution path of the deep tunnel bolt under the co - action of the surrounding rock and the bolt after tunnel excavation;

[0140] The specific process is as follows:

[0141] S3.1. Solve the relative displacement between any point in the bolt and the surrounding rock during the second unloading and the shear stress of the bolt;

[0142] The relative displacement between any point in the bolt and the surrounding rock during the second unloading is expressed as follows:

[0143] ;

[0144] where, is the node number of the neutral point of the bolt; is the deformation of the th layer of surrounding rock corresponding to the neutral point of the bolt after the bolt is installed during the second unloading; is the deformation of the corresponding th layer of surrounding rock during the second unloading after the bolt is installed.

[0145] Furthermore, the judgment method of the position of the neutral point of the bolt is as follows:

[0146] The position of the neutral point is determined according to the self - balance equation of the bolt;

[0147] The self - balance equation of the bolt is as follows:

[0148] ;

[0149] where, 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.

[0150] Furthermore, as shown in Figure 4 when specifically solving the position of the neutral point of the bolt, the specific process is as follows:

[0151] (i). Assume the position of the neutral point is ;

[0152] (ii). According to the expressions of and , calculate the relative displacement and shear stress of each node of the bolt by trial calculation in turn;

[0153] (iii) Substitute the trial result of the shear stress into the self - equilibrium equation of the bolt, and determine whether the shear stress satisfies the self - equilibrium equation;

[0154] (iv) If not satisfied, adjust the position of the neutral point to , and return to step (ii) to recalculate the relative displacements and shear stresses of each node of the bolt until the calculation converges to find a suitable neutral point position , and confirm this neutral point position as the final position.

[0155] If satisfied, directly determine the neutral point position of this bolt as the final position.

[0156] S3.2 Calculate the axial force of the - th unloading of the - th layer of the bolt based on the shear stress of the bolt; ;

[0157] The axial force of the - th layer of the bolt at the - th unloading is expressed as follows: ;

[0158] ;

[0159] S3.3 Calculate the tensile strain of the bolt based on the linear hardening elastoplastic mechanical model of the bolt ;

[0160] The tensile strain of the bolt is expressed as follows:

[0161] ;

[0162] Among them, is the cross - sectional area of the bolt.

[0163] Step Four: Calculate the energy density and total energy of the surrounding rock according to the stress path of the surrounding rock;

[0164] The specific process is as follows:

[0165] S4.1 Obtain the elastic energy density of the - th layer of the surrounding rock, the plastic dissipation energy density and the plastic release energy density after the - th unloading of the surrounding rock according to the calculation result of the stress path of the surrounding rock;

[0166] The elastic energy density , the plastic dissipation energy density and the plastic release energy density are expressed as follows:

[0167] ;

[0168] ;

[0169] ;

[0170] wherein, is the plastic dissipation strain, is the plastic release strain, is the natural constant;

[0171] S4.2. Integrate the energy density component within the plastic zone to obtain the elastic strain energy increment of the plastic zone of the surrounding rock in the plastic deformation stage, the plastic dissipation energy and the plastic release energy ;

[0172] The elastic strain energy increment of the plastic zone of the surrounding rock in the plastic deformation stage, the plastic dissipation energy and the plastic release energy are expressed as follows:

[0173] ;

[0174] ;

[0175] wherein, is the initial elastic strain 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.

[0176] Step Five. Calculate the energy density and total absorbed energy of the bolt according to the stress path of the bolt.

[0177] The specific process is as follows:

[0178] S5.1. According to the calculation result of the bolt stress path, the distribution density of the absorbed energy of the bolt along the length direction;

[0179] The distribution density of the absorbed energy of the bolt along the length direction is expressed as follows:

[0180] ;

[0181] S5.2. Integrate the energy density of any point on the bolt along the length direction to solve the The absorbed energy of a single bolt during the secondary unloading, and further based on the number of bolts included in the tunnel per unit length along the longitudinal direction, the total absorbed energy of the bolts per unit cross-section of the tunnel under plane strain conditions can be obtained. ;

[0182] The total absorbed energy of the bolts per unit cross-section of the tunnel under plane strain conditions has the following expression:

[0183] .

[0184] Where: is the differential.

[0185] 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 modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A calculation method for the energy evolution of deep tunnels considering the synergy between surrounding rock and bolts, characterized in that It includes the following steps: Step 1: Establish a calculation model for deep tunnels considering the synergistic effect 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 R0, the virtual support reaction force acting on the tunnel wall is P i , the in-situ rock stress where the tunnel is located is P0, the layout spacing of adjacent bolts along the tunnel axis is L Z , the angle between adjacent bolts along the circumferential direction of the tunnel perimeter is ω, the length of the bolt is L b and the radius of the anchorage zone is R b ; The surrounding rock strength parameters include: elastic modulus E, Poisson's ratio v, uniaxial compressive strength σ c , peak geological strength index GSI p , rock mass quality characteristic parameter m i and disturbance coefficient D; The bolt material parameters include: the shear stiffness K between the bolt and the grout interface b , the bond strength c between the bolt and the grout interface or between the surrounding rock and the grout interface s , the friction angle of the grout failure surface the elastic modulus E of the bolt b1 , the hardening modulus E of the bolt b2 , the yield strength σ of the bolt by , the ultimate tensile strength σ of the bolt bmax , the yield strain ε of the bolt by and the failure strain ε of the bolt bmax ; Step 2: Solve the total strain of the surrounding rock based on the deep tunnel calculation model and the plastic strain of the j-th layer of the surrounding rock Furthermore, obtain the radial deformation of the j-th layer of the surrounding rock during the i-th unloading Step 3: Based on the radial deformation of the j-th layer of surrounding rock during the i-th unloading Solve for the tensile strain of the bolt Step 4. According to the total strain of the surrounding rock and the plastic strain of the j-th layer of the surrounding rock calculate the elastic energy density of the j-th layer of the surrounding rock after the i-th unloading plastic dissipation energy density and plastic release energy density as well as the increment of elastic strain energy E e(i) in the plastic zone of the surrounding rock during the plastic deformation stage, plastic dissipation energy E pd(i) and plastic release energy E pr(i) ; Step 5. According to the tensile strain of the bolt Calculate the distribution density of the energy absorbed by the bolt along the length direction And the total energy absorbed by the bolts per unit cross-section of the tunnel under plane strain conditions, E b (i) ; The calculation model for deep tunnels established in Step 1 satisfies the following conditions: (Ⅰ). Assume that the tunnel depth is greater than 500 m, 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 bolts 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, τ b is the shear stress per unit length of the bolt; u rb is the relative displacement between a certain point on the bolt and the surrounding rock at this position; K b is the shear stiffness between the bolt and the grout interface or between the surrounding rock and the grout interface; c s 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; D s is the effective diameter of the interface between the bolt and the grouting layer; σ t is the confining pressure per unit length of the bolt. For the bolt embedded in the surrounding rock, the confining pressure on the bolt is equal to the radial stress σ θ 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, σ b is the axial stress of the bolt, and ε b is the tensile strain of the bolt.

2. The deep tunnel energy evolution calculation method considering the synergistic effect of surrounding rock and bolt according to claim 1, characterized in that Solve the radial deformation of the j-th layer of surrounding rock during the i-th unloading The specific process is as follows: S2.

1. Assume that the stress in the bolted area of the surrounding rock satisfies the following equilibrium equation: where N0 is the bolt geometric coefficient, and N0 = πD s / ωL Z ; r is the distance from any position of the surrounding rock to the center of the circle, and σ r is the radial stress of the surrounding rock; The stress in the unbolted 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; σ r +σ θ =2P0; 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. Let the virtual support reaction force \(P\) acting on the tunnel wall i If it takes \(I\) steps to gradually unload the initial rock stress \(P_0\) acting on the tunnel to \(0\), and the number of the surrounding rock layer is \(j\), then the stress of the \(j\)-th layer of the surrounding rock at the \(i\)-th unloading step is obtained by the finite difference method as where \(I\) is the number of unloading steps of the support reaction force unloading, \(j\) is the number of the surrounding rock layer, and \(i=(1, 2, \cdots, I)\); S2.

3. Solve for the elastic strain increment of the j-th layer of the surrounding rock relative to the (j + 1)-th layer according to the calculation results of the surrounding rock stress S2.

4. Simultaneously establish the deformation compatibility equation and the plastic potential function to solve the total strain of the surrounding rock S2.

5. Based on the total strain of surrounding rock Solve the radial deformation of the j-th layer of surrounding rock during the i-th unloading 3. The method for calculating the energy evolution of deep tunnels considering the synergistic effect of surrounding rock and anchor bolts according to claim 2, characterized in that The specific process of solving the stress evolution path of the bolts in the deep tunnel under the synergistic action of the surrounding rock and bolts after tunnel excavation is as follows: S3.

1. Based on the radial deformation of the j-th layer of surrounding rock during the i-th unloading Solve the relative displacement between any point on the bolt and the surrounding rock during the i-th unloading and the shear stress of the bolt; S3.

2. Calculate the axial force of the j-th layer of the bolt at the i-th unloading based on the shear stress of the bolt S3.

3. Calculate the tensile strain of the bolt based on the linear hardening elastoplastic mechanical model of the bolt 4. The calculation method for the energy evolution of deep tunnels considering the collaborative effect of surrounding rock and bolts according to claim 3, characterized in that, The judgment method for the position of the neutral point of the bolt is as follows: The position of the neutral point is determined according to the self-balanced equation of the bolt. The self-balanced equation of the bolt is as follows: Among them, L ρ is the distance between the neutral point of the anchor rod and the anchor head, and L is the distance between any point on the anchor rod and the anchor rod.

5. The calculation method for the energy evolution of deep tunnels considering the collaborative effect of surrounding rock and bolts according to claim 4, characterized in that, 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 ρ″. (ii), according to 's expression and τ b 's expression, calculate the relative displacements and shear stresses of each node of the bolt in turn; substitute the trial calculation results of the shear stress into the self - equilibrium equation of the bolt; (ⅲ). Judge whether the shear stress satisfies the self-balanced equation. (ⅳ). If not, adjust the position of the neutral point to ρ′ and return to (ⅱ); if it satisfies, directly determine the position of the neutral point of the bolt as the final position.

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 2, wherein 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. Obtain the elastic energy density of the j-th layer of surrounding rock after i times of unloading according to the calculation results of the surrounding rock stress path Plastic dissipation energy density And plastic release energy density S4.

2. Integrate the energy density component within the plastic zone range to obtain the increment of elastic strain energy \(E\) of the surrounding rock plastic zone in the plastic deformation stage e(i) , plastic dissipation energy \(E\) pd(i) and plastic release energy \(E\) pr(i) .

7. The method for calculating the energy evolution of a deep tunnel considering the synergistic effect of surrounding rock and bolts according to claim 6, characterized in that The specific process of calculating the energy density and total absorbed energy of the bolt according to the stress path of the bolt is as follows: S5.

1. Distribution density of the energy absorbed by the anchor bolt along the length direction according to the calculation results of the stress path of the anchor bolt S5.

2. Integrate the energy density of any point on the bolt along the length direction to solve the absorbed energy of a single bolt during the i-th unloading. According to the number of rock bolts contained in a unit length along the longitudinal direction of the tunnel, the total absorption energy E of the rock bolts in the unit cross-section of the tunnel under plane strain conditions is obtained b (i) 。

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