A method for quickly determining supporting time of deep-buried tunnel considering three-dimensional strength of rock mass

Abstract

The present application relates to a kind of deep-buried tunnel support opportunity fast determination method considering rock mass three-dimensional strength, comprising: based on tunnel engineering field geological detection, excavation face rock mass parameter digitization in-situ test and analysis, real-time acquisition and dynamic update tunnel excavation face rock mass in-situ mechanical parameter and engineering parameter, and determine rock mass strength parameter;Based on rock mass in-situ mechanical parameter, engineering parameter and rock mass strength parameter, establish the tunnel three-dimensional elastic-plastic mechanics analytical model considering rock mass three-dimensional strength and longitudinal axial stress, solve the maximum deformation of surrounding rock and plastic zone radius;Based on the maximum deformation of surrounding rock and plastic zone radius, determine the tunnel longitudinal surrounding rock deformation curve equation considering rock mass three-dimensional strength and longitudinal axial stress;Based on tunnel surrounding rock deformation stability index and tunnel longitudinal surrounding rock deformation curve equation, determine initial lining, two lining support opportunity, and guide construction driving rate.Compared with prior art, the present application has the advantages of fast calculation, considering factors.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of tunnel support structure design, and particularly relates to a deep-buried tunnel support timing rapid determination method considering three-dimensional strength of rock mass. BACKGROUND

[0002] A large number of and long-term field stress monitoring results show that the excavation process of deep-buried rock mass tunnel is often in a true three-dimensional stress state, and the stress size and direction will change significantly during the tunnel excavation process, further increasing the complexity of the surrounding rock stress. The engineering disaster problem caused by stress redistribution due to excavation unloading is particularly significant in deep-buried tunnels, and the fundamental reason is the nonlinear mechanical response of unloading rock mass under high ground stress and complex stress environment. Shallow rock mass engineering is mostly in the observation and empirical design stage, and deep engineering puts forward higher requirements for dynamic design to cope with deep rock mass with high concealment and strong uncertainty. The variation of calculation parameters is large, the three-dimensional spatial effect of excavation and the uncertainty of longitudinal influence range are large, and the best state of support timing and surrounding rock stability cannot be guaranteed. Compared with shallow tunnels, the three-dimensional spatial effect of deep-buried tunnel excavation and the longitudinal influence range of excavation are very wide, and if the surrounding rock stability support time design directly follows the experience of shallow tunnels, there will be more unreleased deformation after support, which will be acted on the support structure under the action of subsequent excavation, resulting in multiple steel arches to release the subsequent incremental deformation and stress, causing the safety of tunnel surrounding rock, construction period, etc. In addition, the unloading rock mass of shallow burial is mainly in a low stress state, and two-dimensional excavation analysis theory (such as two-dimensional Hoek-Brown strength criterion) is sufficient. However, deep engineering is in a true three-dimensional high stress state, which is a significant three-dimensional and nonlinear system, and accurate analysis must be based on a strength theory that can reflect the essential characteristics of rock mass, such as GZZ rock mass three-dimensional strength theory, to overcome the inapplicability of two-dimensional or linear strength criterion in deep engineering. At the same time, the longitudinal axial stress has a very important influence on the stress, strength, deformation and stability of the surrounding rock, and the existing analysis model mainly uses the plane strain model and does not consider the longitudinal axial stress (often the intermediate principal stress) of the tunnel, resulting in a large difference between the analysis results and the true situation.

[0003] The convergence-confinement method based on the full exertion of the self-bearing capacity of the surrounding rock emphasizes that the surrounding rock and the support jointly bear the excavation load, and becomes the mainstream of the stability analysis and support design of the tunnel, and with the application and popularization of the field monitoring measurement technology and the three-dimensional strength theory of the rock mass, the convergence-confinement method is further improved. The longitudinal deformation curve of the surrounding rock is an important part of the convergence-confinement method, can intuitively reflect the spatial effect of the deformation of the surrounding rock in the tunnel excavation process, and can provide an intuitive theoretical basis for determining the position of the primary support relative to the excavation surface. However, with the increase of the overburden depth and the stress level of the rock mass, the three-dimensional mechanical properties and the nonlinear mechanical characteristics of the rock mass are more obvious. The design and analysis method of the shallow rock mass engineering under the self-weight stress field cannot be directly migrated to the deep rock mass engineering (three-dimensional and nonlinear system). If the support timing of the primary support is too early, the primary support bears a large load, and the support may be damaged, and if the deformation is large, the possibility of the instability and collapse of the surrounding rock is large. It is very important for the fine support design of the deep tunnel to accurately and quickly obtain the LDP curve, correctly understand the three-dimensional spatial effect of the deep tunnel, and formulate the support scheme of the support timing.

[0004] In addition, after the tunnel is excavated, due to the stress release, the initial stress field of the surrounding rock will be redistributed, and when the surrounding rock strength is small or the initial stress is large at different depths, the surrounding rock will be plastically yielded and damaged, and the damage range directly affects the prediction of the plastic deformation on the LDP curve, so it is particularly important to accurately use the rock mass mechanical model and the plastic flow method. The three-dimensional strength effect, the strain softening effect and the dilatancy effect are typical mechanical characteristics of the rock mass after the peak, however, the existing LDP curve estimation method involves less, and it is difficult for the engineering personnel to use the support timing under a certain depth and geological condition from the quantitative angle. SUMMARY

[0005] The purpose of the present application is to provide a deep tunnel support timing quick determination method considering the three-dimensional strength of rock mass, reducing the subjectivity of support timing determination.

[0006] The purpose of the present application can be realized by the following technical solutions:

[0007] A deep tunnel support timing quick determination method considering the three-dimensional strength of rock mass, comprising the following steps:

[0008] Step 1) Based on the tunnel engineering field geological exploration, the in-situ test and analysis of the rock mass parameters of the excavation surface, the in-situ mechanical parameters and engineering parameters of the rock mass of the tunnel excavation surface are obtained and dynamically updated in real time, and the strength parameters of the rock mass are determined based on the in-situ mechanical parameters of the rock mass;

[0009] Step 2) Based on the in-situ mechanical parameters of rock mass, engineering parameters and rock mass strength parameters, a three-dimensional elastic-plastic mechanics analytical model of tunnel considering three-dimensional strength of rock mass and longitudinal axial stress is established to solve the maximum deformation of surrounding rock and the radius of plastic zone;

[0010] Step 3) Based on the maximum deformation of surrounding rock and the radius of plastic zone, the longitudinal deformation curve equation of surrounding rock of tunnel considering three-dimensional strength of rock mass and longitudinal axial stress is determined;

[0011] Step 4) Based on the deformation stability index of surrounding rock of tunnel and the longitudinal deformation curve equation of surrounding rock of tunnel, the supporting time of primary lining and secondary lining is determined, and the construction advancing rate is guided.

[0012] The in-situ mechanical parameters of rock mass include initial ground stress, strain softening coefficient, hardness of rock, uniaxial compressive strength of rock, geological strength index and blasting disturbance coefficient.

[0013] The engineering parameters include tunnel radius and supporting force.

[0014] The calculation method of rock mass strength parameters based on in-situ mechanical parameters of rock mass is as follows:

[0015]

[0016] Wherein, m b , s and a are rock mass strength parameters, m i , GSI and D are in-situ mechanical parameters of rock mass, m i is the hardness of rock, GSI is the geological strength index, and D is the blasting disturbance coefficient.

[0017] The step 2) includes the following steps:

[0018] Step 2-1) Based on the three-dimensional elastic-plastic mechanics analytical model of tunnel considering three-dimensional strength of rock mass and longitudinal axial stress, the radial stress at the boundary between elastic and plastic regions is solved, and the plastic zone is divided into N annuli according to the radial stress, and the difference between the inner and outer radial stress of each annulus is constant, that is, the equidifference radial stress is:

[0019]

[0020] Wherein, σ r is the radial stress, σ ep is the elastic-plastic boundary radial stress, p i is the support reaction of the cavity, N is the number of annuli, which is determined according to the calculation accuracy, the larger N is, the more annuli are divided, and the more accurate the calculation result is; r refers to the distance from the rock mass unit to the center of the tunnel;

[0021] The elastic-plastic boundary is the outer boundary of the first annulus, that is, r (0) =R ep , Rep is the plastic zone radius; at the hole wall, r (N) = R0, R0 is the chamber excavation radius;

[0022] At the elastic-plastic interface, the stress should satisfy both the elastic zone stress equation and the yield criterion, so the initial values of the stress and strain components of the surrounding rock at the elastic-plastic boundary of the surrounding rock are:

[0023]

[0024] where, σ θ is the circumferential stress, σ z is the axial stress, ε θ is the hoop strain, ε z is the axial strain, and ε r is the radial strain, the subscript (0) represents the initial value, p is the in-situ rock stress, q is the out-of-plane axial stress, and G is the shear modulus.

[0025] Step 2-2) The strength criterion adopts the smooth GZZ three-dimensional strength yield criterion considering the intermediate principal stress, and at the elastic-plastic boundary, we have:

[0026]

[0027] Or use:

[0028]

[0029] where, I1, J2 and J3 are the first stress invariant, the second invariant of deviatoric stress and the third invariant of deviatoric stress, respectively, i = 1, 2, 3…N, m b , s, a are the rock mass strength parameters, σ c is the uniaxial compressive strength of the rock,

[0030] When the smooth GZZ criterion is used, the yield characteristics of the surrounding rock are independent of the size order of the principal stresses, and the out-of-plane axial stress σ z may be any principal stress.

[0031] Considering the weakening of the rock mass strength parameter GSI, the initial GSI is considered to be the peak GSI p , and the most important parameter of the plastic internal variable is the plastic shear strain where, is the maximum plastic strain, is the minimum plastic strain, then the GSI is assumed to have a linear softening relationship with γ p as shown below:

[0032]

[0033] where, γ p,*is the maximum plastic shear strain, γ p plastic shear strain, GSI r is the peak GSI, GSI r is the residual GSI:

[0034] GSI r = GSI p exp(-0.0134 GSI p )

[0035] Supplementary equation considering longitudinal axial stress:

[0036]

[0037] where β = 1, θ σ(i) refers to Lode angle, S z(i) refers to z-direction deviatoric stress, β is non-associated flow coefficient,

[0038] Z-direction deviatoric stress S z(i) = σ z(i) -I 1(i) / 3;

[0039] Solving the supplementary equation considering longitudinal axial stress and the strength criterion, the three-direction stress expression in each ring of plastic zone is obtained;

[0040] Step 2-3) Determine the expression of surrounding rock displacement:

[0041] The difference form of the equilibrium equation is:

[0042]

[0043] Since r (i) is an unknown, r (i) = R ep ρ (i) is used instead, and from r (0) = R ep and r (N) = R0, it can be known that ρ (0) = 1, ρ (N) = R0 / R ep , the above formula is rewritten as:

[0044]

[0045] where ρ is the density;

[0046] Based on the calculated Δσ r in step 2-1), the following is obtained:

[0047]

[0048]

[0049] The transformation formula is introduced as:

[0050]

[0051] wherein u r is the radial displacement;

[0052] The geometric equation is expressed as:

[0053]

[0054] According to the non-associated plastic flow method, the following is obtained:

[0055]

[0056] wherein λ is a plastic flow parameter, is the radial elastic strain, is the radial plastic strain, is the hoop elastic strain, is the hoop plastic strain;

[0057] Substituting the geometric equation into the above formula, the differential equation that the i-th ring body should satisfy is obtained by using difference instead of differential and simplifying:

[0058]

[0059] Substituting the transformation formula and the geometric equation into the above formula, the differential equation that the i-th ring body should satisfy is obtained by using difference instead of differential and simplifying:

[0060]

[0061] In the formula, is a known quantity; ψ is a shear dilatancy angle;

[0062] and According to the incremental Hooke's law, the following is obtained:

[0063]

[0064] wherein E is an elastic modulus, and ν is a Poisson's ratio;

[0065] The boundary condition of the differential equation is:

[0066]

[0067] Substituting ρ = ρ (i) into the differential equation that satisfies the boundary condition, the solution of the differential equation is:

[0068]

[0069] where A (i) , B (i) , C (i) are known quantities and are obtained by:

[0070]

[0071] where at the elastic-plastic boundary, then the boundary conditions give ε r(i) and ε θ(i) ;

[0072] After N calculations, the values of ρ (N) and the plastic zone radius R ep =R0 / ρ (N) at the wall are obtained; then r (i) =ρ (i) R ep and are used to obtain r (i) and u r(i) ;

[0073] Step 2-4) Determine the plastic zone radius expression of surrounding rock:

[0074] R ep =r (0) / ρ (N)

[0075] r (i) =R ep ρ (i)

[0076] u r(i) =–ε θ(i) r (i)

[0077] and gradually solve the maximum deformation of surrounding rock, the maximum plastic zone radius of surrounding rock, the circumferential strain and radial stress of each layer when the support pressure is 0.

[0078] The tunnel longitudinal surrounding rock deformation curve equation of the step 3) is:

[0079]

[0080] where u * is the dimensionless deformation of surrounding rock; is the dimensionless plastic zone radius, is the plastic zone radius at the maximum deformation, and R0 is the excavation radius of the cavern; x * =x / R0 is the dimensionless distance from the cross section to the excavation surface, and x≤0 is the unexcavated rock mass; is the displacement release coefficient of the cross section of the surrounding rock at the excavation surface, and u0 is the displacement of the wall.max is the maximum stable displacement of the excavated section away from the face.

[0081] The tunnel surrounding rock deformation stability index comprises:

[0082] Surrounding rock displacement release coefficient u * , i.e. the non-dimensional deformation of the surrounding rock, reflecting the degree of deformation release of the surrounding rock;

[0083] Surrounding rock longitudinal deformation rate k, reflecting the speed of deformation release of the surrounding rock along the longitudinal direction of the tunnel:

[0084] k = du * / dx

[0085] Tunnel face excavation rate V, reflecting the excavation distance per unit time:

[0086] V = dx / dt

[0087] Wherein, x is the distance of the section from the face.

[0088] Surrounding rock cross-sectional deformation rate s, reflecting the speed of vertical deformation of the surrounding rock in the cross section of the tunnel:

[0089] s = du / dt

[0090] Wherein, u is the cross-sectional deformation of the surrounding rock.

[0091] The initial lining and secondary lining support timing is determined according to the following method:

[0092] Surrounding rock deformation index I: when the surrounding rock longitudinal deformation rate k reaches the maximum, the non-dimensional distance of the section from the face is x1, which is considered to be the fastest deformation of the surrounding rock, and the surrounding rock is the most unstable at this time, which is the timing of the initial lining;

[0093] Surrounding rock deformation index II: when u * ≥ 0.9, the non-dimensional distance of the section from the face is x2, which is considered to be gradually stable, and is the first timing of the secondary lining;

[0094] Surrounding rock deformation index III: when the surrounding rock cross-sectional deformation rate s ≤ 1 mm / d, it is considered that the surrounding rock is gradually stable, and the non-dimensional distance of the section from the face at this time is x2', which is the second timing of the secondary lining;

[0095] x1 is the timing of the initial lining, max(x2, x2') is the timing of the secondary lining, wherein x1 < max(x2, x2'), the range of the non-dimensional distance of the section from the face between x1 and max(x2, x2') is the influence range of the LDP curve, which is a transition section of the initial support gradually stable, i.e. the step excavation step distance and length.

[0096] Based on the tunnel surrounding rock deformation stability index and the tunnel longitudinal surrounding rock deformation curve equation, the relationship among the surrounding rock longitudinal deformation rate k, the tunnel face excavation rate V and the cross section surrounding rock vertical deformation rate s is obtained as follows:

[0097]

[0098] The construction excavation rate is guided based on the above formula.

[0099] The cross section surrounding rock deformation rate s is calculated by the excavation model or obtained by the surrounding rock deformation monitoring in the construction site, and the maximum value between the two is taken for safety.

[0100] Compared with the prior art, the present application has the following beneficial effects:

[0101] (1) The present application uses digital in-situ testing technology to quickly obtain mechanical parameters, fully considers the influence of deep unloading rock mass three-dimensional strength and tunnel longitudinal axial stress (intermediate principal stress) on tunnel three-dimensional space effect and LDP curve characteristics, and can reflect the effects of deep rock mass dilatancy characteristics, strain softening, residual strength and geological joint fracture development, etc., more truly considers the nonlinear mechanical characteristics and engineering response of deep true three-dimensional high stress unloading rock mass, can be applied to deep rock mass with high concealment and spatial variability, effectively avoids the over-reliance on shallow tunnel engineering experience and blind use of deep buried tunnel support timing, and improves the reliability and scientificity of deep buried tunnel support design calculation and analysis.

[0102] (2) The present application can quickly calculate the LDP curve and analyze the tunnel excavation three-dimensional space effect and longitudinal influence range, and establish the relationship among the tunnel surrounding rock longitudinal deformation rate, the surrounding rock cross section deformation rate, the maximum surrounding rock deformation and the tunnel excavation rate, which can provide scientific basis and technical support for deep / ultra-deep buried tunnel dynamic design and construction. BRIEF DESCRIPTION OF DRAWINGS

[0103] Figure 1 The present application is a method flowchart;

[0104] Figure 2 It is a deep buried tunnel three-dimensional elastoplastic mechanics analytical model diagram considering rock mass three-dimensional strength and longitudinal axial stress;

[0105] Figure 3 It is a longitudinal displacement curve comparison diagram calculated by considering H-B and GZZ rock mass strength criteria respectively in the embodiment;

[0106] Figure 4 It is a surrounding rock longitudinal deformation curve diagram considering different buried depths in the embodiment. DETAILED DESCRIPTION

[0107] The application will be described in detail below in combination with the drawings and specific embodiments. The embodiments are implemented on the premise of the technical solutions of the application, and detailed implementation modes and specific operation processes are given, but the protection scope of the application is not limited to the following embodiments.

[0108] The embodiment provides a quick determination method for deep-buried tunnel support timing considering three-dimensional strength of a rock mass, as shown in the figure, comprising the following steps: Figure 1

[0109] Step 1) Based on tunnel engineering site geological exploration, digital in-situ test and analysis of rock mass parameters of an excavation surface, real-time acquisition and dynamic update of in-situ mechanical parameters and engineering parameters of the rock mass of the tunnel excavation surface are performed, and rock mass strength parameters are determined based on the in-situ mechanical parameters of the rock mass.

[0110] In the embodiment, the in-situ mechanical parameters of the rock mass include initial ground stress, strain softening coefficient, and the softness and hardness degree m i of the rock, the uniaxial compressive strength σ ci of the rock, the geological strength index GSI, and the blasting disturbance coefficient D; the engineering parameters include the tunnel radius and the support force.

[0111] In the embodiment, the in-situ mechanical parameters and engineering parameters of the rock mass are set as follows: p = 40 MPa; GSI = 50, σ ci = 50 MPa, E = 4.5 GPa, v = 0.35, m i = 6, D = 0, ψ = 8°, R0 = 5 m; p i = 2 MPa.

[0112] Specifically, three-dimensional laser scanning is used to extract geometric information (three-dimensional trace occurrence, group number and distribution form, etc.) of structural planes such as joint fissures of the rock mass of the tunnel excavation surface for each excavation surface, through section information and corresponding digital processing procedures, the joint fissure distribution characteristics of the rock mass of the excavation surface are obtained, and the H-B strength parameters GSI and D are obtained by using the parameter value method recommended by Hoek et al., for reference: Hoek E, Marinos P. Predicting Tunnel Squeezing Problems in Weak Heterogeneous Rock Masses [J]. Tunnels and Tunnelling International. 2000, 32 (11): 45-51, which will not be repeated here.

[0113] The calculation method for determining the rock mass strength parameters based on the in-situ mechanical parameters of the rock mass is as follows:

[0114]

[0115] wherein, m​b , s, and a are rock mass strength parameters.

[0116] The method described above, distinct from the inverse analysis process of geotechnical parameters, falls under the category of forward analysis. This method enables rapid in-situ detection and forward analysis of rock mass parameters, and can update the rock mass strength parameters at the excavation face in real time.

[0117] Step 2) Based on the in-situ mechanical parameters, engineering parameters, and rock mass strength parameters, establish a three-dimensional elastoplastic mechanical analytical model of the tunnel considering the three-dimensional strength and longitudinal axial stress of the rock mass, such as... Figure 2 As shown, solve for the maximum deformation of the surrounding rock and the radius of the plastic zone.

[0118] Step 2-1) Based on the three-dimensional elastoplastic mechanical analytical model of the tunnel considering the three-dimensional strength and longitudinal axial stress of the rock mass, solve for the radial stress at the boundary between the elastic and plastic regions. Divide the radial stress in the plastic region into N equal rings, where the difference between the inner and outer radial stresses of each ring is constant, i.e., the equal radial stresses are:

[0119]

[0120] Where, σ r It is radial stress, σ ep It is the radial stress at the elastic-plastic boundary, p i It is the support reaction force of the tunnel, N is the number of rings, which is determined according to the calculation accuracy. The larger N is, the more rings are divided, and the more accurate the calculation result is; r refers to the distance from the rock mass unit to the center of the tunnel.

[0121] The elastoplastic boundary is the outer boundary of the first annulus, i.e., r. (0) =R ep R ep It is the radius of the plastic zone; at the cave wall, r (N) =R0, where R0 is the excavation radius of the tunnel.

[0122] At the elastoplastic interface, the stress should simultaneously satisfy the stress equation of the elastic zone and the yield criterion. Therefore, the initial values ​​of the stress and strain components of the surrounding rock at the elastoplastic boundary are:

[0123]

[0124] Where, σ θ It is circumferential stress, σ z It is axial stress, ε θ It is circumferential strain, ε z It is axial strain, ε r It is radial strain, the subscript (0) indicates the initial value, p is the original rock stress, q is the out-of-plane axial stress, and G is the shear modulus.

[0125] Step 2-2) The strength criterion adopts the smooth GZZ three-dimensional strength yield criterion considering the intermediate principal stress. Since GZZ can completely degenerate H-B, H-B and GZZ parameters are shared.

[0126] At the elastic-plastic boundary, we have:

[0127]

[0128] Or use:

[0129]

[0130] Where I1, J2 and J3 are the first stress invariant, the deviatoric second invariant and the deviatoric third invariant, respectively, i = 1, 2, 3…N, m b , s, a are rock mass strength parameters, σ c is the uniaxial compressive strength of rock,

[0131] When the smooth GZZ criterion is adopted, the yield characteristics of surrounding rock are independent of the size order of principal stresses, and the out-of-plane axial stress σ z can be any principal stress.

[0132] Considering the weakening of rock mass strength parameter GSI, the initial GSI is considered as the peak GSI p The most important parameter of the plastic internal variable is the plastic shear strain Where, is the maximum plastic strain, is the minimum plastic strain, then the GSI is assumed to be linearly softened with γ p as shown below:

[0133]

[0134] Where γ p,* is the maximum plastic shear strain, γ p is the plastic shear strain, GSI r is the peak GSI, GSI r is the residual GSI, which can be calculated by equation (6):

[0135]

[0136] The supplementary equation considering the longitudinal axial stress is:

[0137]

[0138] Where β = 1, θ σ(i) refers to the Lode angle, S z(i) refers to the z-direction deviatoric stress, and β is the non-associated flow coefficient,

[0139] The deviatoric stress S in the Z direction z(i) =σ z(i) -I 1(i) / 3.

[0140] Solving the supplementary equations considering longitudinal axial stress and the strength criterion yields the triaxial stress expression for each ring in the plastic region.

[0141] Step 2-3) Determine the expression for the surrounding rock displacement:

[0142] The difference form of the equilibrium equation is:

[0143]

[0144] Because r (i) If it is an unknown, then use r. (i) =R ep ρ (i) Instead, by r (0) =R ep and r (N) =R0, we know that ρ (0) =1,ρ (N) =R0 / R ep Rewrite the above formula as:

[0145]

[0146] Where ρ is density.

[0147] Based on the Δσ calculated in step 2-1) r Find:

[0148]

[0149]

[0150] Introducing the transformation formula:

[0151]

[0152] Among them, u r It is radial displacement.

[0153] The geometric equation is then expressed as:

[0154]

[0155] From the non-associated plastic flow method, we obtain:

[0156]

[0157] Where λ is the plastic flow parameter, is the radial elastic strain, is the radial plastic strain, is the hoop elastic strain, is the hoop plastic strain.

[0158] Substituting equation (10) into the geometric equation (9) gives:

[0159]

[0160] Substituting the transformation equation (8) and the geometric equation (9) into the above equation (11) and replacing the differential with the difference, the differential equation that the i-th ring body should satisfy is obtained as:

[0161]

[0162] where, are known quantities;

[0163]

[0164] ψ is the dilatancy angle;

[0165] and From the incremental Hooke's law, we have:

[0166]

[0167] where E is the elastic modulus and v is the Poisson's ratio.

[0168] The boundary conditions of the differential equation (12) are:

[0169]

[0170] Substituting ρ = ρ (i) into the differential equation that satisfies the boundary conditions, we have:

[0171]

[0172] where A (i) , B (i) , and C (i) are known quantities, which are obtained from equation (17):

[0173]

[0174] where at the elastic-plastic boundary, then through the boundary condition (15), we have ε r(i) and ε θ(i) .

[0175] After N calculations, we obtain ρ (N)and plastic zone radius R ep = R0 / p (N) ; and r (i) = p (i) R ep and r (i) is obtained r(i) .

[0176] Step 2-4) determining the expression of the plastic zone radius of the surrounding rock:

[0177] R ep = r (0) / p (N)

[0178] r (i) = R ep p (i) (18)

[0179] u r(i) = - e θ(i) r (i)

[0180] and gradually solving the maximum deformation of the surrounding rock, the maximum plastic zone radius of the surrounding rock, the circumferential strain and the radial stress of each layer when the support pressure is 0.

[0181] The comparison chart of the longitudinal displacement curves calculated by considering the H-B and GZZ rock mass strength criteria respectively is shown in Figure 3 , wherein the longitudinal displacement calculated by the H-B criterion belongs to the prior art, and is not described herein again in order to avoid the purpose of the present application being blurred.

[0182] Step 3) determining the tunnel longitudinal deformation curve (LDP) equation considering the three-dimensional strength of the rock mass and the longitudinal axial stress based on the maximum deformation and the plastic zone radius of the surrounding rock:

[0183]

[0184] In the formula, u * is the dimensionless deformation of the surrounding rock; is the dimensionless plastic zone radius, is the plastic zone radius at the maximum deformation, R0 is the excavation radius of the chamber; x * = x / R0 is the dimensionless distance of the section from the excavation surface, x≤0 is the unexcavated rock mass; is the displacement release coefficient of the section of the surrounding rock of the excavation surface, u0 is the displacement of the wall, u max is the maximum stable displacement of the excavated section away from the excavation surface.

[0185] Using the radius of the plastic zone of the surrounding rock calculated in step 2) and the maximum displacement of the surrounding rock after tunnel excavation, the LDP curve equation considering the intermediate principal stress under different working conditions is obtained. This is combined with the different values ​​calculated at different burial depths in step 2). Draw different The LDP curve below, as shown Figure 4 As shown.

[0186] when At that time, the surrounding rock is in an elastic stress state, and the corresponding LDP curve describes the three-dimensional spatial effect of shallow tunnel excavation. The influence range of the excavation face is (1~2)R0. With... As the diameter increases, the LDP curve gradually flattens out, corresponding to the three-dimensional spatial effect of deep-buried tunnels, and the influence range of the excavation face gradually increases.

[0187] Step 4) Based on the tunnel surrounding rock deformation stability index and the longitudinal surrounding rock deformation curve equation, determine the timing of primary and secondary lining support and guide the construction tunneling rate.

[0188] Step 4-1) Determine the deformation stability index of the surrounding rock of the tunnel:

[0189] Surrounding rock displacement release coefficient u * This refers to the dimensionless deformation of the surrounding rock, which reflects the degree of deformation release in the surrounding rock.

[0190] The longitudinal deformation rate k of the surrounding rock reflects how quickly the deformation of the surrounding rock is released along the longitudinal direction of the tunnel:

[0191] k = du * / dx

[0192] The tunnel face excavation rate V reflects the excavation distance per unit time:

[0193] V = dx / dt

[0194] Where x is the distance between the cross section and the excavation face.

[0195] The deformation rate s of the surrounding rock cross section reflects the rate of vertical deformation of the surrounding rock in the tunnel cross section:

[0196] s = du / dt

[0197] Where u is the cross-sectional deformation of the surrounding rock. The cross-sectional deformation rate s of the surrounding rock is obtained by calculation from the excavation model or by monitoring the deformation of the surrounding rock at the construction site. For safety reasons, the maximum value between the two is taken.

[0198] Step 4-2) Based on the tunnel surrounding rock deformation stability index and the tunnel longitudinal surrounding rock deformation curve equation, determine the timing of primary and secondary lining support.

[0199] Determination of the deformation index of surrounding rock I: when the longitudinal deformation rate k of surrounding rock reaches the maximum, the dimensionless distance of the section from the excavation surface is x1, which is considered as the fastest deformation of surrounding rock, and the surrounding rock is the most unstable at this time, which is the timing of the initial lining construction.

[0200] Determination of the deformation index of surrounding rock II: when u * ≥ 0.98, the dimensionless distance of the section from the excavation surface is x2, which is considered as the gradual stability of the surrounding rock, and it is the first timing of the alternative secondary lining construction.

[0201] Determination of the deformation index of surrounding rock III: when the transverse deformation rate s of surrounding rock is ≤ 1 mm / d, it is considered that the surrounding rock gradually tends to be stable, and at this time the dimensionless distance of the section from the excavation surface is x2', which is the second timing of the alternative secondary lining construction.

[0202] x1 is the timing of the initial lining construction, max(x2, x2') is the timing of the secondary lining construction, wherein x1 < max(x2, x2'), the dimensionless distance of the section from the excavation surface in the range between x1 and max(x2, x2') is the influence range of the LDP curve, which is the transition section of the gradual stability of the primary support, i.e. the step method excavation step distance and length.

[0203] Step 4-3) Based on the tunnel surrounding rock deformation stability index and the tunnel longitudinal surrounding rock deformation curve equation, the relationship among the longitudinal deformation rate k of surrounding rock, the tunnel face excavation rate V and the transverse deformation rate s of surrounding rock is obtained as follows:

[0204]

[0205] Based on the above formula, the construction excavation rate is guided.

[0206] According to Figure 4 It can be obtained that, The larger the displacement release coefficient at the excavation surface is, the smaller the displacement release coefficient at the excavation surface is, and at the same time, the deformation of the deep-buried tunnel surrounding rock is much larger than that of the shallow-buried tunnel, indicating that the subsequent excavation process of the deep-buried tunnel will produce more significant space effect. Figure 4 In the tunnel, there is a certain difference in the displacement release coefficient at the position 2.5R0 from the excavation surface, and The corresponding displacement release coefficients are 0.98 and 0.43 respectively. In the shallow-buried tunnel, the deformation at 2.5R0 is almost completely released, while for the deep-buried and super-deep-buried tunnels, the deformation at 2.5R0 is released by less than half. If the shallow-buried tunnel support design experience is followed, the influence range of the excavation space effect of the deep-buried tunnel is underestimated, which will cause the steel arch and other support systems to bear a large load in the subsequent excavation process, thereby causing the steel arch to be replaced many times, releasing stress and deformation, and seriously affecting the safety of the project and the construction progress. Therefore, when When R0= 10 m, the initial lining support timing is x1= 0, and the secondary lining support timing is x2= 2.5R0. When R0= 10 m, the initial lining support timing is x1= 0, and the secondary lining support timing is x2= 20.3R0.

[0207] The preferred embodiments of the present application have been described in detail. It should be understood that modifications and variations can be made by those skilled in the art without creating spurious equivalents to fall within the scope of the present application. Therefore, any technical solutions obtained by logical analysis, reasoning or limited experiments based on the concept of the present application in the prior art should be within the scope of protection of the present application.

Claims

1. A method for rapidly determining the timing of deep-buried tunnel support considering the three-dimensional strength of rock mass, characterized in that, Includes the following steps: Step 1) Based on the on-site geological exploration of the tunnel project, digital in-situ testing and analysis of rock mass parameters at the excavation face, the in-situ mechanical and engineering parameters of the rock mass at the tunnel excavation face are acquired and dynamically updated in real time, and the rock mass strength parameters are determined based on the in-situ mechanical parameters of the rock mass. Step 2) Based on the in-situ mechanical parameters, engineering parameters and rock mass strength parameters, establish a three-dimensional elastoplastic mechanical analytical model of the tunnel considering the three-dimensional strength and longitudinal axial stress of the rock mass, and solve for the maximum deformation of the surrounding rock and the radius of the plastic zone. Step 3) Based on the maximum deformation of the surrounding rock and the radius of the plastic zone, determine the equation of the longitudinal surrounding rock deformation curve of the tunnel that takes into account the three-dimensional strength of the rock mass and the longitudinal axial stress. Step 4) Based on the tunnel surrounding rock deformation stability index and the tunnel longitudinal surrounding rock deformation curve equation, determine the timing of primary and secondary lining support and guide the construction tunneling rate. Step 2) includes the following steps: Step 2-1) Based on the three-dimensional elastoplastic mechanical analytical model of the tunnel considering the three-dimensional strength and longitudinal axial stress of the rock mass, solve for the radial stress at the boundary between the elastic and plastic regions. Divide the radial stress in the plastic region into N equal rings, where the difference between the inner and outer radial stresses of each ring is constant, i.e., the arithmetic radial stresses are: in, σ r It is radial stress. σ ep It is the radial stress at the elastic-plastic boundary. p i It is the reaction force of the cavern support. N It is the number of rings, determined based on the calculation precision. N The larger the value, the more rings are divided, and the more accurate the calculation result. r This refers to the distance from the rock mass unit to the center of the tunnel. The elastoplastic boundary is the outer boundary of the first annulus, i.e. r (0) = R ep , R ep It is the radius of the plastic zone; at the cave wall, r (N) = R 0 , R 0 It is the radius of the tunnel excavation; At the elastoplastic interface, the stress should simultaneously satisfy the stress equation of the elastic zone and the yield criterion. Therefore, the initial values ​​of the stress and strain components of the surrounding rock at the elastoplastic boundary are: in, σ θ It is circumferential stress. σ z It is axial stress. ε θ It is circumferential strain. ε z It is axial strain. ε r It represents radial strain, and the subscript (0) indicates the initial value. p It is the original rock stress. q It is out-of-plane axial stress. It is the shear modulus; Step 2-2) The strength criterion adopts a smooth GZZ three-dimensional strength yield criterion that considers the intermediate principal stress. At the elastoplastic boundary, we have: Alternatively, you can use: In the formula, I 1 , J 2 and J 3 These are the first stress invariant, the second deviatoric stress invariant, and the third deviatoric stress invariant, respectively. i =1,2,3… N , m b , s , a These are rock mass strength parameters. For the uniaxial compressive strength of rock, ; When using the smooth GZZ criterion, the yield characteristics of the surrounding rock are independent of the order of principal stresses, and the out-of-plane axial stress... σ z It can be any principal stress; Considering rock mass strength parameters GSI The weakening, initial GSI Considered peak GSI p The most important parameter of the plastic internal variable is the plastic shear strain. ,in, It is the maximum plastic strain. If it is the minimum plastic strain, then assume GSI Follow γ p The following linear softening relationship exists: In the formula, It is the maximum plastic shear strain. Plastic shear strain, GSI r Peak value GSI , GSI r For the remainder GSI : Supplementary equation considering longitudinal axial stress: In the formula, β =1, It refers to the Lode angle. This refers to the deviatoric stress in the z-direction. It is an uncorrelated flow coefficient. ； Deviatoric stress in the Z direction ; Solving the supplementary equations considering longitudinal axial stress and the strength criterion yields the triaxial stress expression for each ring in the plastic region; Steps 2-3) Determine the expression for the surrounding rock displacement: The difference form of the equilibrium equation is: because If it is an unknown, then adopt Instead, by and It can be seen that, , Rewrite the above formula as: in, ρ It is density; Based on the calculation in step 2-1) Find: Introducing the transformation formula: in, u r It is radial displacement; The geometric equation is then expressed as: From the non-associated plastic flow method, we obtain: in, λ These are plastic flow parameters. It is radial elastic strain. It is radial plastic strain. It is circumferential elastic strain. It is circumferential plastic strain; Substituting into the geometric equation, we get: Substituting the transformation formula and geometric equation into the above equation, and using difference instead of differential, we simplify to obtain the first... i The differential equation that the ring rock mass should satisfy is: In the formula, , are known quantities; , ψ It is the shear expansion angle; and Obtained from incremental Hooke's law: in, E It is the elastic modulus. ν It is Poisson's ratio; The boundary conditions for the differential equation are: Will ρ = ρ (i) Substituting the values, the solution to the differential equation satisfying the boundary conditions is: In the formula, A (i) , B (i) , C (i) All quantities are known and can be obtained using the following formula: In the formula, at the elastic-plastic boundary, Then, by using boundary conditions, we can obtain... ε r(i) and ε θ(i) ; pass N After the calculation, the location of the cave wall was obtained. ρ (N) and plastic zone radius R ep = R 0 / ρ (N) Then by r (i) = ρ (i) R ep and Seeking r (i) and u r(i) ; Steps 2-4) Determine the expression for the radius of the plastic range of the surrounding rock: R ep = r (0) / ρ (N) r (i) = R ep ρ (i) u r(i) = – ε θ(i) r (i) The maximum surrounding rock deformation, the maximum radius of the plastic zone of the surrounding rock, the circumferential strain and radial stress of each layer are solved step by step when the support pressure is 0.

2. The method for rapidly determining the timing of deep-buried tunnel support considering the three-dimensional strength of rock mass according to claim 1, characterized in that, The in-situ mechanical parameters of the rock mass include initial geostress, strain softening coefficient, rock hardness, uniaxial compressive strength of the rock, geological strength index, and blasting disturbance coefficient.

3. The method for rapidly determining the timing of deep-buried tunnel support considering the three-dimensional strength of rock mass according to claim 1, characterized in that, The engineering parameters include tunnel radius and support force.

4. The method for rapidly determining the timing of deep-buried tunnel support considering the three-dimensional strength of rock mass according to claim 1, characterized in that, The calculation method for determining rock mass strength parameters based on in-situ mechanical parameters of the rock mass is as follows: in, m b ,s,a These are rock mass strength parameters. m i , GSI , D All of these are in-situ mechanical parameters of the rock mass. m i It refers to the hardness or softness of the rock. GSI It is a geological strength indicator. D It is the blasting disturbance coefficient.

5. The method for rapidly determining the timing of deep-buried tunnel support considering the three-dimensional strength of rock mass according to claim 1, characterized in that, The equation for the longitudinal surrounding rock deformation curve of the tunnel in step 3) is: In the formula, u * The deformation of the surrounding rock is dimensionless; Let be the radius of the dimensionless plastic region. The radius of the plastic zone at the point of maximum deformation. R 0 represents the excavation radius of the tunnel; The dimensionless distance between the cross-section and the excavation face is examined. The rock mass is unexcavated. This is the displacement release coefficient of the surrounding rock at the excavation face cross section. u 0 represents the displacement of the tunnel wall. u max This represents the maximum stable displacement of the excavated section far from the excavation face.

6. The method for rapidly determining the timing of deep-buried tunnel support considering the three-dimensional strength of rock mass according to claim 1, characterized in that, The deformation stability indicators of the surrounding rock of the tunnel include: Surrounding rock displacement release coefficient , which is dimensionless deformation of the surrounding rock, reflects the degree of deformation release of the surrounding rock; Longitudinal deformation rate of surrounding rock k This reflects the rate at which the deformation of the surrounding rock is released along the longitudinal direction of the tunnel. tunnel face excavation rate V This reflects the tunneling distance per unit time. in, x This refers to the distance between the cross-section and the excavation face. Deformation rate of surrounding rock cross section s This is reflected in the rate of vertical deformation of the surrounding rock in the tunnel cross section: in, u It is the deformation of the cross section of the surrounding rock.

7. The method for rapidly determining the timing of deep-buried tunnel support considering the three-dimensional strength of rock mass according to claim 6, characterized in that, The timing of the primary and secondary lining support is determined according to the following method: Rock deformation index 1: When the longitudinal deformation rate of the surrounding rock k When it reaches its maximum, the dimensionless distance between the cross-section and the excavation face is x 1 It is believed that the surrounding rock deforms the fastest and is the most unstable at this time, which is the time to carry out the initial lining. Rock deformation index two: when At that time, the dimensionless distance between the cross-section and the excavation face is x 2 They believed that the surrounding rock was gradually stabilizing, which was the first opportunity to construct the alternative secondary lining. Rock deformation index three: When the deformation rate of the surrounding rock cross section At this point, it is assumed that the surrounding rock gradually stabilizes, and the dimensionless distance between the cross-section and the excavation face is... This is the second opportunity to construct the alternative secondary lining; x 1 For the timing of initial lining application, max( x 2 , The timing of the secondary lining construction is as follows: x 1 <max( x 2 , The dimensionless distance between the cross-section and the excavation face is... x 1 and max( x 2 , The range between ) is the influence range of the LDP curve, which serves as the transition section for the gradual stabilization of the initial support, i.e., the step distance and length of the bench method excavation.

8. The method for rapidly determining the timing of deep-buried tunnel support considering the three-dimensional strength of rock mass according to claim 6, characterized in that, Based on the deformation stability index of the tunnel surrounding rock and the equation of the longitudinal deformation curve of the surrounding rock, the longitudinal deformation rate of the surrounding rock is obtained. k Tunnel face excavation rate V and the vertical deformation rate of the surrounding rock in the cross section s The relationship between the three is as follows: The above formula guides the construction and tunneling rate.

9. The method for rapidly determining the timing of deep-buried tunnel support considering the three-dimensional strength of rock mass according to claim 6, characterized in that, The deformation rate of the surrounding rock cross section s The results are obtained from calculations based on the excavation model or from monitoring the deformation of the surrounding rock at the construction site. For safety reasons, the maximum value between the two is taken.

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