Method and equipment for determining stress and displacement of composite lining tunnel

Abstract

The present invention provides a method and device for determining stress and displacement of a composite lining tunnel, wherein the region of the composite lining tunnel includes surrounding rock, primary support and secondary lining; the contact surface between the surrounding rock and the primary support is the first contact surface; the contact surface between the primary support and the secondary lining is the second contact surface; the inner boundary of the secondary lining is the third contact surface; the method comprises: obtaining tunnel cross-sectional structural parameters, far-field stress parameters, material parameters of each region of the tunnel, boundary conditions and contact conditions of each contact surface and determining stress continuity conditions and displacement continuity conditions based on these; determining stress functions of each region based on the stress continuity conditions and displacement continuity conditions to analyze stress and displacement on each contact surface. By determining through the continuous conditions on each contact surface, stress and displacement can be accurately calculated based on only fixed parameters and conditions of each region of the tunnel without the need for numerical simulation and experimental research, thereby solving the problem that the prior art is difficult to apply to composite lining tunnels.

Description

Technical Field

[0001] The present application belongs to the technical field of tunnel construction, and in particular to a method and device for determining stress and displacement of a composite lining tunnel. Background Art

[0002] With the rapid development of highways and railways, the demand for tunnels is increasing, and controlling the stress and displacement of tunnels is a necessary condition to ensure the safe operation of tunnels.

[0003] In the prior art, there are many research results on unsupported tunnels and tunnels with one layer of lining, and their stress and displacement can be quickly obtained. However, for composite lining tunnels that are widely used in practical applications, the prior art generally uses numerical simulation and experimental research to determine the stress and displacement. The determination process is complicated and not convenient for practical application. Summary of the invention

[0004] In view of this, the present invention provides a method and device for determining stress and displacement of a composite lining tunnel, aiming to solve the problem of complex process of determining stress and displacement of a composite lining tunnel in the prior art.

[0005] A first aspect of an embodiment of the present invention provides a method for determining stress and displacement of a composite lining tunnel, wherein the region of the composite lining tunnel includes surrounding rock, primary support and secondary lining; the contact surface between the inner boundary of the surrounding rock and the outer boundary of the primary support is a first contact surface; the contact surface between the inner boundary of the primary support and the outer boundary of the secondary lining is a second contact surface; the inner boundary of the secondary lining is a third contact surface; the method comprises:

[0006] Obtain tunnel cross-sectional structural parameters, far-field stress parameters, material parameters of each tunnel region, boundary conditions and contact conditions of each contact surface;

[0007] Determine the stress continuity condition and displacement continuity condition based on the tunnel section structural parameters, far-field stress parameters, material parameters of each area of ​​the tunnel, boundary conditions and contact conditions of each contact surface;

[0008] Determine the stress function of each region according to the stress continuity condition and the displacement continuity condition;

[0009] The stress and displacement on each contact surface are determined based on the stress function of each area.

[0010] A second aspect of an embodiment of the present invention provides a stress and displacement determination device for a composite lining tunnel, wherein the region of the composite lining tunnel includes surrounding rock, primary support and secondary lining; the contact surface between the inner boundary of the surrounding rock and the outer boundary of the primary support is a first contact surface; the contact surface between the inner boundary of the primary support and the outer boundary of the secondary lining is a second contact surface; the inner boundary of the secondary lining is a third contact surface; the device comprises:

[0011] A data acquisition module is used to obtain tunnel cross-sectional structural parameters, far-field stress parameters, material parameters of each area of ​​the tunnel, and boundary conditions and contact conditions of each contact surface;

[0012] A condition determination module is used to determine stress continuity conditions and displacement continuity conditions based on tunnel section structural parameters, far-field stress parameters, material parameters of each area of ​​the tunnel, boundary conditions and contact conditions of each contact surface;

[0013] A function determination module, used to determine the stress function of each region according to the stress continuity condition and the displacement continuity condition;

[0014] The function solving module is used to determine the stress and displacement on each contact surface according to the stress function of each area.

[0015] A third aspect of an embodiment of the present invention provides a terminal device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the steps of the method for determining stress and displacement of a composite lining tunnel as described in the first aspect above are implemented.

[0016] A fourth aspect of an embodiment of the present invention provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the steps of the method for determining stress and displacement of a composite lining tunnel as described in the first aspect above are implemented.

[0017] The embodiment of the present invention provides a method and device for determining stress and displacement of a composite lining tunnel, wherein the region of the composite lining tunnel includes surrounding rock, primary support and secondary lining; the contact surface between the inner boundary of the surrounding rock and the outer boundary of the primary support is the first contact surface; the contact surface between the inner boundary of the primary support and the outer boundary of the secondary lining is the second contact surface; the inner boundary of the secondary lining is the third contact surface; the method includes: obtaining tunnel cross-sectional structural parameters, far-field stress parameters, material parameters of each region of the tunnel, boundary conditions and contact conditions of each contact surface; determining stress continuity conditions and displacement continuity conditions according to tunnel cross-sectional structural parameters, far-field stress parameters, material parameters of each region of the tunnel, boundary conditions and contact conditions of each contact surface; determining stress functions of each region according to stress continuity conditions and displacement continuity conditions; determining stress and displacement on each contact surface according to stress functions of each region. By determining the continuity conditions on the contact surface of the surrounding rock, primary support and secondary lining, stress and displacement can be accurately calculated based on only fixed parameters and conditions of each region of the tunnel without the need for numerical simulation and experimental research, thereby solving the problem that the prior art is difficult to apply to composite lining tunnels. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0019] Figure 1 is a load structure diagram of a composite lining tunnel provided by an embodiment of the present invention;

[0020] Figure 2 is a flow chart of the implementation of the method for determining stress and displacement of a composite lining tunnel provided by an embodiment of the present invention;

[0021] Figure 3 is a stress curve diagram of a first contact surface provided by an embodiment of the present invention;

[0022] Figure 4 is a displacement curve diagram of a first contact surface provided by an embodiment of the present invention;

[0023] Figure 5 is a stress curve diagram of the second contact surface provided by an embodiment of the present invention;

[0024] Figure 6 is a displacement curve diagram of the second contact surface provided by an embodiment of the present invention;

[0025] Figure 7 is a stress curve diagram of a third contact surface provided by an embodiment of the present invention;

[0026] Figure 8 is a displacement curve diagram of a third contact surface provided by an embodiment of the present invention;

[0027] Fig. 9 It is a schematic structural diagram of a device for determining stress and displacement of a composite lining tunnel provided by an embodiment of the present invention;

[0028] Fig.10 It is a schematic diagram of the structure of a terminal device provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0029] In the following description, specific details such as specific system structures, technologies, etc. are provided for the purpose of illustration rather than limitation, so as to provide a thorough understanding of the embodiments of the present invention. However, it should be clear to those skilled in the art that the present invention may be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted to prevent unnecessary details from obstructing the description of the present invention.

[0030] Figure 1: is a load structure diagram of a composite lining tunnel provided by an embodiment of the present invention. Figure 1 As shown, in some embodiments, the area of ​​the composite lining tunnel includes surrounding rock R, primary support L1 and secondary lining L2; the contact surface between the inner boundary of the surrounding rock R and the outer boundary of the primary support L1 is the first contact surface; the contact surface between the inner boundary of the primary support L1 and the outer boundary of the secondary lining L2 is the second contact surface; and the inner boundary of the secondary lining L2 is the third contact surface.

[0031] In this embodiment, the composite lining refers to a tunnel lining that is constructed in two layers, inner and outer. After the tunnel is excavated, the outer flexible support (generally shotcrete support) that is in close contact with the surrounding rock is first constructed in a timely manner, also known as the initial support (i.e., the initial support L1), which allows the surrounding rock to deform to a certain extent without causing excessive deformation that causes loosening pressure. After the deformation of the surrounding rock is basically stable, the inner lining (generally cast in a mold), also known as the secondary support (i.e., the second lining L2), is constructed. Between the two layers of lining, a waterproof layer is set as needed, or a waterproof concrete inner lining can be poured without a waterproof layer.

[0032] In this embodiment, according to elastic theory, the deep buried tunnel can be simplified into a plane strain model of infinitely large flat surrounding rock with holes subjected to bidirectional compression stress, where the vertical pressure at infinity is P and the lateral pressure coefficient is λ.

[0033] Figure 2 FIG. 1 is a flow chart of the method for determining stress and displacement of a composite lining tunnel provided by an embodiment of the present invention. Figure 2 As shown in the figure, the stress and displacement determination method for composite lining tunnels is applied to Figure 1 The design and analysis process of the composite lining tunnel shown in the figure includes:

[0034] S201, obtaining tunnel cross-sectional structural parameters, far-field stress parameters, material parameters of each area of ​​the tunnel, and boundary conditions and contact conditions of each contact surface.

[0035] In this embodiment, the tunnel section structural parameters are used to reflect the shape and size of the tunnel section, the far-field stress parameters are determined based on the pressure and lateral pressure coefficients at vertical infinity, and the material parameters of each area of ​​the tunnel are used to determine the shear elastic modulus and coefficient of each area.

[0036] S202, determining stress continuity conditions and displacement continuity conditions according to tunnel cross-sectional structural parameters, far-field stress parameters, material parameters of each region of the tunnel, boundary conditions and contact conditions of each contact surface.

[0037] In this embodiment, an expression of a stress function with unknown coefficients is pre-stored, the expression is substituted into the boundary conditions, and written in the form of an equation based on the contact conditions, tunnel cross-sectional structural parameters, far-field stress parameters, and material parameters of each region of the tunnel, retaining the terms with exponents of the unit circle from -n to n, and the stress continuity conditions and displacement continuity conditions can be obtained.

[0038] S203, determining the stress function of each region according to the stress continuity condition and the displacement continuity condition.

[0039] In this embodiment, the stress continuity condition and the displacement continuity condition can obtain multiple equation groups, which can be used to solve the undetermined coefficients of the stress function of each region, thereby determining the stress function of each region.

[0040] S204, determining the stress and displacement on each contact surface according to the stress function of each region.

[0041] In this embodiment, when solving the stress function, a complex variable function method is generally used. When using the complex variable function method to solve the mechanical response of the tunnel, the most critical step is to solve the mapping function of the tunnel. Only an ellipse has an accurate mapping function.

[0042] In this embodiment, the mapping function of the composite lining tunnel is:

[0043]

[0044] Where z = x + iy, ζ = ρe iθ , x, y, ρ and θ represent the rectangular coordinates and polar coordinates on the z and ζ planes respectively. k is the tunnel cross-sectional structural parameter, which is related to the cross-sectional shape and size of the tunnel; m is the number of terms in the mapping function.

[0045] In this embodiment, the stress functions of the surrounding rock, primary support and secondary lining that meet the continuity conditions and boundary conditions under the action of non-hydrostatic pressure are obtained by the complex function method, and then the analytical solutions of stress and displacement are obtained. Therefore, without the need for numerical simulation and experimental research, the stress and displacement can be accurately calculated based on only some fixed parameters and conditions in each area of ​​the tunnel, thereby solving the problem that the existing technology is difficult to apply to composite lining tunnels.

[0046] In some embodiments, S202 may include:

[0047] Determine the displacement continuity condition of the first contact surface according to the tunnel section structural parameters, far-field stress parameters, material parameters of the surrounding rock R, material parameters of the initial support L1, boundary conditions and contact conditions of the first contact surface;

[0048] Determine the stress continuity condition of the first contact surface according to the tunnel cross-section structural parameters, the far-field stress parameters, the boundary conditions and the contact conditions of the first contact surface;

[0049] Determine the displacement continuity condition of the second contact surface according to the tunnel section structural parameters, the material parameters of the primary support L1, the material parameters of the secondary lining L2, the boundary conditions and contact conditions of the second contact surface;

[0050] Determining the stress continuity condition of the second contact surface according to the tunnel cross-section structural parameters, the boundary conditions and the contact conditions of the second contact surface;

[0051] Determine the stress continuity condition of the third contact surface based on the tunnel section structural parameters and the boundary conditions of the inner boundary of the second lining L2;

[0052] According to the tunnel section structural parameters and the material parameters of the surrounding rock R, the continuity conditions of the inner boundary displacement of the surrounding rock R caused by tunnel excavation are determined.

[0053] In some embodiments, the boundary condition of the first contact surface is:

[0054] ρ=1 (2)

[0055] ζ=e iθ =σ (3)

[0056] Among them, ρ is the polar diameter of the composite lining tunnel on the mapping plane, θ is the polar angle of the composite lining tunnel on the mapping plane, ζ is the variable on the mapping plane, σ is the unit circumference, and i is an imaginary number;

[0057] The contact condition of the first contact surface is complete contact.

[0058] In this embodiment, according to the boundary conditions and contact conditions, it can be concluded that the stress and displacement on the first contact surface are continuous, that is, the normal displacement, tangential displacement, normal stress and tangential stress are equal. That is, the displacement continuity condition of the first contact surface is:

[0059]

[0060] The stress continuity condition of the first contact surface is:

[0061]

[0062] Among them, κ1 is the first coefficient, G1 is the first shear elastic modulus, κ1 and G1 are determined by the material parameters of the surrounding rock R; κ2 is the second coefficient, G2 is the second shear elastic modulus, κ2 and G2 are determined by the material parameters of the primary support L1;

[0063] B, B′, C′ are far-field stress parameters, C k is the tunnel section structural parameter, W j and Wj ′ by C k Determine; m is the number of items in the mapping function of the composite lining tunnel, n is the number of preset reserved items, i is an imaginary number, and j is a sequence number;

[0064] a j and b j is the first unknown coefficient of the stress function of the surrounding rock R, d j 、f j , g j 、h j is the second unknown coefficient of the stress function of the initial support L1.

[0065] In this embodiment, let the displacement continuity condition equation of the first contact surface have two ends σ i The coefficients of the (-n≤i≤n) terms are equal, and we can get 2n+1 equations. Let the stress continuity condition equation of the first contact surface have both ends σ i The coefficients of the (-n≤i≤n) terms are equal, and we can get 2n+1 equations.

[0066] In some embodiments, the boundary condition of the second contact surface is:

[0067] ζ=R1σ (6)

[0068] Among them, ζ is the variable on the mapping plane, σ is the unit circle, and R1 is the first boundary parameter;

[0069] Since the waterproof layer between the primary support and the secondary lining cannot withstand shear force, the contact condition of the second contact surface is smooth contact.

[0070] In this embodiment, it can be obtained that the normal displacement and the normal stress are equal, the shear stress is equal to 0, and the tangential displacement is not necessarily equal. That is, the displacement continuity condition of the second contact surface is:

[0071]

[0072] The stress continuity condition of the second contact surface is:

[0073]

[0074]

[0075] Among them, κ2 is the second coefficient, G2 is the second shear elastic modulus, κ2 and G2 are determined by the material parameters of the primary support L1; κ3 is the third coefficient, G3 is the third shear elastic modulus, κ3 and G3 are determined by the material parameters of the secondary lining L2;

[0076] C k is the tunnel section structural parameter, M j and M j ′ by C kDetermine; m is the number of items in the mapping function of the composite lining tunnel, n is the number of preset reserved items, and j is the sequence number;

[0077] d j 、f j , g j 、h j is the second unknown coefficient of the stress function of the primary support L1, p j ,q j 、s j ,t j is the third unknown coefficient of the stress function of the second lining L2.

[0078] In this embodiment, the real parts of the left and right ends of equation (15) are respectively represented by half of the sum of the real parts and their conjugates. i and σ -i The coefficients of (0≤i≤n) are all equal, and we can get n+1 equations. Let equation (16) have two ends σ i The coefficients of the (-n≤i≤n) terms are equal, and 2n+1 equations can be obtained. In equation (17), the imaginary part of the function is expressed as half of the difference between it and its conjugate. Let σ in equation (17) be i and σ -i The coefficients of (1≤i≤n) are equal, and we can get n equations.

[0079] In some embodiments, the boundary condition of the inner boundary of the second lining L2 is:

[0080] ζ=R2σ (10)

[0081] Among them, ζ is the variable on the mapping plane, σ is the unit circle, and R2 is the second boundary parameter;

[0082] The inner boundary of the second lining L2 is a free boundary.

[0083] In this embodiment, it can be concluded that both the normal stress and the shear stress are 0, so the stress continuity condition of the third contact surface is:

[0084]

[0085] Among them, L j and L j ′ by C k OK, C k is the tunnel section structural parameter; m is the number of items in the mapping function of the composite lining tunnel, n is the number of preset reserved items, and j is the sequence number;

[0086] p j ,q j 、s j ,t jis the third unknown coefficient of the stress function of the second lining L2.

[0087] In this embodiment, let σ on both ends of equation (19) i The coefficients of the (-n≤i≤n) terms are equal, and we can get 2n+1 equations.

[0088] In the above embodiment, a total of 10n+5 equations can be obtained, but there are a total of 10n+6 unknown coefficients, so another equation needs to be obtained.

[0089] Since the displacement of the surrounding rock at infinity caused by tunnel excavation is equal to the rigid body displacement of the inner boundary of the surrounding rock, the displacement is zero. In some embodiments, the displacement continuity condition of the inner boundary displacement of the surrounding rock R caused by tunnel excavation is:

[0090]

[0091] Among them, κ1 is the first coefficient, G1 is the first shear elastic modulus, and κ1 and G1 are determined by the material parameters of the surrounding rock R;

[0092] W j and W j ′ by C k OK, C k is the tunnel section structural parameter; m is the number of items in the mapping function of the composite lining tunnel, n is the number of preset reserved items, and j is the sequence number;

[0093] a j and b j is the first unknown coefficient of the stress function of the surrounding rock R.

[0094] In this embodiment:

[0095]

[0096] in, The lowest exponent of σ is 2, The expansion of -2 .

[0097] The rigid body displacement of the inner boundary of the surrounding rock caused by excavation is 0, that is, the constant term in the expanded formula on the right side of equation (20) is equal to 0:

[0098]

[0099] In some embodiments, the stress function of the surrounding rock R is:

[0100]

[0101] ψ1(ζ)=(B′+iC′)ω(ζ)+ψ0(ζ) (16)

[0102]

[0103]

[0104] The stress function of the initial support L1 is:

[0105]

[0106]

[0107] The stress function of the second lining L2 is:

[0108]

[0109]

[0110] in, and ψ1(ζ) is the stress function of the surrounding rock R, and ψ0(ζ) are analytical functions that map the area outside the unit circle of the plane, and ψ2(ζ) is the stress function of the primary support L1, and ψ3(ζ) is the stress function of the second lining L2;

[0111] ζ is the variable on the mapping plane, B, B′, C′ are far-field stress parameters, i is an imaginary number, a j and b j is the first unknown coefficient of the stress function of the surrounding rock R; d j 、f j , g j 、h j is the second unknown coefficient of the stress function of the primary support L1; p j ,q j 、s j ,t j is the third unknown coefficient of the stress function of the second lining L2.

[0112] In this embodiment, B=P(1+λ) / 4, B′=-P(1-λ) / 2, C′=0, and all the coefficients to be determined are real numbers.

[0113] In this embodiment, for the convenience of calculation, the following is introduced:

[0114]

[0115]

[0116] The superscript “′” indicates that the first-order derivative is required, ζ is the variable on the mapping plane, and ψ(ζ) are stress functions in each region.

[0117] In the rectangular coordinate system, the stress component σ x , σ y and τ xy for:

[0118] σ x +σ y =4Re[Φ(ζ)] (25)

[0119]

[0120] Among them, the upper horizontal line “-” represents conjugation, “Re” represents the real part of the complex number, and i is an imaginary number.

[0121] In rectangular coordinates, the displacement components u and v are:

[0122]

[0123] Among them, u and v are vertical displacement and horizontal displacement respectively, G is the shear elastic modulus, and κ is the coefficient; for plane strain problems, κ=3-4μ, and μ is Poisson's ratio.

[0124] In curvilinear coordinates, the stress component σ ρ , σ θ and τ ρθ for

[0125] σ ρ +σ θ =4Re[Φ(ζ)] (28)

[0126]

[0127] In curvilinear coordinates, the displacement component u ρ and u θ for

[0128]

[0129] The stress function in the above stress component and displacement component expressions is and ψ(ζ) are the stress functions of surrounding rock, primary support and secondary lining respectively and ψ1(ζ), and ψ2(ζ), and ψ3(ζ), the shear elastic modulus G and coefficient κ are replaced by G1 and κ1, G2 and κ2, G3 and κ3 of surrounding rock, primary support and secondary lining respectively, and the stress and displacement components of surrounding rock, primary support and secondary lining can be obtained.

[0130] The traction force on the boundary is:

[0131]

[0132] in, and is the surface force component on the boundary.

[0133] In some embodiments, the method further comprises:

[0134] The minimum thickness of the primary support L1 and the secondary lining L2 is determined according to the stress and displacement and the allowable stress of the lining material to modify the design of the composite lining tunnel.

[0135] In this embodiment, by determining the minimum thickness of the primary support L1 and the secondary lining L2, the primary support and the secondary lining in the design of the composite lining tunnel can be changed with reference to the minimum thickness, thereby taking into account both the economy and safety of the tunnel.

[0136] The following is an example of a double-track composite lining tunnel for a passenger-dedicated railway with a speed of 250 kilometers per hour and with Class IV surrounding rock. The method for determining the stress and displacement of a composite lining tunnel is described below through an implementation example, but it is not intended to be limiting.

[0137] In this implementation example, according to the railway tunnel specification, the material parameters of the surrounding rock are: elastic modulus E1 = 3.7 GPa, Poisson's ratio μ1 = 0.325, the material parameters of the primary support are: elastic modulus E2 = 23 GPa, Poisson's ratio μ2 = 0.2, the material parameters of the secondary lining are: elastic modulus E3 = 31.5 GPa, Poisson's ratio μ3 = 0.2, P = 0.148762 MPa, and the lateral pressure coefficient λ = 0.2. The mapping function coefficients of the composite lining are C1 = 0.7268, C2 = 6.7015, C3 = -0.5140, C4 = 0.2968, C5 = -0.1282, C6 = 0.0290, C7 = 0.0105, C8 = -0.0152, C9 = 0.0083, C 10 =-0.0024, C 11 =-0.0002, C 12 =0.0001, C 13 =-0.0004, C 14 =0.0009, R1=0.9632, R2=0.8975.

[0138] Substituting the above data into the above method for determining the stress and displacement of the composite lining tunnel, the stress and displacement of the tunnel can be obtained.

[0139] Figure 3 : is a stress curve diagram of the first contact surface provided by an embodiment of the present invention. Figure 3 As shown, the horizontal axis is Figure 1 The azimuth angle α is shown, and the vertical axis is stress. The normal stress on the contact surface between the surrounding rock and the primary support, the inner boundary of the surrounding rock and the outer boundary of the primary support and and shear stress and It can be seen that the normal stress and shear stress are equal.

[0140] Figure 4 : is a displacement curve diagram of the first contact surface provided by an embodiment of the present invention. Figure 4 As shown, the horizontal axis is the azimuth and the vertical axis is the displacement. The normal displacement between the inner boundary of the surrounding rock and the outer boundary of the primary support on the contact surface between the surrounding rock and the primary support and and tangential displacement and It can be seen that the normal displacement and the tangential displacement are equal.

[0141] Among them, Figure 3 and Figure 4 In all cases, ρ=1.

[0142] Figure 5 : is a stress curve diagram of the second contact surface provided by an embodiment of the present invention. Figure 5 As shown, the horizontal axis is the azimuth and the vertical axis is the stress. On the contact surface between the primary support and the secondary lining, the normal stress at the inner boundary of the primary support and the outer boundary of the secondary lining is and and shear stress and It can be seen that the normal stresses are equal and the shear stresses are all zero.

[0143] Figure 6 : is a displacement curve diagram of the second contact surface provided by an embodiment of the present invention. Figure 6 As shown, the horizontal axis is the azimuth and the vertical axis is the displacement. The normal displacement between the inner boundary of the primary support and the outer boundary of the secondary lining on the contact surface between the primary support and the secondary lining and and tangential displacement and From the curve, we can see that the normal displacements are equal, but the tangential displacements are not equal.

[0144] Among them, Figure 5 and Figure 6 In both cases, ρ=0.9632.

[0145] Figure 7 : is a stress curve diagram of the third contact surface provided by the embodiment of the present invention. Figure 7 As shown, the horizontal axis is the azimuth and the vertical axis is the stress. and shear stress Normal stress and shear stress are both zero. Shear stress on all vertical axes is zero, satisfying the symmetry condition.

[0146] Figure 8: is a displacement curve diagram of the third contact surface provided by the embodiment of the present invention. Figure 8 As shown, the horizontal axis is the azimuth and the vertical axis is the displacement. Normal displacement of the inner boundary of the second lining and tangential displacement The displacement trends of each boundary are consistent and the values ​​are close. The maximum settlement, uplift and peripheral displacement occur at the arch crown, arch bottom and arch waist respectively. On the vertical axis, the tangential displacement is equal to zero, satisfying the symmetry condition.

[0147] Among them, Figure 7 and Figure 8 In both cases, ρ=0.8975.

[0148] In this implementation example, the stress functions of the surrounding rock, primary support and secondary lining that meet the continuity and boundary conditions under the action of non-hydrostatic pressure are obtained by the method of complex variable functions, and then the analytical solutions of stress and displacement are obtained. Taking the railway composite lining tunnel under the IV-level surrounding rock as an example, the mapping function of the composite lining tunnel is first obtained by searching the boundary point method. The analytical solution of stress and displacement distribution is given, which is in good agreement with the numerical solution calculated by the finite element software. The results show that the ratio of the maximum normal positive stress of the secondary lining to the outer boundary of the primary support (load sharing ratio) is 0.7414. The normal displacement change trends of the secondary lining, primary support and the inner boundary of the surrounding rock are consistent, and the values ​​are close. The maximum settlement and uplift occur at the top and bottom of the arch respectively. The tangential positive stress of the secondary lining is compressive stress, and the tangential positive stress of the primary support is tensile stress and compressive stress. The maximum tangential positive stress of the primary support and the secondary lining is less than the allowable stress of the concrete. For the sake of economy, the thickness of the primary support and the secondary lining can be appropriately reduced. The research results provide a theoretical basis for safe and economical tunnel design.

[0149] It should be understood that the order of execution of the steps in the above embodiment does not necessarily mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiment of the present invention.

[0150] Fig. 9 Schematic diagram of the structure of the stress and displacement determination device of the composite lining tunnel provided by the embodiment of the present invention. Fig. 9 As shown, in some embodiments, the region of the composite lining tunnel includes surrounding rock, primary support and secondary lining; the contact surface between the inner boundary of the surrounding rock and the outer boundary of the primary support is the first contact surface; the contact surface between the inner boundary of the primary support and the outer boundary of the secondary lining is the second contact surface; the inner boundary of the secondary lining is the third contact surface; the stress and displacement determination device 9 of the composite lining tunnel includes:

[0151] The data acquisition module 910 is used to obtain tunnel cross-sectional structural parameters, far-field stress parameters, material parameters of each area of ​​the tunnel, and boundary conditions and contact conditions of each contact surface;

[0152] Condition determination module 920, used to determine stress continuity conditions and displacement continuity conditions according to tunnel cross-section structural parameters, far-field stress parameters, material parameters of each area of ​​the tunnel, boundary conditions and contact conditions of each contact surface;

[0153] Function determination module 930, used to determine the stress function of each region according to the stress continuity condition and the displacement continuity condition;

[0154] The function solving module 940 is used to determine the stress and displacement on each contact surface according to the stress function of each area.

[0155] Optionally, the condition determination module 920 is specifically configured to:

[0156] Determine the displacement continuity condition of the first contact surface according to the tunnel section structural parameters, far-field stress parameters, material parameters of the surrounding rock, material parameters of the primary support, boundary conditions and contact conditions of the first contact surface;

[0157] Determine the stress continuity condition of the first contact surface according to the tunnel cross-section structural parameters, the far-field stress parameters, the boundary conditions and the contact conditions of the first contact surface;

[0158] Determine the displacement continuity condition of the second contact surface according to the tunnel section structural parameters, the material parameters of the primary support, the material parameters of the secondary lining, the boundary conditions and contact conditions of the second contact surface;

[0159] Determining the stress continuity condition of the second contact surface according to the tunnel cross-section structural parameters, the boundary conditions and the contact conditions of the second contact surface;

[0160] Determine the stress continuity condition of the third contact surface based on the tunnel section structural parameters and the boundary conditions of the inner boundary of the second lining;

[0161] According to the tunnel section structural parameters and the material parameters of the surrounding rock, the continuity conditions of the inner boundary displacement of the surrounding rock caused by tunnel excavation are determined.

[0162] Optionally, the boundary condition of the first contact surface is:

[0163] ρ=1

[0164] ζ=e iθ =σ

[0165] Among them, ρ is the polar diameter of the composite lining tunnel on the mapping plane, θ is the polar angle of the composite lining tunnel on the mapping plane, ζ is the variable on the mapping plane, σ is the unit circumference, and i is an imaginary number;

[0166] The contact condition of the first contact surface is complete contact;

[0167] The displacement continuity condition of the first contact surface is:

[0168]

[0169] The stress continuity condition of the first contact surface is:

[0170]

[0171] Among them, κ1 is the first coefficient, G1 is the first shear elastic modulus, κ1 and G1 are determined by the material parameters of the surrounding rock; κ2 is the second coefficient, G2 is the second shear elastic modulus, κ2 and G2 are determined by the material parameters of the primary support;

[0172] B, B′, C′ are far-field stress parameters, C k is the tunnel section structural parameter, W j and W j ′ by C k Determine; m is the number of items in the mapping function of the composite lining tunnel, n is the number of preset reserved items, i is an imaginary number, and j is a sequence number;

[0173] a j and b j is the first unknown coefficient of the stress function of the surrounding rock, d j 、f j , g j 、h j is the second unknown coefficient of the stress function of the primary support.

[0174] Optionally, the boundary condition of the second contact surface is:

[0175] ζ=R1σ

[0176] Among them, ζ is the variable on the mapping plane, σ is the unit circle, and R1 is the first boundary parameter;

[0177] The contact condition of the second contact surface is smooth contact;

[0178] The displacement continuity condition of the second contact surface is:

[0179]

[0180] The stress continuity condition of the second contact surface is:

[0181]

[0182] Among them, κ2 is the second coefficient, G2 is the second shear elastic modulus, κ2 and G2 are determined by the material parameters of the primary support; κ3 is the third coefficient, G3 is the third shear elastic modulus, κ3 and G3 are determined by the material parameters of the secondary lining;

[0183] C k is the tunnel section structural parameter, M j and M j′ by C k Determine; m is the number of items in the mapping function of the composite lining tunnel, n is the number of preset reserved items, and j is the sequence number;

[0184] d j 、f j , g j 、h j is the second unknown coefficient of the stress function of the primary support, p j ,q j 、s j ,t j is the third unknown coefficient of the stress function of the second lining.

[0185] Optionally, the boundary conditions on the inner boundary of the second lining are:

[0186] ζ=R2σ

[0187] Among them, ζ is the variable on the mapping plane, σ is the unit circle, and R2 is the second boundary parameter;

[0188] The inner boundary of the second lining is a free boundary;

[0189] The stress continuity condition of the third contact surface is:

[0190]

[0191] Among them, L j and L j ′ by C k OK, C k is the tunnel section structural parameter; m is the number of items in the mapping function of the composite lining tunnel, n is the number of preset reserved items, and j is the sequence number;

[0192] p j ,q j 、s j ,t j is the third unknown coefficient of the stress function of the second lining.

[0193] Optionally, the displacement continuity condition for the inner boundary displacement of the surrounding rock caused by tunnel excavation is:

[0194]

[0195] Among them, κ1 is the first coefficient, G1 is the first shear elastic modulus, and κ1 and G1 are determined by the material parameters of the surrounding rock;

[0196] W j and W j ′ by C k OK, C k is the tunnel section structural parameter; m is the number of items in the mapping function of the composite lining tunnel, n is the number of preset reserved items, and j is the sequence number;

[0197] a j and b j is the first unknown coefficient of the stress function of the surrounding rock.

[0198] Optionally, the stress function of the surrounding rock is:

[0199]

[0200] ψ1(ζ)=(B′+iC′)ω(ζ)+ψ0(ζ)

[0201]

[0202]

[0203] The stress function of the initial support is:

[0204]

[0205]

[0206] The stress function of the secondary lining is:

[0207]

[0208]

[0209] in, and ψ1(ζ) is the stress function of the surrounding rock, and ψ0(ζ) are analytical functions that map the area outside the unit circle of the plane, and ψ2(ζ) is the stress function of the primary support, and ψ3(ζ) is the stress function of the second lining;

[0210] ζ is the variable on the mapping plane, B, B′, C′ are far-field stress parameters, i is an imaginary number, a j and b j is the first unknown coefficient of the stress function of the surrounding rock; d j 、f j , g j 、h j is the second unknown coefficient of the stress function of the primary support; p j ,q j 、s j ,t j is the third unknown coefficient of the stress function of the second lining.

[0211] Optionally, the stress and displacement determination device 9 for a composite lining tunnel further includes: a thickness determination module 950 .

[0212] The thickness determination module 950 is used to determine the minimum thickness of the primary support and the secondary lining according to the stress and displacement and the allowable stress of the lining material, so as to modify the design scheme of the composite lining tunnel.

[0213] The stress and displacement determination device for a composite lining tunnel provided in this embodiment can be used to execute the above method embodiments, and its implementation principle and technical effects are similar, so this embodiment will not be repeated here.

[0214] Fig.10 Schematic diagram of a terminal device provided by an embodiment of the present invention. Fig.10 As shown, an embodiment of the present invention provides a terminal device 10, and the terminal device 10 of this embodiment includes: a processor 1000, a memory 1010, and a computer program 1020 stored in the memory 1010 and executable on the processor 1000. When the processor 1000 executes the computer program 1020, the steps in the above-mentioned various composite lining tunnel determination method embodiments are implemented, for example Figure 2 Alternatively, when the processor 1000 executes the computer program 1020, the functions of each module / unit in the above-mentioned system embodiments are implemented, for example Fig. 9 Functions of modules 910 to 940 are shown.

[0215] Exemplarily, the computer program 1020 may be divided into one or more modules / units, one or more modules / units are stored in the memory 1010, and are executed by the processor 1000 to complete the present invention. One or more modules / units may be a series of computer program instruction segments capable of completing specific functions, and the instruction segments are used to describe the execution process of the computer program 1020 in the terminal device 10.

[0216] The terminal device 10 may be a single chip microcomputer, MCU, desktop computer, notebook, PDA, and other computing devices. The terminal may include, but is not limited to, a processor 1000 and a memory 1010. Those skilled in the art will appreciate that Fig.10 It is only an example of the terminal device 10 and does not constitute a limitation on the terminal device 10. It may include more or fewer components than shown in the figure, or a combination of certain components, or different components. For example, the terminal may also include input and output devices, network access devices, buses, etc.

[0217] The processor 1000 may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor, etc.

[0218] The memory 1010 may be an internal storage unit of the terminal device 10, such as a hard disk or memory of the terminal device 10. The memory 1010 may also be an external storage device of the terminal device 10, such as a plug-in hard disk, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, a flash card (FlashCard), etc. equipped on the terminal device 10. Further, the memory 1010 may also include both an internal storage unit of the terminal device 10 and an external storage device. The memory 1010 is used to store computer programs and other programs and data required by the terminal. The memory 1010 may also be used to temporarily store data that has been output or is to be output.

[0219] An embodiment of the present invention provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the steps in the above-mentioned embodiment of the stress and displacement determination system for a composite lining tunnel are implemented.

[0220] The computer readable storage medium stores a computer program 1020, which includes program instructions. When the program instructions are executed by the processor 1000, all or part of the processes in the above-mentioned embodiment method are implemented. The computer program 1020 can also be used to instruct related hardware to complete. The computer program 1020 can be stored in a computer readable storage medium. When the computer program 1020 is executed by the processor 1000, the steps of each of the above-mentioned method embodiments can be implemented. Among them, the computer program 1020 includes computer program code, which can be in source code form, object code form, executable file or some intermediate form. The computer readable medium may include: any entity or device capable of carrying computer program code, recording medium, USB flash drive, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), electric carrier signal, telecommunication signal and software distribution medium. It should be noted that the content contained in the computer-readable medium can be appropriately increased or decreased according to the requirements of legislation and patent practices in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practices, computer-readable media does not include electrical carrier signals and telecommunications signals.

[0221] The computer-readable storage medium may be an internal storage unit of the terminal of any of the foregoing embodiments, such as a hard disk or memory of the terminal. The computer-readable storage medium may also be an external storage device of the terminal, such as a plug-in hard disk, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, a flash card (Flash Card), etc. equipped on the terminal. Further, the computer-readable storage medium may also include both an internal storage unit of the terminal and an external storage device. The computer-readable storage medium is used to store computer programs and other programs and data required by the terminal. The computer-readable storage medium may also be used to temporarily store data that has been output or is to be output.

[0222] It should be understood that the order of execution of the steps in the above embodiment does not necessarily mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiment of the present invention.

[0223] The technicians in the relevant field can clearly understand that for the convenience and simplicity of description, only the division of the above-mentioned functional units and modules is used as an example for illustration. In practical applications, the above-mentioned function allocation can be completed by different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiment can be integrated in a processing unit, or each unit can exist physically separately, or two or more units can be integrated in one unit. The above-mentioned integrated unit can be implemented in the form of hardware or in the form of software functional units. In addition, the specific names of the functional units and modules are only for the convenience of distinguishing each other, and are not used to limit the scope of protection of this application. The specific working process of the units and modules in the above-mentioned system can refer to the corresponding process in the aforementioned method embodiment, which will not be repeated here.

[0224] In the above embodiments, the description of each embodiment has its own emphasis. For parts that are not described or recorded in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0225] Those of ordinary skill in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

[0226] In the embodiments provided by the present invention, it should be understood that the disclosed devices / terminals and methods can be implemented in other ways. For example, the device / terminal embodiments described above are only schematic, for example, the division of modules or units is only a logical function division, and there may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0227] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0228] In addition, each functional unit in each embodiment of the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.

[0229] If the integrated module / unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the present invention implements all or part of the processes in the above-mentioned embodiment method, and can also be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium, and the computer program can implement the steps of the above-mentioned various method embodiments when executed by the processor. Among them, the computer program includes computer program code, and the computer program code can be in source code form, object code form, executable file or some intermediate form. The computer-readable medium may include: any entity or device capable of carrying computer program code, recording medium, U disk, mobile hard disk, disk, optical disk, computer memory, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), electric carrier signal, telecommunication signal and software distribution medium. It should be noted that the content contained in the computer-readable medium can be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, the computer-readable medium does not include electric carrier signals and telecommunication signals.

[0230] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. Such modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention, and should be included in the protection scope of the present invention.

Claims

1. A method for determining stress and displacement of a composite lining tunnel, characterized in that: The area of ​​the composite lining tunnel includes surrounding rock, primary support and secondary lining; the contact surface between the inner boundary of the surrounding rock and the outer boundary of the primary support is the first contact surface; the contact surface between the inner boundary of the primary support and the outer boundary of the secondary lining is the second contact surface; the inner boundary of the secondary lining is the third contact surface; the method includes: Obtain tunnel cross-sectional structural parameters, far-field stress parameters, material parameters of each tunnel region, boundary conditions and contact conditions of each contact surface; Determine the stress continuity condition and displacement continuity condition based on the tunnel section structural parameters, far-field stress parameters, material parameters of each area of ​​the tunnel, boundary conditions and contact conditions of each contact surface; Determine the stress function of each region according to the stress continuity condition and the displacement continuity condition; Determine the stress and displacement on each contact surface based on the stress function of each area; Determining the stress continuity condition and the displacement continuity condition according to the tunnel cross-sectional structural parameters, the far-field stress parameters, the material parameters of each area of ​​the tunnel, the boundary conditions and the contact conditions of each contact surface includes: Determine the displacement continuity condition of the first contact surface according to the tunnel section structural parameters, far-field stress parameters, material parameters of the surrounding rock, material parameters of the primary support, boundary conditions and contact conditions of the first contact surface; Determine the stress continuity condition of the first contact surface according to the tunnel cross-section structural parameters, the far-field stress parameters, the boundary conditions and the contact conditions of the first contact surface; Determine the displacement continuity condition of the second contact surface according to the tunnel section structural parameters, the material parameters of the primary support, the material parameters of the secondary lining, the boundary conditions and contact conditions of the second contact surface; Determining the stress continuity condition of the second contact surface according to the tunnel cross-section structural parameters, the boundary conditions and the contact conditions of the second contact surface; Determine the stress continuity condition of the third contact surface based on the tunnel section structural parameters and the boundary conditions of the inner boundary of the second lining; Determine the continuity conditions of the inner boundary displacement of the surrounding rock caused by tunnel excavation based on the tunnel section structural parameters and the material parameters of the surrounding rock; The boundary condition of the first contact surface is: ρ=1 ζ=e iθ =s Wherein, ρ is the polar diameter of the composite lining tunnel on the mapping plane, θ is the polar angle of the composite lining tunnel on the mapping plane, ζ is a variable on the mapping plane, σ is the unit circumference, and i is an imaginary number; The contact condition of the first contact surface is complete contact; The displacement continuity condition of the first contact surface is: The stress continuity condition of the first contact surface is: Wherein, κ1 is the first coefficient, G1 is the first shear elastic modulus, and κ1 and G1 are determined by the material parameters of the surrounding rock; κ2 is the second coefficient, G2 is the second shear elastic modulus, and κ2 and G2 are determined by the material parameters of the primary support; B, B′, C′ are the far-field stress parameters, C k is the tunnel cross-sectional structural parameter, W j and W j ′ by C k Determine; m is the number of items in the mapping function of the composite lining tunnel, n is the number of preset reserved items, i is an imaginary number, and j is a sequence number; a j and b j is the first unknown coefficient of the stress function of the surrounding rock, d j 、f j , g j 、h j is the second unknown coefficient of the stress function of the primary support; The boundary condition of the second contact surface is: ζ=R1σ Wherein, R1 is the first boundary parameter; The contact condition of the second contact surface is smooth contact; The displacement continuity condition of the second contact surface is: The stress continuity condition of the second contact surface is: Wherein, κ3 is the third coefficient, G3 is the third shear elastic modulus, and κ3 and G3 are determined by the material parameters of the second lining; M j and M j ′ by C k Sure; p j ,q j 、s j ,t j is the third unknown coefficient of the stress function of the second lining; The boundary conditions of the inner boundary of the second lining are: ζ=R2σ Wherein, R2 is the second boundary parameter; The inner boundary of the second lining is a free boundary; The stress continuity condition of the third contact surface is: Among them, L j and L j ′ by C k Sure; The displacement continuity condition of the inner boundary displacement of the surrounding rock caused by tunnel excavation is:

2. The method for determining stress and displacement of a composite lining tunnel according to claim 1, characterized in that: The stress function of the surrounding rock is: ψ1(ζ)=(B′+iC′)ω(ζ)+ψ0(ζ) The stress function of the primary support is: The stress function of the second lining is: in, and ψ1(ζ) is the stress function of the surrounding rock, and ψ0(ζ) are analytical functions that map the area outside the unit circle of the plane, and ψ2(ζ) is the stress function of the primary support, and ψ3(ζ) is the stress function of the second lining; ζ is a variable on the mapping plane, B, B′, C′ are the far-field stress parameters, i is an imaginary number, a j and b j is the first unknown coefficient of the stress function of the surrounding rock; d j 、f j , g j 、h j is the second unknown coefficient of the stress function of the primary support; p j ,q j 、s j ,t j is the third unknown coefficient of the stress function of the second lining.

3. The method for determining stress and displacement of a composite lining tunnel according to claim 1 or 2, characterized in that: The method further comprises: The minimum thickness of the primary support and the secondary lining is determined based on the stress and displacement and the allowable stress of the lining material to modify the design of the composite lining tunnel.

4. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the method for determining stress and displacement of a composite lining tunnel as described in any one of claims 1 to 3 are implemented.

5. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the method for determining stress and displacement of a composite lining tunnel as described in any one of claims 1 to 3 above are implemented.

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