Reinforced concrete lining design method considering water load increment process

Abstract

The invention relates to a reinforced concrete lining design method considering a water load increment process, which comprises the following steps of: calculating and judging a contact state between a lining and surrounding rock in a construction completion period according to a relational expression among circumferential stress of the lining, outer wall deformation and inner wall deformation of the surrounding rock; according to the judgment result of the contact state, the stress and the maximum crack width of the reinforcing steel bar after the hydrostatic load increment is applied under different conditions are calculated; continuously applying the dynamic water load increment, calculating the dynamic water load when the gap between the lining and the surrounding rock is closed, and then calculating the reinforcement stress and the maximum crack width of the concrete according to the continuous displacement condition; and determining an optimal reinforcement design scheme of the reinforced concrete lining according to the requirements of the normal use limit state in combination with the requirements of safety and economy. According to the method, based on the permeable lining theory, the effect of the dynamic water load on the cracked lining is considered in combination with the orthotropic constitutive structure, the optimal lining scheme is determined, and the method is suitable for structural design of the reinforced concrete lining of the pressure tunnel.

Description

Technical Field

[0001] The invention relates to the field of hydraulic structure design and is suitable for reinforced concrete lining design of pressure tunnels. Background Art

[0002] As a commonly used lining form in hydraulic tunnels, reinforced concrete lining plays a vital role in the construction and operation of hydraulic tunnels. In an environment with good hydrogeological conditions, the use of reinforced concrete lining can give full play to the bearing capacity of the surrounding rock itself, and has high economy and adaptability. In the development of reinforced concrete lining design theory, the water load can generally be divided into two theories: surface force and body force: the surface force theory regards the concrete lining as an impermeable medium, and the water load acts on the inner surface of the lining in the form of boundary surface force; the body force theory regards the concrete lining as a porous micro-permeable medium, and the water load acts on the structure in the form of body force. The traditional reinforced concrete lined tunnel is designed according to the crack resistance requirements, and the ability of the surrounding rock to bear water load is not fully realized and utilized, resulting in excessive lining thickness and steel consumption. With the development of body force theory, the tunnel design theory based on the permeable lining theory has gradually matured. Different from the traditional surface force theory, the permeable lining theory regards the lining and the surrounding rock as permeable media. Especially when the lining cracks under the action of high internal water pressure, the infiltration of internal water will cause the internal and external water pressures of the lining to be basically balanced. The surrounding rock will become the main bearing body of the water load, which greatly reduces the requirements for the bearing capacity of the lining.

[0003] In the existing reinforced concrete lining design methods, whether based on the surface force theory or the permeable lining theory, usually only the bearing characteristics of the lining during the water filling operation period are focused on, and different forms of loads are often generalized. In fact, the bonding strength between the reinforced concrete lining and the surrounding rock is limited. Under the external pressure of external water pressure, grouting pressure and other external pressures during the construction period, the lining and the surrounding rock may have been separated and a certain gap may be formed, which will have an unignorable impact on the bearing characteristics of the lining; in addition, during the operation of the water diversion tunnel, especially the pumped storage power station, it is inevitable to experience start-up and shutdown, load increase, working condition conversion, equipment and power system failure, etc., which will cause unignorable dynamic water loads. Its action time is short and it often does not have time to form the internal water seepage process. If it is considered according to the body load, it cannot reflect its action characteristics and may underestimate its force on the lining structure.

[0004] In summary, the current reinforced concrete lining still has the following defects: (1) Lack of understanding of the conditional joint bearing process between lining and surrounding rock under the action of water load increment during the entire process from construction completion to water filling and operation;

[0005] (2) The changes in the contact state between the lining and the surrounding rock during the construction period were not taken into account; (3) The action forms of static water load and dynamic water load were not distinguished, and the effect of dynamic water load was underestimated. Summary of the invention

[0006] The purpose of the present invention is to overcome the shortcomings of existing design methods and provide a reinforced concrete lining design method that takes into account the water load increment process. Based on the permeable lining theory, the dynamic combination process of lining and surrounding rock from the construction completion period to the water filling operation period is considered to design the reinforced concrete lining structure of a pressurized tunnel.

[0007] The technical solution provided by the present invention is as follows:

[0008] In a first aspect, the present invention provides a reinforced concrete lining design method considering a water load increment process, comprising the following steps:

[0009] According to the relationship between the hoop stress of the lining and the deformation of the outer wall and the inner wall of the surrounding rock under the action of the seepage water pressure increment and the surface force increment, combined with the hydraulic continuity condition and displacement continuity condition between the lining and the surrounding rock, the contact state between the lining and the surrounding rock during the construction completion period is calculated and judged;

[0010] According to the judgment results of the contact state, the stress and maximum crack width of the steel bar after applying the hydrostatic load increment under different conditions are calculated;

[0011] Continue to apply the hydrodynamic load increments to calculate the hydrodynamic load when the gap between the lining and the surrounding rock is closed, and then calculate the steel stress and the maximum crack width of the concrete according to the displacement continuity condition;

[0012] According to the requirements of normal use limit state, combined with safety and economy requirements, the optimal reinforcement design scheme of reinforced concrete lining is determined.

[0013] In a possible implementation, under the action of the seepage water pressure increment, the relationship between the hoop stress of the lining and the outer wall deformation and the inner wall deformation of the surrounding rock is as follows:

[0014]

[0015] The relationship between the hoop stress of the lining and the deformation of the outer wall and the inner wall of the surrounding rock under the action of the surface force increment is as follows:

[0016]

[0017] Among them, σ θ,P is the hoop stress of the lining under the action of penetration force, σ θ,F is the hoop stress of the surrounding rock under the action of penetration force; ΔP i , ΔP o are the water seepage pressure increments on the inner and outer surfaces of the lining respectively; r i 、r o are the inner and outer radius of the lining, respectively, and r o / r i =t;ΔF i , ΔF o are the surface force increments of the inner and outer surfaces of the lining respectively; μ c , μ r are the Poisson’s ratios of lining concrete and surrounding rock, respectively; is the radial displacement of the outer wall of the lining under the action of the penetration force, is the radial displacement of the inner wall of the surrounding rock under the action of penetration force; is the radial displacement of the outer wall of the lining under the action of the surface force, is the radial displacement of the inner wall of the surrounding rock under the action of surface force; The superscript c represents the lining concrete, the superscript r represents the surrounding rock, μ is the Poisson’s ratio of the lining concrete or surrounding rock, and E is the corresponding elastic modulus;

[0018]

[0019] In a possible implementation, in the method of combining hydraulic continuity conditions and displacement continuity conditions to calculate and determine the contact state between the lining and the surrounding rock during the construction completion period, the hydraulic continuity condition is Q c1 =Q r1 , the displacement continuity condition is Among them, Q c1 is the lining seepage, Q r1 is the surrounding rock seepage;

[0020] Seepage water pressure P at the lining-surrounding rock interface S1 With boundary force T S1 for:

[0021]

[0022] Among them, k c , k r is the permeability coefficient of lining and surrounding rock, R is the hydraulic permeability radius, and P0 is the seepage water pressure at the hydraulic permeability radius R;

[0023] If-T S1 ≤T0, the lining and the surrounding rock remain in a bonded state; if -T S1 >T0, the lining will be separated from the surrounding rock, where T0 is the bonding strength of the lining-surrounding rock interface.

[0024] In a possible implementation, the method of calculating the stress and maximum crack width of the steel bar after applying the hydrostatic load increment under different conditions according to the judgment result of the contact state includes:

[0025] (1) During the construction completion period, the lining and surrounding rock have not separated

[0026] After the hydrostatic load increment is applied, the load increment of the lining and surrounding rock is recorded as ΔPi =P H , ΔP o =P S2 , ΔF i =0, ΔF o =T S2 ;

[0027]

[0028] σ s =N / A s

[0029] The calculation formula for the maximum crack width of the lining is as follows:

[0030]

[0031] Where: Q c2 is the lining seepage under hydrostatic pressure, Q r2 is the seepage volume of surrounding rock under hydrostatic pressure; n is the number of cracks; g is the acceleration of gravity; υ is the kinematic viscosity coefficient of seepage water; P H is the maximum static water load during operation, P S2 T is the water seepage pressure on the outer wall of the lining under the action of hydrostatic pressure; S2 is the interfacial force before the lining and surrounding rock separate under the action of hydrostatic pressure, ω max is the maximum crack width of the lining; γ is the bulk density of the seepage water; N is the resultant force of the lining section; σ s A is the reinforcement stress at the lining crack position; s is the total area of ​​steel bars; ψ is the steel bar strain non-uniformity coefficient; E s is the elastic modulus of the steel bar; l f is the average crack spacing; d is the steel bar diameter; ρ s is the lining reinforcement ratio; ν is the steel bar surface shape coefficient; f tk is the standard value of concrete tensile strength; r s is the radius of the annular reinforcement ring; α1 and α2 are coefficients;

[0032] From the above formula, we know that P H By iteratively solving P S2 , and then solve the remaining variables; if -T S2 >T0, the lining is separated from the surrounding rock. At this time, let T S2 = 0 is substituted into the above equations and solved iteratively again to obtain the stress of the steel bar and the maximum crack width;

[0033] (2) During the construction completion period, the lining and surrounding rock have been separated

[0034] If the gap between the lining and the surrounding rock is closed before the lining cracks, the force T acting on the lining and surrounding rock interface before closing is S2 = 0, the lining will separate from the surrounding rock again after cracking. At this time, T S2 = 0 is substituted into the formula in (1) and solved it iteratively;

[0035] If the lining cracks before the gap closes, record the load increment ΔP1 = P H , ΔP2=P S2 , ΔF1=0, ΔF2=0; T S2 = 0 is substituted into formula (1) and solved iteratively to obtain the stress of the steel bar and the maximum crack width.

[0036] Furthermore, the method of continuing to apply the hydrodynamic load increment, calculating the hydrodynamic load when the gap between the lining and the surrounding rock is closed, and then calculating the steel stress and the maximum crack width of the concrete according to the displacement continuity condition meets the following conditions: the lining and the surrounding rock have been separated; the lining concrete ring after cracking is regarded as an orthotropic material and loses its bearing capacity in the annular direction; the boundary conditions are p4=0, p1 is the surface force load of the inner wall of the lining concrete, is the dynamic water load when the lining is closed, and p4 is the surface force load on the outer wall of the lining; after continuing to apply the dynamic water load increment, the displacement increment of the lining and surrounding rock meets the displacement continuity condition is the radial displacement of the outer wall of the lining concrete, u r is the radial displacement of the inner wall of the surrounding rock.

[0037] Furthermore, in the method of continuing to apply the dynamic water load increment, calculating the dynamic water load when the gap between the lining and the surrounding rock is closed, and then calculating the steel bar stress and the maximum crack width of the concrete according to the displacement continuity condition, the steel bar stress is:

[0038] σ s,all =σ s +Δσ s

[0039] Δσ s =(r i P D -r o T S3 ) / A s

[0040] Among them, σ s,all is the stress of the steel bar under the combined effect of static water load and dynamic water load, σ s is the reinforcement stress at the lining crack position under hydrostatic pressure, Δσ s is the reinforcement stress increment at the lining crack position under the action of dynamic water pressure, P D is the maximum dynamic water load during operation, A s is the total area of ​​steel bars; TS3 is the force acting on the interface between lining and surrounding rock under the action of dynamic water load, μ s is the steel bar Poisson’s ratio, is the dynamic water load when the gap between the lining and the surrounding rock is closed, r1, r2, r3, r4 are the radii of the inner wall of the lining, the inner wall of the equivalent steel lining, the outer wall of the equivalent steel lining, and the outer wall of the lining, respectively, μ c is the Poisson's ratio of lining concrete, E c is the elastic modulus of lining concrete;

[0041] Substitute the steel bar stress into the crack width calculation formula to solve and obtain the crack width.

[0042] In a second aspect, the present invention provides a reinforced concrete lining design device taking into account a water load increment process, comprising:

[0043] Module 1 is used to calculate and determine the contact state between the lining and the surrounding rock during the construction completion period based on the relationship between the hoop stress of the lining and the outer wall deformation and the inner wall deformation of the surrounding rock under the action of the seepage water pressure increment and the surface force increment, combined with the hydraulic continuity condition and displacement continuity condition between the lining and the surrounding rock;

[0044] Module 2 is used to calculate the stress and maximum crack width of the steel bar after applying the hydrostatic load increment under different conditions according to the judgment results of the contact state;

[0045] Module 3 is used to continue to apply the dynamic water load increment, calculate the dynamic water load when the gap between the lining and the surrounding rock is closed, and then calculate the steel bar stress and the maximum crack width of the concrete according to the displacement continuity condition;

[0046] Module 4 is used to determine the optimal reinforcement design scheme for reinforced concrete lining according to the normal use limit state requirements combined with safety and economy requirements.

[0047] In a third aspect, the present invention provides an electronic 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 program, the reinforced concrete lining design method taking into account the water load increment process as described above is implemented.

[0048] In a fourth aspect, the present invention provides a non-transitory computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the reinforced concrete lining design method considering the water load increment process as described above is implemented.

[0049] In a fifth aspect, a computer program product comprises a computer program, wherein when the computer program is executed by a processor, the method for designing reinforced concrete linings taking into account the water load increment process as described above is implemented.

[0050] Compared with the existing design method, the beneficial effects of the present invention are:

[0051] 1. Compared with the traditional lining design method based on the surface force theory, the present invention takes into account the effect of internal water seepage based on the permeable lining theory, effectively reduces the amount of steel bars used, and at the same time considers the effect of dynamic water load in the form of surface force, giving the lining sufficient safety reserve.

[0052] 2. Based on the permeable lining theory, the effect of water load increment in the whole process from the completion of construction to the water filling operation period is considered, revealing the conditional joint bearing characteristics between the lining and the surrounding rock, making the lining design closer to the actual load action process.

[0053] 3. Based on the orthogonal anisotropic constitutive model, the calculation model of cracked reinforced concrete lining under dynamic water load was derived. Compared with the existing lining design method, the effect of various loads on the lining structure during operation was fully considered. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 is a flow chart of the method of the present invention;

[0055] Figure 2 Schematic diagram of water load increment process;

[0056] Figure 3 It is a schematic diagram of the orthotropic cracking reinforced concrete model;

[0057] Figure 4 It is a structural schematic diagram of a reinforced concrete lining design device considering a water load increment process provided by the present invention;

[0058] Figure 5 It is a structural schematic diagram of the electronic device provided by the present invention. DETAILED DESCRIPTION

[0059] In order to facilitate the understanding of the present invention, the technical solution of the invention is further specifically described below through examples. The content of the present invention is not limited thereto.

[0060] like Figure 1 As shown in the figure, a reinforced concrete lining design method considering the water load increment process is presented.

[0061] Before the calculation step begins, the following formula is clarified based on the thick-walled cylinder theory:

[0062] According to the thick-walled cylinder theory, under the increment of seepage water pressure, the hoop stress of the lining and the deformation of the outer wall and the inner wall of the surrounding rock satisfy the following relationship:

[0063]

[0064] It should be noted that cracking or uncracked refers to whether the lining concrete is cracked or not.

[0065] Under the action of the surface force increment, the hoop stress of the lining, the outer wall deformation, and the inner wall deformation of the surrounding rock satisfy the following relationship:

[0066]

[0067] Among them, σ θ,P is the hoop stress of the lining under the action of penetration force, σ θ,F is the hoop stress of the surrounding rock under the action of penetration force; ΔP i , ΔP o are the water seepage pressure increments on the inner and outer surfaces of the lining respectively; r i 、r o are the inner and outer radius of the lining, respectively, and r o / r i =t;ΔF i , ΔF o are the surface force increments of the inner and outer surfaces of the lining respectively; μ c , μ r are the Poisson’s ratios of lining concrete and surrounding rock, respectively; is the radial displacement of the outer wall of the lining under the action of the penetration force, is the radial displacement of the inner wall of the surrounding rock under the action of penetration force; is the radial displacement of the outer wall of the lining under the action of the surface force, is the radial displacement of the inner wall of the surrounding rock under the action of surface force; The superscript c represents the lining concrete, the superscript r represents the surrounding rock, μ is the Poisson’s ratio of the lining concrete or surrounding rock, and E is the corresponding elastic modulus;

[0068]

[0069] The design method comprises the following steps:

[0070] Step 1: According to the lining and surrounding rock Figure 2 The relationship between the hoop stress of the lining and the deformation of the outer wall and the inner wall of the surrounding rock under the action of the seepage water pressure increment and the surface force increment shown in the figure is used to calculate the contact state between the lining and the surrounding rock during the construction completion period in combination with the hydraulic continuity condition and displacement continuity condition between the lining and the surrounding rock.

[0071] The load increment ΔP of the lining and surrounding rock during the construction completion period is recorded as i =0,ΔP o =P S1 , ΔF i =0, ΔF o =T S1 ;

[0072] Where: P S1is the seepage water pressure of the lining outer wall during the construction completion period, T S1 It is the force acting on the lining-surrounding rock interface during the construction completion period (i.e. boundary force).

[0073] The inner and outer walls of the lining are initially in a water-free state. The water load increment is the water head of the inner and outer walls. The seepage expression of the lining and surrounding rock is:

[0074]

[0075] Where: Q c is the lining seepage; k c , k r are the permeability coefficients of lining and surrounding rock respectively; γ is the bulk density of seepage water; n is the number of lining cracks; g is the gravitational acceleration, which is 10m / s 2 υ is the kinematic viscosity coefficient of the seepage water body, which is 1.308×10 - 6 m 2 / s;ω max is the maximum crack width of the lining; R is the hydraulic penetration radius; P0 is the seepage water pressure at the hydraulic penetration radius R.

[0076] Combining equations (2), (3), (7) and (8), we introduce the hydraulic continuity condition Q c1 =Q r1 Continuity condition with displacement Among them, Q c1 is the lining seepage during the construction completion period, Q r1 It is the surrounding rock seepage during the construction completion period.

[0077] Then the seepage water pressure and boundary force at the lining-surrounding rock interface are:

[0078]

[0079] If-T S1 ≤T0, the lining and the surrounding rock remain in a bonded state; if -T S1 >T0, the lining will be separated from the surrounding rock, where T0 is the bonding strength of the lining-surrounding rock interface.

[0080] Step 2: Based on the judgment results of the contact state, calculate the stress and maximum crack width of the steel bar after applying the hydrostatic load increment under different conditions.

[0081] It should be noted that the steel bars refer to the single layer of steel bars arranged close to the inner wall of the lining, and the maximum crack width refers to the crack width corresponding to the position of maximum stress of the steel bars.

[0082] There are two cases:

[0083] (1) During the construction completion period, the lining and surrounding rock have not separated

[0084] The load increment ΔP of the lining and surrounding rock under the hydrostatic pressure is i =P H , ΔP o =P S2 , ΔF i =0, ΔF o =T S2 ;

[0085] Before the lining cracks, the hydraulic continuity condition and displacement continuity condition are introduced by combining equations (2), (3), (7) and (8), and the seepage water pressure and boundary force at the lining-surrounding rock interface are:

[0086]

[0087] Then the lining section force N and the steel bar stress σ s They are:

[0088]

[0089] Where: E s 、E c are the elastic modulus of steel bars and lining concrete respectively; A s , A are the cross-sectional areas of the reinforcement and lining respectively.

[0090] After the lining cracks, it is first assumed that the lining is not separated from the surrounding rock, and the displacement continuity condition and hydraulic continuity condition are introduced to obtain:

[0091]

[0092] Then the resultant force of the lining section and the stress of the steel bar are:

[0093]

[0094] σ s =N / A s (18)

[0095] According to the "Design Code for Hydraulic Tunnels" (NB / T 10391-2020), the calculation formula for the maximum crack width of the lining is introduced as follows:

[0096]

[0097] Where: Q c2 is the lining seepage under hydrostatic pressure, Q r2 is the seepage volume of surrounding rock under hydrostatic pressure; n is the number of cracks; g is the gravitational acceleration; υ is the kinematic viscosity coefficient of seepage water, which is 1.308×10 -6 m 2 / s;P His the maximum static water load during operation, P S2 T is the water seepage pressure on the outer wall of the lining under the action of hydrostatic pressure; S2 is the interfacial force before the lining and surrounding rock separate under the action of hydrostatic pressure; ω max is the maximum crack width of the lining; γ is the bulk density of the seepage water; N is the resultant force of the lining section; σ s A is the steel bar stress at the lining crack position under hydrostatic pressure; s is the total area of ​​steel bars; ψ is the steel bar strain non-uniformity coefficient; E s is the elastic modulus of the steel bar; l f is the average crack spacing; d is the steel bar diameter; ν is the steel bar surface shape coefficient, which is 0.7 for threaded steel bars; ρ s is the lining reinforcement ratio; f tk is the standard value of concrete tensile strength; r s is the radius of the annular reinforcement ring; the coefficients α1 and α2 are taken as 0.16 and 0.6 respectively according to axial tension.

[0098] From equations (16) to (19), we can see that equation (16) is about P H , P S2 The implicit equation of P is known. H P can be solved by iteration S2 , and then solve for the remaining variables. If we obtain -T S2 >T0, the lining is separated from the surrounding rock. At this time, let T S2 Substituting =0 into the above equations and solving them iteratively again, we can obtain the stress of the steel bar and the maximum crack width.

[0099] (2) During the construction completion period, the lining and surrounding rock have been separated

[0100] If the gap is closed before the lining cracks, the interface force T S2 = 0, after the lining cracks, it is necessary to consider whether the lining and the surrounding rock will separate again. Existing engineering data and scientific research show that if the lining and the surrounding rock have separated during the construction completion period, the lining will separate from the surrounding rock again after cracking. At this time, T S2 Substitute =0 into equations (16) to (19) and solve them iteratively.

[0101] If the lining cracks before the gap closes, record the load increment ΔP1 = P H , ΔP2=P S2 , ΔF1=0, ΔF2=0. S2 =0 is substituted into equations (16) to (19) and solved iteratively to obtain the stress of the steel bar and the maximum crack width.

[0102] Step three: Continue to apply the dynamic water load increment, calculate the dynamic water load when the gap between the lining and the surrounding rock is closed, and then calculate the steel bar stress and the maximum crack width of the concrete according to the displacement continuity condition.

[0103] It should be noted that step three is to continue applying the dynamic water load increment while maintaining the static water load increment.

[0104] Assuming that the lining and the surrounding rock have been separated in step 2 (if the lining and the surrounding rock are not separated, ξ0 = 0), the gap ξ0 between the lining and the surrounding rock is obtained from equations (1) and (3):

[0105]

[0106] The tensile stress equivalent method is used to convert the steel bar into an equivalent steel lining with a thickness of d. Figure 3 The following parameters are introduced: r1, r2, r3, and r4 represent the radius of the inner wall of the lining, the inner wall of the equivalent steel lining, the outer wall of the equivalent steel lining, and the outer wall of the lining, respectively; p1, p2, p3, and p4 represent the surface force loads at r1, r2, r3, and r4, respectively.

[0107] It should be noted that the steel bars are converted into equivalent steel linings, which are the steel bars arranged close to the inner wall of the lining.

[0108] For the cracked lining concrete ring, it is regarded as an orthotropic material, which loses its bearing capacity in the annular direction, and the strain generated by the annular force is 0. Its physical equation is:

[0109]

[0110] Among them, ε θ is the hoop strain of the concrete ring, E c,θ is the hoop elastic modulus of the lining concrete ring, σ θ is the hoop stress of the lining concrete ring, ε r is the radial strain of the lining concrete ring, μ c is the Poisson's ratio of the lining concrete ring, E c is the elastic modulus of the lining concrete ring, σ r is the radial stress of the lining concrete ring.

[0111] Substituting the plane strain geometric equation in polar coordinates into the physical equation of cracked concrete, we get:

[0112]

[0113] Among them, E c,θ is the hoop elastic modulus of the lining concrete ring, u is the radial displacement of the calculation point, r is the distance from the calculation point to the center of the lining circle, σ r is the radial stress of the lining concrete ring;

[0114] Substituting the plane strain equilibrium equation in polar coordinates, we get:

[0115]

[0116] Introducing the orthogonal anisotropy condition E c,θ = 0 and simplify to get:

[0117]

[0118] Solving the equilibrium differential equation gives the general solution:

[0119] u=D1lnr+D2 (27)

[0120] Where D1 and D2 are arbitrary constants of the general solution of the above expression;

[0121] The boundary condition σ r，r1 =p1,σ r，r2 =p2 Substitute into

[0122]

[0123] in, is the radial stress of the inner wall of the lining concrete, p1 is the surface force load of the inner wall of the lining concrete, is the radial stress of the lining concrete at the inner wall of the equivalent steel lining, and p2 is the surface force load of the lining concrete at the inner wall of the equivalent steel lining;

[0124] Radial displacement of cracked concrete ring u c,r The general solution is:

[0125]

[0126] Where B is an arbitrary constant of the general solution of the above expression;

[0127] At the same time, the equivalent outer surface displacement of the steel lining is obtained by solving the radial displacement of the outer side of the thick-walled cylinder under the action of the surface force. for:

[0128]

[0129] Among them, μ s is the Poisson's ratio of the equivalent steel lining (i.e., steel bar), E s is the elastic modulus of the equivalent steel lining (i.e., steel bar);

[0130] Introducing the displacement continuity condition between the lining concrete and the equivalent steel lining, we get:

[0131]

[0132] in, is the radial displacement of the lining concrete at the inner and outer walls of the equivalent steel lining, is the radial displacement of the inner and outer walls of the equivalent steel lining;

[0133] Substitute into equation (30) and equation (31):

[0134]

[0135] Among them, B1 and B2 are arbitrary constants of the general solution of the above expression;

[0136] For cracked lining concrete, ignoring its annular bearing capacity, it can be obtained:

[0137] p1r1=p2r2,p3r3=p4r4 (35)

[0138] Introducing boundary conditions p4=0, then:

[0139]

[0140] in, The radial deformation of the outer wall of the lining, is the dynamic water load when the gap between the lining and the surrounding rock is closed, P D is the maximum dynamic water load during operation.

[0141] Determine the dynamic water load when the lining is closed Subsequent hydrodynamic load (For the case where the lining is not separated from the surrounding rock, ) under the action of the lining and surrounding rock displacement increments meet the displacement continuity condition u r is the radial displacement of the inner wall of the surrounding rock, that is:

[0142]

[0143] Substitution Obtain

[0144]

[0145] Among them, T S3 It is the force acting on the interface between lining and surrounding rock under the action of dynamic water load.

[0146] At this time, the total stress of the steel bar is:

[0147] Δσ s =(r i P D -r o T S3 ) / A s (39)

[0148] σ s,all =σ s +Δσ s (40)

[0149] Among them, σ s,all is the stress of the steel bar under the combined effect of static water load and dynamic water load, σ s is the reinforcement stress at the lining crack position under hydrostatic pressure, Δσ s A is the stress increment of the reinforcement at the lining crack under the action of dynamic water pressure, s is the total area of ​​steel bars.

[0150] Substitute it into crack width calculation formula (19) again to solve.

[0151] Step 4: Determine the optimal design of reinforced concrete lining according to the requirements of the normal use limit state, combined with the requirements of safety and economy. In the above steps, if the lining is not cracked, the structural reinforcement can be carried out according to the minimum reinforcement ratio requirements.

[0152] This will be described below with reference to specific embodiments.

[0153] Example 1

[0154] (1) Calculation conditions

[0155] The reinforced concrete lining of the circular cross-section water diversion tunnel of a pumped storage power station has an inner radius of 4.75m and a wall thickness of 0.8m. C30 concrete is used, with an elastic modulus of 30GPa, a Poisson's ratio of 0.167, and a permeability coefficient of 1×10 -9 m / s; the surrounding rock is Class III, with an elastic modulus of 9 GPa, a Poisson's ratio of 0.27, and a permeability of 1×10 -7 m / s, the surrounding rock penetration radius is taken as 60 times the excavation hole diameter, and the water pressure at the penetration radius is 1MPa; the bonding strength between the lining and the surrounding rock is 0.5MPa, and a single layer of HRB400 steel bars is planned to be arranged on the inner side, with an elastic modulus of 206GPa, a Poisson's ratio of 0.3, and a protective layer thickness of 50mm. The maximum static water load during operation is 5.2MPa, and the maximum dynamic water load is 1.5MPa.

[0156] (2) Design process

[0157] Step 1: Based on the experience of similar projects, the initial reinforcement scheme is 10 28mm HRB400 steel bars on one side. According to the external water conditions, the lining and the surrounding rock have been separated during the construction completion period, and the gap between the lining and the surrounding rock is 1.8mm. At this time, the reinforced concrete lining is in a compressive state as a whole, and the compressive stress of the steel bar is 33.42MPa.

[0158] Step 2: Apply hydrostatic load incremental head.

[0159] Firstly, the sequence between closure of the lining-surrounding rock gap and cracking of the lining was calculated. The calculation results showed that the lining had cracked before closing with the surrounding rock, and the cracking load was 1.27MPa. When the hydrostatic load increased to 5.2MPa, the seepage water pressure of the lining outer wall was 5.06MPa, the steel bar stress was 115.17MPa, the maximum crack width was 0.088mm, and the gap between the lining and the surrounding rock was 3.8mm.

[0160] Step three: Apply dynamic water load incremental head.

[0161] First, the dynamic water load corresponding to the re-closure of the lining and surrounding rock is calculated. The calculation results show that when the dynamic water load reaches 0.23MPa, the gap between the lining and the surrounding rock is closed, and then the joint bearing process begins; when the dynamic water load reaches 1.5MPa, the interaction force between the lining and the surrounding rock reaches 1.05MPa, the steel bar stress reaches 330.42MPa, and the maximum crack width reaches 0.66mm.

[0162] By adopting different reinforcement schemes, the calculation results are as follows:

[0163] When the reinforcement scheme is to arrange a single layer of 10 28mm HRB400 steel bars close to the inner wall of the lining, the steel stress is 330.42MPa and the maximum crack width is 0.66mm;

[0164] When the reinforcement scheme is to arrange a single layer of 10 25mm HRB400 steel bars close to the inner wall of the lining, the steel bar stress is 334.81MPa and the maximum crack width is 0.59mm;

[0165] When the reinforcement scheme is to arrange a single layer of 10 22mm HRB400 steel bars close to the inner wall of the lining, the steel stress is 338.82MPa and the maximum crack width is 0.47mm;

[0166] When the reinforcement scheme is to arrange a single layer of 10 20mm HRB400 steel bars close to the inner wall of the lining, the steel stress is 341.27MPa and the maximum crack width is 0.52mm.

[0167] For the above reinforcement scheme, arranging a single layer of 10 22mm HRB400 steel bars close to the inner wall of the lining is a better choice.

[0168] Example 2

[0169] (1) Calculation conditions

[0170] The reinforced concrete lining of the circular cross-section water diversion tunnel of a pumped storage power station has an inner radius of 4m and a wall thickness of 0.6m. C30 concrete is used, with an elastic modulus of 30GPa, a Poisson's ratio of 0.167, and a permeability coefficient of 1×10 -9m / s; the surrounding rock is Class III, with an elastic modulus of 9 GPa, a Poisson's ratio of 0.27, and a permeability of 1×10 -7 m / s, the surrounding rock penetration radius is taken as 60 times the excavation hole diameter, and the water pressure at the penetration radius is 1MPa; the bonding strength between the lining and the surrounding rock is 1MPa, and a single layer of HRB400 steel bars is planned to be arranged on the inner side, with an elastic modulus of 206GPa, a Poisson's ratio of 0.3, and a protective layer thickness of 50mm. The maximum static water load during operation is 3.5MPa, and the maximum dynamic water load is 0.8MPa.

[0171] (2) Design process

[0172] Step 1: Based on the experience of similar projects, the initial reinforcement scheme is 10 25mm HRB400 steel bars on one side. According to the external water conditions, it is found that the lining is not separated from the surrounding rock during the construction completion period, and the lining expands outward with the surrounding rock, and is in a tensile state as a whole, and the tensile stress of the steel bar is 10.98MPa.

[0173] Step 2: Apply hydrostatic load incremental head.

[0174] First, the hydrostatic load corresponding to the cracking of the lining is calculated. The calculation results show that the cracking load of the lining is 0.21MPa. At this time, the lining and the surrounding rock are still not separated, and they deform outward together; when the hydrostatic load reaches 2.61MPa, the lining is separated from the surrounding rock, and the seepage water pressure of the lining outer wall is 2.49MPa; when the hydrostatic load increases to 3.5MPa, the seepage water pressure of the lining outer wall is 3.37MPa, the steel bar stress is 109.85MPa, the maximum crack width is 0.069mm, and the gap between the lining and the surrounding rock is 2.1mm.

[0175] Step three: Apply dynamic water load incremental head.

[0176] First, the dynamic water load corresponding to the re-closure of the lining and surrounding rock is calculated. The calculation results show that when the dynamic water load reaches 0.14MPa, the gap between the lining and the surrounding rock is closed, and then the joint bearing process begins; when the dynamic water load reaches 0.8MPa, the interaction force between the lining and the surrounding rock reaches 0.55MPa, the steel bar stress reaches 243.65MPa, and the maximum crack width reaches 0.30mm.

[0177] By adopting different reinforcement schemes, the calculation results are as follows:

[0178] When the reinforcement scheme is to arrange a single layer of 10 25mm HRB400 steel bars close to the inner wall of the lining, the steel stress is 243.65MPa and the maximum crack width is 0.30mm;

[0179] When the reinforcement scheme is to arrange a single layer of 8 25mm HRB400 steel bars close to the inner wall of the lining, the steel stress is 244.19MPa and the maximum crack width is 0.26mm;

[0180] When the reinforcement scheme is to arrange a single layer of 10 22mm HRB400 steel bars close to the inner wall of the lining, the steel stress is 247.81MPa and the maximum crack width is 0.25mm.

[0181] When the reinforcement scheme is to arrange a single layer of 8 22mm HRB400 steel bars close to the inner wall of the lining, the steel stress is 247.48MPa and the maximum crack width is 0.30mm.

[0182] For the above reinforcement scheme, arranging a single layer of 10 22mm HRB400 steel bars close to the inner wall of the lining is a better choice.

[0183] A reinforced concrete lining design device considering the water load increment process provided by the present invention is described below. The reinforced concrete lining design device considering the water load increment process described below and the reinforced concrete lining design method considering the water load increment process described above can be referenced to each other.

[0184] Figure 4 is a structural schematic diagram of a reinforced concrete lining design device considering a water load increment process provided by an embodiment of the present invention, such as Figure 4 As shown, it includes: module one 41, module two 42, module three 43 and module four 44, wherein:

[0185] Module 1 41 is used to calculate and determine the contact state between the lining and the surrounding rock during the construction completion period according to the relationship between the hoop stress of the lining and the outer wall deformation and the inner wall deformation of the surrounding rock under the action of the seepage water pressure increment and the surface force increment, combined with the hydraulic continuity condition and displacement continuity condition between the lining and the surrounding rock;

[0186] Module 2 42 is used to calculate the stress and maximum crack width of the steel bar after applying the hydrostatic load increment under different conditions according to the judgment result of the contact state;

[0187] Module three 43 is used to continue to apply the dynamic water load increment, calculate the dynamic water load when the gap between the lining and the surrounding rock is closed, and then calculate the steel bar stress and the maximum crack width of the concrete according to the displacement continuity condition;

[0188] Module 4 44 is used to determine the optimal reinforcement design scheme for reinforced concrete lining according to the normal use limit state requirements combined with safety and economy requirements.

[0189] Figure 5 An example of a physical structure diagram of an electronic device is shown in FIG. Figure 5 As shown, the electronic device may include: a processor 510, a communication interface 520, a memory 530 and a communication bus 540, wherein the processor 510, the communication interface 520 and the memory 530 communicate with each other through the communication bus 540. The processor 510 may call the logic instructions in the memory 530 to execute the reinforced concrete lining design method considering the water load increment process.

[0190] In addition, the logic instructions in the above-mentioned memory 530 can be implemented in the form of a software functional unit and can be stored in a computer-readable storage medium when it is sold or used as an independent product. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, etc. Various media that can store program codes.

[0191] On the other hand, the present invention also provides a computer program product, which includes a computer program. The computer program can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute the reinforced concrete lining design method considering the water load increment process provided by the above-mentioned methods.

[0192] On the other hand, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, is implemented to execute the reinforced concrete lining design method considering the water load increment process provided by the above-mentioned methods.

[0193] The device embodiments described above are merely illustrative, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. Ordinary technicians in this field can understand and implement it without paying creative labor.

[0194] Through the description of the above implementation methods, those skilled in the art can clearly understand that each implementation method can be implemented by means of software plus a necessary general hardware platform, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solution is essentially or the part that contributes to the prior art can be embodied in the form of a software product, and the computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a disk, an optical disk, etc., including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0195] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these 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.

Claims

1. A reinforced concrete lining design method considering the water load increment process, characterized in that: The following steps are involved: According to the relationship between the hoop stress of the lining and the deformation of the outer wall and the inner wall of the surrounding rock under the action of the seepage water pressure increment and the surface force increment, combined with the hydraulic continuity condition and displacement continuity condition between the lining and the surrounding rock, the contact state between the lining and the surrounding rock during the construction completion period is calculated and judged; According to the judgment results of the contact state, the stress and maximum crack width of the steel bar after applying the hydrostatic load increment under different conditions are calculated; Continue to apply the hydrodynamic load increments to calculate the hydrodynamic load when the gap between the lining and the surrounding rock is closed, and then calculate the steel stress and the maximum crack width of the concrete according to the displacement continuity condition; According to the requirements of normal use limit state, combined with safety and economy requirements, the optimal reinforcement design scheme of reinforced concrete lining is determined.

2. The reinforced concrete lining design method considering the water load increment process according to claim 1 is characterized in that: Under the action of the seepage water pressure increment, the relationship between the hoop stress of the lining and the outer wall deformation and the inner wall deformation of the surrounding rock is as follows: The relationship between the hoop stress of the lining and the deformation of the outer wall and the inner wall of the surrounding rock under the action of the surface force increment is as follows: Among them, σ θ,P is the hoop stress of the lining under the action of penetration force, σ θ,F is the hoop stress of the surrounding rock under the action of penetration force; ΔP i , ΔP o are the water seepage pressure increments on the inner and outer surfaces of the lining respectively; r i 、r o are the inner and outer radius of the lining, and r o / r i =t;ΔF i , ΔF o are the surface force increments of the inner and outer surfaces of the lining respectively; μ c , μ r are the Poisson’s ratios of lining concrete and surrounding rock, respectively; is the radial displacement of the outer wall of the lining under the action of the penetration force, is the radial displacement of the inner wall of the surrounding rock under the action of penetration force; is the radial displacement of the outer wall of the lining under the action of the surface force, is the radial displacement of the inner wall of the surrounding rock under the action of surface force; The superscript c represents the lining concrete, the superscript r represents the surrounding rock, μ is the Poisson’s ratio of the lining concrete or surrounding rock, and E is the corresponding elastic modulus; 3. The reinforced concrete lining design method considering the water load increment process according to claim 2 is characterized in that: In the method for calculating and judging the contact state between the lining and the surrounding rock during the construction completion period by combining the hydraulic continuity condition and the displacement continuity condition, the hydraulic continuity condition is Q c1 =Q r1 , the displacement continuity condition is Among them, Q c1 is the lining seepage, Q r1 is the surrounding rock seepage; Seepage water pressure P at the lining-surrounding rock interface S1 With boundary force T S1 for: Among them, k c , k r is the permeability coefficient of lining and surrounding rock, R is the hydraulic permeability radius, and P0 is the seepage water pressure at the hydraulic permeability radius R; If-T S1 ≤T0, the lining and the surrounding rock remain in a bonded state; if -T S1 >T0, the lining will be separated from the surrounding rock, where T0 is the bonding strength of the lining-surrounding rock interface.

4. The reinforced concrete lining design method considering the water load increment process according to claim 3 is characterized in that: The method for calculating the stress and maximum crack width of the steel bar after applying the hydrostatic load increment under different conditions according to the judgment result of the contact state includes: (1) During the construction completion period, the lining and surrounding rock have not separated After the hydrostatic load increment is applied, the load increment of the lining and surrounding rock is recorded as ΔP i =P H , ΔP o =P S2 , ΔF i =0, ΔF o =T S2 ; s s =N / A s The calculation formula for the maximum crack width of the lining is as follows: Where: Q c2 is the lining seepage under hydrostatic pressure, Q r2 is the seepage volume of surrounding rock under hydrostatic pressure; n is the number of cracks; g is the acceleration of gravity; υ is the kinematic viscosity coefficient of seepage water; P H is the maximum static water load during operation, P S2 T is the water seepage pressure on the outer wall of the lining under the action of hydrostatic pressure; S2 is the interfacial force before the lining and surrounding rock separate under the action of hydrostatic pressure, ω max is the maximum crack width of the lining; γ is the bulk density of the seepage water; N is the resultant force of the lining section; σ s A is the reinforcement stress at the lining crack position; s is the total area of ​​steel bars; ψ is the steel bar strain non-uniformity coefficient; E s is the elastic modulus of the steel bar; l f is the average crack spacing; d is the steel bar diameter; ρ s is the lining reinforcement ratio; ν is the steel bar surface shape coefficient; f tk is the standard value of concrete tensile strength; r s is the radius of the annular steel ring; the bulk density of the seepage water body α1 and α2 are coefficients; From the above formula, we know that P H By iteratively solving P S2 , and then solve the remaining variables; if -T S2 >T0, the lining is separated from the surrounding rock. At this time, let T S2 = 0 is substituted into the above equations and solved iteratively again to obtain the stress of the steel bar and the maximum crack width; (2) During the construction completion period, the lining and surrounding rock have been separated If the gap between the lining and the surrounding rock is closed before the lining cracks, the force T acting on the lining and surrounding rock interface before closing is S2 = 0, the lining will separate from the surrounding rock again after cracking. At this time, T S2 = 0 is substituted into the formula in (1) and solved it iteratively; If the lining cracks before the gap closes, record the load increment ΔP1 = P H , ΔP2=P S2 , ΔF1=0, ΔF2=0; T S2 = 0 is substituted into formula (1) and solved iteratively to obtain the stress of the steel bar and the maximum crack width.

5. The reinforced concrete lining design method considering the water load increment process according to claim 4 is characterized in that: The method of continuing to apply the hydrodynamic load increment, calculating the hydrodynamic load when the gap between the lining and the surrounding rock is closed, and then calculating the steel stress and the maximum crack width of the concrete according to the displacement continuity condition, meets the following conditions: the lining and the surrounding rock have been separated; for the cracked lining concrete ring, it is regarded as an orthotropic material and loses its bearing capacity in the annular direction; the boundary conditions are p4=0, p1 is the surface force load of the inner wall of the lining concrete, is the dynamic water load when the lining is closed, and p4 is the surface force load on the outer wall of the lining; after the dynamic water load increment is continuously applied, the displacement increment of the lining and the surrounding rock meets the displacement continuity condition is the radial displacement of the outer wall of the lining concrete, u r is the radial displacement of the inner wall of the surrounding rock.

6. The reinforced concrete lining design method considering the water load increment process according to claim 4 is characterized in that: In the method of continuing to apply the dynamic water load increment, calculating the dynamic water load when the gap between the lining and the surrounding rock is closed, and then calculating the steel bar stress and the maximum crack width of the concrete according to the displacement continuity condition, the steel bar stress is: s s,all =s s +Ds s Δσ s =(r i P D -r o T S3 ) / A s Among them, σ s,all is the stress of the steel bar under the combined effect of static water load and dynamic water load, σ s is the reinforcement stress at the lining crack position under hydrostatic pressure, Δσ s is the reinforcement stress increment at the lining crack position under the action of dynamic water pressure, P D is the maximum dynamic water load during operation, A s is the total area of ​​steel bars; T S3 is the force acting on the interface between lining and surrounding rock under the action of dynamic water load, μ s is the steel bar Poisson’s ratio, is the dynamic water load when the gap between the lining and the surrounding rock is closed, r1, r2, r3, r4 are the radii of the inner wall of the lining, the inner wall of the equivalent steel lining, the outer wall of the equivalent steel lining, and the outer wall of the lining, respectively, μ c is the Poisson's ratio of lining concrete, E c is the elastic modulus of lining concrete; Substitute the steel bar stress into the crack width calculation formula to solve and obtain the crack width.

7. A reinforced concrete lining design device considering the water load increment process, characterized in that: include: Module 1 is used to calculate and determine the contact state between the lining and the surrounding rock during the construction completion period based on the relationship between the hoop stress of the lining and the outer wall deformation and the inner wall deformation of the surrounding rock under the action of the seepage water pressure increment and the surface force increment, combined with the hydraulic continuity condition and displacement continuity condition between the lining and the surrounding rock; Module 2 is used to calculate the stress and maximum crack width of the steel bar after applying the hydrostatic load increment under different conditions according to the judgment results of the contact state; Module 3 is used to continue to apply the dynamic water load increment, calculate the dynamic water load when the gap between the lining and the surrounding rock is closed, and then calculate the steel bar stress and the maximum crack width of the concrete according to the displacement continuity condition; Module 4 is used to determine the optimal reinforcement design scheme for reinforced concrete lining according to the normal use limit state requirements combined with safety and economy requirements.

8. An electronic 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 program, the reinforced concrete lining design method considering the water load increment process as described in any one of claims 1 to 6 is implemented.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the reinforced concrete lining design method considering the water load increment process as described in any one of claims 1 to 6 is implemented.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the reinforced concrete lining design method considering the water load increment process as described in any one of claims 1 to 6 is implemented.

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