Shear-bearing capacity calculation method for the circumferential joint of a shield tunnel

Abstract

The present invention discloses a shear-bearing capacity calculation method for the circumferential joint of a shield tunnel, belonging to the technical field of shield tunnels, which includes: selecting the target circumferential joint of the shield tunnel; obtaining the spatial dimensions and bearing strength parameters of the segments, steel bars, and connectors in the target circumferential joint; constructing a shear-resistant model of the circumferential joint at different bearing stages according to the spatial dimensions in the circumferential joint; and calculating the shear-bearing capacity of the circumferential joint according to the shear-resistant model of the circumferential joint at different bearing stages. By constructing the shear-resistant model of the circumferential joint at different bearing stages to calculate the shear-bearing capacity of the circumferential joint, the present invention has strong theoretical guiding significance for the safe construction of shield tunnels; it also has important guiding significance for the parameter setting of shield tunnels, including the specific settings of concrete strength, tensile steel bars in the concrete rupture zone, segment thickness, connectors, etc.

Description

Technical Field

[0001] The present invention belongs to the technical field of shield tunnels, and particularly relates to a shear-bearing capacity calculation method for the circumferential joint of a shield tunnel. Background Art

[0002] A shield tunnel is a fully mechanized construction method in the cut-and-cover method. It is to push a shield machine underground, and the surrounding rock is borne by the shield shell and segment to prevent collapse into the tunnel. At the same time, the soil is excavated by a cutting device in front of the excavation face, transported out of the tunnel by an earth-moving machine, jacked forward by a jack at the rear, and precast concrete segments are assembled to form a tunnel structure.

[0003] During the construction of a shield tunnel, due to the disturbance of the surrounding rock mass and soil, the rock mass and soil will generate a huge shear force on the segments. Therefore, the shear-bearing capacity of the segment joints is very important. However, the existing technology lacks a method for calculating the shear-bearing capacity of segment joints and cannot provide theoretical support for segment design. Summary of the Invention

[0004] The purpose of the present invention is to provide a shear-bearing capacity calculation method for the circumferential joint of a shield tunnel to solve the problem that the existing technology lacks a method for calculating the shear-bearing capacity of segment joints.

[0005] To achieve the above purpose, the technical solution adopted by the present invention is:

[0006] A shear-bearing capacity calculation method for the circumferential joint of a shield tunnel, comprising the following steps:

[0007] S1. Select the target circumferential joint of the shield tunnel;

[0008] S2. Obtain the spatial dimensions and bearing strength parameters of the segments, steel bars, and connectors in the target circumferential joint;

[0009] S3. Construct a shear-resistant model of the circumferential joint at different bearing stages according to the spatial dimensions in the circumferential joint;

[0010] S4. Calculate the shear-bearing capacity of the circumferential joint according to the shear-resistant model of the circumferential joint at different bearing stages.

[0011] Further, in S1, the target circumferential joint includes a segment joint; the segment joint includes a first segment and a second segment, and a positioning tenon and a longitudinal bolt are provided between the circumferential joints of the first segment and the second segment; and the connection between the first segment and the second segment is realized through the positioning tenon and the longitudinal bolt;

[0012] The circumferential joint surface of the first segment is prefabricated with a quasi-rectangular mortise groove, and the circumferential joint surface of the second segment is prefabricated with a circular mortise hole. The mortise groove and the mortise hole are used to place the positioning tenon.

[0013] Further, S2 specifically includes:

[0014] The spatial dimensions of the segment include the thickness of the segment, the radial height L of the mortise groove from the inner arc side of the first segment R , the width L of the upper plane of the mortise groove D , the height L from the center of the bolt hole on the joint surface to the inner arc surface r , the thickness C of the segment protective layer. The bearing strength parameters of the segment include the design value f of the tensile strength of the concrete t ;

[0015] The spatial dimensions of the steel bars include the number i of steel bars that can provide vertical tensile force around the positioning tenon, the diameter A of the i-th steel bar Si , the included angle θ between the i-th steel bar and the vertical direction Si , and the bearing strength parameters of the steel bars include the design value f of the tensile strength of the steel bars y ;

[0016] The connecting piece includes a positioning tenon and a bolt; the spatial dimensions of the positioning tenon include the inner diameter D Dn and the outer diameter D Dw at the joint of the positioning tenon, and the bearing strength parameter of the positioning tenon includes the shear strength f D of the positioning tenon; the spatial dimension of the bolt includes the diameter D B of the bolt, and the bearing strength parameter of the bolt includes the tensile strength f B of the bolt.

[0017] Further, S3 specifically includes:

[0018] The circumferential joint shear model is used to calculate the minimum shear bearing capacity in the most unfavorable stress direction of the circumferential joint, that is, to calculate the concrete and steel bars above the mortise groove of the first segment to bear the extrusion load of the connecting piece;

[0019] The circumferential joint shear model includes a concrete shear model, a steel bar shear model, and a connecting piece shear model;

[0020] The concrete shear model is a quadrangular prism AEGB-CFHD, caused by the positioning tenon extruding the concrete above the mortise groove of the first segment. The quadrangular prism is an isosceles trapezoid AEGB on the joint surface;

[0021] The steel bar shear model is a quadrangular pyramid O-EMNG, caused by the bolt extruding the concrete above the mortise groove of the first segment. The quadrangular pyramid is an isosceles triangle OEG on the joint surface;

[0022] The connecting piece shear model is jointly composed of the shear mechanical equations of the positioning tenon and the bolt.

[0023] Further, in the quadrangular prism AEGB-CFHD, AB = L D , EG = L C , GH = C, and the height of the isosceles trapezoid AEGB is L R ; the height of the quadrangular pyramid O-EMNG is L r , EM = L L ;

[0024] L L and L c are obtained from experimental test statistics; when L R is 116 mm, L r is 160 mm, and L D is 66 mm, the experimental test of L L0 is 370 mm, and the experimental test expression of L c is:

[0025] L C0 = 494 - 0.1827×N

[0026] According to geometric relationships and similarity ratios, when the radial height on the inner arc side of the first segment is L R , the calculation formula of L c is:

[0027]

[0028] L L The calculation formula is:

[0029]

[0030] where N is the longitudinal axial force.

[0031] Further, the quadrangular prism AEGB-CFHD is for concrete shear bearing. In the quadrangular prism, the rectangles AEFC and BDHG are concrete tensile surfaces, and the trapezoid CFHD is a shear surface under compression;

[0032] The quadrangular pyramid O-EMNG is for steel bar shear bearing, considering the steel bars passing through the quadrangular pyramid and capable of providing vertical forces;

[0033] In the shear model of the connector, the positioning tenon provides shear bearing capacity; because the bolt has sufficient deformation space, it is mainly in tension after deformation and provides tensile bearing capacity.

[0034] Further, according to the shear model of the circumferential joint in the concrete shear stage, calculate the shear bearing capacity of the circumferential joint in the concrete shear stage:

[0035] Q u1 = f t C(LC -L D ) + 0.35f t L R (L D +L C ) + μN + K(N)

[0036] Among them, Q u1 is the shear bearing capacity in the shear stage of concrete; μ is the friction coefficient between the concrete joint surfaces; K(N) is the increment of the shear load of the trapezoid CFHD in the prismatic structure caused by the longitudinal axial force;

[0037] K(N) is obtained through experimental tests, and its calculation formula is:

[0038]

[0039] Furthermore, the shear bearing capacity of the connector is:

[0040]

[0041] Among them, Q u2 is the shear bearing capacity of the connector.

[0042] Furthermore, according to the shear model of the circumferential joint in the shear stage of the steel bar, the shear bearing capacity of the joint in the shear stage of the steel bar is calculated as:

[0043]

[0044] Among them, Q u3 is the shear bearing capacity of the joint in the shear stage of the steel bar.

[0045] Furthermore, in S4, according to the minimum shear bearing capacity in the shear stage of concrete, the shear bearing capacity of the connector, and the shear bearing capacity of the joint in the shear stage of the steel bar, the shear bearing capacity of the circumferential joint is calculated as:

[0046] Q u = min{max[Q u1 ; Q u3 ; Q u2}

[0047] Among them, Q u is the minimum shear bearing capacity in the most unfavorable stress direction of the circumferential joint.

[0048] The shear bearing capacity calculation method of the circumferential joint of the shield tunnel provided by the present invention has the following beneficial effects:

[0049] The present invention calculates the shear bearing capacity of the circumferential joint by constructing shear models of the circumferential joint at different bearing stages, which has strong theoretical guiding significance for the safe construction of shield tunnels; it also has important guiding significance for the parameter setting of shield tunnels, including the specific setting of concrete strength, tensile reinforcement in the concrete rupture zone, segment thickness, connectors, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is a flow chart of the shear bearing capacity calculation method for the circumferential joint of the shield tunnel of the present invention.

[0051] Figure 2 It is a structural diagram of the segment of the shield tunnel of the present invention, where ① is the circumferential joint; ② is the longitudinal bolt; ③ is the positioning tenon.

[0052] Figure 3 It is the concrete shear model of the present invention.

[0053] Figure 4 It is the steel bar shear model of the present invention.

[0054] Figure 5 It is the inclination angle of the steel bar in the steel bar shear model of the present invention.

[0055] Figure 6 It is Q under different longitudinal axial forces in the present invention u1 、Q u2 、Q u3 and Q u variation curves. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0056] The following describes the specific embodiments of the present invention to facilitate those skilled in the art to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions created using the concept of the present invention are within the scope of protection.

[0057] Embodiment

[0058] This embodiment provides a shear bearing capacity calculation method for the circumferential joint of a shield tunnel. Referring to Figure 1 , it specifically includes the following steps:

[0059] Step S1: Select the target circumferential joint of the shield tunnel, which specifically includes the following content:

[0060] Referring to Figure 2, in this embodiment, the outer diameter of the shield tunnel is 8.3 m and the inner diameter is 7.5 m; the thickness of the segment is 0.4 m, the width is 1.8 m, and one ring of segments is divided into 1 + 2 + 4 blocks. The segment rings are connected by 19 evenly distributed longitudinal bolts. To control the number of variables in the study, this embodiment selects Figure 2 the segment joint connected by 1 longitudinal bolt within the red line area in

[0061] as the target object. Among them, the segment joint includes a first segment and a second segment. Specifically, a positioning tenon and a longitudinal bolt are provided between the circumferential joints of the first segment and the second segment; the connection between the first segment and the second segment is realized through the positioning tenon and the longitudinal bolt; the first segment is the Figure 2 segment 1 in Figure 2 and the second segment is the

[0062] segment 2 in

[0063] A quasi-rectangular mortise groove is prefabricated on the circumferential joint surface of the first segment, and a circular mortise hole is prefabricated on the circumferential joint surface of the second segment. The mortise groove and the mortise hole are used to place the positioning tenon, satisfying that the mortise holes are at the same height, the mortise groove is in line-contact with the positioning tenon, and the mortise hole is in surface-contact with the positioning tenon. Figure 2

[0064] Step S2: Obtain the spatial dimensions and bearing strength parameters of the segments, steel bars, and connectors in the target circumferential joint, which specifically include the following contents:

[0065] Referring to Figure 2 , the spatial dimensions of the segment include the thickness of the segment, the radial height L R from the mortise groove to the inner arc side of the first segment, the width L D of the upper plane of the mortise groove, the height L r from the center of the bolt hole on the joint surface to the inner arc surface, and the segment cover thickness C. The bearing strength parameters of the segment include the design value f t of the tensile strength of the concrete.

[0066] The spatial dimensions of the steel bar include the number i of steel bars that can provide vertical tensile force around the positioning tenon and the diameter A Si ​, the included angle θ between the i-th steel bar and the vertical direction Si , the bearing strength parameters of the steel bar include the design value of the tensile strength of the steel bar f y .

[0067] The connecting piece includes a positioning tenon and a bolt; the spatial dimensions of the positioning tenon include the inner diameter D Dn and the outer diameter D Dw at the joint, and the bearing strength parameters of the positioning tenon include the shear strength f D of the positioning tenon; the spatial dimensions of the bolt include the diameter D B of the bolt, and the bearing strength parameters of the bolt include the tensile strength f B of the bolt.

[0068] In this embodiment, the net distance between the mortise groove, the mortise hole and the inner arc surface of the segment is 116 mm, and the net distance from the outer arc surface is 196 mm. The inner arc side of the segment is the weak part of the shear resistance of the segment ring joint. In addition, the width of the mortise groove is larger than that of the mortise hole, and the inner arc side of the first segment in the mortise groove is the weakest part of the shear resistance of the ring joint. When the shear force borne by the segment is less than the shear bearing capacity of the inner arc side of the mortise groove of the first segment, the force of the segment is in an absolutely safe range.

[0069] Based on this, referring to Figure 3 , in this embodiment, a shear test is carried out on the selected target ring joint to verify the accuracy of the calculation method of the present invention. Among them, the inner arc side, the outer arc side and the free ring joint surface on the left side of the first segment are all restricted by the reaction beam of the loading table, restricting their displacement in the vertical and horizontal directions. Two vertical jacks and two horizontal jacks are respectively installed on the outer arc side and the free ring joint surface of the second segment, which are respectively used to apply shear load and longitudinal axial force. Under this loading scheme, the inner arc side of the mortise groove of the first segment will bear the shear load.

[0070] Step S3, construct a shear resistance model of the ring joint at different bearing stages, which specifically includes the following contents:

[0071] The shear resistance model of the ring joint is used to calculate the minimum shear resistance bearing capacity in the most unfavorable stress direction of the ring joint, that is, the concrete and steel bars above the mortise groove of the first segment bear the extrusion load of the connecting piece.

[0072] The shear resistance model of the ring joint includes a concrete shear resistance model, a steel bar shear resistance model and a connecting piece shear resistance model;

[0073] For the construction of the concrete shear resistance model, it is as follows:

[0074] Referring to Figure 3, according to the failure characteristics of the segment, the concrete rupture body is simplified into a prism structure, that is, the concrete shear model is a quadrangular prism AEGB-CFHD, which is caused by the positioning tenon squeezing the concrete above the first segment tenon groove; the quadrangular prism is an isosceles trapezoid AEGB at the joint surface;

[0075] The quadrangular prism AEGB-CFHD is for the concrete shear bearing. In the quadrangular prism, the rectangles AEFC and BDHG are the concrete tensile surfaces, and the trapezoid CFHD is the shear surface under compression;

[0076] In the quadrangular prism AEGB-CFHD, AB = L D , EG = L C , GH = C, and the height of the trapezoid AEGB is L R . The height of the quadrangular pyramid O-EMNG is L r , EM = L L .

[0077] L L and the said L c are from experimental test statistics; when L R is 116 mm, L r is 160 mm, and L D is 66 mm, the experimental test of L L0 is 370 mm, and the experimental test expression of L c is:

[0078] L C0 = 494 - 0.1827×N (1)

[0079] where N is the longitudinal axial force, with the unit of kN, and the unit of L c0 is mm. According to the geometric relationship and similarity ratio, when the radial height on the inner arc side of segment 1 is L R , the calculation formula of L c is:

[0080]

[0081] L L The calculation formula is:

[0082]

[0083] Specifically, referring to Figure 3 , the bottom and top surfaces of the prism are both trapezoids. The width of the concrete rupture body at the tenon groove is L D , and the length in the circumferential direction of the inner arc surface is L C , that is, the width of the main rupture zone. The length of the concrete rupture body in the longitudinal direction of the segment is C, and the height in the radial direction of the joint surface is L R。The concrete rupture body mainly has 3 shear planes. Among them, the rectangular planes ACEF and BDGH are tensile planes, and the trapezoidal plane CDFH is the shear plane in a compressive state;

[0084] According to the force relationship in the vertical direction of the joint surface, the shear resistance of the circumferential joint needs to satisfy:

[0085] Q u1 -F f =F D1 ×cosθ D1 +F D2 ×cosθ D2 +F D3 (4)

[0086] In the formula:

[0087] Q u1 is the minimum shear bearing capacity in the concrete shear stage, and its calculation formula is:

[0088] Q u1 =Q - G (5)

[0089] Q is the shear load during loading; F f is the frictional force between the joint surfaces, and its calculation formula is:

[0090] F f =μ×N (6)

[0091] In the formula: μ is the friction coefficient between the concrete joint surfaces; N is the longitudinal axial force; G is the self-weight of segment 2; F D1 is the maximum tensile force of the rectangle AEFC; θ D1 is the angle between F D1 and the vertical direction; F D2 is the maximum tensile force of the rectangle BDHG; θ D2 is the angle between F D2 and the vertical direction; F D3 is the shear bearing capacity of the trapezoid CFHD.

[0092] F D1 The calculation formula of is:

[0093] F D1 =f t ×A D1 (7)

[0094] In the formula: f t is the design value of the tensile strength of concrete; A D1 is the area of the rectangle AEFC;

[0095] F D2 The calculation formula of is:

[0096] FD2 = f t × A D2 (8)

[0097] Where: A D2 is the area of the rectangle BDHG;

[0098] According to the geometric relationship, the calculation formulas for A D1 and θ D1 are respectively:

[0099]

[0100] Where: C is the protective layer thickness of the joint surface of segment 1; L R is the height of the broken body in the radial direction of the joint surface; L C is the length of the broken body in the circumferential direction of the inner arc surface; L D is the width of the broken body at the mortise and tenon groove;

[0101] According to the geometric characteristics of the broken body, there is:

[0102] A D2 = A D1 (11)

[0103] θ D2 = θ D1 (12)

[0104] Therefore, there is:

[0105] F D2 = F D1 (13)

[0106] Since F D3 is the shear resistance load of the trapezoid CFHD under the compression state, and its shear strength is significantly different from that of pure shear. Since the shear strength of the structure is positively correlated with the axial force. Different from the friction force between the joint surfaces, the increase of the longitudinal axial force not only increases the pressure between the joint surfaces, but also the concrete is in two-way stress under the compression-shear load, which is more conducive to improving the shear strength of the concrete. Therefore, F D3 can be expressed as:

[0107] F D3 = V0 + K(N) (14)

[0108] Where: V0 is the pure shear load of the trapezoid CFHD; K(N) is the shear load increment of the trapezoid CFHD caused by the longitudinal axial force; The calculation of V0 is obtained according to the "Code for Design of Concrete Structures", that is:

[0109] V0 = 0.7 × β h × f t × A D3(15)

[0110] Where: β h is the sectional height influence coefficient, taking 1.0; A D3 is the area of trapezoid CFHD, and its calculation formula is:

[0111]

[0112] Substitute Eqs. (7) to (16) into Eq. (4), and the shear bearing capacity of the concrete shear model can be obtained:

[0113] Q u1 = f t × C × (L C - L D ) + 0.35 × β h × f t × L R × (L D + L C ) + μ × N + K(N) (17)

[0114] There is an unknown function K(N) in this expression, which needs to satisfy K(N) = 0 when N = 0; K(N) can be obtained through the shear experiment under the concrete compression state.

[0115] This embodiment provides a calculation method for K(N):

[0116] When there is only one set of compression-shear test data of the circumferential joint, the function K(N) can be set as:

[0117] K(N) = k × N (18)

[0118] Where k is a constant coefficient.

[0119] When there are multiple sets of test data, the function K(N) can be set as:

[0120] K(N) = k(N) × N (19)

[0121] Where k(N) is a function of the longitudinal axial force N and can be obtained through mathematical statistics. Obviously, the more test data, the more accurate the value of the function K(N).

[0122] K(N) is obtained through experimental testing, and its calculation formula is:

[0123]

[0124] For the construction of the shear model of the connector; the shear model of the connector is jointly composed of the shear mechanical equations of the positioning tenon and the bolt. In the shear model of the connector, the positioning tenon provides the shear bearing capacity; the bolt has sufficient deformation space and is mainly in tension after deformation, providing the tensile bearing capacity;

[0125] Therefore, the bearing capacity of the force-transferring component, that is, the shear bearing capacity of the positioning tenon and the bolt, is as follows:

[0126] Q u2 = F D + F B + F f (21)

[0127] In the formula, Q u2 is the shear bearing capacity of the force-transferring component, and its calculation formula is:

[0128] Q u2 = Q - G (22)

[0129] In the formula, F D is the shear bearing capacity of the positioning tenon; F B is the shear bearing capacity of the bolt.

[0130] Finally, the shear bearing capacity of the connector is obtained as:

[0131]

[0132] Among them, Q u2 is the shear bearing capacity of the connector.

[0133] For the construction of the steel bar shear model;

[0134] Referring to Figure 4 , the steel bar shear model is a quadrangular pyramid O-EMNG, which is caused by the bolt extruding the concrete above the first segment tenon groove. The quadrangular pyramid is an isosceles triangle OEG on the joint surface; the quadrangular pyramid O-EMNG is the steel bar shear bearing, considering the steel bars passing through the quadrangular pyramid and capable of providing vertical forces;

[0135] The steel bar shear stage occurs after the concrete shear stage, and the shear load is mainly borne by the steel bars in the rupture area. According to the mechanical equilibrium equation, the steel bars capable of providing vertical tensile forces are mainly considered in the steel bar shear stage. As Figure 4 shown, the tearing of the internal concrete of the segment is mainly caused by the longitudinal bolts. Therefore, the concrete rupture body is simplified to a pyramid structure, that is, a quadrangular pyramid OEMNG, to construct the shear model of the circumferential joint in the steel bar shear stage;

[0136] That is, the shear load is borne by the steel bars passing through the quadrangular pyramid OEMNG, as shown by the red line in Figure 4 .

[0137] According to the mechanical equilibrium in the vertical direction of the segment circumferential joint, the shear resistance of the joint in the steel bar shear stage needs to satisfy:

[0138]

[0139] In the formula, Q u3 is the shear bearing capacity of the joint in the shear stage of the steel bar, and its calculation formula is:

[0140] Q u3 = Q - G (25)

[0141] F Si is the tension of the i-th steel bar passing through the quadrangular prism OEMNG; θ Si is the included angle between the i-th steel bar and the vertical direction;

[0142] F Si The calculation formula of is:

[0143] F Si = f y ×A Si (26)

[0144] f y is the design value of the tensile strength of the steel bar; A Si is the cross-sectional area of the i-th steel bar.

[0145] Step S4: Calculate the shear bearing capacity of the circumferential joint according to the shear model of the circumferential joint in different bearing stages, specifically:

[0146] As can be seen from the above formula, the parameters corresponding to the shear bearing of the circumferential joint are obtained through three channels, namely the "Code for Design of Concrete Structures", segment design and experimental statistics. The parameters involved in the calculation formula in Table 1. Among them, the segment is made of C50 concrete, and its density is 24.2 kN / m 3 . The volume of the second segment is calculated according to Figure 2 dimensions, and the inclination angles of the construction steel bars (θ S1 to θ S4 ) are as Figure 5 shown. The width L L of the prism rupture body in the circumferential and longitudinal directions takes the average value in Table 1, and the width L C of the prism rupture body in the circumferential direction is calculated by formula (2).

[0147] Table 1 Parameters involved in formulas (1) to (26)

[0148]

[0149]

[0150] In addition, there are three experiment-related parameters that need to be specifically explained. The friction coefficient between the circumferential joints is obtained through experiments, that is, the ratio of the maximum static friction force of the joint to the longitudinal axial force. The maximum static friction force takes the shear force corresponding to the obvious increase in the circumferential joint offset, as shown in Table 3. Finally, the friction coefficient takes the average value of the experimental values, that is, μ = 0.2. K(N) is calculated by formula (20), that is:

[0151]

[0152] Load statistics at each stage in Test Table 3

[0153]

[0154] Since the mortise and tenon groove provides displacement space for the longitudinal bolts, the maximum tensile strength of the longitudinal bolts is taken as 800 MPa. The shear bearing capacity of the positioning tenons is measured according to the standard "Thermal insulation products for building applications - Determination of shear properties" (GB / T 32382 - 2015). The maximum shear loads of 3 positioning tenon components are 198 kN, 184 kN, and 183 kN respectively, and the average value is 188.3 kN. That is, the maximum shear strengths of the 3 positioning tenon components are 51.969 MPa, 48.294 MPa, and 48.032 MPa respectively, and the average value is 49.432 MPa. Based on the above parameters, Q u1 、Q u2 and Q u31 are expressed as follows:

[0155]

[0156] Q u2 = 753.8 + 0.2N (29)

[0157] Q u3 = 168.16 + 0.2N (30)

[0158] That is, according to the minimum shear bearing capacity in the concrete shear stage, the shear bearing capacity of the force - transfer component, and the joint shear bearing capacity in the steel - bar shear stage, the shear bearing capacity of the circumferential joint is calculated as:

[0159] Q u = min{max[Q u1 ; Q u3 ; Q u2} (31)

[0160] According to Equation (31), the shear bearing capacity calculation formula for the circumferential joint is:

[0161]

[0162] Among them, Q u is the shear bearing capacity of the circumferential joint.

[0163] The theoretical value of the shear bearing capacity of the circumferential joint can be obtained by calculating with Equation (32). The theoretical value and experimental value of the shear bearing capacity of the circumferential joint are shown in Table 4. By comparison, it is found that the theoretically calculated value and the experimental value are in good agreement, and the error between the two does not exceed 1.1%. This shows that the shear bearing capacity calculation method of the circumferential joint proposed in the present invention is reasonable and accurate, as shown in Table 4;

[0164] Table 4 Shear Model Verification

[0165]

[0166] In this embodiment, to further study the shear mechanical characteristics of the circumferential joint, Q u1 , Q u2 , Q u3 and Q u are simultaneously shown in Figure 6 . As can be seen from Figure 6 , the shear bearing curve of the circumferential joint consists of three curves, and the shear bearing capacity of the circumferential joint increases with the increase of the longitudinal axial force. Among them, in the lower longitudinal axial force section (0 ≤ N < 277.1 kN), Q u2 is the lowest. At this time, after the segment concrete fails, the steel bars continue to resist shear, similar to the tensile failure mode of the "reinforced beam" of the concrete member, belonging to plastic failure. In the medium longitudinal axial force section (277.1 kN ≤ N < 928.3 kN), Q u1 is the lowest. At this stage, the shear bearing capacity of the circumferential joint is controlled by the segment concrete, and the concrete failure will mark the shear failure of the circumferential joint. At this time, the shear failure of the segment joint has no sign, similar to the tensile failure mode of the "under-reinforced beam" of the concrete member, belonging to brittle failure. In the larger longitudinal axial force section (N ≥ 928.3 kN), the connecting components, including bolts and positioning tenons, will become the weak parts of the circumferential joint (Q u3 ). At this stage, the shear bearing capacity of the circumferential joint is controlled by the connecting components. In summary, it can be seen that with different longitudinal axial forces, the failure modes of the circumferential joint are also different. With the increase of the longitudinal axial force, the circumferential joint can be divided into 3 control stages, namely, the steel bar control stage, the concrete control stage, and the connecting component control stage.

[0167] Based on the above analysis, parameters such as enhanced concrete strength, tensile reinforcement in the concrete fracture zone, segment thickness, and connectors can all increase the shear resistance of the circumferential joint. It should be noted that the longitudinal axial force between the circumferential joints is closely related to the geology. In the low longitudinal axial force section, enhancing the tensile reinforcement in the concrete fracture zone has the most obvious effect on improving the circumferential joint shear resistance. In the medium longitudinal axial force section, enhancing the tensile reinforcement in the concrete fracture zone will control the length of the compressed concrete section. At the same time, enhancing the connectors will extend the length of the high shear resistance stage, and increasing the segment thickness will overall improve the circumferential joint shear resistance. Therefore, these three methods can all improve the shear resistance of the circumferential joint in the medium longitudinal axial force section. For geological sections with large longitudinal axial force and shear load, enhancing the connectors is the most effective method to improve the circumferential joint shear strength. Except for the above measures, other strengthening measures may not have obvious effects on enhancing the circumferential joint shear resistance.

[0168] Although the specific implementation manners of the invention have been described in detail with reference to the accompanying drawings, it should not be construed as a limitation on the protection scope of this patent. Within the scope described in the claims, various modifications and deformations that can be made by those skilled in the art without creative efforts still fall within the protection scope of this patent.

Claims

1. A method for calculating the shear bearing capacity of annular joints in a shield tunnel, characterized in that: The following steps are involved: S1. Select the target annular joint of the shield tunnel; S2, obtaining the spatial dimensions and bearing strength parameters of the pipe segments, steel bars, and connectors in the target annular joint; S3. Constructing the shear resistance model of the annular joint at different load-bearing stages according to the spatial dimensions in the annular joint S3 specifically includes: The shear resistance model of the annular joint is used to calculate the minimum shear bearing capacity of the annular joint in the most unfavorable stress direction, that is, to calculate the extrusion load of the concrete and steel bars of the first pipe segment above the mortise and tenon groove to bear the said connecting piece; The shear model of the annular joint includes a concrete shear model, a steel bar shear model and a connector shear model; The concrete shear model is a quadrangular prism AEGB-CFHD, which is caused by the positioning tenon squeezing the concrete above the tenon groove of the first pipe segment, and the quadrangular prism is an isosceles trapezoid AEGB on the joint surface; The steel bar shear model is a tetrahedral pyramid O-EMNG, which is caused by the bolts squeezing the concrete above the tenon groove of the first pipe segment, and the tetrahedral pyramid is an isosceles triangle OEG on the joint surface; The shear resistance model of the connector is composed of shear resistance mechanics equations of the locating tenon and the bolt; In the tetrahedral AEGB-CFHD, AB= L D , L D is the width of the upper plane of the mortise; EG= L C , L C is the length of the inner arc surface in the circumferential direction; GH= C , C is the thickness of the segment protection layer; the height of the isosceles trapezoid AEGB is L R , L R is the radial height of the mortise and tenon groove from the inner arc side of the first segment; the height of the quadrangular pyramid O-EMNG is L r , L r It is the height from the center of the bolt hole on the joint surface to the inner arc surface; EM= L L ; L L and L c Derived from experimental test statistics; L R 116mm, L r 160mm, L D When it is 66mm, L L0 The experimental test is 370mm, L c The experimental test expression is: According to the geometric relationship and similarity ratio, the radial height on the inner arc side of the first segment is L R hour, L c The calculation formula is: L L The calculation formula is: in, N is the longitudinal axial force; S4. Calculate the shear bearing capacity of the girth joint according to the shear model of the girth joint at different load-bearing stages.

2. The shear bearing calculation method of the shield tunnel annular joint according to claim 1 is characterized by: The target annular joint in S1 includes a segment joint; the segment joint includes a first segment and a second segment, a positioning tenon and a longitudinal bolt are provided between the annular joints of the first segment and the second segment; and the first segment and the second segment are connected by the positioning tenon and the longitudinal bolt; The annular seam surface of the first pipe segment is prefabricated with a quasi-rectangular tenon groove, and the annular seam surface of the second pipe segment is prefabricated with a circular tenon hole, and the tenon groove and the tenon hole are used to accommodate the positioning tenon.

3. The shear bearing calculation method of the shield tunnel annular joint according to claim 1 is characterized in that: The S2 specifically includes: The spatial dimensions of the pipe segment include the thickness of the pipe segment, the radial height of the tongue and groove from the inner arc side of the first pipe segment, the width of the upper plane of the tongue and groove, the height from the center of the bolt hole on the joint surface to the inner arc surface, and the thickness of the pipe segment protective layer. The bearing strength parameters of the pipe segment include the design value of the tensile strength of the concrete. f t ; The spatial dimensions of the steel bars include the number of steel bars around the locating tenon that can provide vertical tension. i , No. i The diameter of the steel bar A Si , No. i Angle between the root steel bar and the vertical direction θ Si The bearing strength parameters of the steel bars include the design value of the tensile strength of the steel bars. f y ; The connecting piece includes a positioning tenon and a bolt; the spatial dimensions of the positioning tenon include the inner diameter of the positioning tenon at the joint D Dn and outer diameter D Dw The bearing strength parameters of the positioning tenon include the shear strength of the positioning tenon. f D ; The spatial dimensions of the bolt include the diameter of the bolt D B The bearing strength parameters of the bolt include the tensile strength of the bolt f B .

4. The shear bearing calculation method of the shield tunnel annular joint according to claim 3 is characterized in that: The quadrangular prism AEGB-CFHD is the concrete shear bearing, the rectangular AEFC and the rectangular BDHG in the quadrangular prism are the concrete tensile surfaces, and the trapezoidal CFHD is the shear surface under compression; The tetrahedral pyramid O-EMNG is a steel bar shear bearing, and steel bars that pass through the tetrahedral pyramid and can provide vertical force are considered; In the shear resistance model of the connector, the positioning tenon provides shear resistance; the bolt has sufficient deformation space and is mainly subjected to tension after deformation, thus providing tensile resistance.

5. The shear bearing calculation method of the shield tunnel annular joint according to claim 4 is characterized in that: According to the shear model of the annular joint in the concrete shear stage, the shear bearing capacity of the annular joint in the concrete shear stage is calculated: in, Q u1 is the shear bearing capacity of concrete in the shear stage; μ is the friction coefficient between concrete joint surfaces; K(N) is the shear load increment of the trapezoidal CFHD in the prismatic structure caused by the longitudinal axial force; K(N) Obtained through experimental testing, the calculation formula is: 。 6. The shear bearing calculation method of the shield tunnel annular joint according to claim 5 is characterized in that: The shear bearing capacity of the connector is: in, Q u2 is the shear resistance of the connector.

7. The shear bearing calculation method of the shield tunnel annular joint according to claim 6 is characterized in that: According to the shear model of the circumferential joint in the steel bar shear stage, the shear bearing capacity of the joint in the steel bar shear stage is calculated as: in, Q u3 It is the shear bearing capacity of the joint during the steel bar shear stage.

8. The shear bearing calculation method of the shield tunnel annular joint according to claim 7 is characterized in that: In S4, the shear bearing capacity of the annular joint is calculated based on the minimum shear bearing capacity of the concrete in the shear stage, the shear bearing capacity of the connector and the shear bearing capacity of the joint in the shear stage of the steel bar: in, It is the minimum shear bearing capacity of the circumferential joint in the most unfavorable stress direction.

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