A method for calculating the internal forces of special segment structures in upward shield construction

Abstract

The present invention discloses a method for calculating the internal forces of a special segment structure during upward shield construction. The method determines the vertical load and lateral load of the special segment structure; based on the fact that the special segment ring structure is a quadratic indeterminate structure, a displacement coordination equation at the elastic center is established, and the elastic center method is used to analyze the internal forces of the special segment ring; the segments at the openings of the special segment ring structure are approximated as curved thin plates, the stress conditions of the special segment structure are analyzed, and the internal force calculation of the lateral load is corrected; the internal forces of the special segment structure under the action of the vertical load are calculated; and the segment ring internal forces under the action of the lateral load and the vertical load are superimposed to obtain the final internal forces of the special segment. The calculation method proposed by the present invention is simple and has strong applicability, and takes into account the special loads caused by upward shield construction and the influence of the construction opening.

Description

Technical Field

[0001] The invention belongs to the technical field of underground tunnel engineering and relates to a method for calculating the internal force of a special segment structure in upward shield construction. Background Art

[0002] With the modernization of cities, today's underground space construction technology has shown diversified development. Various pipeline facilities are buried underground in large and medium-sized cities. Under such complex conditions, if traditional methods are used to excavate vertical shafts on the surface, it will inevitably bring inconvenience to transportation and the lives of surrounding residents. In response to this demand, the upward shield method came into being. The upward shield method mainly uses a shield machine to start from an existing underground horizontal shield tunnel and excavate vertical shafts upward. The upward shield method is used in Japan's Midosuji Project. The project requires excavating a main line tunnel with a total length of approximately 4km and 8 vertical shafts in a busy traffic environment. This construction method has brought huge economic benefits due to its advantages such as small ground space occupation, low construction cost and short construction period.

[0003] Compared to conventional horizontal shield tunnel segments, the internal forces in special segments of horizontal shield tunnels are more complex and require unique design requirements. Improper analysis and design of segment internal forces can cause cracks or even damage in the horizontal tunnel during upward shield construction, directly impacting the quality and lifespan of the shield tunnel. Therefore, special segment design requirements for special segments in horizontal shield tunnels corresponding to upward shield construction areas require separate internal force calculation and analysis.

[0004] Most existing research focuses on the horizontal shield method, with little research on the upward shield method. The study "Study on the Design Method of Horizontal Shield Tunnel Segments in the Vertical Pipe Jacking Method" divides the horizontal tunnel segments into sections based on their basic stress characteristics and calculates their internal forces using the free deformation method. The shortcomings of this method include:

[0005] 1) The effect of formation resistance is not considered;

[0006] 2) The impact of construction openings on the internal forces of horizontal tunnel segments is not considered.

[0007] The special vertical loads caused by upward shield construction directly act on the segment structure in special sections of the horizontal shield, and the construction opening and ground resistance have a significant impact on the internal forces of the segments. Therefore, the internal force calculation method used for the general horizontal shield method cannot be used in upward shield construction. It is necessary to propose a new internal force calculation method for the segment structure in special sections of the upward shield construction, taking into account the special loads caused by upward shield construction and the influence of the construction opening. Summary of the Invention

[0008] In view of the shortcomings of the existing technology, the present invention proposes a method for calculating the internal forces of a special segment structure in upward shield construction.

[0009] To achieve the above technical objectives, the technical solution of the present invention is as follows: the present invention proposes a method for calculating the internal forces of a special segment structure in an upward shield tunneling method, the method specifically comprising the following steps:

[0010] Step 1: Determine the vertical and lateral loads of the segment structure in a specific section;

[0011] Step 2: Based on the fact that the special segment ring structure is a quadratic indeterminate structure, the displacement coordination equation at the elastic center is established, and the internal force of the special segment ring is analyzed using the elastic center method;

[0012] Step 3: Approximate the segments at the opening of the special segment ring structure as curved thin plates, analyze the stress conditions of the special segment structure, calculate the triangularly distributed lateral water and soil pressure, uniformly distributed lateral water and soil pressure, and stratum resistance, and correct the internal force calculation of the lateral load;

[0013] Step 4: Calculate the internal forces of the special segment structure under vertical loads; the vertical loads mainly include vertical excavation soil unloading and foundation reaction force, jacking reaction force and foundation reaction force;

[0014] Step 5: Superimpose the internal forces of the segment ring under the action of lateral load and vertical load to obtain the internal forces of the final special segment.

[0015] Furthermore, the special segment is an annular segment with a circular opening formed by upward shield construction during horizontal shield tunneling.

[0016] Furthermore, the vertical load of the special segment structure includes the self-weight g and the foundation reaction p g , vertical water and soil pressure q1 and foundation reaction force p1, soil unloading q2 caused by vertical excavation and foundation reaction force p2, jacking reaction force P and foundation reaction force p p .

[0017] Furthermore, the jacking reaction force is composed of the weight of the vertical shield machine, the weight of the jack, the weight of the vertical shield segments, the front thrust and the friction force.

[0018] Furthermore, (1) it is assumed that the ground resistance is distributed in the range of π / 4 to 3π / 4 from the top of the ring to the left and right, and its magnitude is in accordance with the local deformation theory, that is, the ground resistance is proportional to the passive displacement of the ground; (2) it is assumed that the lateral water and soil pressure is distributed between 0 and π from the top of the ring to the left and right; (3) the vertical load is uniformly distributed along the horizontal projection of the ring; and (4) the soil unloading caused by vertical excavation is simplified to a line load.

[0019] Furthermore, the displacement coordination equation at the elastic center is:

[0020]

[0021] Where: δ 11 , δ 21 Refers to the displacement of the basic structure along the X1 and X2 directions under the action of unit force X1 = 1 alone; δ 21 , δ 22 Refers to the displacement of the basic structure along the X1 and X2 directions when the unit force X2 = 1 acts alone; Δ1p and Δ2p are the displacements of the basic structure along the X1 and X2 directions respectively when the load acts alone;

[0022] Calculate the M at the angle θ between the segment ring and the vertical axis of the special section θ 、N θ , the formula is as follows:

[0023] M θ =M P +X1-X2R cosθ (2)

[0024] N θ =X2cosθ+N P (3)

[0025] Where: M P 、N P are the bending moment and axial force generated by external load on the segment ring; M θ 、N θ They are the bending moment and axial force at the angle θ between the cross-section segment ring and the vertical axis; θ is the angle between the cross-section segment ring and the vertical axis; among them, the bending moment is positive when the inner side is tensile, and the axial force is positive when the pressure is.

[0026] Furthermore, the calculation process of the triangular distribution lateral water and soil pressure q3 is as follows:

[0027] First, the axial force at the ring opening caused by the triangularly distributed lateral water and soil pressure is calculated. The axial force calculation formula for a complete circular ring under the action of the triangularly distributed lateral water and soil pressure is:

[0028]

[0029] Where: N q3t is the axial force of the complete ring under the triangular distribution of lateral water and soil pressure; q3 is the triangular distribution of lateral water and soil pressure; R c is the calculated radius of the horizontal shield tunnel;

[0030] The axial force correction coefficient λ of the opening segment is introduced, and its value is the ratio of the inner diameter of the opening to the arc length of the curved thin plate. After the axial force correction coefficient λ of the opening segment is introduced, the axial force loss value N caused by the opening is calculated. q3c Calculate as follows:

[0031]

[0032] Where: N q3c It is the axial force lost due to the opening after the axial force correction coefficient λ of the opening segment is introduced under the action of triangularly distributed lateral water and soil pressure;

[0033] Therefore, after considering the opening effect, the axial force caused by the triangularly distributed lateral water and soil pressure at the ring opening point is calculated according to the following formula:

[0034] N q3 =N q3t -N q3c (6)

[0035] Where: N q3 To consider the axial force at the ring opening point caused by the triangularly distributed lateral water and soil pressure after the opening is affected;

[0036] The calculation formula for the axial force of the remaining points under the action of triangular distributed lateral water and soil pressure is:

[0037]

[0038] Where: N' q3 To consider the axial forces at other points caused by the triangularly distributed lateral water and soil pressure after the opening is affected;

[0039] When 0≤θ≤π, after introducing the bending moment influence coefficient μ of the open segment, the calculation formula of the bending moment of the open segment ring under the action of triangular distributed lateral water and soil pressure is:

[0040]

[0041] Where: M q3 The bending moment of the open segment ring caused by the triangularly distributed lateral water and soil pressure after considering the influence of the opening.

[0042] Furthermore, the calculation process of the uniformly distributed lateral water and soil pressure q4 is as follows:

[0043] First, the axial force at the ring opening caused by the uniformly distributed lateral water and soil pressure is calculated. The axial force calculation formula for a complete circular ring under the action of the uniformly distributed lateral water and soil pressure is:

[0044] N q4t =q4R c cos 2 θ (9)

[0045] Where: N q4t is the axial force of the complete ring under the uniform lateral water and soil pressure; q4 is the uniform lateral water and soil pressure;

[0046] The loss of axial force is:

[0047]

[0048] Where: N q4c is the axial force lost due to the opening under the action of uniformly distributed lateral water and soil pressure;

[0049] Therefore, the axial force caused by the uniformly distributed lateral water and soil pressure at the ring opening point after considering the opening effect is calculated according to the following formula:

[0050] N q4 =N q4t -N q4c (11)

[0051] Where: N q4 The axial force at point A2 caused by the uniformly distributed lateral water and soil pressure after considering the effect of the opening;

[0052] After the axial force correction coefficient λ of the open segment is introduced into the remaining points, the axial force calculation formula of the open segment ring under the uniformly distributed lateral water and soil pressure is:

[0053] N' q4 =λq3R c cos 2 θ (12)

[0054] Where: N' q4 The axial forces at other points are caused by the uniformly distributed lateral water and soil pressure after considering the effect of the opening;

[0055] When 0≤θ≤π, after introducing the bending moment influence coefficient μ of the open segment, the bending moment calculation formula under the uniformly distributed lateral water and soil pressure is:

[0056]

[0057] Where: M q4 The bending moment of the open segment ring caused by the uniformly distributed lateral water and soil pressure after considering the influence of the opening.

[0058] Furthermore, the formation resistance q r The specific calculation process is:

[0059] According to the calculation of the horizontal displacement at the horizontal diameter point of the segment ring in the modified conventional method, and combined with the load system, the calculation formula for the horizontal displacement at the horizontal diameter point of the segment ring in the special section during the upward shield method construction is:

[0060]

[0061] Where: p1, p2, p pare the foundation reaction force corresponding to the vertical water and soil pressure, the foundation reaction force corresponding to the unloading of the soil caused by vertical excavation, and the foundation reaction force corresponding to the jacking reaction force; g is the deadweight of the horizontal shield segment; k is the stratum (elastic) bed coefficient; η is the bending moment adjustment coefficient; EI is the bending stiffness per unit width; δ is the horizontal displacement of the horizontal diameter point of the segment ring;

[0062] The axial force at the ring opening point caused by the formation resistance is calculated; the axial force calculation formula for a complete ring under the action of formation resistance is:

[0063] N qrt =0.3536cosθkδR c (15)

[0064] Where: N qrt is the axial force of the complete ring under the action of the formation resistance;

[0065] Loss of axial force:

[0066]

[0067] Where: N qrc is the axial force lost due to the opening under the action of formation resistance;

[0068] Therefore, the axial force caused by the formation resistance at point A2 after considering the opening effect can be calculated according to the following formula:

[0069] N qr =N qrt -N qrc (17)

[0070] Where: N qr The axial force around the opening point caused by the formation resistance after considering the opening effect;

[0071] When π / 12<θ<π / 4, after the axial force correction coefficient λ of the opening segment is introduced into the remaining points, the calculation formula of the axial force caused by the formation resistance is:

[0072] N' qr =0.3536λcosθkδR c (18)

[0073] Where: N' qr To consider the axial forces at other points caused by the formation resistance after the opening is affected;

[0074] When π / 4≤θ≤π / 2, after introducing the axial force correction coefficient λ of the open segment, the calculation formula of the axial force caused by the formation resistance is:

[0075] N' qr =(-0.7071cosθ+cos 2 θ+0.7071sin2 θcosθ)λkδR c (19)

[0076] When 0≤θ<π / 4, after introducing the bending moment influence coefficient μ of the open segment, the calculation formula of the bending moment caused by the formation resistance is:

[0077] M qr =(1+μ)(0.2346-0.3536cosθ)kδR c 2 (20)

[0078] Where: M qr To consider the bending moment of the opening segment ring caused by the formation resistance after the opening is affected;

[0079] When π / 4≤θ≤π / 2, after introducing the bending moment influence coefficient μ of the open segment, the calculation formula of the bending moment caused by the formation resistance is:

[0080] M qr =(1+μ)(-0.3487+0.5sin 2 θ+0.2357cos 3 θ)kδR c 2 (twenty one).

[0081] Furthermore, the step 4 is specifically as follows:

[0082] The calculation formulas for the axial force and bending moment at the ring opening point and the arch bottom are as follows:

[0083] N PA =0.00467PR c (twenty two)

[0084] M PA =0.00232PR c 2 (twenty three)

[0085] N PB =0 (24)

[0086] M PB =0.05531PR c 2 (25)

[0087] Where: N PA 、M PA 、N PB 、M PB are the axial force and bending moment at the ring opening point and the arch bottom point under the action of jacking reaction force and foundation reaction force respectively;

[0088] The vertical load causes the axial force N at other pointsg 、N q1 、N q2 、N P for:

[0089]

[0090] N q1 =q1R c sin 2 θ (27)

[0091] N q2 =-q2R c sin 2 θ (28)

[0092] N P =-PR c sin 2 θ (29)

[0093] Where: N g 、N q1 、N q2 Axial forces caused by self-weight and foundation reaction, vertical water and soil pressure and foundation reaction, vertical excavation soil unloading and foundation reaction; N P is the axial force at other points caused by the jacking reaction force and the foundation reaction force; P is the jacking reaction force;

[0094] In addition, the vertical load causes bending moments M at other points g 、M q1 、M q2 、M P for:

[0095]

[0096] Where: M g 、M q1 、M q2 The bending moments caused by self-weight and foundation reaction, vertical water and soil pressure and foundation reaction, vertical excavation soil unloading and foundation reaction; M P The remaining bending moment is caused by the jacking reaction force and foundation reaction force.

[0097] Compared with the existing technology, the present invention has the following advantages: the calculation method proposed in the present invention is simple and highly applicable. It takes into account the special loads caused by the upward shield method and the influence of the construction opening, and proposes a method for calculating the internal forces of the special segment structure during upward shield construction. Based on the modified conventional method, the opening of the special segment is approximated as a "curved thin plate". The axial force correction factor and bending moment influence factor of the opening segment are introduced to modify the calculation formula of the internal force of the opening segment. By superimposing the bending moment and axial force of the special segment under various loads, the internal forces at each point of the special segment structure can be obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0098] Figure 1 Schematic diagram of the reference points of the lining segment rings in special sections;

[0099] Figure 2 Schematic diagram of the internal force calculation method for the open segment ring;

[0100] Figure 3 This is a schematic diagram for calculating the axial force at the opening segment;

[0101] Figure 4 is the bending moment curve caused by various loads;

[0102] Figure 5 This is the axial force curve caused by various loads. DETAILED DESCRIPTION

[0103] Exemplary embodiments will be described in detail herein, examples of which are illustrated in the accompanying drawings. In the following description, when referring to the drawings, like numbers in different figures represent like or similar elements unless otherwise indicated. The embodiments described in the following exemplary embodiments are not intended to represent all possible embodiments consistent with the present invention. Rather, they are merely examples of apparatus and methods consistent with certain aspects of the present invention, as detailed in the appended claims.

[0104] The existing horizontal shield tunnel segment designs at home and abroad can be summarized into the following nine methods: conventional method, modified conventional method, improved conventional method, multi-hinge ring method, elastic hinge ring method, beam-spring method, shell-spring method, flat shell-joint element-foundation system method, flat shell-elastic hinge-foundation system method. After comprehensive analysis of different design and calculation methods for shield segments, the modified conventional method is generally accepted and recognized by the public because of its simpler calculation process and more practical results. Therefore, the present invention combines the existing research on the internal force design of shield tunnel segments, based on the modified conventional method, and taking into account the influence of the opening in the upward shield construction method, proposes a method for calculating the internal forces of the horizontal shield segment ring in the special section of the upward shield construction.

[0105] The following describes in detail a method for calculating the internal force of a special segment structure in an upward shield tunneling method according to the present invention in conjunction with the accompanying drawings. The features of the following embodiments and implementations may be combined with each other unless they conflict.

[0106] The internal force calculation method of the special segment structure in the upward shield method construction mainly includes the following steps: wherein, the special segment is an annular segment with a circular opening formed by the upward shield method construction during the horizontal shield tunnel excavation.

[0107] Step 1: Determine the load system of the special segment structure.

[0108] During the construction of the upward shield method, the special segment ring is mainly subjected to the following seven pairs of loads: ① Self-weight g and foundation reaction p g ; ② Vertical water and soil pressure q1 and foundation reaction force p1; ③ Soil unloading q2 and foundation reaction force p2 caused by vertical excavation; ④ Jacking reaction force P and foundation reaction force p p ; ⑤ triangular distribution lateral water and soil pressure q3; ⑥ uniform distribution lateral water and soil pressure q4; ⑦ stratum resistance q r According to the direction of load action, loads ① to ④ are collectively referred to as vertical loads, and loads ⑤ to ⑦ are collectively referred to as lateral loads.

[0109] The assumptions for various loads are as follows: (1) The ground resistance is assumed to be distributed in the range of π / 4 to 3π / 4 from the top of the ring to the left and right (triangular distribution), and its magnitude is based on the local deformation theory, that is, the ground resistance is proportional to the passive displacement of the ground; (2) The lateral water and soil pressure is assumed to be distributed between 0 and π from the top of the ring to the left and right; (3) The vertical load is uniformly distributed along the horizontal projection of the ring; (4) The soil unloading caused by vertical excavation is simplified to a line load.

[0110] Step 2: Establish the internal force calculation formula for the special segment structure.

[0111] Considering that the special segment ring structure is a quadratic indeterminate structure, the elastic center method is used to analyze the internal forces of the special segment ring. The displacement coordination equation at the elastic center is established:

[0112]

[0113] The M at the angle θ between the segment ring and the vertical axis of the special section can be obtained. θ 、N θ :

[0114] M θ =M P +X1-X2R cosθ (2)

[0115] N θ =X2 cosθ+N P (3)

[0116] Where: M P 、N P are the bending moment and axial force generated by external loads on the segment ring in the basic structure; M θ 、N θ The bending moment and axial force are the angle θ between the segment ring and the vertical axis, respectively. θ is the angle between the segment ring and the vertical axis. The bending moment is positive when the inner side is tensile, and the axial force is positive when the inner side is compressive.

[0117] The internal force calculation of representative points on the special segment ring is carried out, which are located at the opening, arch top, arch bottom and arch waist of the special segment ring. Figure 1 .

[0118] Step 3: Analyze the stress conditions of the special segment structure.

[0119] Considering that the opening of the upward shield method is small, the segment at the opening is approximated as a "curved thin plate". The absence of this "curved thin plate" will significantly increase the deformation of the structure under lateral load and "release" the internal force. Therefore, the present invention considers the effect of the opening on the basis of the calculation of the internal force of the complete ring (see Figure 2 ), calculate the triangular distribution lateral water and soil pressure, uniform distribution lateral water and soil pressure and stratum resistance, and focus on revising the internal force calculation formula of lateral load. Specifically:

[0120] 1) Triangular distribution lateral water and soil pressure q3

[0121] First, the axial force at the ring opening A2 caused by the triangularly distributed lateral water and soil pressure is calculated. The formula for calculating the axial force of a complete circular ring under the action of triangularly distributed lateral water and soil pressure is:

[0122]

[0123] Where: N q3t is the axial force of the complete ring under the triangular distribution of lateral water and soil pressure (kN); q3 is the triangular distribution of lateral water and soil pressure (kN / m); R c is the calculated radius of the horizontal shield tunnel (m), which is equal to the average of the inner radius and the outer radius.

[0124] The axial force calculation of the open segment ring requires subtracting the average axial force N of the open segment from the axial force calculation of the complete ring. q3c ,See Figure 3 .

[0125] In addition, since the open segment is approximated as a "curved thin plate" in the above text, and the actual open segment is circular, the axial force correction coefficient λ of the open segment is introduced, which is the ratio of the inner diameter of the opening to the arc length of the "curved thin plate". Therefore, after introducing the axial force correction coefficient λ, the axial force loss value N caused by the opening is q3c It can be calculated as follows:

[0126]

[0127] Where: N q3c It is the axial force lost due to the opening after the axial force correction coefficient λ of the opening segment is introduced under the action of triangularly distributed lateral water and soil pressure (kN).

[0128] Therefore, after considering the effect of the opening at point A2, the axial force caused by the triangularly distributed lateral water and soil pressure can be calculated using the following formula:

[0129] N q3 =Nq3t -N q3c (6)

[0130] Where: N q3 It is the axial force (kN) at point A2 caused by the triangularly distributed lateral water and soil pressure after considering the effect of the opening.

[0131] In addition, considering that the opening will reduce the axial force of the segment ring to a certain extent, after introducing the axial force correction coefficient λ of the opening segment, the axial force calculation formula of the remaining points under the action of triangular distributed lateral water and soil pressure is:

[0132]

[0133] Where: N' q3 It is the axial force (kN) at the remaining points caused by the triangularly distributed lateral water and soil pressure after considering the influence of the opening.

[0134] Since the segment ring section on the vertical symmetry axis only sinks vertically without horizontal displacement or rotation, the bottom section of the ring can be regarded as the fixed end. By solving the mechanical problems of both the "cantilever effect" and the fixed end, it can be concluded that the bending moments at the segment ring ends in the two cases are ql 2 / 12,ql 2 / 2 (q is the lateral load, l is the diameter of the pipe ring), and the "cantilever effect" in the open working condition will increase the pipe segment bending moment by 5ql 2 / 12, thereby introducing the opening segment bending moment influence coefficient μ, whose value is equal to the increase coefficient of the segment bending moment under the "cantilever effect".

[0135] Therefore, when 0≤θ≤π, after introducing the bending moment influence coefficient μ of the open segment, the calculation formula of the bending moment of the open segment ring under the action of triangular distributed lateral water and soil pressure is:

[0136]

[0137] Where: M q3 The bending moment (kN·m) of the open segment ring caused by the triangularly distributed lateral water and soil pressure after considering the effect of the opening.

[0138] 2) Uniformly distributed lateral water and soil pressure q4

[0139] First, the axial force at point A2 caused by the uniformly distributed lateral water and soil pressure is calculated. The formula for calculating the axial force of a complete circular ring under the action of the uniformly distributed lateral water and soil pressure is:

[0140] N q4t =q4R c cos 2 θ (9)

[0141] Where: N q4tis the axial force of the complete ring under the uniformly distributed lateral water and soil pressure (kN); q4 is the uniformly distributed lateral water and soil pressure (kN / m).

[0142] Loss of axial force:

[0143]

[0144] Where: N q4c is the axial force lost due to the opening under the action of uniformly distributed lateral water and soil pressure (kN).

[0145] Therefore, the axial force caused by the uniformly distributed lateral water and soil pressure at point A2 after considering the effect of the opening can be calculated according to the following formula:

[0146] N q4 =N q4t -N q4c (11)

[0147] Where: N q4 It is the axial force (kN) at point A2 caused by the uniformly distributed lateral water and soil pressure after considering the influence of the opening.

[0148] After the axial force correction coefficient λ of the open segment is introduced into the remaining points, the axial force calculation formula of the open segment ring under the uniformly distributed lateral water and soil pressure is:

[0149] N' q4 =λq3R c cos 2 θ (12)

[0150] Where: N' q4 It is the axial force (kN) at the remaining points caused by the uniformly distributed lateral water and soil pressure after considering the influence of the opening.

[0151] When 0≤θ≤π, after introducing the bending moment influence coefficient μ of the open segment, the bending moment calculation formula under the uniformly distributed lateral water and soil pressure is:

[0152]

[0153] Where: M q4 It is the bending moment (kN·m) of the open segment ring caused by the uniformly distributed lateral water and soil pressure after considering the effect of the opening.

[0154] 3) Formation resistance q r

[0155] According to the calculation of the horizontal displacement at the horizontal diameter point of the segment ring in the modified conventional method and combined with the load system in this paper, the calculation formula for the horizontal displacement at the horizontal diameter point of the segment ring in the special section during the upward shield method construction is:

[0156]

[0157] Where: p1, p2, p p are the foundation reaction forces corresponding to the vertical water and soil pressure, the foundation reaction forces corresponding to the unloading of the soil caused by vertical excavation, and the foundation reaction forces corresponding to the jacking reaction forces (kN / m); g is the deadweight of the horizontal shield segment (kN / m); k is the stratum base coefficient per unit length (m) in the direction perpendicular to the tunnel cross section (kN / m 2 ); η is the bending moment adjustment coefficient; EI is the bending stiffness per unit width (kN·m 2 );δHorizontal displacement of the horizontal diameter point of the segment ring (m).

[0158] First, calculate the axial force at point A2 caused by the ground resistance. The formula for calculating the axial force of a complete ring under the action of ground resistance is:

[0159] N qrt =0.3536cosθkδR c (15)

[0160] Where: N qrt is the axial force of the complete ring under the action of formation resistance (kN).

[0161] Loss of axial force:

[0162]

[0163] Where: N qrc It is the axial force lost due to the opening under the action of formation resistance (kN).

[0164] Therefore, the axial force caused by the formation resistance at point A2 after considering the opening effect can be calculated according to the following formula:

[0165] N qr =N qrt -N qrc (17)

[0166] Where: N qr It is the axial force (kN) at point A2 caused by the formation resistance after considering the impact of the opening.

[0167] When π / 12<θ<π / 4, after the axial force correction coefficient λ of the opening segment is introduced into the remaining points, the calculation formula of the axial force caused by the formation resistance is:

[0168] N' qr =0.3536λcosθkδR c (18)

[0169] Where: N' qr It is the axial force (kN) at the remaining points caused by the formation resistance after considering the influence of the opening.

[0170] When π / 4≤θ≤π / 2, after introducing the axial force correction coefficient λ of the open segment, the calculation formula of the axial force caused by the formation resistance is:

[0171] N' qr =(-0.7071cosθ+cos 2 θ+0.7071sin 2 θcosθ)λkδR c (19)

[0172] When 0≤θ<π / 4, after introducing the bending moment influence coefficient μ of the open segment, the calculation formula of the bending moment caused by the formation resistance is:

[0173] M qr =(1+μ)(0.2346-0.3536cosθ)kδR c 2 (20)

[0174] Where: M qr It is the bending moment (kN·m) of the opening segment ring caused by the formation resistance after considering the influence of the opening.

[0175] When π / 4≤θ≤π / 2, after introducing the bending moment influence coefficient μ of the open segment, the calculation formula of the bending moment caused by the formation resistance is:

[0176] M qr =(1+μ)(-0.3487+0.5sin 2 θ+0.2357cos 3 θ)kδR c 2 (twenty one)

[0177] Step 4: Calculate the internal forces of the special segment structure under vertical load.

[0178] The special vertical loads caused by the upward shield method primarily include vertical unloading of excavated soil, foundation reaction forces, jacking forces, and foundation reaction forces. The jacking force is composed of the weight of the vertical shield machine, the weight of the jacks, the weight of the vertical shield segments, frontal thrust, and friction. To prevent damage to the horizontal shield tunnel during upward shield construction, a leveling layer is required at the bottom of the horizontal tunnel to disperse the jacking reaction forces.

[0179] According to the magnitude and position of the jacking reaction force, the internal force calculation is divided into points A2, B2 and other points. First, the internal forces of points A2 and B2 under the action of the jacking reaction force and the foundation reaction force are calculated.

[0180] Considering that the axial force and bending moment values ​​of the vault under the action of the jacking reaction force and the foundation reaction force are relatively small under the action of the complete circular ring, and that point A2 is close to the vault, the axial force and bending moment at point A2 can be approximately calculated using the internal force calculation formula of the vault. The calculation formulas for the axial force and bending moment at points A2 and B2 are as follows:

[0181] N PA =0.00467PR c (twenty two)

[0182] M PA =0.00232PR c 2 (twenty three)

[0183] N PB =0 (24)

[0184] M PB =0.05531PR c 2 (25)

[0185] Where: N PA 、M PA 、N PB 、M PB are the axial force (kN) and bending moment (kN·m) at points A2 and B2 under the action of jacking reaction force and foundation reaction force, respectively.

[0186] The vertical load causes the axial force N at other points g 、N q1 、N q2 、N P for:

[0187]

[0188] N q1 =q1R c sin 2 θ (27)

[0189] N q2 =-q2R c sin 2 θ (28)

[0190] N P =-PR c sin 2 θ (29)

[0191] Where: N g 、N q1 、N q2 Axial forces caused by self-weight and foundation reaction, vertical water and soil pressure and foundation reaction, vertical excavation soil unloading and foundation reaction (kN); NP is the axial force (kN) at other points caused by the jacking reaction force and the foundation reaction force; P is the jacking reaction force (kN / m).

[0192] In addition, the bending moment M at other points caused by vertical load can be obtained: g 、M q1 、M q2 、M P for:

[0193]

[0194] Where: M g 、M q1 、M q2 Bending moments caused by self-weight and foundation reaction, vertical water and soil pressure and foundation reaction, vertical excavation soil unloading and foundation reaction (kN·m); M P The remaining bending moment (kN·m) is caused by the jacking reaction force and foundation reaction force.

[0195] Step 5: Superimpose the internal forces of the segment ring under the action of lateral load and vertical load to obtain the internal forces of each point of the segment ring (ring opening, arch crown, arch bottom, and arch waist) of the final special section.

[0196] Example 1

[0197] An example is selected to calculate the internal forces of the lining segments of a special section of a horizontal tunnel. Considering that the soil around the tunnel is sandy, according to the Basic Data of Bridges and Culverts in the Highway Design Manual of China, the base bed coefficient is 5×10 4 kN·m -3 , then the stratum base coefficient per unit length (m) in the direction perpendicular to the tunnel cross section is 5×10 4 kN·m -2 Without considering the effect of ground overload, soil weight γ=19kN·m -3 , static earth pressure coefficient K0=0.43. Starting from the horizontal shield tunnel with a depth of 9m, the outer radius of the horizontal shield tunnel is R1=4.5m, the inner radius is R2=4m, and the radius R is calculated. c =4.25m, and the length of each ring segment is 2m. The lining ring of the special section of the horizontal shield tunnel is made of concrete with a weight of γ = 25kN·m -3 .

[0198] The upward shield tunnel construction is carried out by excavating 18 rings, each ring of segments is 0.5m long, with an outer radius of r1 = 1m and an inner radius of r2 = 0.9m. The vertical shield tunnel segments are also made of concrete with a weight of γ = 25kN·m -3. The leveling layer is made of steel, and the top surface size is 3m×3m. The main parameters of the vertical shield machine are as follows: the weight of the shield machine is 25.0t, and 8 QF140 / 500 jacks are selected, each weighing 110kg. In addition, to ensure the upward excavation of the shield machine, its front thrust needs to be 5 to 20kPa greater than the overburden, and 10kPa is taken. The friction coefficient f=0.2 during the upward excavation process. After calculation, the bending moment influence coefficient μ of the opening segment is A2 =μ B2 =0.42, μ C2 =μ D2 =0.17, the axial force correction coefficient of the open segment λ=0.8.

[0199] According to formulas (4) to (33), by setting θ = π / 12, π / 2, π in the formula, the axial forces and bending moments at points A2, B2, C2, and D2 of the open segment ring can be obtained. The calculation results are shown in Table 1.

[0200] Table 1: Calculated internal forces at reference points of segment rings at openings

[0201]

[0202] The absolute value of the sum of the segment annular internal forces under the seven loads is referred to as the final result. Table 1 shows that in terms of bending moments, the absolute sum of the bending moments at points A2, B2, C2, and D2 due to lateral loads is 13.6 times, 42.4 times, and 7.3 times the final result, respectively. The absolute sum of the bending moments at points A2, B2, C2, and D2 due to vertical loads is 14.6 times, 47.3 times, and 10.1 times the final result, respectively. In terms of axial forces, the absolute sum of the axial forces at points A2, B2, C2, and D2 due to lateral loads accounts for 93.5%, 98.3%, and 0% of the final result, respectively. The axial forces at points A2, B2, C2, and D2 due to vertical loads account for 6.5%, 1.7%, and 100% of the final result, respectively.

[0203] The bending moments and axial forces caused by the various loads in Table 1 are as follows Figure 4 and Figure 5 As shown. In terms of bending moment: the bending moment value of point A2 is between point B2 and points C2 and D2. The changes in the bending moments of points B2 and C2 and D2 basically show opposite trends. Under the action of vertical soil pressure, the bending moments of points C2 and D2 show the minimum value, and the bending moment of point B2 shows the maximum value. In terms of axial force: under the action of various loads, the change trend of the axial force values ​​of points A2 and B2 is relatively gentle, while the changes in the axial force values ​​of points C2 and D2 vary greatly. Among them, the axial forces of points C2 and D2 show the maximum value under the action of vertical soil pressure; the axial forces of points C2 and D2 show the minimum value under the action of jacking reaction force.

[0204] In addition, the final results of the bending moments at points A2, B2, C2, and D2 are similar, while the final results of the axial forces vary significantly. The final results of the axial forces at points C2 and D2 are the largest, the final result of the bending moment at point A2 is the smallest, and the final result of the bending moment at point B2 is somewhere in between.

[0205] This example shows that the method of the present invention takes into account the influence of the construction opening, stratum resistance and special loads of the upward shield method, and can provide a theoretical reference for the internal force calculation and design of the special section segment structure of the upward shield method.

[0206] The above embodiments are intended only to illustrate the design concepts and features of the present invention. Their purpose is to enable those skilled in the art to understand the contents of the present invention and implement them accordingly. The scope of protection of the present invention is not limited to the above embodiments. Therefore, any equivalent changes or modifications made based on the principles and design concepts disclosed in the present invention are within the scope of protection of the present invention.

Claims

1. A method for calculating the internal forces of a special segment structure in an upward shield tunneling method, characterized in that: The method specifically comprises the following steps: Step 1: Determine the vertical load and lateral load of the special segment structure; the vertical load of the special segment structure includes its own weight g and its corresponding first foundation reaction p g , vertical water and soil pressure q1 and its corresponding second foundation reaction force p1, soil unloading q2 caused by vertical excavation and its corresponding third foundation reaction force p2, jacking reaction force P and its corresponding fourth foundation reaction force p p ; Step 2: Based on the fact that the special segment ring structure is a quadratic indeterminate structure, the displacement coordination equation at the elastic center is established, and the internal force of the special segment ring is analyzed using the elastic center method; Step 3: Approximate the segments at the opening of the special segment ring structure as curved thin plates, analyze the stress conditions of the special segment structure, calculate the triangularly distributed lateral water and soil pressure, uniformly distributed lateral water and soil pressure, and stratum resistance, and correct the internal force calculation of the lateral load; The calculation process of the triangular distribution lateral water and soil pressure q3 is as follows: First, the axial force at the ring opening caused by the triangularly distributed lateral water and soil pressure is calculated. The axial force calculation formula for a complete circular ring under the action of the triangularly distributed lateral water and soil pressure is: Where: N q3t is the axial force of the complete ring under the triangular distribution of lateral water and soil pressure; q3 is the triangular distribution of lateral water and soil pressure; R c is the calculated radius of the horizontal shield tunnel; The axial force correction coefficient λ of the opening segment is introduced, and its value is the ratio of the inner diameter of the opening to the arc length s of the curved thin plate. After the axial force correction coefficient λ of the opening segment is introduced, the axial force loss value N caused by the opening is q3c Calculate as follows: Where: N q3c It is the axial force lost due to the opening after the axial force correction coefficient λ of the opening segment is introduced under the action of triangularly distributed lateral water and soil pressure; Therefore, after considering the opening effect, the axial force caused by the triangularly distributed lateral water and soil pressure at the ring opening point is calculated according to the following formula: N q3 =N q3t -N q3c Where: N q3 To consider the axial force at the ring opening point caused by the triangularly distributed lateral water and soil pressure after the opening is affected; The calculation formula for the axial force of the remaining points under the action of triangular distributed lateral water and soil pressure is: Where: N' q3 To consider the axial forces at other points caused by the triangularly distributed lateral water and soil pressure after the opening is affected; When 0≤θ≤π, after introducing the bending moment influence coefficient μ of the open segment, the calculation formula of the bending moment of the open segment ring under the action of triangular distributed lateral water and soil pressure is: Where: M q3 To consider the bending moment of the opening segment ring caused by the triangularly distributed lateral water and soil pressure after the opening is affected; The calculation process of the uniformly distributed lateral water and soil pressure q4 is as follows: First, the axial force at the ring opening caused by the uniformly distributed lateral water and soil pressure is calculated. The axial force calculation formula for a complete circular ring under the action of the uniformly distributed lateral water and soil pressure is: N q4t =q4R c cos 2 i Where: N q4t is the axial force of the complete ring under the uniform lateral water and soil pressure; q4 is the uniform lateral water and soil pressure; The loss of axial force is: Where: N q4c is the axial force lost due to the opening under the action of uniformly distributed lateral water and soil pressure; Therefore, the axial force caused by the uniformly distributed lateral water and soil pressure at the ring opening point after considering the opening effect is calculated according to the following formula: N q4 =N q4t -N q4c Where: N q4 The axial force at point A2 caused by the uniformly distributed lateral water and soil pressure after considering the effect of the opening; After the axial force correction coefficient λ of the open segment is introduced into the remaining points, the axial force calculation formula of the open segment ring under the uniformly distributed lateral water and soil pressure is: N' q4 =λq3R c cos 2 i Where: N' q4 The axial forces at other points are caused by the uniformly distributed lateral water and soil pressure after considering the effect of the opening; When 0≤θ≤π, after introducing the bending moment influence coefficient μ of the open segment, the bending moment calculation formula under the uniformly distributed lateral water and soil pressure is: Where: M q4 To consider the bending moment of the open segment ring caused by the uniformly distributed lateral water and soil pressure after the opening is affected; Formation resistance q r The specific calculation process is: According to the calculation of the horizontal displacement at the horizontal diameter point of the segment ring in the modified conventional method, and combined with the load system, the calculation formula for the horizontal displacement at the horizontal diameter point of the segment ring in the special section during the upward shield method construction is: Where: p1, p2, p p are the foundation reaction force corresponding to the vertical water and soil pressure, the foundation reaction force corresponding to the unloading of the soil caused by vertical excavation, and the foundation reaction force corresponding to the jacking reaction force; g is the deadweight of the horizontal shield segment; k is the stratum (elastic) bed coefficient; η is the bending moment adjustment coefficient; EI is the bending stiffness per unit width; δ is the horizontal displacement of the horizontal diameter point of the segment ring; The axial force at the ring opening point caused by the formation resistance is calculated; the axial force calculation formula for a complete ring under the action of formation resistance is: N qrt =0.3536cosθkδR c Where: N qrt is the axial force of the complete ring under the action of the formation resistance; Loss of axial force: Where: N qrc is the axial force lost due to the opening under the action of formation resistance; Therefore, the axial force caused by the formation resistance at point A2 after considering the opening effect can be calculated according to the following formula: N qr =N qrt -N qrc Where: N qr The axial force around the opening point caused by the formation resistance after considering the opening effect; When π / 12<θ<π / 4, after the axial force correction coefficient λ of the opening segment is introduced into the remaining points, the calculation formula of the axial force caused by the formation resistance is: N' qr =0.3536λcosθkδR c Where: N' qr To consider the axial forces at other points caused by the formation resistance after the opening is affected; When π / 4≤θ≤π / 2, after introducing the axial force correction coefficient λ of the open segment, the calculation formula of the axial force caused by the formation resistance is: N' qr =(-0.7071cosθ+cos 2 θ+0.7071sin 2 θcosθ)λkδR c When 0≤θ<π / 4, after introducing the bending moment influence coefficient μ of the open segment, the calculation formula of the bending moment caused by the formation resistance is: M qr =(1+μ)(0.2346-0.3536cosθ)kδR c 2 Where: M qr To consider the bending moment of the opening segment ring caused by the formation resistance after the opening is affected; When π / 4≤θ≤π / 2, after introducing the bending moment influence coefficient μ of the open segment, the calculation formula of the bending moment caused by the formation resistance is: M qr =(1+μ)(-0.3487+0.5sin 2 θ+0.2357cos 3 θ)kδR c 2 Step 4: Calculate the internal forces of the special segment structure under vertical loads; the vertical loads include vertical excavation soil unloading and foundation reaction force, jacking reaction force and foundation reaction force; The step 4 is specifically as follows: The calculation formulas for the axial force and bending moment at the ring opening point and the arch bottom are as follows: N PA =0.00467PR c M PA =0.00232PR c 2 N PB ＝0 M PB =0.05531PR c 2 Where: N PA 、M PA 、N PB 、M PB are the axial force and bending moment at the ring opening point and the arch bottom point under the action of jacking reaction force and foundation reaction force respectively; The vertical load causes the axial force N at other points g 、N q1 、N q2 、N P for: N q1 =q1R c sin 2 i N q2 =-q2R c sin 2 i N P =-PR c sin 2 θ Where: N g 、N q1 、N q2 are the axial forces caused by self-weight and foundation reaction, vertical water and soil pressure and foundation reaction, vertical excavation soil unloading and foundation reaction; N P is the axial force at other points caused by the jacking reaction force and the foundation reaction force; P is the jacking reaction force; In addition, the vertical load causes bending moments M at other points g 、M q1 、M q2 、M P for: Where: M g 、M q1 、M q2 are the bending moments caused by self-weight and foundation reaction, vertical water and soil pressure and foundation reaction, vertical excavation soil unloading and foundation reaction; M P The remaining bending moment is caused by the jacking reaction and foundation reaction; Step 5: Superimpose the internal forces of the segment ring under the action of lateral load and vertical load to obtain the internal forces of the final special segment.

2. The internal force calculation method for a special segment structure in upward shield construction according to claim 1 is characterized in that: The special segment is an annular segment with a circular opening formed by upward shield construction during horizontal shield tunneling.

3. The internal force calculation method for a special segment structure in upward shield construction according to claim 1 is characterized in that: The jacking reaction force is composed of the weight of the vertical shield machine, the weight of the jack, the weight of the vertical shield segments, the front thrust and the friction force.

4. The internal force calculation method for a special segment structure in upward shield construction according to claim 1 is characterized in that: (1) Assume that the ground resistance is distributed in the range of π / 4 to 3π / 4 from the top of the ring to the left and right, and its magnitude is in accordance with the local deformation theory, that is, the ground resistance is proportional to the passive displacement of the ground; (2) Assume that the lateral water and soil pressure is distributed between 0 and π from the top of the ring to the left and right; (3) The vertical load is uniformly distributed along the horizontal projection of the ring; (4) The soil unloading caused by vertical excavation is simplified to a line load.

5. The internal force calculation method for a special segment structure in upward shield construction according to claim 1 is characterized in that: The displacement coordination equation at the elastic center is: Where: δ 11 , δ 21 Refers to the displacement of the basic structure along the X1 and X2 directions under the action of unit force X1 = 1 alone; δ 21 , δ 22 Refers to the displacement of the basic structure along the X1 and X2 directions when the unit force X2 = 1 acts alone; Δ1p and Δ2p are the displacements of the basic structure along the X1 and X2 directions respectively when the load acts alone; Calculate the M at the angle θ between the segment ring and the vertical axis of the special section θ 、N θ , the formula is as follows: M θ =M P +X1-X2R cosθ <h2 style=";text-align:left;direction:ltr">N<h2 style=";text-align:left;direction:ltr"> θ <h2 style=";text-align:left;direction:ltr"> =X2cosθ+N<h2 style=";text-align:left;direction:ltr"> P Where: M P 、N P are the bending moment and axial force generated by external load on the segment ring; M θ 、N θ They are the bending moment and axial force at the angle θ between the cross-section segment ring and the vertical axis; θ is the angle between the cross-section segment ring and the vertical axis; among them, the bending moment is positive when the inner side is tensile, and the axial force is positive when the pressure is.

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