A method for verifying the grouting pressure of the gap at the tail of shield during shield construction

Abstract

The present invention relates to the technical field of tunnel shield construction, and in particular to a method for calibrating grouting pressure of a gap at the tail of a shield during shield construction. The method comprises the following steps: firstly calculating a critical value of an inter-ring shear force according to an inter-ring joint model of an assembled tunnel; then calculating a theoretical value of shear force at each longitudinal position of the assembled tunnel according to a designed grouting pressure and a longitudinal mechanical model of the assembled tunnel; and then comparing each theoretical value of shear force with the critical value of the inter-ring shear force. If any theoretical value of shear force is greater than the critical value of the inter-ring shear force, the designed grouting pressure is reduced, thereby avoiding shear yield of bolts at the inter-ring joints due to excessive shear force during shield construction.

Description

Technical Field

[0001] The invention relates to the technical field of tunnel shield construction, in particular to a method for calibrating grouting pressure of a shield tail gap in shield construction. Background Art

[0002] Shield tunneling, with its high degree of mechanization and automation, is a widely adopted excavation technique for underground transportation projects both domestically and internationally. During shield construction, a cutterhead is installed in front of the shield machine to cut the soil, while an assembly machine is located behind the machine to assemble the annular reinforced concrete segments into a prefabricated tunnel. To facilitate construction, the outer diameter of the shield machine casing is often larger than that of the prefabricated tunnel. This creates an annular gap between the prefabricated tunnel and the surrounding strata, known as the shield tail gap.

[0003] To ensure the stability of the assembled tunnel and the surrounding strata, the annular voids must be filled through simultaneous grouting. Controlling the grouting pressure during simultaneous grouting is a key technology in shield construction. Excessive grouting pressure can damage the assembled tunnel's lining structure. Therefore, to ensure shield construction safety, the grouting pressure must be controlled at an appropriate value.

[0004] Currently, the grouting pressure is determined by considering only the deformation of the surrounding strata and the overall upward displacement of the assembled tunnel, without considering the stress characteristics of the inter-ring joints. However, the assembled tunnel is a discontinuous structure composed of segments and bolts, and its deformation mainly occurs at the inter-ring joints. Excessive shear force usually leads to shear dislocation, which can cause leakage in the inter-ring joints. Summary of the Invention

[0005] The technical problem to be solved by the present invention is that the existing method for determining grouting pressure does not take into account the stress characteristics of the inter-ring joints of the assembled tunnel, resulting in shear dislocation and deformation of the inter-ring joints due to excessive shear force during shield construction.

[0006] In order to solve the above technical problems, the present invention provides a method for calibrating the grouting pressure of the gap at the tail of a shield during shield construction, comprising the following steps:

[0007] Calculate the critical value of inter-ring shear force based on the inter-ring joint model of assembled tunnel;

[0008] Calculating theoretical values ​​of shear force at various longitudinal positions of the assembled tunnel based on the designed grouting pressure and the longitudinal mechanical model of the assembled tunnel;

[0009] The theoretical values ​​of the shear force are compared with the critical value of the inter-annular shear force. If any of the theoretical values ​​of the shear force is greater than the critical value of the inter-annular shear force, the designed grouting pressure is reduced.

[0010] As a preferred solution, the longitudinal mechanical model of the assembled tunnel is an elastic foundation beam model, which includes a slurry unsolidified area on the left and a slurry solidified area on the right. The base bed coefficient of the slurry unsolidified area gradually increases from left to right, and the base bed coefficient of the slurry solidified area is fixed.

[0011] As a preferred solution, the longitudinal mechanical model of the assembled tunnel includes n units sequentially connected from left to right along the longitudinal direction of the assembled tunnel:

[0012]

[0013] Among them, S n is the shear force and deformation expression matrix of the nth unit, S n-1 is the shear force and deformation expression matrix of the n-1th unit, T n is the stress-strain transfer matrix between the nth unit and the n-1th unit, F1 n is the initial value influence matrix of external load between the nth unit and the n-1th unit, is the external load slope influence matrix between the nth unit and the n-1th unit.

[0014] As a preferred solution, the boundary condition of the longitudinal mechanical model of the assembled tunnel is that the left endpoint of the longitudinal mechanical model of the assembled tunnel is a hinged end, and the right endpoint of the longitudinal mechanical model of the assembled tunnel is a fixed end.

[0015] As a preferred solution, the following formula is used to solve the theoretical shear force Q at each longitudinal position of the assembled tunnel:

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[0096] Where x is the distance between the calculation point on the longitudinal mechanical model of the assembled tunnel and the left end of the longitudinal mechanical model of the assembled tunnel, in meters; C is the equivalent shear stiffness, in kN / rad; D is the equivalent bending stiffness, in kN·m / rad; K is the base coefficient at the calculation point, in kN / m 2 ; q is the initial value of the floating load in kN, unit; Δq / ΔL is the load gradient, unit is kN / m.

[0097] As a preferred solution, C=πG S (D0 2 -d 2 ) / 4;

[0098] Among them, G S is the shear modulus of the segment, in kPa; D0 is the outer diameter of the tunnel, in m; d is the inner diameter of the tunnel, in m.

[0099] As a preferred solution, D = ηπE S (D0 2 -d 2 ) / 64;

[0100] Among them, η is the effective longitudinal stiffness, E S is the elastic modulus of the segment, in kPa; D0 is the outer diameter of the tunnel, in m; d is the inner diameter of the tunnel, in m.

[0101] As a preferred solution, q = 1000 × BPD0;

[0102] Among them, q is the floating load, unit is kN; B is the ring width of the pipe segment, unit is m; P is the grouting pressure, unit is MPa; D0 is the outer diameter of the tunnel, unit is m.

[0103] As a preferred solution, the inter-ring joint model includes:

[0104]

[0105] Wherein, τ is the shear strength of the bolt, in MPa; n b is the number of bolts, unit: G b is the shear modulus of the bolt, in kPa; A b is the bolt area, unit is m 2 ;n g is the number of tenons and mortises, in units; κ g is the shear correction factor, dimensionless; G g is the shear modulus of the mortise and tenon, unit is kPa; A g is the area of ​​the mortise and tenon, unit: m 2 ; f is the friction force of the joint between the rings, unit is kN.

[0106] Compared with the prior art, the present invention has the following beneficial effects:

[0107] The present invention provides a method for verifying the grouting pressure of the gap between the shield tails during shield construction. The method first calculates a critical value of the inter-ring shear force based on an inter-ring joint model of an assembled tunnel. Then, the theoretical value of the shear force at each longitudinal position of the assembled tunnel is calculated based on the designed grouting pressure and a longitudinal mechanical model of the assembled tunnel. Subsequently, the theoretical values ​​of the shear force are compared with the critical value of the inter-ring shear force. If any theoretical value of the shear force is greater than the critical value of the inter-ring shear force, the designed grouting pressure is reduced, thereby avoiding shear dislocation and deformation at the inter-ring joints due to excessive shear force during shield construction. BRIEF DESCRIPTION OF THE DRAWINGS

[0108] Figure 1 This is a flow chart of the shield tail gap grouting pressure calibration method for shield construction of the present invention;

[0109] Figure 2 This is a schematic diagram of the longitudinal mechanical model of the assembled tunnel of the present invention;

[0110] Figure 3 This is a side view of the inter-ring joint model of the assembled tunnel of the present invention before deformation;

[0111] Figure 4 This is a side view of the inter-ring joint model of the assembled tunnel of the present invention after deformation;

[0112] Figure 5 This is a front view of the inter-ring joint model of the assembled tunnel of the present invention;

[0113] Figure 6 This is the calculation result data diagram of the inter-ring joint model;

[0114] Figure 7 This is a data diagram of the calculation results of the longitudinal mechanical model of the assembled tunnel;

[0115] In the figure, 100 is a bolt; 200 is a tenon. DETAILED DESCRIPTION

[0116] The following embodiments of the present invention are described in further detail with reference to the accompanying drawings and examples. The following examples are used to illustrate the present invention but are not intended to limit the scope of the present invention.

[0117] In the description of the present invention, it should be understood that the terms "upper", "lower", "left", "right", "top", "bottom", etc., indicating the orientation or positional relationship, are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. It should be understood that the terms "first", "second", etc. are used in the present invention to describe various information, but such information should not be limited to these terms, which are only used to distinguish the same type of information from each other. For example, without departing from the scope of the present invention, "first" information may also be referred to as "second" information, and similarly, "second" information may also be referred to as "first" information.

[0118] like Figure 1As shown, the shield tail gap grouting pressure calibration method of the present invention for shield construction first calculates the critical value of the inter-ring shear force based on the inter-ring joint model of the assembled tunnel; then calculates the theoretical value of the shear force at each longitudinal position of the assembled tunnel based on the designed grouting pressure and the longitudinal mechanical model of the assembled tunnel; then compares each theoretical value of the shear force with the critical value of the inter-ring shear force. If any theoretical value of the shear force is greater than the critical value of the inter-ring shear force, the designed grouting pressure is reduced, thereby avoiding shear dislocation and deformation at the inter-ring joint due to excessive shear force during shield construction.

[0119] The longitudinal mechanical model of the assembled tunnel is an elastic foundation beam model, which includes a slurry unsolidified area on the left and a slurry solidified area on the right. The base bed coefficient of the slurry unsolidified area increases gradually from left to right, while the base bed coefficient of the slurry solidified area is fixed. Figure 2 As shown, in the unsolidified slurry zone, the base coefficient gradually increases from left to right, while the upward load on the segments gradually decreases from left to right. In the solidified slurry zone, the slurry has completed consolidation and hardening, and the base coefficient no longer changes. The foundation of the elastic foundation beam adopts a Winkel elastic foundation, and the continuous beam adopts a Timoshenko beam that takes shear deformation into account. Due to the variable base coefficient and variable load involved, a calculation method similar to the finite element method can be used, namely the transfer matrix method. The continuous beam on the elastic foundation is discretized into n beam units, which are first discretized and then integrated. The specific longitudinal mechanical model of the assembled tunnel includes n units connected sequentially from left to right along the longitudinal direction of the assembled tunnel:

[0120]

[0121] Among them, S n is the shear force and deformation expression matrix of the nth unit, S n-1 is the shear force and deformation expression matrix of the n-1th unit, T n is the stress-strain transfer matrix between the nth unit and the n-1th unit, F1 n is the initial value influence matrix of external load between the nth unit and the n-1th unit, is the external load slope influence matrix between the nth unit and the n-1th unit.

[0122] Specifically, S0 is the initial parameter matrix of the left endpoint of the continuous beam, which is an unknown quantity, S0 = [v0; θ0; M0; Q0], where v0 represents the deflection of the left endpoint, unit; θ0 represents the cross-sectional rotation of the left endpoint, unit rad; M0 represents the bending moment of the left endpoint, unit kN·m; Q represents the shear force of the left endpoint, unit kN; Tn F1 is the stress-strain transfer matrix between the nth unit and the n-1th unit; nis the initial value influence matrix of external load between the nth unit and the n-1th unit, is the external load slope influence matrix between the nth unit and the n-1th unit, T n 、F1 n and are all known quantities. Therefore, according to It can be seen that the internal force and deformation at any position of each beam element can be expressed by the initial parameter matrix at the left end point of the continuous beam:

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[0127] Combine the above S1 to S n The formulas can then be derived:

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[0129] The boundary conditions for the above formula are set as follows: the left endpoint of the assembled tunnel longitudinal mechanical model is the hinged end, and the right endpoint of the assembled tunnel longitudinal mechanical model is the fixed end. Since the bending moment and deflection of the hinged end are both 0, and the deflection and rotation angle of the fixed end are both 0, therefore:

[0130] S0=[0;θ0;0;Q0] (2)

[0131] S n =[0;0;M n ;Q n ] (three)

[0132] By combining the above formulas (1), (2) and (3), we can obtain the theoretical value of the shear force Q at any point in the longitudinal direction of the tunnel.

[0133] In this embodiment, C=πG S (D0 2 -d 2 ) / 4;

[0134] Among them, G S is the shear modulus of the segment, in kPa; D0 is the outer diameter of the tunnel, in m; d is the inner diameter of the tunnel, in m.

[0135] D=ηπE S (D0 2 -d 2 ) / 64;

[0136] Where η is the effective longitudinal stiffness, which is set to 0.1; E S is the elastic modulus of the segment, in kPa; D0 is the outer diameter of the tunnel, in m; d is the inner diameter of the tunnel, in m

[0137] q = 1000 × BPD0;

[0138] Where q is the floating load, unit is kN; B is the ring width of the segment, unit is m; P is the grouting pressure, unit is MPa; D0 is the outer diameter of the tunnel, unit is m

[0139] In this embodiment:

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[0220] Where x is the distance from the calculation point on the longitudinal mechanical model of the assembled tunnel to the left end of the longitudinal mechanical model of the assembled tunnel, with the unit of m; C is the equivalent shear stiffness, with the unit of kN / rad; D is the equivalent flexural stiffness, with the unit of kN·m / rad; K is the subgrade coefficient at the location of the calculation point, with the unit of kN / m 2 ; q is the initial value of the uplift load, with the unit of kN; Δq / ΔL is the load gradient, with the unit of kN / m.

[0221] In this embodiment, as Figures 3 to 5 shown, when the circumferential joint is subjected to shear force, there are three forces in total to bear the shear force, namely the circumferential friction force, the shear resistance of the male and female tenons 200, and the shear resistance of the bolts 100. In this embodiment, it is assumed that first the circumferential friction force plays the role of shear resistance, and then the male and female tenons and bolts play the role of shear resistance. When the segment is subjected to a shear force Q and undergoes shear deformation, under the action of the bolt pre-tightening force, friction force will be generated. The relationship between the maximum static friction force f and the axial force N is f = μN, where μ is the friction coefficient of the segment of the circumferential joint, and the value is 0.3. Therefore, whether the circumferential joint of the segment undergoes deformation is related to the magnitude relationship between the applied shear force Q and the maximum static friction force f. When the shear force is small and satisfies the relationship Q < f, the shear force is not sufficient to overcome the maximum static friction force, so the joint does not slip, and it is considered that the joint does not undergo shear dislocation deformation; when the shear force is large and satisfies the relationship Q ≥ f, the maximum static friction force is no longer sufficient to resist the action of the shear force, so the joint starts to slide. At this time, the bolts and the male and female tenons play the role of resisting the shear force; when the shear force Q continues to increase and is greater than the maximum static friction f generated by applying the axial force at the circumferential joint, and the bolts at the joint start to slip, there is usually an installation gap of 1 mm to 2 mm between the bolts, female tenons and male tenons in actual engineering, so usually it will slip 1 mm to 2 mm, and only then will the bolts contact the bolt hole wall, and the female tenons and male tenons will contact, and these three will play a role together; at this time:

[0222]

[0223] Wherein, τ is the shear strength of the bolt, in MPa; n b is the number of bolts, in pieces; G b is the shear modulus of the bolt, in kPa; A b is the cross-sectional area of ​​the bolt, in m 2 ;n g is the number of tenons and mortises, in units; κ g is the shear correction factor, dimensionless; G g is the shear modulus of the mortise and tenon, unit is kPa; A g is the area of ​​the mortise and tenon, unit: m 2 ; f is the friction force between the ring joints, unit is kN.

[0224] The critical value of the inter-ring shear force can be solved by formula (4). The grouting pressure can be verified by comparing the theoretical value of the shear force Q at any point in the longitudinal direction of the tunnel with the critical value of the inter-ring shear force.

[0225] The specific calculation cases using the shield tail gap grouting pressure calibration method of the present invention are as follows:

[0226] A typical shield tunnel project is selected as a calculation example. The outer diameter of the tunnel is 13.8m, the inner diameter of the tunnel is 12.6m, the ring width of the segment is 2m, and the elastic modulus of the segment E is S 3.45×10 7 kPa, segment shear modulus G S 1.32×10 7 kPa, number of bolts n b There are 56 bolts with a bolt diameter of d b is 0.036m, bolt length l b is 0.7m, the elastic modulus of the bolt E b is 2.06×108kPa, the bolt shear modulus G b 0.78×10 8 kPa, the base bed coefficient is 1×10 5 kN / m2, the allowable shear stress τ of the bolt is 370MPa, the length of the unsolidified slurry zone is 12m, and the bolt preload is 380kN. The cross-sectional area of ​​the tenon is 0.047m 2 , a total of 28.

[0227] First, calculate the deformation and stress characteristics of the ring joint, and the results are as follows Figure 6 As shown by Figure 6 It can be seen that when the shear force Q of the inter-ring joint is greater than 73000kN, the bolt will show shear yield phenomenon, and this shear force is regarded as the critical value of the shear deformation of the inter-ring joint.

[0228] Then, four grouting pressures are set at 0.1 MPa, 0.3 MPa, 0.5 MPa, and 0.7 MPa, and the shear force distribution along the longitudinal direction of the tunnel under each working condition is solved, as shown in the following example: Figure 7 As shown by Figure 7 It is known that when the grouting pressure exceeds 0.5 MPa, it will cause local shear failure of the longitudinal bolts. Therefore, in order to keep the tunnel in normal working condition, the grouting pressure of synchronous grouting should not exceed 0.5 MPa.

[0229] In summary, the shield tail gap grouting pressure calibration method of the present invention first calculates the critical value of the inter-ring shear force based on the inter-ring joint model of the assembled tunnel; then calculates the theoretical value of the shear force at each longitudinal position of the assembled tunnel based on the designed grouting pressure and the longitudinal mechanical model of the assembled tunnel; then compares each theoretical value of the shear force with the critical value of the inter-ring shear force. If any theoretical value of the shear force is greater than the critical value of the inter-ring shear force, the designed grouting pressure is reduced, thereby avoiding shear dislocation and deformation at the inter-ring joint due to excessive shear force during shield construction.

[0230] The above description is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and substitutions can be made without departing from the technical principles of the present invention. These improvements and substitutions should also be regarded as the scope of protection of the present invention.

Claims

1. A method for calibrating the grouting pressure of the gap at the tail of a shield during shield construction, characterized in that: The following steps are involved: Calculate the critical value of inter-ring shear force based on the inter-ring joint model of assembled tunnel; Calculating theoretical values ​​of shear force at various longitudinal positions of the assembled tunnel based on the designed grouting pressure and the longitudinal mechanical model of the assembled tunnel; Compare each of the theoretical shear force values ​​with the critical value of the inter-ring shear force. If any of the theoretical shear force values ​​is greater than the critical value of the inter-ring shear force, reduce the designed grouting pressure. The longitudinal mechanical model of the assembled tunnel is an elastic foundation beam model, which includes a slurry unsolidified zone on the left and a slurry solidified zone on the right. The base bed coefficient of the slurry unsolidified zone gradually increases from left to right, and the base bed coefficient of the slurry solidified zone is fixed. The longitudinal mechanical model of the assembled tunnel includes n units connected sequentially from left to right along the longitudinal direction of the assembled tunnel: Among them, S n is the shear force and deformation expression matrix of the nth unit, S n-1 is the shear force and deformation expression matrix of the n-1th unit, T n is the stress-strain transfer matrix between the nth unit and the n-1th unit, F1 n is the initial value influence matrix of external load between the nth unit and the n-1th unit, is the external load slope influence matrix between the nth unit and the n-1th unit; The inter-ring joint model includes: Wherein, τ is the shear strength of the bolt, in MPa; n b is the number of bolts, unit: G b is the shear modulus of the bolt, in kPa; A b is the bolt area, unit is m 2 ;n g is the number of tenons and mortises, in units; κ g is the shear correction factor, dimensionless; G g is the shear modulus of the mortise and tenon, unit is kPa; A g is the area of ​​the mortise and tenon, unit: m 2 ; f is the friction force of the joint between the rings, unit is kN.

2. The shield tail gap grouting pressure calibration method for shield construction according to claim 1 is characterized in that: The boundary condition of the assembled tunnel longitudinal mechanical model is that the left endpoint of the assembled tunnel longitudinal mechanical model is a hinged end, and the right endpoint of the assembled tunnel longitudinal mechanical model is a fixed end.

3. The method for verifying the grouting pressure of the shield tail gap during shield construction according to claim 1, wherein: The following formulas are used to solve the theoretical shear force Q at each longitudinal position of the assembled tunnel: hour: hour: hour: Where x is the distance between the calculation point on the longitudinal mechanical model of the assembled tunnel and the left end of the longitudinal mechanical model of the assembled tunnel, in meters; C is the equivalent shear stiffness, in kN; D is the equivalent bending stiffness, in kN·m / rad; K is the base coefficient at the calculation point, in kN / m 2 ; q is the initial value of the floating load, unit is kN / m; Δq / ΔL is the load gradient, unit is kN / m 2 .

4. The method for verifying the grouting pressure of the shield tail gap during shield construction according to claim 3, wherein: C=πG S (D0 2 -d 2 ) / 4; Among them, G S is the shear modulus of the segment, in kPa; D0 is the outer diameter of the tunnel, in m; d is the inner diameter of the tunnel, in m.

5. The method for verifying the grouting pressure of the shield tail gap during shield construction according to claim 3, characterized in that: D=ηπE S (D0 2 -d 2 ) / 64; Where η is the effective longitudinal stiffness, which is a dimensionless unit; E S is the elastic modulus of the segment, in kPa; D0 is the outer diameter of the tunnel, in m; d is the inner diameter of the tunnel, in m.

6. The method for verifying the grouting pressure of the gap at the tail of a shield during shield construction according to claim 3, wherein: q = 1000 × BPD0; Among them, q is the floating load, unit is kN; B is the ring width of the pipe segment, unit is m; P is the grouting pressure, unit is MPa; D0 is the outer diameter of the tunnel, unit is m.

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