A design method for shock-absorbing grouting in shield tunnels in composite strata

Abstract

The present invention discloses a shock-absorbing grouting design method for a composite stratum shield tunnel, comprising the following steps: establishing a beam-spring structure numerical model; determining the stiffness of a grouting layer frame spring based on a traditional grouting slurry to obtain a combined resistance coefficient of the stratum-grouting layer; calculating and analyzing the safety performance of pipe segments and joints to obtain displacement and internal force calculation results of the shield tunnel in the composite stratum; if the calculation results meet safety regulations, it indicates that selecting a traditional slurry material for grouting can meet the seismic requirements of the shield tunnel; if the calculation results do not meet safety regulations, determining stiffness differences based on typical sections, dynamically adjusting parameters of the combined resistance coefficient of the stratum-grouting layer until the safety regulations are met, calculating the difference between the two, and determining the optimal difference between the two; calculating the frame spring stiffness based on the adjusted value, and then determining the elastic modulus of the grouting material based on the frame spring stiffness formula; and determining the type of grouting material based on the elastic modulus of the grouting material.

Description

Technical Field

[0001] The invention belongs to the field of underground engineering shock-absorbing construction design, and in particular relates to a shield tunnel shock-absorbing grouting design method under complex strata. Background Art

[0002] During the actual construction process, shield tunnels inevitably pass through high-intensity earthquake zones, where earthquake damage is severe and post-earthquake repair is difficult. Under the action of earthquakes, the tunnel moves with the surrounding strata. Its safety mainly depends on the deformation of the surrounding strata and its ability to resist deformation. Especially in complex strata, the propagation speed and stiffness of seismic waves in different strata vary greatly. Therefore, the internal forces and displacements generated by the structure at the site where the geological conditions suddenly change are large, making the structure more susceptible to damage. Therefore, improving the seismic resistance of shield tunnels in complex strata is an important part of the shield tunnel design process. There are three main approaches to the seismic resistance and shock absorption design of existing shield tunnels, as follows:

[0003] (1) Strengthen the ground through grouting and other means to improve its deformation resistance. However, in actual engineering, grouting reinforcement of the ground is often costly, labor-intensive, and the reinforcement quality is unstable.

[0004] (2) For the seismic design of shield tunnels in heterogeneous medium strata, seismic components can be added to the weak points, or flexible segment rings or steel segment rings can be used to adapt to the displacement of the surrounding strata through their own deformation, thereby reducing the internal forces of the structure caused by earthquakes. However, this requires a complex design process, and such components are often only suitable for specific stratum combination conditions. When the stratum combination conditions change, such components are difficult to use again. In addition, such construction processes are relatively complex and have poor universality, which increases the design process and construction costs of shield tunnel construction.

[0005] (3) Related research and examples have shown that the installation of an isolation layer can effectively reduce the damage to shield tunnels during earthquakes. By utilizing the key process of grouting behind the shield tunnel wall, asphalt-based grouting materials are used to form a softer isolation layer between the stratum and the tunnel, thereby preventing the displacement and force of stratum deformation from being transmitted to the segments, thereby protecting the tunnel structure. Related research has proven the feasibility of this operation. However, for more complex sites, there is no systematic design solution for the grouting parameters. Summary of the Invention

[0006] In order to solve the technical problems existing in the prior art, the purpose of the present invention is to provide an energy-absorbing and shock-absorbing structure grouting design method suitable for complex strata in response to the shock absorption needs of shield tunnels, so that it is more suitable for the protection of tunnel structures in earthquakes in complex strata, while improving the feasibility of the structure.

[0007] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0008] A design method for shock-absorbing grouting of a composite stratum shield tunnel comprises the following steps:

[0009] Step 1: Obtain relevant parameters of the shield tunnel in complex strata; select a typical section of the shield tunnel in a representative complex stratum;

[0010] Step 2: Establish a numerical model of the beam-spring structure; determine the stiffness of the stratum spring by determining the stratum structure, and determine the stiffness of the grouting layer frame spring based on the traditional grouting slurry to obtain the combined resistance coefficient of the stratum-grouting layer;

[0011] Step 3: Apply the combined stratum-grouting layer resistance coefficient and seismic force to the beam-spring structure numerical model, perform calculations and analysis on the safety performance of the segments and joints, obtain the displacement and internal force calculation results of the shield tunnel in the composite stratum, and perform strength verification;

[0012] Step 4: If the calculation result meets the safety requirements, it means that the selection of traditional grouting materials for grouting can meet the seismic requirements of the shield tunnel, and the traditional grouting slurry can be used for grouting construction; if the calculation result does not meet the safety requirements, the stiffness difference is determined based on the typical section, and the parameters of the stratum-grouting layer combination resistance coefficient are dynamically adjusted. Step (3) is repeated until the safety requirements are met. At this time, the difference between the stratum-grouting layer combination resistance coefficient before and after the adjustment is calculated to determine the optimal difference between the two; the grouting layer frame spring stiffness is calculated based on the adjusted stratum-grouting layer combination resistance coefficient, and then the elastic modulus of the grouting material is determined based on the frame spring stiffness formula;

[0013] Step 5: Determine the type of grouting material based on the elastic modulus of the grouting material.

[0014] As a further technical solution, step 2 simulates the shield tunnel as a homogeneous circular ring beam, the annular joint can be simulated by elastic hinges, and the surrounding rock and soil can be simulated by stratum springs; the grouting layer frame springs are connected in series with the stratum springs to simulate the grouting layer and soil constraints.

[0015] As a further technical solution, the formation spring stiffness of different formations is determined by the formula:

[0016] k 1i =K 1i Ld

[0017] Where:

[0018] k 1i —formation spring stiffness (N / m);

[0019] K 1i —Base coefficient (N / m 3 );

[0020] L—central spring spacing of foundation (m);

[0021] d—Calculated length of the stratum along the longitudinal direction of the underground structure (m).

[0022] As a further technical solution, the stiffness calculation formula of the grouting layer spring is as follows:

[0023] k 2i =EI

[0024] E—elastic modulus;

[0025] I—Interface moment of inertia.

[0026] As a further technical solution, the calculation formula for the combined resistance coefficient of the stratum-grouting layer is as follows:

[0027]

[0028] k 1i — formation spring stiffness;

[0029] k 2i —Spring stiffness of the grouting layer.

[0030] As a further technical solution, when using the static method for calculation, the seismic effects include the seismic inertia force of the lining's own weight, the seismic inertia force of the overlying soil column, and the seismic lateral earth pressure increment.

[0031] As a further technical solution, the lining self-weight seismic inertia force includes the horizontal and vertical seismic inertia forces of the segment self-weight;

[0032] E ih =A h m is =C i C s Am is

[0033] E iv =K v E ih =K v C i C s Am is

[0034] C i —Seismic importance coefficient;

[0035] C s —Site seismic peak acceleration adjustment coefficient;

[0036] A—peak value of horizontal basic ground acceleration;

[0037] m is—mass of the tunnel segment at the calculation point (kg);

[0038] k v —Ratio of the vertical peak acceleration to the horizontal peak acceleration.

[0039] As a further technical solution, the seismic inertia force of the overlying soil column includes the horizontal seismic force of the overlying soil column and the vertical seismic force of the overlying soil column; the horizontal seismic force of the overlying soil column is:

[0040] F ih =A h Q i / g

[0041] The vertical seismic force of the overlying soil column is:

[0042] F iv =K v A h Q i / g

[0043] A h —Horizontal design ground motion peak acceleration

[0044] g—acceleration due to gravity;

[0045] k v —Ratio of vertical peak acceleration to horizontal peak acceleration;

[0046] Q i —vertical earth pressure of the overlying soil column;

[0047] As a further technical solution, the lateral earth pressure increment during an earthquake includes the inner earth pressure increment and the outer earth pressure increment:

[0048] The inner earth pressure increment is:

[0049] Δe 1i =C i C s γh 1i (λ1-λ)

[0050] The outer earth pressure increment is:

[0051] Δe 2i =C i C s γh 2i (λ2-λ′)(9)

[0052] λ, λ′—inner and outer constant lateral pressure coefficients;

[0053] h 1i 、h 2i—The distance from any point i inside or outside the segment to the ground surface (m).

[0054] C i —Seismic importance coefficient;

[0055] C s —Site adjustment coefficient;

[0056] γ—surrounding rock mass;

[0057] λ1, λ2—lateral pressure coefficients during internal and external earthquakes.

[0058] As a further technical solution, in step 3, when performing strength verification, the opening and displacement of the shield segment joints should not exceed the design allowable values, the displacement of the axial steel bars at the expansion joints should be less than the yield displacement, the rotation angle at the expansion joints should be less than the yield rotation angle, and the joint opening should be less than the allowable opening of the ductile sealing gasket.

[0059] Compared with the existing technology, the shield tunnel vibration reduction design method of the present invention has the following advantages:

[0060] 1. Based on the stiffness coupling theory, this invention proposes a shield tunnel construction design method and proposes a basis for selecting grouting materials based on the existing shield tunnel construction technology. It makes maximum use of the existing technology, greatly reduces the cost of process improvement, and quantitatively analyzes the seismic performance of the grouting layer, providing a theoretical basis for the shock absorption effect of the shield tunnel.

[0061] 2. The seismic measures of the present invention are based on the grouting reinforcement method. During construction, slurry that meets the safety factor method is selected for grouting. Compared with the use of special pipe segments and seismic-resistant structures, the design method of this scheme has a wider range of application and can be adapted to complex strata with multiple layers of different strata, effectively reducing construction costs and meeting the needs of reducing costs and increasing efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 Flowchart of the shock-absorbing grouting design of the present invention;

[0063] Figure 2 A simplified diagram of the stratum distribution at a typical cross section of the shield tunnel of the present invention;

[0064] Figure 3 A simplified diagram of the load-structure model of the present invention;

[0065] Figure 4 A schematic diagram of the grouting layer spring and the stratum spring connected in series according to the present invention;

[0066] Figure 5 The combined resistance coefficient adjustment flow chart proposed by the present invention;

[0067] In the figure: 1-first stratum; 2-shield tunnel; 3-second stratum; 4-third stratum; 5-grouting layer; 6-second stratum construction spring; 7-equivalent circular ring beam of shield tunnel; 8-third stratum construction spring; 9-equivalent elastic hinge of annular joint; 10-segment deadweight; 11-inner soil pressure increment; 12-outer soil pressure increment; 13-seismic inertia force of upper soil column; 14-grouting layer construction spring; 15-stratum spring; 16-first stratum construction spring. DETAILED DESCRIPTION

[0068] The present invention will be described below with reference to the accompanying drawings, specifically as follows:

[0069] (1) Conduct a detailed geological survey of the construction site to collect information on the stratigraphic structure, surrounding rock grade, elastic modulus of different stratigraphic layers, site seismic fortification intensity, and segment elastic modulus of the shield tunnel area.

[0070] (2) According to the design data, a typical section of the shield tunnel under a representative complex stratum is selected (typical section method: section at the joint at the demarcation point; section at the place where the spring stiffness of the stratum is greatly different; section at the place where the terrain is undulating) to determine the stratum distribution at the typical section. Taking a complex stratum with three different stratum combinations as an example, the stratum distribution diagram is shown in the figure below; it includes the first stratum 1, the second stratum 3, and the third stratum 4; in the three strata, the positions of the shield tunnel 2 and the grouting layer 5 in the three strata are as follows: Figure 2 As shown;

[0071] Establish a numerical model of beam-spring structure and simulate the tunnel structure as a homogeneous circular beam. Figure 3 In (shield tunnel equivalent circular ring beam 7), the ring joint can be simulated by elastic hinge (see Figure 3 The annular joint is equivalent to the elastic hinge 9), and the surrounding rock and soil are simulated by springs (see the second layer frame spring 6, the first layer frame spring 16, and the third layer frame spring 8 for details). The beam-spring model is as follows Figure 3 shown.

[0072] (3) There are grouting layers 5 and soil constraints around the tunnel, so the construction spring is simulated by connecting the grouting layer construction spring 14 and the ground spring 15 in series, as shown in the schematic diagram. Figure 4 shown.

[0073] For the stratum spring, due to the complex stratum conditions where the tunnel is located, the stiffness of different strata varies greatly, and the spring stiffness established is also quite different. The spring stiffness of different strata is determined by the formula:

[0074] k 1i =K 1i Ld (1)

[0075] Where:

[0076] k 1i —formation spring stiffness (N / m);

[0077] K 1i —Base coefficient (N / m 3 ), can be taken according to the current national standard "Code for Geotechnical Engineering Investigation of Urban Rail Transit" GB50307;

[0078] L—central spring spacing of foundation (m);

[0079] d—Calculated length of the stratum along the longitudinal direction of the underground structure (m).

[0080] For the grouting layer spring, the calculation formula for the spring stiffness is as follows:

[0081] k 2i =EI (2)

[0082] E—elastic modulus

[0083] I—Intersection moment of inertia

[0084] According to the stiffness coupling effect, the stratum spring stiffness and the grouting layer spring stiffness constitute the stratum-grouting layer combined resistance coefficient, which is used as an indicator for the seismic verification of the beam-spring model. The calculation formula of the stratum-grouting layer combined resistance coefficient is shown in (1):

[0085]

[0086] k 1i — Formation spring stiffness Spring stiffness

[0087] k 2i —Spring stiffness of grouting layer

[0088] When using the static method for calculation, the earthquake action should include the seismic inertia force of the lining's own weight, the seismic inertia force of the overlying soil column, and the earthquake lateral earth pressure increment:

[0089] Furthermore, the lining self-weight seismic inertia force includes the lining self-weight horizontal seismic inertia force and the vertical seismic inertia force. The specific calculation formulas are as follows (4) and (5):

[0090] E ih =A h m is =C i C s Am is (4)

[0091] E iv =K v E ih =K v Ci C s Am is (5)

[0092] E ih —Horizontal seismic inertia force due to the deadweight of the lining;

[0093] E iv —Vertical seismic inertia force due to lining self-weight;

[0094] C i —Seismic importance coefficient;

[0095] C s —Site seismic peak acceleration adjustment coefficient;

[0096] A—peak value of horizontal basic ground acceleration;

[0097] m is —mass of the tunnel segment at the calculation point (kg);

[0098] k v —Ratio of vertical peak acceleration to horizontal peak acceleration

[0099] In the calculation of the seismic inertia force of the overlying soil column, it is assumed that the seismic inertia force on the overlying soil column acts on the center of mass of the soil column unit. When calculating the internal force of the structure, since this force does not act directly on the structure, it is necessary to use the force translation theorem to transform the seismic inertia force on the overlying soil column to the structure, and then apply the transformed nodal force and added point bending moment to the structure.

[0100] The horizontal seismic force of the overlying soil column is as follows:

[0101] F ih =A h Q i / g (6)

[0102] The vertical seismic force of the overlying soil column is as follows:

[0103] F iv =K v A h Q i / g (7)

[0104] A h —Horizontal design ground motion peak acceleration

[0105] g—acceleration due to gravity;

[0106] k v —Ratio of vertical peak acceleration to horizontal peak acceleration;

[0107] Q i—vertical earth pressure of the overlying soil column;

[0108] The lateral earth pressure increment during an earthquake should be calculated according to the following formula and applied in an antisymmetric manner. The solution is as follows:

[0109] 1) The increment of the inner earth pressure is as follows:

[0110] Δe 1i =C i C s γh 1i (λ1-λ) (8)

[0111] 2) The increment of the outer soil pressure is as follows:

[0112] Δe 2i =C i C s γh 2i (λ2-λ′)(9)

[0113] Where: λ, λ′—inner and outer constant lateral pressure coefficients;

[0114] h 1i 、h 2i —The distance from any point i inside or outside the segment to the ground surface (m).

[0115] C i —Seismic importance coefficient;

[0116] C s —Site adjustment coefficient;

[0117] γ—surrounding rock mass;

[0118] λ1, λ2—lateral pressure coefficients during internal and external earthquakes.

[0119] (4) The above parameters and numerical models are imported into numerical calculation software, where the grouting slurry parameters are preferentially assumed to be traditional slurry parameters. According to the solution steps of the static method, the seismic action is equivalent to a static load and applied to the beam-spring model. The safety performance of the segments and joints is calculated and analyzed by the numerical calculation software, and the displacement and internal force calculation results of the shield tunnel in the composite stratum are obtained.

[0120] According to the specification "Code for Seismic Design of Highway Tunnels" JTG / T2232-01-2019, the safety factor method is used for strength verification, and the structural strength should comply with the provisions of the following formula.

[0121]

[0122] S()—action effect function related to the load acting on the structure;

[0123] R()—structural resistance effect function related to the strength of structural materials and geometric dimensions of components;

[0124] F r —Combination value of loads acting on the structure;

[0125] f—strength value of the material;

[0126] α k —Geometric parameter values ​​of the structure;

[0127] C—ultimate constraint value of the structure;

[0128] γ0—component working condition coefficient, value is 1.0;

[0129] γ1—additional safety factor of the structure, with a value of 1.0;

[0130] γ m —Partial coefficient of the action on the structure

[0131] γ f —Material performance partial coefficient

[0132] According to the code, the deformation calculation under earthquake combination should comply with the following formula

[0133] S q ”C(11)

[0134] S q —Effect value of earthquake action combination

[0135] C—Corresponding limits specified in the design for deformation, displacement, etc.

[0136] The opening and displacement of shield segment joints should not exceed the design allowable values. The displacement of the axial steel bars (bolts) at the expansion joints should be less than the yield displacement, the rotation angle at the expansion joints should be less than the yield rotation angle, the joint opening should be ≤2mm (rock formations or with important buildings (structures) nearby), or ≤4mm (large-section shield tunnels or located in soft soil formations), and should be less than the allowable opening of the ductile sealing gasket.

[0137] (5) Determine whether the traditional grout selected in step (4) meets the seismic safety requirements of shield tunnels; if the calculation results meet the above safety requirements, it means that the selection of traditional grouting materials for grouting can meet the seismic requirements of shield tunnels, and traditional grouting grouting can be used for grouting construction; if the calculation results do not meet the above safety requirements, determine the stiffness difference based on the typical section and dynamically adjust the combined resistance coefficient K of the stratum-grouting layer. i Parameters, then repeat step (4) until the safety regulations are met (import calculation software to obtain the results of internal stress displacement), then calculate the K before and after adjustment i The difference between them is used to determine the optimal difference between the two.i Use formula (3) to calculate the spring stiffness k 2i , and then determine the elastic modulus E of the grouting material according to the spring stiffness formula (2). For specific steps, refer to Figure 5 ;

[0138] (6) Determine the type of grouting material based on the slurry elastic modulus E inverted in step (5). Some grouting material options are shown in Table 1 below:

[0139] Table 1 Elastic modulus of grouting materials

[0140]

[0141] Based on the stiffness coupling theory, this invention innovatively proposes a shield tunnel construction design method. On the basis of the existing shield tunnel construction technology, it proposes a basis for selecting grouting materials, making maximum use of the existing technology, greatly reducing the cost of process improvement, and quantitatively analyzing the seismic performance of the grouting layer, providing a theoretical basis for the shock absorption effect of the shield tunnel.

[0142] 2. The seismic measures in this design are based on the grouting reinforcement method. During construction, grouting is performed using a slurry that meets the safety factor method. Compared with the use of special segments and seismic-resistant structures, this design method has a wider scope of application and can be adapted to complex strata with multiple layers of different strata, effectively reducing construction costs and meeting the needs of cost reduction and efficiency improvement.

Claims

1. A design method for shock-absorbing grouting of composite stratum shield tunnels, characterized in that: The following steps are involved: Step 1: Obtain relevant parameters of composite stratum shield tunnel; Select a typical section of a shield tunnel located under representative complex strata; Step 2: Establish a numerical model of the beam-spring structure. Determine the stiffness of the stratum spring by determining the stratum structure, and determine the stiffness of the grouting layer spring based on the traditional grouting slurry to obtain the combined resistance coefficient of the stratum-grouting layer. Simulate the shield tunnel as a homogeneous circular ring beam, simulate the annular joint with an elastic hinge, and simulate the surrounding rock and soil with stratum springs. Use the grouting layer spring and stratum spring in series to simulate the grouting layer and soil constraints. Step 3: Apply the combined resistance coefficient of the stratum-grouting layer and the seismic force to the beam-spring structure numerical model, calculate and analyze the safety performance of the pipe segments and joints, obtain the displacement and internal force calculation results of the shield tunnel in the composite stratum, and perform strength verification; the combined resistance coefficient of the stratum-grouting layer K i The calculation formula is as follows: ; k 1i — Formation spring stiffness Spring stiffness; k 2i — Grouting layer frame spring stiffness; Step 4: If the calculation result meets the safety requirements, it means that the selection of traditional grouting materials for grouting can meet the seismic requirements of the shield tunnel, and the traditional grouting slurry can be used for grouting construction; if the calculation result does not meet the safety requirements, the stiffness difference is determined based on the typical section, and the parameters of the stratum-grouting layer combination resistance coefficient are dynamically adjusted. Step (3) is repeated until the safety requirements are met. At this time, the difference between the stratum-grouting layer combination resistance coefficient before and after the adjustment is calculated to determine the optimal difference between the two; the grouting layer frame spring stiffness is calculated based on the adjusted stratum-grouting layer combination resistance coefficient, and then the elastic modulus of the grouting material is determined based on the frame spring stiffness formula; Step 5: Determine the type of grouting material based on the elastic modulus of the grouting material.

2. The composite stratum shield tunnel shock absorption grouting design method according to claim 1, characterized in that: The formation spring stiffness of different formations is determined by the formula: Where: k 1i — formation spring stiffness; K 1i —base bed coefficient; L — Spacing of concentrated springs in the foundation; d —The calculated length of the stratum along the longitudinal direction of the underground structure.

3. The design method for shock-absorbing grouting of composite stratum shield tunnels according to claim 1, characterized in that: The stiffness of the grouting layer spring k 2i The calculation formula is as follows: E— elastic modulus; I— Moment of inertia of area.

4. The design method for shock-absorbing grouting of composite stratum shield tunnels according to claim 1, characterized in that: When the static method is used for calculation, the seismic effects include the seismic inertia force of the lining's own weight, the seismic inertia force of the overlying soil column, and the seismic lateral earth pressure increment.

5. The composite stratum shield tunnel shock absorption grouting design method according to claim 4 is characterized in that: The lining self-weight seismic inertia force includes the lining self-weight horizontal seismic inertia force and the lining self-weight vertical seismic inertia force; E ih —Horizontal seismic inertia force due to the deadweight of the lining; E iv —Vertical seismic inertia force due to lining self-weight; C i —Seismic importance coefficient; C s —Site seismic peak acceleration adjustment coefficient; A —Peak value of horizontal basic ground acceleration; m is —Quality of the calculated points of the tunnel segments; K v —Ratio of vertical peak acceleration to horizontal peak acceleration; A h —Horizontal design peak acceleration of seismic motion.

6. The composite stratum shield tunnel shock absorption grouting design method according to claim 4, characterized in that: The seismic inertia force of the overlying soil column includes the horizontal seismic force of the overlying soil column and the vertical seismic force of the overlying soil column; the horizontal seismic force of the overlying soil column F ih for: Vertical seismic force of overlying soil column F iv for: A h — horizontal design ground motion peak acceleration; g — acceleration due to gravity; k v —Ratio of vertical peak acceleration to horizontal peak acceleration; Q i —Vertical earth pressure of overlying soil column.

7. The design method for shock-absorbing grouting of composite stratum shield tunnels according to claim 6, characterized in that: The lateral earth pressure increment during an earthquake includes the inner earth pressure increment and the outer earth pressure increment: The inner earth pressure increment is: （8） The outer earth pressure increment is: （9） 、 —Inner and outer constant lateral pressure coefficients; 、 —Any point inside or outside the segment i distance to the ground surface; —Seismic importance coefficient; —Site adjustment coefficient; γ — weight of surrounding rock; 、 — Lateral pressure coefficients during internal and external earthquakes.

8. The design method for shock-absorbing grouting of composite stratum shield tunnels according to claim 1, characterized in that: In step 3, when performing strength verification, the opening and displacement of the shield segment joints should not exceed the design allowable values, the displacement of the axial steel bars at the expansion joint should be less than the yield displacement, the rotation angle at the expansion joint should be less than the yield rotation angle, and the joint opening should be less than the allowable opening of the ductile sealing gasket.

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