A method for designing a tunnel structure under rockfall impact

Abstract

The application discloses a tunnel structure design method under rockfall impact, and the application is characterized by the following aspects: a calculation method of rockfall impact load, in particular, a calculation model of impact duration and impact force considering the parameters (thickness, elastic modulus, Poisson's ratio and density) of a buffer layer; a structure collaborative stress analysis model based on deformation coordination, in particular, an analysis model formed by displacement boundary conditions between an arch protection and secondary lining and by elastic resistance coefficients between the secondary lining and an arch bridge structure. The application can accurately calculate the rockfall impact load, and through a protection system, effectively buffers, diffuses and transfers the load, ensures the safety of the tunnel structure under rockfall impact, and provides clear theoretical support and a design process for similar projects.

Description

Technical Field

[0001] This invention relates to the field of tunnel and underground engineering technology, and in particular to a tunnel structure design method under rockfall impact. Background Technology

[0002] When high-speed railways, highways, and other transportation tunnels pass through karst areas, they often face the threat of falling rocks from the roof of giant karst caves. The impact load of falling rocks is characterized by its instantaneous nature, high energy, and unpredictability. Traditional tunnel structures are unable to effectively resist such extreme impacts, seriously affecting construction and operational safety.

[0003] Traditional design treats structures such as arches, linings, and bridge spans as independent load-bearing units, neglecting their deformation coordination and load transfer paths under impact loads. This leads to conservative structural designs or potential safety hazards. Moreover, the design process relies on experience, resulting in low repeatability and standardization.

[0004] In summary, there is a lack of systematic theoretical support and standardized design procedures for tunnel structure design under rockfall impact. Summary of the Invention

[0005] The purpose of this invention is to provide a tunnel structure design method under rockfall impact, which solves the problem that existing tunnel structure designs lack systematic theoretical support and standardized design processes.

[0006] This invention is implemented as follows: This invention provides a tunnel structure design method under rockfall impact, characterized in that the method includes the following steps:

[0007] S1. Comprehensive Investigation and Determination of Rockfall Characteristics: Determine the shape, size, filling condition, and positional relationship of the cavity to the tunnel; determine the maximum volume, mass, and maximum falling height of potential rocks.

[0008] S2. Using engineering analogy, preliminary design of the protective structure is carried out: The protective structure includes, from bottom to top, the tunnel bottom arch bridge, the tunnel reinforced concrete secondary lining, the initial support, the arch support structure, the backfill layer, and the buffer layer. The type and thickness of the buffer layer are preliminarily determined.

[0009] S3. Initial load calculation of rockfall impact: Assuming that the velocity of the rockfall becomes 0 after impacting the buffer layer and no rebound occurs, the initial load of the rockfall impact is calculated based on the rockfall impact velocity and impact duration.

[0010] S4. Calculation of rockfall impact load transfer: The transferred load refers to the load transferred to the structural part after the initial rockfall impact load diffuses through the buffer layer. The rockfall impact load transfer is calculated based on the maximum depth of the rock embedded in the buffer layer and the rockfall impact intensity.

[0011] S5. Structural stress analysis and safety check: The internal forces of the structure are calculated using the "load-structure" method through Midas GTX NX. Through continuous trial calculations, the parameters of the main structure are determined.

[0012] S6. Add auxiliary measures to complete the overall design.

[0013] A further technical solution of the present invention is: in step S1, the shape, size, filling condition and positional relationship of the cavity with the tunnel are determined by geological survey and three-dimensional laser scanning.

[0014] A further technical solution of the present invention is that the buffer layer in step S2 can be selected from at least one of sandbags, plain concrete, and waste tires.

[0015] A further technical solution of the present invention is: the tunnel bottom arch bridge includes an arch bridge structure, an arch base foundation, anchor bolts and a filling layer, the arch base foundation is placed at both ends of the arch bridge structure, the filling layer is filled between the arch bridge structure and the tunnel reinforced concrete secondary lining, and the anchor bolts are placed on both sides of the filling layer for reinforcement.

[0016] A further technical solution of the present invention is that the filling layer is made of C30 concrete.

[0017] A further technical solution of the present invention is: in step S3, the calculation of the impact velocity of the falling rock (m / s):

[0018]

[0019] In the formula, The slope coefficient is... ,in Where is the slope angle, and K is the rolling resistance coefficient of the falling rock along the slope, with a value range of 0 to 1; The acceleration due to gravity is m / s². 2 ; The height of the falling rock is in meters (m).

[0020] Calculate the impact duration (s):

[0021]

[0022] In the formula, Calculate the thickness of the buffer layer, in meters (m). Let be the reciprocating velocity of the compression wave in the buffer layer, in m / s, and its calculation formula is:

[0023]

[0024] In the formula, , , The Poisson's ratio, elastic modulus (MPa), and density (kg / m³) of the buffer layer are given. 3 );

[0025] Calculate the initial impact load of falling rocks (kN):

[0026]

[0027] In the formula, Let t represent the mass of the falling rock.

[0028] A further technical solution of the present invention is: in step S4, the maximum depth (m) of the rock embedded in the buffer layer:

[0029]

[0030] In the formula: The internal friction angle of the buffer layer is (°); The density of the buffer layer is kN / m 3 F represents the projected area (m) of the surface of the rock embedded in the buffer layer on a plane perpendicular to the impact direction. 2 According to the principle of volume equivalence, the falling rocks are converted into spheres with a radius of R;

[0031] The calculation of the impact intensity of the falling rock (kPa):

[0032]

[0033] In the formula, The minimum calculated thickness of the buffer layer is m; when hour, ;when hour, . The angle of impact of falling rocks is calculated as approximately 40° to the vertical.

[0034] A further technical solution of the present invention is: the main structure of step S5 includes an arch support structure, a secondary lining, and an arch bridge structure;

[0035] The calculation of the arch support structure is as follows: the load it bears is divided into the structure's self-weight, the gravity of plain concrete, the impact load transmitted by falling rocks, and the pressure of the surrounding rock; the arch support is simulated by beam elements, and the interaction between the surrounding rock and the structure is simulated by 1m long compression spring elements, with full constraint at the end of the compression springs; the arch foot is embedded in the bedrock on both sides of the karst cavity and is considered as a fixed support; the bending moment, axial force, and displacement under load are verified to ensure that the safety factor and crack width meet the specifications.

[0036] Secondary lining calculation: The maximum vertical displacement of the arch support is applied as a forced displacement boundary condition to the arch of the secondary lining. At the same time, the elastic resistance and surrounding rock pressure provided by the lower arch bridge are considered to verify its bending moment, axial force and displacement, and ensure that the safety factor and crack width meet the specifications.

[0037] Arch bridge structural calculations: bearing dead loads and live loads from the secondary lining, verifying the stress of the main arch ring, crack width and arch base stress, and ensuring that the tensile stress of the steel bars, the maximum compressive stress of the concrete, the crack width of the concrete, the maximum compressive stress of the base and other indicators meet the specifications.

[0038] The beneficial effects of this invention are as follows: The method for calculating rockfall impact loads in this invention, particularly the impact duration and impact force calculation model considering buffer layer parameters (thickness, elastic modulus, Poisson's ratio, density); and the structural collaborative stress analysis model based on deformation coordination, especially the analysis models constructed by displacement boundary conditions between the arch support and the secondary lining, and by elastic resistance coefficients between the secondary lining and the arch bridge structure. This allows for accurate calculation of rockfall impact loads and, through the protection system, achieves effective buffering, diffusion, and transfer of the load, ensuring the safety of the tunnel structure under rockfall impacts, and providing clear theoretical support and design procedures for similar projects.

[0039] This solution provides a complete package from rockfall impact load calculation to structural design, with a clear design process and strong operability. Through integrated collaborative design, the arch support, lining, and arch bridge work together, significantly improving the structure's resistance to rockfall impacts. The calculation results meet the safety requirements of the relevant codes. Precise load calculations and collaborative stress analysis avoid material waste, optimize structural dimensions, and achieve both safety and economy, aligning with green building principles. Attached Figure Description

[0040] Figure 1 A flowchart of a tunnel structure design method under rockfall impact;

[0041] Figure 2 A schematic diagram illustrating the calculation method for the impact load transfer of falling rocks;

[0042] Figure 3 This is a schematic cross-sectional view of the tunnel structure in the described embodiment;

[0043] Figure 4 This is a schematic longitudinal section of the tunnel structure in the described embodiment;

[0044] Figure 5 This is a calculation model diagram of the arch support structure in the described embodiment;

[0045] Figure 6The diagram shows the calculation results of the arch support in the embodiment described above; where (a) is the arch support bending moment (unit: kN·m), (b) is the arch support axial force (unit: kN), and (c) is the arch support vertical displacement (maximum 1.8mm) (unit: mm).

[0046] Figure 7 This is the secondary lining calculation model for the described embodiment;

[0047] Figure 8 The diagram shows the calculation results of the secondary lining in the described embodiment; where (a) is the lining bending moment (unit: kN.m) and (b) is the lining axial force (unit: kN).

[0048] Figure 9 The above is a computational model of the arch bridge in the described embodiment.

[0049] Attached reference numerals: 1. Initial support, 2. Secondary lining, 3. Arch support structure, 4. Arch bridge structure, 5. Arch abutment foundation, 6. Anchor bolt, 7. Filling layer, 8. Large pipe shed, 9. Backfill layer, 10. Buffer layer, 11. Detour tunnel, 12. Detour tunnel connecting passage, 13. Solution cavity. Detailed Implementation

[0050] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention.

[0051] The high-speed railway tunnel is located in Xiangyang City, Hubei Province. It is a single-bore, double-track tunnel designed for a speed of 350 km / h, with a total length of 5506m and a maximum burial depth of approximately 320m. The tunnel traverses the Lower Triassic Daye Formation (T1d) limestone, with karst formations exhibiting strong and well-developed karst characteristics. Construction revealed a giant karst cavity, which has a rhomboid to elliptical planar shape, approximately 13m long and 12m wide, and is vertically barrel-shaped with a vertical height of approximately 105m. It is a "deep and narrow" type of karst cavity, with clay at the bottom and no water or airflow.

[0052] S1: The survey determined that the maximum length, width and height of the falling rock was 3m×1m×1m, the mass was 7.5t, and the falling height was 105m.

[0053] S2: Based on engineering analogies, a preliminary structural design scheme is formulated: The overall scheme adopts a combination of "bottom bridge span + middle tunnel + upper arch support," namely "tunnel bottom arch bridge + tunnel reinforced concrete secondary lining 2 + initial support 1 + arch support structure 3 + backfill layer 9 + buffer layer 10." Schematic diagrams of the cross and longitudinal sections of the protection system are shown below. Figure 3 , Figure 4 .

[0054] S3: Initial load calculation for rockfall impact. The buffer layer uses 4.5m thick sandbags.

[0055] (1) Calculate the impact velocity of the falling rock (m / s):

[0056] m / s

[0057] In the formula, The slope coefficient is taken as 1 in this calculation, considering the most unfavorable situation, that is, the slope angle is 90° and the falling rocks do not collide with the slope.

[0058] (2) Calculate the impact duration (s):

[0059] s

[0060] In the formula, Calculate the thickness of the buffer layer, in meters (m). Let be the reciprocating velocity of the compression wave in the buffer layer, in m / s, and its calculation formula is: m / s.

[0061] (3) Calculate the initial impact load of the falling rock (kN):

[0062] kN

[0063] In the formula, Let t represent the mass of the falling rock.

[0064] S4: Calculation of transferred load from rockfall impact. The transferred load refers to the load transferred to the structural components after the initial rockfall impact load diffuses through the buffer layer. This involves calculating the maximum depth of the rockfall embedded in the buffer layer and the impact intensity of the rockfall.

[0065] (1) Maximum depth (m) of falling rocks embedded in the buffer layer:

[0066]

[0067] In the formula: The internal friction angle of the buffer layer is (°); The density of the buffer layer is kN / m 3 F represents the projected area (m) of the surface of the rock embedded in the buffer layer on a plane perpendicular to the impact direction. 2 If, according to the principle of volume equivalence, the falling rock is converted into a sphere with a radius of R, then: when hour, ;when hour, The value used in this calculation is 1.

[0068] (2) Calculation of rockfall impact intensity (kPa):

[0069]

[0070] In the formula, The minimum calculated thickness of the buffer layer is m; when hour, ;when hour, This calculation: m; The angle of impact of falling rocks is calculated as approximately 40° to the vertical.

[0071] S5: Structural stress analysis and safety check.

[0072] The load-structure method was used to calculate the internal forces of the structure using Midas GTX NX, and the main structural parameters were determined through continuous trial calculations.

[0073] (1) Calculation of the arch support structure: The loads borne are divided into the structure's self-weight, the gravity of C20 concrete, the impact load transmitted by falling rocks, and the pressure of the surrounding rock. The arch support is simulated by beam elements, and the interaction between the surrounding rock and the structure is simulated by 1m long compression spring elements (elastic reaction coefficient is taken as 300MPa / m), with full constraint at the end of the compression spring. The arch foot is embedded in the bedrock on both sides of the karst cavity and is considered as a fixed support. The bending moment, axial force, and displacement under the load are checked to ensure that the safety factor and crack width meet the code requirements. The results are shown in Table 1.

[0074] Table 1 Structural verification results

[0075]

[0076] It can be seen that the safety factor of the arch support structure is greater than 2.4, and the maximum crack width is less than 0.2 mm, which meets the requirements for bearing capacity and normal use. At the same time, the stress exerted by the arch foot on the bedrock is 1.99 MPa, which is less than 2.2 MPa, and meets the requirements.

[0077] (2) Calculation of secondary lining: The secondary lining bears the structural self-weight, the additional force caused by the displacement of the arch support, the surrounding rock pressure, and the elastic resistance provided by the lower arch bridge. Among them, the displacement of the arch support is only considered as the vertical downward displacement (1.8mm). When the arch support moves vertically upward, it has already separated from the secondary lining structure. Therefore, the vertical upward displacement is considered as 0, that is, a displacement boundary condition is applied to the arch of the secondary lining. At the same time, in order to simplify the calculation, the downward displacement is considered as the maximum vertical displacement of the arch support. The calculation model is as follows: Figure 7 As shown in Table 2, the calculation results for the secondary lining structure are presented.

[0078] Table 2 Calculation Results of Secondary Lining Structure

[0079]

[0080] The above analysis shows that the safety factor of the secondary lining is greater than 2.4 and the maximum crack width is less than 0.2 mm, which meets the requirements of load-bearing capacity and normal use.

[0081] (3) Arch Bridge Structure Calculation: The bridge bears the structural self-weight, elastic reaction force of the secondary lining base plate, train and track loads, and the arch feet of the bridge span structure are fixedly constrained. Its simplified model is as follows: Figure 9 As shown. After dividing the load transferred from the tunnel structure to the bridge into dead load and live load, the dead load from left to right is 152, 56, 56, 57, 158 kN / m. 2 The impact live loads transmitted to the bridge from falling rocks are 110, 28, 0, 10, and 56 kN / m from left to right. 2 Calculation models were established using the aforementioned loads, named Model 1 through Model 5. A separate model, "Model 6," was created where all loads were evenly distributed across the entire width of the arch, with a uniformly distributed load of 98 kN / m. 2 The corresponding live load from falling rocks is 31 kN / m. 2 The impact load of falling rocks is applied using the influence line, considering only the buffer layer spreading the impact load along the track direction for a length of 10.5m. The arch ring is modeled and analyzed based on a lateral distance of 1m.

[0082] ① RC calculation of the main arch ring

[0083] Based on the most unfavorable load combination, RC calculations were performed on the main arch ring. Eight φ28mm steel bars were installed within 1m of the upper and lower edges of the arch ring, with a spacing of 125mm. The RC calculation results of the arch foot and arch top of the main arch ring are shown in Tables 3 and 4, respectively.

[0084] Table 3 Calculation results of the RC of the main arch foot for each model

[0085]

[0086] Table 4 Calculation results of RC at the crown of the main arch ring for each model

[0087]

[0088] ② Arch seat verification

[0089] According to Article 5.2.2 of TB10093-2017 "Code for Design of Foundations and Substructures of Railway Bridges and Culverts", the arch seat was verified, and the results are shown in Table 5.

[0090] Table 5 Calculation results of arch base

[0091]

[0092] As shown in Table 5, all the indicators of the substrate meet the relevant requirements.

[0093] S6: Add auxiliary measures to complete the overall design.

[0094] The project adopts a combined approach of "bottom bridge + middle tunnel + upper arch support," consisting of a tunnel bottom arch bridge, a 0.7m thick reinforced concrete secondary lining, a 32cm thick initial support (with internal I25a steel frames spaced 0.6m apart), a 2m thick C35 reinforced concrete arch support, a 4m thick backfill of C20 concrete (with internal 8 φ159mm advanced large pipe sheds, 25m long, 9° outward angle, 7mm wall thickness, 0.5cm circumferential spacing, and an embedment length of at least 5m into intact bedrock), and a 5.5m thick buffer layer (1m thick polymer material + 4.5m thick sandbags, with the maximum embedment depth of the buffer layer determined by falling rocks). The arch abutment foundation is an enlarged foundation using C40 shrinkage-compensating concrete; the reinforced concrete slab arch uses C50 shrinkage-compensating concrete; the arch axis uses a catenary with an arch axis coefficient of 1.6. A waterproof layer is installed on the top surface of the main arch ring, using polymer-modified bitumen waterproof membrane. The arch is filled with C30 concrete, backfilled to 0.5m above the arch top, and the top surface of the backfill follows the longitudinal slope of the line.

[0095] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for designing tunnel structures under rockfall impact, characterized in that: The method includes the following steps: S1. Comprehensive Investigation and Determination of Rockfall Characteristics: Determine the shape, size, filling condition, and positional relationship of the cavity to the tunnel; determine the maximum volume, mass, and maximum falling height of potential rocks. S2. Using engineering analogy, a preliminary design of the protective structure is carried out: The protective structure includes, from bottom to top, the tunnel bottom arch bridge, the tunnel secondary lining, the initial support, the arch support structure, the backfill layer, and the buffer layer. The type and thickness of the buffer layer are preliminarily determined. S3. Initial load calculation of rockfall impact: Assuming that the velocity of the rockfall becomes 0 after impacting the buffer layer and no rebound occurs, the initial load of the rockfall impact is calculated based on the rockfall impact velocity and impact duration. S4. Calculation of rockfall impact load transfer: The transferred load refers to the load transferred to the structural part after the initial rockfall impact load diffuses through the buffer layer. The rockfall impact load transfer is calculated based on the maximum depth of the rock embedded in the buffer layer and the rockfall impact intensity. S5. Structural stress analysis and safety check: The internal forces of the structure are calculated using the "load-structure" method through Midas GTX NX. Through continuous trial calculations, the parameters of the main structure are determined. S6. Add auxiliary measures to complete the overall design.

2. The tunnel structure design method under rockfall impact according to claim 1, characterized in that: In step S1, geological surveys and three-dimensional laser scanning are used to determine the shape, size, filling condition, and positional relationship of the cavity to the tunnel.

3. The tunnel structure design method under rockfall impact according to claim 1, characterized in that: In step S2, the buffer layer can be selected from at least one of sandbags, plain concrete, and discarded tires.

4. The tunnel structure design method under rockfall impact according to claim 2, characterized in that: The tunnel bottom arch bridge includes an arch bridge structure, an arch foundation, anchor bolts, and a filling layer. The arch foundation is placed at both ends of the arch bridge structure. The filling layer is used to fill the space between the arch bridge structure and the secondary tunnel lining. The anchor bolts are placed on both sides of the filling layer for reinforcement.

5. The tunnel structure design method under rockfall impact according to claim 4, characterized in that: The filling layer is made of C30 concrete.

6. The tunnel structure design method under rockfall impact according to claim 1, characterized in that: In step S3, the calculation of the rockfall impact velocity (m / s) is as follows: In the formula, The slope coefficient is... ,in Where is the slope angle, and K is the rolling resistance coefficient of the falling rock along the slope, with a value range of 0 to 1; The acceleration due to gravity is m / s². 2 ; The height of the falling rock is in meters (m). Calculate the impact duration (s): In the formula, Calculate the thickness of the buffer layer, in meters (m). Let be the reciprocating velocity of the compression wave in the buffer layer, in m / s, and its calculation formula is: In the formula, , , The Poisson's ratio, elastic modulus (MPa), and density (kg / m³) of the buffer layer are given. 3 ); Calculate the initial impact load of falling rocks (kN): In the formula, Let t represent the mass of the falling rock.

7. The tunnel structure design method under rockfall impact according to claim 1, characterized in that: In step S4, the maximum depth (m) of the rock embedded in the buffer layer: In the formula: The internal friction angle of the buffer layer is (°); The density of the buffer layer is kN / m 3 ; F represents the projected area (m) of the surface of the rock embedded in the buffer layer on a plane perpendicular to the impact direction. 2 According to the principle of volume equivalence, the falling rocks are converted into spheres with a radius of R; The calculation of the impact intensity of the falling rock (kPa): In the formula, The minimum calculated thickness of the buffer layer is m; when hour, ;when hour, . The angle of impact of falling rocks is calculated as approximately 40° to the vertical.

8. The tunnel structure design method under rockfall impact according to claim 4, characterized in that: The main structure of step S5 includes an arch support structure, a secondary lining, and an arch bridge structure. The calculation of the arch support structure is as follows: the load it bears is divided into the structure's self-weight, the gravity of plain concrete, the impact load transmitted by falling rocks, and the pressure of the surrounding rock; the arch support is simulated by beam elements, and the interaction between the surrounding rock and the structure is simulated by 1m long compression spring elements, with full constraint at the end of the compression spring; the arch foot is embedded in the bedrock on both sides of the karst cavity and is considered as a fixed support. Verify its bending moment, axial force and displacement under load to ensure that the safety factor and crack width meet the specifications. Secondary lining calculation: The maximum vertical displacement of the arch support is applied as a forced displacement boundary condition to the arch of the secondary lining. At the same time, the elastic resistance and surrounding rock pressure provided by the lower arch bridge are considered to verify its bending moment, axial force and displacement, and ensure that the safety factor and crack width meet the specifications. Arch bridge structural calculations: bearing dead loads and live loads from the secondary lining, verifying the stress of the main arch ring, crack width and arch base stress, and ensuring that the tensile stress of the steel bars, the maximum compressive stress of the concrete, the crack width of the concrete, the maximum compressive stress of the base and other indicators meet the specifications.

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