Method for determining surrounding rock pressure of underwater deeply-buried unequal-span bifurcated tunnel
By establishing a mechanical model and a calculation formula for underwater deep buried unequal trans-bian tunnels and surrounding rock pressure, the problem of surrounding rock pressure calculation in underwater unequal trans-bian tunnels is solved, providing a theoretical basis, and improving the reliability of design and construction.
Patent Information
- Application Number
- CN202510519693.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-24
- Publication Date
- 2025-08-01
AI Technical Summary
The existing technology lacks effective methods to calculate the surrounding rock pressure of unequal trans-bian tunnels underwater, especially under deep underwater burial conditions, resulting in a lack of theoretical basis for design and construction.
By establishing a mechanical model of underwater deep buried unequal span bifurcated tunnels, geometric relationships and surrounding rock pressure calculation formulas, including additional equilibrium arch height, pressure calculation, etc., a theoretical calculation method is provided.
It provides a theoretical basis for the design and construction of subwater deep buried non-equal span bifurcation tunnels, and can calculate surrounding rock pressures at different relative positions and sizes, improving project safety and construction reliability.
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Figure CN120409001A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of tunnel design and construction, and particularly relates to a method for determining the surrounding rock pressure of an underwater deeply-buried unequal-span bifurcated tunnel. Background Art
[0002] An underwater unequal-span tunnel is a special tunnel structure, which often appears when the tunnel bifurcates from a single direction to two or more directions. According to different structural characteristics and cross-sectional sizes, such tunnel projects can be divided into a large-span section and a small clear distance section. The two sections generally converge at the bifurcation. The characteristics of the large-span section are large span and large traffic capacity, and the characteristics of the small clear distance section are flexible direction and good traffic guidance. Designing the two tunnels with unequal spans has the advantage of meeting the traffic demands in different directions, with reliable structure, low carbon and environmental protection, superior cost, and is conducive to improving the operation efficiency of traffic facilities.
[0003] For an underwater unequal-span tunnel, due to the rich water in the stratum and the changing spacing, its stress mode is more complex than that of a separated double-tunnel and a small clear distance tunnel, and the surrounding rock pressure is dynamically adjusted under the influence of various physical and mechanical parameters. In the existing "Code for Design of Highway Tunnels", "Code for Design of Railway Tunnels", and "Code for Design of Highway Underwater Tunnels", there is no calculation content for the surrounding rock pressure of bifurcated tunnels. The "Code for Design of Highway Tunnels" only gives a simple introduction to bifurcated tunnels; the corresponding calculation method for the surrounding rock pressure, especially the surrounding rock pressure of unequal-span bifurcated tunnels, is lacking. Summary of the Invention
[0004] The purpose of the present invention is to provide a method for determining the surrounding rock pressure of an underwater deeply-buried unequal-span bifurcated tunnel in view of the above technical problems existing in the prior art.
[0005] The above object of the present invention is achieved by the following technical solutions: The method for determining the surrounding rock pressure of an underwater deeply-buried unequal-span bifurcated tunnel of the present invention includes the following steps in sequence: (1) Establish a mechanical model of an underwater deeply-buried unequal-span bifurcated tunnel and determine the geometric relationship. In the model, when the burial depth of the underwater unequal-span bifurcated tunnel is large enough, the water-resistant layer formed by the upper surrounding rock is relatively thick, which can effectively block the upper surface water, and the formation of the collapse arch is hardly affected by the water level. Among them, the geometric relationship is determined by the following formula: ; In the formula: l m is the effective bearing width of the middle rock pillar; l is the clear distance between the two tunnels of the unequal-span bifurcated tunnel; h a is the height of the large-span tunnel; h b is the height of the small-span tunnel;θ is the fracture surface angle, which is determined by θ = 45° - φ / 2, where φ is the calculated friction angle of the surrounding rock; W a is the balance arch span of the large-span tunnel; b a is the span of the large-span tunnel; W b is the balance arch span of the small-span tunnel; b b is the span of the small-span tunnel; W m is the additional balance arch span; (2) Calculate the additional balance arch height, which is determined by the following formula: ; In the formula: H m is the additional balance arch height; H m ' is the ultimate balance arch height, which is determined by the following formula: ; In the formula: f is the surrounding rock firmness coefficient, also known as the Protodyakonov coefficient; (3) Calculate the additional balance arch pressure, which is determined by the following formula: ; In the formula: q m is the maximum additional pressure generated by the additional balance arch; γ is the unit weight of the surrounding rock; d is the vertical distance between the crowns of the large-span and small-span tunnels in the bifurcated tunnel, that is, the model considers the case where the buried depths of the unequal-span double tunnels are different; H a is the balance arch height of the large-span tunnel, which is determined by ; H b is the balance arch height of the small-span tunnel, which is determined by ; q s is the pressure acting on the rock pillar, which is determined by the following formula: ; In the formula: R q is the compressive strength of the rock pillar; α is the enhancement coefficient caused by the reinforcement effect; (4) Calculate the additional pressure on the outer side and the additional pressure on the inner side of the large-span tunnel, which is determined by the following formula: ; ; In the formula: q ma1 is the additional pressure on the outer side of the large-span tunnel; q ma2 is the additional pressure on the inner side of the large-span tunnel; (5) Calculate the additional pressure on the outer side and the inner side of the small-span tunnel, which is determined by the following formula: ; ; In the formula: q mb1 is the additional pressure on the outer side of the small-span tunnel; q mb2 is the additional pressure on the inner side of the small-span tunnel; (6) Calculate the vertical surrounding rock pressure and the horizontal surrounding rock pressure of the large-span tunnel, which is determined by the following formula: ; ; ; ; In the formula: q a1 is the vertical surrounding rock pressure on the outer side of the large-span tunnel; q a2 is the vertical surrounding rock pressure on the inner side of the large-span tunnel; q a is the basic pressure of the large-span tunnel, determined by the formula ; e a1i is the horizontal surrounding rock pressure on the outer side of the large-span tunnel; e a2i is the horizontal surrounding rock pressure on the inner side of the large-span tunnel; h ai is the vertical distance from the calculation point to the crown of the large-span tunnel; (7) Calculate the vertical surrounding rock pressure and the horizontal surrounding rock pressure of the small-span tunnel, which is determined by the following formula: ; ; ; ; In the formula: q b1 is the vertical surrounding rock pressure on the outer side of the small-span tunnel; q b2 is the vertical surrounding rock pressure on the inner side of the small-span tunnel; q bis the basic pressure of the small-span tunnel, determined by Equation ; e b1i is the horizontal surrounding rock pressure on the outside of the small-span tunnel; e b2i is the horizontal surrounding rock pressure on the inside of the small-span tunnel; h bi is the vertical distance from the calculation point to the crown of the small-span tunnel.
[0006] Compared with the prior art and research methods, the present invention has the following advantages: The research object of the prior art mainly analyzes the surrounding rock pressure of equal-span tunnels with small clear distances. There is little research on unequal-span bifurcated tunnels, and even less research on the surrounding rock pressure of underwater unequal-span bifurcated tunnels.
[0007] The present invention provides a theoretical calculation method for determining the surrounding rock pressure of underwater deeply buried unequal-span bifurcated tunnels; by changing the relative positions and relative sizes of the two tunnels in the bifurcated tunnel, the surrounding rock pressure under different relative positions and different relative sizes can be obtained, thereby providing a theoretical basis for the design and construction of underwater deeply buried unequal-span bifurcated tunnels. The method of the present invention can be applied to the calculation of the surrounding rock pressure and safety assessment of deeply buried underground projects with unequal-span small spacings, such as adjacent roadways in mining, adjacent tunnels in hydraulic engineering, adjacent interval tunnels in subways, etc. BRIEF DESCRIPTION OF THE DRAWINGS
[0008] Figure 1 is the calculation diagram of the surrounding rock pressure of the underwater deeply buried unequal-span tunnel of the present invention.
[0009] In the figure, a is the large-span tunnel; b is the small-span tunnel; h a is the height of the large-span tunnel; b a is the span of the large-span tunnel; W a is the balanced arch span of the large-span tunnel; θ is the rupture surface angle; H a is the balanced arch height of the large-span tunnel; h b is the height of the small-span tunnel; b b is the span of the small-span tunnel; H b is the balanced arch height of the small-span tunnel; H m is the additional balanced arch height; H m ' is the limit balanced arch height; l m is the effective bearing width of the middle rock pillar;l a is the inner damage width of the large-span tunnel; l b is the inner damage width of the small-span tunnel; l is the net distance between the two tunnels of the unequal-span bifurcated tunnel; d is the vertical distance between the crowns of the large-span and small-span tunnels in the bifurcated tunnel; W m is the additional balance arch span.
[0010] Figure 2 This is the calculation diagram of the additional balance arch pressure of the present invention.
[0011] In the figure, q m is the maximum additional pressure generated by the additional balance arch; q s is the pressure acting on the rock pillar; q a is the basic pressure of the large-span tunnel; q b is the basic pressure of the small-span tunnel; e a1 is the lateral horizontal surrounding rock pressure of the large-span tunnel; e b1 is the lateral horizontal surrounding rock pressure of the small-span tunnel.
[0012] Figure 3 This is the calculation diagram of the surrounding rock pressure of the large-span tunnel of the underwater deep-buried unequal-span bifurcated tunnel of the present invention.
[0013] In the figure, q a1 is the vertical pressure on the outside of the large tunnel, q a2 is the vertical pressure on the inside of the large tunnel, e a1i is the horizontal pressure on the outside of the large tunnel, e a2i is the horizontal pressure on the inside of the large tunnel.
[0014] Figure 4 This is the calculation diagram of the surrounding rock pressure of the small-span tunnel of the underwater deep-buried unequal-span bifurcated tunnel of the present invention.
[0015] In the figure, q b1 is the vertical pressure on the outside of the large tunnel, q b2 is the vertical pressure on the inside of the large tunnel, e b1i is the horizontal pressure on the outside of the large tunnel, e b2i is the horizontal pressure on the inside of the large tunnel.
[0016] Figure 5This is for the influence of different sizes of the two holes of the bifurcated tunnel in the implementation example of the present invention on the vertical surrounding rock pressure.
[0017] Figure 6 This is for the influence of the vertical distance between the crowns of the two holes of the bifurcated tunnel (i.e., relative position, different buried depths) in the implementation example of the present invention on the vertical surrounding rock pressure. Specific implementation manner
[0018] The following further describes the present invention in conjunction with the drawings and embodiments.
[0019] The specific data of this embodiment project are as follows: unit weight of surrounding rock γ = 19 kN / m³, calculated friction angle φ = 45°, distance between the two holes of the unequal-span bifurcated tunnel l = 10 m, reinforcement enhancement coefficient of rock pillar α = 1.1, height of large-span hole h a = 9.55 m, span of large-span hole b a = 11.9 m, height of small-span hole h b = 9.2 m, span of small-span hole b a Let the vertical distance between the crowns of the large-span hole and the small-span hole in the bifurcated tunnel be d = 0.175 m.
[0020] Refer to Figure 1 , the method for determining the surrounding rock pressure of the underwater deeply buried unequal-span bifurcated tunnel in this embodiment is as follows: Step 1: Establish a mechanical model of the underwater deeply buried unequal-span bifurcated tunnel and determine the geometric relationship. In the model, when the buried depth of the underwater unequal-span bifurcated tunnel is large enough, the water-resistant layer formed by the upper surrounding rock is relatively thick, which can effectively block the upper surface water, and the formation of the collapse arch is hardly affected by the water level. Among them, the geometric relationship is determined by the following formula: ; In the formula: l m is the effective bearing width of the middle rock pillar; l is the net distance between the two holes of the unequal-span bifurcated tunnel; h a is the height of the large-span hole; h b is the height of the small-span hole; θ is the rupture surface angle, which is determined by θ = 45° - φ / 2, where φ is the calculated friction angle of the surrounding rock; W ais the span of the equilibrium arch of the large-span tunnel; b a is the span of the large-span tunnel; W b is the span of the equilibrium arch of the small-span tunnel; b b is the span of the small-span tunnel; W m is the span of the additional equilibrium arch; Step 2. Calculate the height of the additional equilibrium arch, which is determined by the following formula: ; In the formula: H m is the height of the additional equilibrium arch; H m ' is the height of the limit equilibrium arch, which is determined by the following formula: ; In the formula: f is the coefficient of rock mass firmness, also known as the Protodyakonov coefficient; Step 3. Calculate the pressure of the additional equilibrium arch, which is determined by the following formula: ; In the formula: q m is the maximum value of the additional pressure generated by the additional equilibrium arch; γ is the unit weight of the surrounding rock; d is the vertical distance between the crowns of the large-span and small-span tunnels in the bifurcated tunnel, that is, the model considers the case of different buried depths of unequal-span double tunnels; H a is the height of the equilibrium arch of the large-span tunnel, determined by ; H b is the height of the equilibrium arch of the small-span tunnel, determined by ; q s is the pressure acting on the rock pillar, determined by the following formula: ; In the formula: R q is the compressive strength of the rock pillar; α is the enhancement coefficient caused by the reinforcement effect; Step 4. Calculate the additional pressure on the outer side and the additional pressure on the inner side of the large-span tunnel, which are determined by the following formula: ; ; In the formula: q ma1 is the additional pressure on the outer side of the large-span tunnel; q ma2is the additional pressure on the inner side of the large-span cavity; Step 5. Calculate the additional pressure on the outer side and the additional pressure on the inner side of the small-span cavity, which are determined by the following formula: ; ; In the formula: q mb1 is the additional pressure on the outer side of the small-span cavity; q mb2 is the additional pressure on the inner side of the small-span cavity; Step 6. Calculate the vertical surrounding rock pressure and the horizontal surrounding rock pressure of the large-span cavity, which are determined by the following formula: ; ; ; ; In the formula: q a1 is the vertical surrounding rock pressure on the outer side of the large-span cavity; q a2 is the vertical surrounding rock pressure on the inner side of the large-span cavity; q a is the basic pressure of the large-span cavity, determined by the formula ; e a1i is the horizontal surrounding rock pressure on the outer side of the large-span cavity; e a2i is the horizontal surrounding rock pressure on the inner side of the large-span cavity; h ai is the vertical distance from the calculation point to the crown of the large-span cavity; Step 7. Calculate the vertical surrounding rock pressure and the horizontal surrounding rock pressure of the small-span cavity, which are determined by the following formula: ; ; ; ; In the formula: q b1 is the vertical surrounding rock pressure on the outer side of the small-span cavity; q b2 is the vertical surrounding rock pressure on the inner side of the small-span cavity; q b is the basic pressure of the small-span cavity, determined by the formula ; e b1i is the horizontal surrounding rock pressure on the outer side of the small-span cavity; e b2i is the horizontal surrounding rock pressure on the inner side of the small-span cavity;h bi To calculate the vertical distance from a point to the crown of the small-span tunnel.
[0021] According to the above method steps, by changing the span of the large-span a-tunnel of the bifurcated tunnel, the influence of different sizes of the two tunnels of the bifurcated tunnel on the vertical surrounding rock pressure can be obtained, as shown in Figure 5 As shown, with the increase of the span of the large-span tunnel, the vertical pressure and the horizontal pressure increase approximately linearly; the increase rate of the vertical pressure in the large-span tunnel is significantly greater than that in the small-span tunnel. This is because when the span of the large-span tunnel increases, not only the self-supporting arch increases, but also the additional balancing arch increases. The increased load is mainly borne by the large-span tunnel. At the same time, the increase in the height of the additional balancing arch also causes an increase in the additional load on the small-span tunnel.
[0022] According to the above method steps, by changing the vertical distance between the crowns of the two tunnels of the bifurcated tunnel (i.e., the relative position, different burial depths), the influence on the vertical surrounding rock pressure can be obtained, as shown in Figure 6 As shown, the vertical distance is inversely proportional to the surrounding rock pressure. When the distance changes from negative to positive, the surrounding rock pressure will gradually decrease. When it gradually increases from a positive value, the pressure still continues to decrease. This is because the smaller the vertical position of the two tunnels, the lower the position of the large-span tunnel and the higher the position of the small-span tunnel, the greater the effect of the additional balancing arch formed, and the greater the additional pressure. While the higher the position of the large-span tunnel and the lower the position of the small-span tunnel, the smaller the effect of the additional arch.
Claims
1. A method for determining the surrounding rock pressure of an underwater deeply buried unequal-span bifurcated tunnel, characterized in that Including the following steps in sequence: (1) Establish a mechanical model of an underwater deeply buried unequal-span bifurcated tunnel and determine the geometric relationships. In the model, when the burial depth of the underwater unequal-span bifurcated tunnel is large enough, the water-resisting layer formed by the upper surrounding rock is relatively thick, which can effectively block the upper surface water, and the formation of the collapse arch is hardly affected by the water level. Among them, the geometric relationships are determined by the following formula: ； In the formula: l m is the effective bearing width of the middle rock pillar; l is the net distance between the two tunnels of the unequal-span bifurcated tunnel; h a is the height of the large-span tunnel; h b is the height of the small-span tunnel; θ is the fracture surface angle, which is determined by θ = 45° - φ / 2, where φ is the calculated friction angle of the surrounding rock; W a is the balanced arch span of the large-span tunnel; b a is the span of the large-span tunnel; W b is the balanced arch span of the small-span tunnel; b b is the span of the small-span tunnel; W m is the additional balanced arch span; (2) Calculate the height of the additional equilibrium arch, which is determined by the following formula: ； Wherein: H m is the additional balance arch height; H m ' is the ultimate balance arch height, which is determined by the following formula: ； Wherein: f is the coefficient of rock mass firmness, also known as the Protodyakonov coefficient; (3) Calculate the pressure of the additional equilibrium arch, which is determined by the following formula: ； Wherein: q m is the maximum additional pressure generated by the additional balance arch; γ is the unit weight of surrounding rock; d is the vertical distance between the crowns of the large-span and small-span tunnels in the bifurcated tunnel, that is, the model considers the case where the buried depths of the unequal-span double tunnels are different; H a is the height of the balance arch of the large-span tunnel, determined by ; H b is the height of the balance arch of the small-span tunnel, determined by ; q s is the pressure acting on the rock pillar, determined by the following formula: ； In the formula: R q is the compressive strength of the rock pillar; α is the enhancement coefficient caused by the reinforcement effect; (4) Calculate the additional pressure on the outer side and the additional pressure on the inner side of the large-span hole, which are determined by the following formula: ； ； Where: q ma1 is the additional pressure on the outer side of the large-span cavity; q ma2 is the additional pressure on the inner side of the large-span cavity; (5) Calculate the additional pressure on the outer side and the additional pressure on the inner side of the small-span hole, which are determined by the following formula: ； ； In the formula: q mb1 is the additional pressure on the outer side of the small-span hole; q mb2 is the additional pressure on the inner side of the small-span hole; (6) Calculate the vertical surrounding rock pressure and the horizontal surrounding rock pressure of the large-span hole, which are determined by the following formula: ； ； ； ； In the formula: q a1 is the vertical surrounding rock pressure on the outer side of the large-span tunnel; q a2 is the vertical surrounding rock pressure on the inner side of the large-span tunnel; q a is the basic pressure of the large-span tunnel, determined by the formula ; e a1i is the horizontal surrounding rock pressure on the outer side of the large-span tunnel; e a2i is the horizontal surrounding rock pressure on the inner side of the large-span tunnel; h ai is the vertical distance from the calculation point to the crown of the large-span tunnel; (7) Calculate the vertical surrounding rock pressure and the horizontal surrounding rock pressure of the small-span hole, which are determined by the following formula: ； ； ； ； In the formula: q b1 is the vertical surrounding rock pressure on the outside of the small-span tunnel; q b2 is the vertical surrounding rock pressure on the inside of the small-span tunnel; q b is the basic pressure of the small-span tunnel, determined by Equation ; e b1i is the horizontal surrounding rock pressure on the outside of the small-span tunnel; e b2i is the horizontal surrounding rock pressure on the inside of the small-span tunnel; h bi is the vertical distance from the calculation point to the crown of the small-span tunnel.