Top arch surrounding rock loosening and collapsing depth calculation method considering stress holding effect

Abstract

The invention provides a method for calculating the loosening and collapsing depth of top arch surrounding rock. The method comprises the steps that S1, the arch crown height a, the tunnel radius b and the boundary angle theta 1 of an equivalent four-center arc are obtained; s2, on the basis of the data obtained in the step S1, drawing is conducted through a four-center method, and an elliptical caving arch is formed; s3, carrying out stress balance analysis on the self-stabilizing surrounding rock in the vertical direction to obtain a balance equation; s4, the balance equation is analyzed, a transcendental equation only containing one unknown quantity is obtained, and the unknown quantity is the included angle theta h between the surrounding rock friction force direction of the self-stabilizing surrounding rock and the vertical direction; and S5, solving the equilibrium equation through a numerical analysis method to obtain the slump depth. The cavern top arch surrounding rock collapse cavity depth can be accurately predicted, the surrounding rock supporting force is determined, and a reasonable dynamic design basis is provided for tunnel construction penetrating through a fault fracture zone.

Description

Technical Field

[0001] The invention relates to the technical field of tunnel engineering construction, and in particular to a method for calculating the loosening and collapse depth of top arch surrounding rock taking into account stress reinforcement effect. Background Art

[0002] The construction of water diversion tunnels for water diversion projects is an important means to achieve optimal allocation of water resources. The water diversion tunnel has a long route and a deep burial depth. It is inevitable that it will pass through unfavorable geological tunnel sections including fault fracture zones and soft rocks. During the construction period, geological disasters such as surrounding rock collapse and large deformation of soft rocks are prone to occur. The use of support measures such as advanced pipe sheds and small guide tubes can effectively prevent the deformation and collapse of the arch surrounding rock. However, in actual construction, there are still arch deformation and collapse damage caused by insufficient support strength or untimely support. Therefore, studying the stability of the cavern arch in soft and broken strata, analyzing the arch effect of the surrounding rock and proposing appropriate support measures have always been one of the key issues of hydraulic rock engineering.

[0003] Numerical methods, model test methods and physical test methods are usually used in the existing technology. Numerical methods quantitatively analyze the influence of rock properties, ground stress and rock joints on the position and shape of pressure arches. Model test methods study the arching effect of sand in the top arch of shield tunnels. Physical test methods study the correlation between the failure depth of surrounding rock of super-large section tunnels and the scope of arching effect.

[0004] However, the above methods all require building models and conducting experiments, which are slow and costly in the analysis process, and have corresponding implementation difficulties for engineering applications. Summary of the invention

[0005] The present invention proposes a method for calculating the loosening and collapse depth of the arch surrounding rock taking into account the stress reinforcement effect, so as to solve the technical problems of the prior art in that the application speed is slow, the cost is high and the implementation is difficult.

[0006] In order to solve the above technical problems, the present invention provides a method for calculating the loosening and collapse depth of the top arch surrounding rock, comprising the following steps:

[0007] Step S1: Obtain the arch height a, the tunnel radius b and the boundary angle θ1 of the equivalent four-center arc;

[0008] Step S2: Based on the data obtained in step S1, a four-center method is used to construct an elliptical collapse arch;

[0009] Step S3: Perform force balance analysis on the self-stabilizing surrounding rock in the vertical direction to obtain a balance equation;

[0010] Step S4: Analyze the equilibrium equation to obtain a transcendental equation containing only one unknown quantity, which is the angle θ between the friction force direction of the self-stabilizing surrounding rock and the vertical direction.h ;

[0011] Step S5: Solve the equilibrium equation by numerical analysis to obtain the collapse depth.

[0012] Preferably, in step S1, the expression of the collapsed vault height a is:

[0013]

[0014] In the formula, is the equivalent friction angle of rock mass, b is the radius of the tunnel;

[0015] The expression of the boundary angle θ1 of the equivalent four-center arc is:

[0016]

[0017] Where R is the radius of the large arc of the four-center method, r is the radius of the small arc of the four-center method, and b is the radius of the tunnel.

[0018] Preferably, step S2 includes: in the horizontal direction, two points at a distance (Rb) from the center of the tunnel are used as the first center of the circle; in the vertical direction, a point at a distance r from the arch top and close to the center of the tunnel is used as the second center of the circle; the first center of the circle takes R as the radius, the second center of the circle takes r as the radius, and θ1 is used as the dividing angle at the first center of the circle, and an elliptical collapsed arch is constructed by drawing using the four-center method.

[0019] Preferably, the expression of the equilibrium equation is:

[0020] F1 cosθ-F2 sinθ=G;

[0021] Where F1 is the friction force of the surrounding rock on the detached body within the self-stabilizing height, F2 is the surrounding rock pressure on the detached body within the self-stabilizing height, G is the deadweight of the rock mass within the self-stabilizing height, and θ represents the central angle.

[0022] Preferably, step S4 comprises:

[0023] Step S41: Analyze a micro-segment on the collapse arch line to obtain the first decomposition formula of F1cosθ-F2sinθ in the equilibrium equation;

[0024] Step S42: obtaining a second decomposition formula of the deadweight G of the rock mass within the self-stabilizing height in the equilibrium equation according to the area and weight of the surrounding rock self-stabilizing body;

[0025] Step S43: Arrange the first decomposition formula and the second decomposition formula to obtain a formula containing only one unknown quantity θ h The transcendental equation, θ h It represents the angle between the friction direction of the self-stabilizing surrounding rock and the vertical direction.

[0026] Preferably, the expression of the first decomposition formula is:

[0027]

[0028]

[0029] In the formula, r represents the radius of the small arc of the four-center method, and R represents the radius of the large arc of the four-center method. represents the equivalent cohesion of rock mass, represents the equivalent friction angle of rock mass, represents the radial comprehensive stress of surrounding rock, represents the tangential comprehensive stress of the surrounding rock, h represents the collapse depth, h' represents the self-stabilizing height, σ θ , σ r They are the tangential stress and radial stress after circular cavern excavation, respectively.

[0030] Preferably, the expression of the second decomposition formula is:

[0031]

[0032] In the formula, γ represents the rock mass density.

[0033] Preferably, the expression of the transcendental equation is:

[0034]

[0035]

[0036] F = bR.

[0037] Preferably, the expression of the slump depth h is:

[0038] h=Rsinθ h -b.

[0039] Preferably, the collapse volume V of the top arch surrounding rock is calculated by the following expression:

[0040]

[0041] The beneficial effects of the present invention include at least: as a method parallel to numerical simulation and physical simulation, the method of the present invention has the advantages of fast analysis speed and low cost, and is also easy to apply in engineering. Based on the systematic combing of the arch effect of underground caverns, the present invention proposes to use the four-center method to construct an elliptical collapse arch, and consider the analytical solution of the collapse depth of underground caverns with the redistribution of excavation unloading stress in the calculation and analysis, and apply it to actual engineering to accurately derive the collapse depth, providing a simple and reliable analytical idea for the top arch support design of soft surrounding rock tunnels. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 A schematic diagram of a method flow of an embodiment of the present invention;

[0043] Figure 2 Schematic diagram of the deviation of the approximate ellipse using the four-center method according to an embodiment of the present invention;

[0044] Figure 3 A schematic diagram of calculating the apses of an approximate ellipse according to an embodiment of the present invention;

[0045] Figure 4 It is a schematic diagram of the force balance analysis of the elliptical collapse arch according to an embodiment of the present invention. DETAILED DESCRIPTION

[0046] The following is a clear and complete description of the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work belong to the protection scope of the present invention.

[0047] like Figure 1 As shown, an embodiment of the present invention provides a method for calculating the loosening and collapse depth of the arch surrounding rock considering the stress reinforcement effect, comprising the following steps:

[0048] Step S1: Obtain the arch height a, the tunnel radius b and the boundary angle θ1 of the equivalent four-center arc.

[0049] Step S2: Based on the data obtained in step S1, a four-center method is used to construct an elliptical collapse arch.

[0050] Specifically, within the range of the elliptical collapse arch, there is also a self-stabilizing height h', so that the surrounding rock within this critical height will enter a new equilibrium state. At this time, the rock mass far away from the excavation surface is clamped by the stress around the hole after redistribution. Within the range of the elliptical collapse arch, there is also a self-stabilizing height h', so that the surrounding rock within this height range is in a critical equilibrium state under the clamping effect of its own gravity and the rock stress around the hole.

[0051] However, the elliptical collapse arch is different from the common triangular collapse arch in that the angle between the tangent line of the ellipse and the vertical direction is constantly changing. In order to facilitate the calculation of integrals, the embodiment of the present invention uses a four-center circle method to connect four arcs into an approximate ellipse to achieve the effect of simulating an elliptical collapse arch.

[0052] The "four-center method" is to draw an ellipse by using four arc segments to form an approximate ellipse. This drawing method theoretically ensures the smooth connection of the four arc segments, but there must be a certain deviation from the actual ellipse. The deviation is small near the minor axis of the ellipse, and the deviation is large near the major axis of the ellipse. When the ratio of the major and minor axes of the drawn ellipse is close to 1, the deviation of the "four-center method" is smaller. According to the actual collapse range and collapse depth of the arch surrounding rock at the project site, the top of the arch surrounding rock collapse cavity is closer to the minor axis of the ellipse, so the error is relatively small from the actual situation.

[0053] The deviation between the ellipse drawn by the "four-center method" and the actual ellipse is as follows: Figure 2 As shown in the figure, the blue line represents the approximate ellipse drawn by the “four-center method”, and the red line represents the actual ellipse.

[0054] in:

[0055] The radius of the great circle (O2) is:

[0056]

[0057] The radius of the small arc (O1) is:

[0058]

[0059] In the same redistributed secondary stress field, the upper vertex of the elliptical collapse arch and the vertex of the triangular collapse arch are at the same point, that is, this point is a critical equilibrium point under the current stress environment. Figure 3 The approximate ellipse shown in the figure calculates the apsidal line. in is the equivalent friction angle of rock mass, and b is the radius of the tunnel.

[0060] When drawing, in the horizontal direction, two points at a distance (Rb) from the center of the tunnel are used as the first center of the circle; in the vertical direction, a point at a distance r from the arch top and close to the center of the tunnel is used as the second center of the circle; the first center of the circle has R as the radius, the second center of the circle has r as the radius, and θ1 is used as the dividing angle at the first center of the circle, and an elliptical collapsed arch is constructed by the four-center method.

[0061] Step S3: Perform force balance analysis on the self-stabilizing surrounding rock in the vertical direction to obtain a balance equation.

[0062] Specifically, when the top arch surrounding rock of the elliptical collapse arch is only subject to the action of gravity, due to the clamping effect of the secondary stress field around the cavern, when the top arch surrounding rock collapses to a certain depth h, the rock mass within the range of the elliptical collapse arch is in a relatively balanced state, such as Figure 4 shown.

[0063] Similarly, in this embodiment, half of the self-stable surrounding rock (semi-detached body) is taken for analysis. When only the deadweight of the surrounding rock is considered, the equation can be listed based on the force balance in the vertical direction as follows:

[0064] F1cosθ-F2sinθ=G(3)

[0065] Where: F1 is the friction force of the surrounding rock on the detached body within the self-stabilizing height, F2 is the surrounding rock pressure on the detached body within the self-stabilizing height, G is the deadweight of the rock mass within the self-stabilizing height, and θ represents the central angle.

[0066] Step S4: Analyze the equilibrium equation to obtain a transcendental equation containing only one unknown quantity, which is the angle θ between the friction force direction of the self-stabilizing surrounding rock and the vertical direction. h .

[0067] Specifically, according to Figure 4 Taking a micro-segment analysis on the collapse arch line, we can get the left side of the equilibrium equation as:

[0068]

[0069] Where: is the equivalent cohesion of rock mass, is the equivalent friction angle of the rock mass (radian), the radial comprehensive stress of the surrounding rock and tangential combined stress R and r are the radii of the arc of the approximate elliptical arch.

[0070] After the deep buried tunnel is excavated, due to the unloading effect of the surrounding rock, a secondary stress field is formed around the cavern. The tangential stress and radial stress σ after the circular cavern is excavated are obtained. θ and σ r :

[0071]

[0072] In the formula, σ ci Indicates the uniaxial compressive strength of intact rock, s, k, m b is the HB rock mass parameter, r0 is the tunnel excavation radius.

[0073] According to equations (4) and (8), the radial and tangential stress distribution of the surrounding rock varies with the radius r. The radial comprehensive stress of the surrounding rock within the self-stabilizing height h' is obtained by integrating first and then taking the average value. and tangential combined stress have:

[0074]

[0075] Substituting f1 and f2 into equation (4) respectively, we can get:

[0076]

[0077] Then, according to the area and weight of the surrounding rock self-stabilizing body, the self-weight of the surrounding rock within the self-stabilizing height can be obtained:

[0078]

[0079] In the formula, γ represents the rock mass density.

[0080] According to formula (3), after sorting, we can get a formula that only contains θ h A transcendental equation with an unknown quantity is shown below.

[0081]

[0082] in,

[0083]

[0084] F=bR (19)

[0085] Step S5: Solve the equilibrium equation by numerical analysis to obtain the collapse depth.

[0086] Specifically, since equation (13) is a transcendental equation, it is difficult to obtain an analytical solution for the collapse cavity depth h by solving this equation. The embodiment of the present invention uses a numerical analysis method to solve the implicit solution θ of the collapse cavity depth h. h , and then through θ h The numerical value of is used to obtain the collapse depth h of the surrounding rock in the elliptical collapse arch.

[0087] The collapse depth h of the surrounding rock in the elliptical collapse arch can be obtained through geometric relationships. The collapse volume V of the surrounding rock of the top arch considering the clamping effect of excavation unloading stress can be obtained through calculation, as shown in the following formula.

[0088] h=Rsinθ h -b (20)

[0089]

[0090] In specific implementation, the self-stabilizing height h' is randomly input to obtain the corresponding collapse depth h, and the solution is completed when h'+h=ab.

[0091] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. Only the preferred embodiments of the present invention are expressed. The description is more specific and detailed, but it cannot be understood as limiting the scope of the patent of the present invention. As long as there is no contradiction in the combination of these technical features, they should be considered as the scope recorded in this specification.

[0092] It should be noted that, for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, and these modifications and improvements all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be subject to the attached claims.

Claims

1. A method for calculating the loosening and collapse depth of the arch surrounding rock taking into account the stress reinforcement effect, characterized in that: The following steps are involved: Step S1: Obtain the arch height a, the tunnel radius b and the boundary angle θ1 of the equivalent four-center arc; Step S2: Based on the data obtained in step S1, a four-center method is used to construct an elliptical collapse arch; Step S3: Perform force balance analysis on the self-stabilizing surrounding rock in the vertical direction to obtain a balance equation; Step S4: Analyze the equilibrium equation to obtain a transcendental equation containing only one unknown quantity, which is the angle θ between the friction force direction of the self-stabilizing surrounding rock and the vertical direction. h ; Step S5: Solve the equilibrium equation by numerical analysis to obtain the collapse depth.

2. The method for calculating the loosening and collapse depth of the arch surrounding rock considering the stress reinforcement effect according to claim 1 is characterized in that: In step S1, the expression of the collapsed vault height a is: In the formula, is the equivalent friction angle of rock mass, b is the radius of the tunnel; The expression of the boundary angle θ1 of the equivalent four-center arc is: Where R is the radius of the large arc of the four-center method, r is the radius of the small arc of the four-center method, and b is the radius of the tunnel.

3. The method for calculating the loosening and collapse depth of the arch surrounding rock taking into account the stress reinforcement effect according to claim 2 is characterized in that: Step S2 includes: in the horizontal direction, two points at a distance (Rb) from the center of the tunnel are used as the first center of the circle; in the vertical direction, a point at a distance r from the arch top and close to the center of the tunnel is used as the second center of the circle; the first center of the circle takes R as the radius, the second center of the circle takes r as the radius, and θ1 is used as the dividing angle at the first center of the circle, and an elliptical collapsed arch is constructed by the four-center method.

4. The method for calculating the loosening and collapse depth of the arch surrounding rock considering the stress reinforcement effect according to claim 1 is characterized in that: The expression of the equilibrium equation is: F1cosθ-F2sinθ=G; Where F1 is the friction force of the surrounding rock on the detached body within the self-stabilizing height, F2 is the surrounding rock pressure on the detached body within the self-stabilizing height, G is the deadweight of the rock mass within the self-stabilizing height, and θ represents the central angle.

5. The method for calculating the loosening and collapse depth of the arch surrounding rock taking into account the stress reinforcement effect according to claim 4 is characterized in that: Step S4 includes: Step S41: Analyze a micro-segment on the collapse arch line to obtain the first decomposition formula of F1cosθ-F2sinθ in the equilibrium equation; Step S42: obtaining a second decomposition formula of the deadweight G of the rock mass within the self-stabilizing height in the equilibrium equation according to the area and weight of the surrounding rock self-stabilizing body; Step S43: Arrange the first decomposition formula and the second decomposition formula to obtain a formula containing only one unknown quantity θ h The transcendental equation, θ h It represents the angle between the friction direction of the self-stabilizing surrounding rock and the vertical direction.

6. The method for calculating the loosening and collapse depth of the arch surrounding rock taking into account the stress reinforcement effect according to claim 5 is characterized in that: The expression of the first decomposition formula is: In the formula, r represents the radius of the small arc of the four-center method, and R represents the radius of the large arc of the four-center method. represents the equivalent cohesion of rock mass, represents the equivalent friction angle of rock mass, represents the radial comprehensive stress of surrounding rock, represents the tangential comprehensive stress of the surrounding rock, h represents the collapse depth, h' represents the self-stabilizing height, σ θ , σ r They are the tangential stress and radial stress after circular cavern excavation, respectively.

7. The method for calculating the loosening and collapse depth of the arch surrounding rock taking into account the stress reinforcement effect according to claim 6 is characterized in that: The expression of the second decomposition formula is: In the formula, γ represents the rock mass density.

8. The method for calculating the loosening and collapse depth of the arch surrounding rock taking into account the stress reinforcement effect according to claim 7, characterized in that: The expression of the transcendental equation is: F = bR.

9. The method for calculating the loosening and collapse depth of the arch surrounding rock taking into account the stress reinforcement effect according to claim 8, characterized in that: The expression of the collapse depth h is: h=Rsinθ h -b。 10. The method for calculating the loosening and collapse depth of the arch surrounding rock taking into account the stress reinforcement effect according to claim 9, characterized in that: The collapse volume V of the surrounding rock of the arch is calculated by the following expression:

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