Calculation method of crown rock loose collapse depth considering stress superposition effect

Abstract

This invention provides a method for calculating the collapse depth of the surrounding rock of a top arch. Step S1: Obtain the arch height *a*, tunnel radius *b*, and the boundary angle θ1 of the equivalent four-centered circular arc. Step S2: Based on the data obtained in Step S1, construct an elliptical collapse arch using the four-centered method. Step S3: Perform a force balance analysis on the self-stabilizing surrounding rock in the vertical direction to obtain the equilibrium equation. Step S4: Analyze the equilibrium equation to obtain a transcendental equation containing only one unknown: the angle θ between the direction of the frictional force of the self-stabilizing surrounding rock and the vertical direction. h Step S5: Solve the equilibrium equations using numerical analysis to obtain the collapse depth. This method can accurately predict the collapse depth of the surrounding rock cavity in the tunnel arch and determine the supporting force of the surrounding rock, providing a reasonable dynamic design basis for tunnel construction across fault fracture zones.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of tunnel engineering construction, in particular to a calculation method of crown arch surrounding rock loose collapse depth considering stress holding effect. BACKGROUND

[0002] The water conveyance tunnel of the construction water diversion project is an important means to realize the optimal allocation of water resources. The water conveyance tunnel has a long route and a large burial depth, and inevitably passes through unfavorable geological sections including fault fracture zones and soft rock, which are prone to geological disasters such as surrounding rock collapse and large deformation of soft rock during the construction period. The use of support measures such as advanced pipe shed and small guide pipe can effectively prevent the deformation and collapse of the crown arch surrounding rock. However, in actual construction, there are still crown arch deformation and collapse failures caused by insufficient support strength or untimely support. Therefore, the stability of the crown arch of the tunnel in the soft and broken stratum, the analysis of the arch effect of the surrounding rock and the proposal of appropriate support measures have always been one of the key problems in hydraulic and rock engineering.

[0003] In the prior art, numerical methods, model test methods and physical test methods are usually used. The numerical method quantitatively analyzes the influence of lithology, ground stress and rock joint on the position and shape of the pressure arch. The model test method studies the sand arch effect of the crown arch of the shield tunnel. The physical test method studies the correlation between the damage depth of the surrounding rock of the super-large cross-section tunnel and the action range of the arch effect.

[0004] However, the above methods all need to construct models and conduct experiments, and the speed is slow and the cost is high in the analysis process, and there is a corresponding implementation difficulty for engineering application. SUMMARY

[0005] The present application provides a calculation method of crown arch surrounding rock loose collapse depth considering stress holding effect, to solve the technical problems of slow speed, high cost and difficult implementation in the application of the prior art.

[0006] To solve the above technical problems, the present application provides a calculation method of crown arch surrounding rock loose collapse depth, comprising the following steps:

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

[0008] Step S2: based on the data obtained in step S1, drawing an elliptical collapse arch by four-center method;

[0009] Step S3: performing stress balance analysis on the self-stable surrounding rock in the vertical direction to obtain a balance equation;

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

[0011] Step S5: solving the balance equation by numerical analysis method to obtain the collapse depth.

[0012] Preferably, in step S1, the expression of the collapse arch height a is:

[0013]

[0014] In the formula, φ is the equivalent friction angle of the rock mass, and b represents the tunnel radius.

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

[0016]

[0017] In the formula, R represents the radius of the four-center large circular arc, r represents the radius of the four-center small circular arc, and b represents the tunnel radius.

[0018] Preferably, step S2 comprises: in the horizontal direction, taking two points with a distance of (R-b) from the tunnel center as the first center; in the vertical direction, taking a point with a distance of r from the arch and close to the tunnel center as the second center; the first center has a radius of R, the second center has a radius of r, and the first center has a boundary angle of θ1 at the first center, and the four-center method is used to draw an elliptical collapse arch.

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

[0020] F1 cosθ-F2sinθ=G;

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

[0022] Preferably, step S4 comprises:

[0023] Step S41: taking a small section on the collapse arch line for analysis to obtain a first decomposition formula of F1 cosθ-F2sinθ in the balance equation;

[0024] Step S42: according to the area and specific gravity of the self-stable body of the surrounding rock, a second decomposition formula of the weight G of the rock mass within the self-stable height in the balance equation is obtained;

[0025] Step S43: the first decomposition formula and the second decomposition formula are arranged to obtain a transcendental equation containing only one unknown quantity θ, which represents the angle between the direction of the surrounding rock friction force of the self-stable surrounding rock and the vertical direction. h h ​​​

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

[0027]

[0028]

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

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

[0031]

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

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

[0034]

[0035]

[0036] F = b - R.

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

[0038] h = R sin theta h -b.

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

[0040]

[0041] The beneficial effects of the present application at least include: as a method parallel to numerical simulation and physical simulation, the method of the present application has the advantages of fast analysis speed, low cost, and is easy to apply to engineering. Based on the systematic analysis of the arch effect of underground caverns, the present application proposes to construct an elliptical collapse arch by using the four-center method, to consider the stress redistribution of the underground cavern collapse depth during calculation and analysis, and to apply it to practical engineering, accurately deducing the collapse depth, and providing a simple and reliable analysis idea for the crown arch support design of soft surrounding rock tunnels. Attached Figure Description

[0042] Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention;

[0043] Figure 2 This is a schematic diagram of the deviation of the four-center method for approximating an ellipse according to an embodiment of the present invention;

[0044] Figure 3 This is a schematic diagram of the approximate ellipse calculation of the arch line according to an embodiment of the present invention;

[0045] Figure 4 This is a schematic diagram of the force balance analysis of the elliptical collapsed arch according to an embodiment of the present invention. Detailed Implementation

[0046] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0047] like Figure 1 As shown, this embodiment of the invention provides a method for calculating the collapse depth of the surrounding rock of the arch considering the stress-bearing effect, including the following steps:

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

[0049] Step S2: Based on the data obtained in step S1, construct an elliptical collapsed arch using the four-center method.

[0050] Specifically, within the elliptical collapse arch range, there also exists a self-stabilizing height h', causing the surrounding rock within this critical height to enter a new equilibrium state. At this point, the rock mass far from the excavation face is subjected to the clamping effect of the redistributed stress around the tunnel. Within the elliptical collapse arch range, there also exists a self-stabilizing height h', causing the surrounding rock within this height range to be in a critical equilibrium state under the clamping effect of its own weight and the stress of the surrounding rock around the tunnel.

[0051] However, unlike a regular triangular collapsed arch, the angle between the elliptical tangent and the vertical direction of an elliptical collapsed arch is constantly changing. To facilitate integral calculation, this embodiment of the invention employs the four-center circle method, connecting four circular arcs to form an approximate ellipse, thus simulating the effect of an elliptical collapsed arch.

[0052] The "four-center method" for drawing an ellipse uses four circular arcs to form an approximate ellipse. Theoretically, this method ensures a smooth connection between the four arcs, but it inevitably deviates from the actual ellipse. The deviation is smaller near the minor axis and larger near the major axis. The closer the ratio of the major and minor axes of the drawn ellipse is to 1, the smaller the deviation of the "four-center method." Based on the actual collapse range and depth of the surrounding rock at the engineering site, the top of the collapsed cavity of the surrounding rock is closer to the minor axis of the ellipse, thus the error compared to reality is relatively small.

[0053] The deviation between the ellipse drawn using the "four-center method" in drawing software and the actual ellipse is as follows: Figure 2 As shown in the diagram. The blue line represents the approximate ellipse drawn using the "four-center method," while the red line represents the actual ellipse.

[0054] in:

[0055] The radius of the great circle arc (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 collapsed arch coincides with the vertex of the triangular collapsed arch, meaning that this point is a critical equilibrium point under the current stress environment. For example... Figure 3 The approximate ellipse shown is used to calculate the arch line. in denoted as the equivalent friction angle of the rock mass, and b represents the tunnel radius.

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

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

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

[0063] Similarly, the half of the self-stable surrounding rock (half detached body) is taken as an example to analyze. According to the force balance in vertical direction, the equation is:

[0064] F1cosθ-F2sinθ=G(3)

[0065] In the formula, F1 is the friction force of the self-stable height of the detached body, F2 is the pressure of the self-stable height of the detached body, G is the self-weight of the self-stable height of the rock mass, and θ represents the central angle.

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

[0067] Specifically, according to Figure 4 Taking a micro-section on the collapse arch line, the left side of the balance equation can be obtained as:

[0068]

[0069] In the formula, is the equivalent cohesive force of the rock mass, is the equivalent friction angle of the rock mass (radian), the radial comprehensive stress of the surrounding rock is and the tangential comprehensive stress is R and r are the radii of the approximate elliptical arch size circle.

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

[0071]

[0072] In the formula, σ ci represents the uniaxial compressive strength of the intact rock, s, k, and m b are H-B rock mass parameters, and r0 is the tunnel excavation radius.

[0073] According to formula (4) and formula (8), the radial and tangential stress distributions of the surrounding rock change with the radial distance r. By using the method of first integration and then taking the average, the radial comprehensive stress and the tangential comprehensive stress of the surrounding rock within the self-stable height h' are obtained as:

[0074]

[0075] Substituting f1 and f2 into formula (4) respectively, and after rearrangement, the following equation is obtained:

[0076]

[0077] Then, according to the area and the specific gravity of the self-stable body of the surrounding rock, the self-weight of the surrounding rock in the self-stable height can be obtained, which is:

[0078]

[0079] In the formula, γ represents the volume weight of the rock mass.

[0080] According to the formula (3), an only θ h An unknown transcendental equation is shown as follows.

[0081]

[0082] In the formula, θ

[0083]

[0084] F = b - R (19)

[0085] Step S5: the balance equation is solved by the numerical analysis method, and the collapse depth is obtained.

[0086] Specifically, since the formula (13) is a transcendental equation, it is difficult to obtain the analytical solution of the collapse cavity depth h by solving the equation. The embodiment of the present application solves the implicit solution θ h of the collapse cavity depth h by the numerical analysis method, and then the collapse depth h of the surrounding rock in the elliptical collapse arch is obtained by the numerical value of θ h .

[0087] The collapse depth h of the surrounding rock in the elliptical collapse arch is obtained through the geometric relationship, and the collapse volume V of the crown arch surrounding rock considering the clamping effect of the excavation unloading stress is obtained by calculation, which is shown as follows.

[0088] h = Rsinθ h -b (20)

[0089]

[0090] In the specific implementation, the self-stable height h' is randomly input, the corresponding collapse depth h is obtained, and the solution is completed when h'+h=a-b.

[0091] The technical features of the above embodiments can be combined arbitrarily. In order to make the description simple, all possible combinations of the technical features in the above embodiments are not described, only the preferred embodiments of the present application are expressed, and the description is more specific and detailed, but it cannot be understood as a limitation on the scope of the patent. As long as the combination of these technical features does not exist, it should be considered as the scope of the description.

[0092] It should be noted that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the inventive concept, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application patent should be subject to the appended claims.

Claims

1. A method for calculating the loose collapse depth of crown rock considering the stress superposition effect, characterized in that: The method comprises the following steps: Step S1: obtaining a crown arch height a, a tunnel radius b and a boundary angle θ1 of an equivalent four-center circular arc; Step S2: based on the data obtained in step S1, an elliptical crown arch is plotted by four-center method; Step S3: a stress balance analysis is performed on the self-stable surrounding rock in the vertical direction to obtain a balance equation; Step S4: solving the balance equation to obtain a transcendental equation containing only one unknown quantity, i.e. the angle θ between the direction of the surrounding rock friction of the self-stable surrounding rock and the vertical direction h ; Step S5: the balance equation is solved by a numerical analysis method to obtain a collapse depth; The expression of the balance equation is: F1 cosθ-F2sinθ=G; In the formula, F1 is the friction of the detached body in the self-stable height, F2 is the surrounding rock pressure of the detached body in the self-stable height, G is the weight of the rock mass in the self-stable height, and θ represents a central angle; Step S4 comprises: Step S41: a micro-section on the crown arch line is analyzed to obtain a first decomposition formula of F1 cosθ-F2sinθ in the balance equation; Step S42: according to the area and specific gravity of the self-stable body of the surrounding rock, a second decomposition formula of the weight G of the rock mass in the self-stable height in the balance equation is obtained; Step S43: arranging the first and second decompositions to obtain an equation with only one unknown θ h , which is a transcendental equation h , where θ represents the angle between the direction of the surrounding rock friction of the self-stable surrounding rock and the vertical direction. The expression of the first decomposition formula is: wherein r represents the radius of the small circle arc of the four-center method, R represents the radius of the large circle arc of the four-center method, represents the equivalent cohesion of the rock mass, represents the equivalent friction angle of the rock mass, represents the radial comprehensive stress of the surrounding rock, represents the tangential comprehensive stress of the surrounding rock, h represents the collapse depth, h' represents the self-stable height, σ θ , and σ r are the tangential stress and the radial stress after the excavation of the circular cavern, respectively; The expression of the second decomposition formula is: In the formula, γ represents the bulk density of the rock mass.

2. The method of claim 1, wherein the method is characterized in that: In step S1, the expression of the crown arch height a is: In the formula, is the equivalent friction angle of rock mass, and b represents the radius of the tunnel. The expression of the boundary angle θ1 of the equivalent four-center circular arc is: In the formula, R represents the radius of the four-center method large circular arc, r represents the radius of the four-center method small circular arc, and b represents the tunnel radius.

3. The method for calculating the depth of loosening and collapse of the surrounding rock of the arch considering the stress-bearing effect according to claim 2, characterized in that: Step S2 comprises: in the horizontal direction, two points with a distance of (R-b) from the tunnel center are taken as a first center; in the vertical direction, a point with a distance of r from the arch top and close to the tunnel center is taken as a second center; the first center has a radius of R, the second center has a radius of r, and an elliptical crown arch is plotted by four-center method with the first center as the first center and the second center as the second center and with θ1 as the boundary angle.

4. The method of claim 1, wherein the method further comprises: calculating the stress concentration factor of the crown rock mass. The expression of the transcendental equation is: F=b-R.

5. The method for calculating the depth of loosening and collapse of the surrounding rock of the arch considering the stress-bearing effect according to claim 4, characterized in that: The expression of the collapse depth h is: h = R sin θ h -b.

6. The method of claim 5, wherein the method further comprises: The collapse volume V of the arch top surrounding rock is calculated by the following expression:

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