Top arch surrounding rock caving depth calculation method considering excavation unloading stress redistribution

Abstract

The invention provides a top arch surrounding rock collapse depth calculation method considering excavation unloading stress redistribution. The top arch surrounding rock collapse depth calculation method comprises the following steps that S1, the height of a collapse arch before excavation is calculated through a triangle formula; s2, the tunnel radius, the surrounding rock volume weight, the cohesive force and the internal friction angle are collected; and S3, stress decomposition and stress redistribution analysis are carried out after excavation, and the caving depth of the top arch surrounding rock is obtained. The cavern top arch surrounding rock collapse cavity depth can be more 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 collapse depth of a crown arch surrounding rock taking into account the redistribution of excavation unloading stress. 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 collapse depth of the top arch surrounding rock taking into account the redistribution of excavation unloading stress, 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 collapse depth of the top arch surrounding rock taking into account the redistribution of excavation unloading stress, comprising the following steps:

[0007] Step S1: using the triangle formula to calculate the height of the collapsed arch before excavation;

[0008] Step S2: Collecting the tunnel radius, surrounding rock bulk density, cohesion and internal friction angle;

[0009] Step S3: After excavation, force decomposition and stress redistribution analysis are performed to obtain the collapse depth of the top arch surrounding rock.

[0010] Preferably, step S3 comprises:

[0011] Step S31: Perform force analysis on the semi-detached body and construct a vertical equilibrium equation;

[0012] Step S32: taking the self-stabilizing height as an unknown variable, and using the tangential stress and radial stress after the cavern excavation to analyze each force in the equilibrium equation, to obtain an expression for the self-stabilizing height;

[0013] Step S33: The tangential comprehensive stress and radial comprehensive stress after excavation are obtained by integrating first and then taking the average, and the iterative method is used to solve them to obtain the self-stabilizing height and thus calculate the collapse depth.

[0014] Preferably, the expression of the equilibrium equation in step S31 is:

[0015]

[0016] In the formula, F 1 F is the friction force of the surrounding rock on the detached body within the self-stabilizing height, 2 The surrounding rock pressure of the detached body within the self-stabilizing height is applied to it, and G is the deadweight of the rock mass within the self-stabilizing height.

[0017] Preferably, in step S32, the surrounding rock friction force F 1 Parses as:

[0018]

[0019] Where h′ represents the collapse depth, σ θ and σ r are the tangential stress and radial stress after excavation, c is the rock mass cohesion, is the friction angle within the rock mass.

[0020] Preferably, in step S32, the surrounding rock of the detached body within the self-stabilizing height is subjected to the surrounding rock pressure F 2 Parses as:

[0021]

[0022] Preferably, in step S32, the deadweight G of the rock mass within the self-stabilizing height is analyzed as:

[0023]

[0024] Where γ is the rock mass bulk density.

[0025] Preferably, the tangential stress σ θ and radial stress σ r The expression is:

[0026]

[0027] Where r is the radius vector and p is the support force acting on the excavation surface of surrounding rock.

[0028] Preferably, the expressions of the self-stabilizing height h′ and the collapse depth L are:

[0029]

[0030] Where R is the radius of the cavern before excavation. and It is the combined tangential and radial stress of the surrounding rock within the self-stabilizing height h′.

[0031] Preferably, the comprehensive value of the tangential stress after excavation is The combined value of radial stress The expression is:

[0032]

[0033] Where h represents the collapse depth of the arch top before excavation.

[0034] Preferably, the collapsed volume V can also be obtained by the following formula:

[0035]

[0036] 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 analysis of the arch effect of underground caverns, the present invention proposes an analytical solution for the collapse depth of underground caverns considering the redistribution of excavation unloading stress, and applies 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

[0037] Figure 1 A schematic diagram of a method flow of an embodiment of the present invention;

[0038] Figure 2 A schematic diagram of a collapsed arch structure according to an embodiment of the present invention;

[0039] Figure 3 It is a schematic diagram of force analysis of a semi-detached body within a self-stabilizing height according to an embodiment of the present invention;

[0040] Figure 4 A schematic diagram of secondary stress distribution after excavation of a deep-buried circular cavern according to an embodiment of the present invention;

[0041] Figure 5 This is a generalized example diagram of a collapsed cavity according to an embodiment of the present invention;

[0042] Figure 6It is a schematic diagram of the solution result of the top arch collapse depth according to an embodiment of the present invention. DETAILED DESCRIPTION

[0043] 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.

[0044] The surrounding rock of the cavern roof arch will loosen under the disturbance of excavation, causing the rock mass within a certain range to collapse without support. At the same time, the unloading of deep tunnel excavation causes the stress redistribution of the surrounding rock, and the secondary stress field formed has a clamping effect on the surrounding rock of the roof arch. This effect can resist the effect of self-weight load within a certain range and avoid the increase of collapse height. Therefore, within the range of the collapse arch, there is a critical height, so that the rock mass in this height range is in critical equilibrium under the clamping effect of self-weight and surrounding rock stress. According to the above analysis, the existing collapse arch height prediction formulas rarely consider the influencing factor of the secondary stress field of the surrounding rock. Therefore, the embodiments of the present invention provide a method for calculating the collapse depth of the roof arch surrounding rock taking into account the redistribution of stress due to excavation unloading, and a method for calculating the collapse depth of the cavern taking into account the influence of the redistribution of stress due to surrounding rock due to excavation unloading, such as Figure 1 As shown, the following steps are included:

[0045] Step S1: Calculate the height of the collapse arch before excavation using the triangle formula.

[0046] like Figure 2 As shown in the figure, when the collapse arch is a triangle, H is the collapse arch height calculated by the triangle formula when only the deadweight is considered, and h is the collapse depth of the arch top before excavation. At the same time, the self-stabilizing height h' and collapse depth L to be obtained are also marked in the figure.

[0047] Specifically, after the cavern is excavated, the surrounding rock stress is redistributed. The farther away from the excavation surface, the more obvious the clamping effect of the redistributed stress on the rock mass. Therefore, within the range of the collapse arch, there is a self-stabilizing height h', which makes the surrounding rock within this critical height range in a critical equilibrium state under the clamping effect of its own weight and surrounding rock stress.

[0048] Step S2: Collect the tunnel radius, surrounding rock bulk density, cohesion and internal friction angle.

[0049] Step S3: After excavation, force decomposition and stress redistribution analysis are performed to obtain the collapse depth of the top arch surrounding rock.

[0050] Specifically, if Figure 3 As shown in the figure, the force analysis of the semi-detached body is carried out, and the equilibrium equation in the vertical direction is:

[0051]

[0052] In the formula, F 1 F is the friction force of the surrounding rock on the detached body within the self-stabilizing height, 2 The surrounding rock pressure of the detached body within the self-stabilizing height is applied to it, and G is the deadweight of the rock mass within the self-stabilizing height.

[0053] Then, the self-stabilizing height h' is taken as an unknown variable, and the tangential stress and radial stress after the cavern excavation are used to analyze each force in the equilibrium equation and obtain them respectively.

[0054]

[0055]

[0056] Where c is the rock mass cohesion, is the internal friction angle of the rock mass (radian), γ is the rock mass bulk density, σ θ and σ r They are the tangential stress and radial stress after cavern excavation, respectively.

[0057] After the deep tunnel is excavated, a secondary stress field is formed around the cavern due to the unloading effect of the surrounding rock. Based on the MC rock strength criterion and combined with the elastic-plastic mechanics analysis, the secondary stress distribution diagram after the circular cavern excavation can be obtained as follows: Figure 4 As shown, the stress distribution σ along the tangential and radial directions of the tunnel is obtained. θ (r) and σ r (r) is:

[0058]

[0059] In the formula, r is the radius vector, and p is the support force acting on the excavation surface of the surrounding rock.

[0060] According to equations (9) and (10), the radial and tangential stress distribution of the surrounding rock varies with the radius r. The method of integrating first and then taking the average is used to obtain the tangential and radial comprehensive stress of the surrounding rock within the self-stabilizing height h′. and have:

[0061]

[0062] Then, formula (6) to formula (12) are combined to obtain:

[0063]

[0064]

[0065] Where: L is the collapse depth, V is the collapse volume Figure 2 The shaded part in the figure, R represents the radius of the cavern before excavation, and It is the combined tangential and radial stress of the surrounding rock within the self-stabilizing height h′.

[0066] Substituting equations (11) and (12) into equation (13), we get an equation with the self-stabilizing height h′ as the only unknown. The self-stabilizing height h′ can be obtained by using the iterative method, and then substituted into equations (14) and (15) to obtain the collapse depth L and collapse volume V considering the stress redistribution of the surrounding rock after excavation unloading.

[0067] The following is an explanation using a water diversion tunnel of a water diversion project as an example, hereinafter referred to as Project A. It passes through a fault fracture zone. The structural rock in the fault zone is block rock and broken rock. The tunnel section is buried at a depth of about 750m. The initial geostress field analysis results of similar tunnel sections show that the horizontal lateral pressure coefficient of this tunnel section is close to 1.0. The top arch has long and steeply inclined cracks. The crack surface is generally rough and undulating. After excavation and unloading, it is mostly open and filled with 0.2-1cm mud. The rock mass on the upper plate of the fault zone is relatively broken to broken, and the overall structure is broken to thin layered. During the excavation construction process, the top arch continued to fall off, smashing two steel arch frames and extending in front of the heading face. Finally, a collapse cavity with an arc length of about 6.5m, an extension of 3.2m along the tunnel axis, and a depth of about 3m was formed in the arch. Figure 5 shown.

[0068] According to the on-site investigation and preliminary survey and design data, the excavation of this tunnel section revealed that the surrounding rock has been a fault fracture zone tunnel section, and obvious fault compression was found at the interface between the fault zone and the upper and lower plate strata, resulting in a certain thickness of crushed powder rock distribution in some areas. At the same time, the excavation revealed that the rock mass on the upper plate of the fault was broken, and the rock mass structure was fragmented-thin layered. Due to the poor integrity of the rock mass in the fault zone, once the air-facing surface is formed after excavation, under the action of gravity, the arch surrounding rock has no self-stabilizing ability, and due to the insufficient initial support strength and the lack of other effective support measures, it immediately loosens and deforms significantly, and further induces the collapse and instability of the surrounding rock, resulting in deformation and collapse of the surrounding rock.

[0069] According to the design data and engineering geological conditions, the tunnel radius is 5m and the surrounding rock density of the fault zone is 21kN / m 3 , cohesion 0.1MPa, internal friction angle about 18°. Substituting the above parameters into equations (11) to (13), and solving them by iteration method, the depth of the collapse cavity can be calculated to be 3.2m. Then, the self-stabilizing height is calculated to be 4.63m and the single-width collapse volume is 20.74m by equations (14) and (15). 3 The radial and tangential comprehensive stresses of the surrounding rock within the self-stabilizing height can be calculated by equations (14) and (15) to be 0.39 MPa and 0.99 MPa. The calculation results are shown in Figure 6As shown in the figure, when the redistribution of stress caused by surrounding rock excavation is not considered, the collapse depth of the arch reaches 7.83m; after considering the influence of surrounding rock stress redistribution, the collapse depth is reduced to 3.2m, which is very close to the actual collapse depth of 3m, indicating that this method can more accurately predict the range of surrounding rock collapse. Therefore, it can be determined that the surrounding rock support force within a single width should be no less than 435.5kN. It can be seen that if the redistribution of surrounding rock stress caused by cavern excavation is not considered, the required surrounding rock support force will increase significantly, which will significantly increase the support cost and reduce the economic efficiency of engineering measures.

[0070] In summary, the method of the embodiment of the present invention is based on the assumption of a triangular collapse arch, the concept of self-stabilizing height is introduced, and the analytical solution of the radial and tangential stress distribution of the surrounding rock is used to derive the collapse cavity depth and collapse volume formula considering the influence of the surrounding rock unloading stress redistribution, and then the self-stabilizing height is obtained. Case analysis shows that the proposed formula can more accurately predict the collapse cavity depth of the surrounding rock of the cavern top arch, determine the surrounding rock support force, and provide a reasonable dynamic design basis for the construction of tunnels crossing the fault fracture zone.

[0071] 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.

[0072] 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 collapse depth of the arch surrounding rock taking into account the redistribution of excavation unloading stress, characterized in that: The following steps are involved: Step S1: using the triangle formula to calculate the height of the collapsed arch before excavation; Step S2: Collecting the tunnel radius, surrounding rock bulk density, cohesion and internal friction angle; Step S3: After excavation, force decomposition and stress redistribution analysis are performed to obtain the collapse depth of the top arch surrounding rock.

2. The method for calculating the collapse depth of the top arch surrounding rock taking into account the redistribution of excavation unloading stress according to claim 1, characterized in that: Step S3 includes: Step S31: Perform force analysis on the semi-detached body and construct a vertical equilibrium equation; Step S32: taking the self-stabilizing height as an unknown variable, and using the tangential stress and radial stress after the cavern excavation to analyze each force in the equilibrium equation, to obtain an expression for the self-stabilizing height; Step S33: The tangential comprehensive stress and radial comprehensive stress after excavation are obtained by integrating first and then taking the average, and the iterative method is used to solve them to obtain the self-stabilizing height and thus calculate the collapse depth.

3. The method for calculating the collapse depth of the top arch surrounding rock taking into account the redistribution of excavation unloading stress according to claim 2, characterized in that: The expression of the equilibrium equation in step S31 is: 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, and G is the deadweight of the rock mass within the self-stabilizing height.

4. The method for calculating the collapse depth of the arch surrounding rock taking into account the redistribution of excavation unloading stress according to claim 3 is characterized in that: In step S32, the surrounding rock friction force F1 exerted on the detached body within the self-stabilizing height is analyzed as: Where h′ represents the collapse depth, σ θ and σ r are the tangential stress and radial stress after excavation, c is the rock mass cohesion, is the friction angle within the rock mass.

5. The method for calculating the collapse depth of the top arch surrounding rock taking into account the redistribution of excavation unloading stress according to claim 4, characterized in that: In step S32, the surrounding rock pressure F2 of the detached body surrounding rock within the self-stabilizing height is analyzed as follows:

6. The method for calculating the collapse depth of the arch surrounding rock taking into account the redistribution of excavation unloading stress according to claim 5, characterized in that: In step S32, the deadweight G of the rock mass within the self-stabilizing height is analyzed as: Where γ is the rock mass bulk density.

7. The method for calculating the collapse depth of the arch surrounding rock taking into account the redistribution of excavation unloading stress according to claim 6, characterized in that: Tangential stress σ θ and radial stress σ r The expression is: Where r is the radius vector and p is the support force acting on the excavation surface of surrounding rock.

8. The method for calculating the collapse depth of the top arch surrounding rock taking into account the redistribution of excavation unloading stress according to claim 7, characterized in that: The expressions of the self-stabilizing height h' and the collapse depth L are: Where R is the radius of the cavern before excavation. and It is the combined tangential and radial stress of the surrounding rock within the self-stabilizing height h′.

9. The method for calculating the collapse depth of the arch surrounding rock taking into account the redistribution of excavation unloading stress according to claim 8, characterized in that: Comprehensive value of tangential stress after excavation The combined value of radial stress The expression is: Where h represents the collapse depth of the arch top before excavation.

10. A method for calculating the collapse depth of the arch surrounding rock taking into account the redistribution of excavation unloading stress according to claim 9, characterized in that: The collapse volume V can also be calculated using the following formula:

Images