Calculation method of crown rock collapse depth considering excavation unloading stress redistribution

Abstract

The application provides a calculation method of a crown arch surrounding rock collapse depth considering excavation unloading stress redistribution, comprising the following steps: step S1: a triangular formula is used to calculate the collapse arch height before excavation; step S2: a tunnel radius, surrounding rock bulk density, cohesive force and internal friction angle are collected; step S3: stress decomposition and stress redistribution analysis are carried out after excavation, and the crown arch surrounding rock collapse depth is obtained. The crown arch surrounding rock collapse cavity depth of the tunnel can be more accurately predicted, the surrounding rock support force is determined, and a reasonable dynamic design basis is provided for the tunnel construction through a fault fracture zone.

Description

Technical Field

[0001] This invention relates to the field of tunnel engineering construction technology, specifically to a method for calculating the collapse depth of the surrounding rock of the arch considering the redistribution of excavation unloading stress. Background Technology

[0002] Constructing water conveyance tunnels for water diversion projects is a crucial means of optimizing water resource allocation. These tunnels are long and deep, inevitably traversing sections with challenging geological conditions, including fault fracture zones and soft rock. During construction, they are prone to geological disasters such as surrounding rock collapse and large deformations of soft rock. Employing advanced pipe roofing and small-diameter pipe supports can effectively prevent deformation and collapse of the surrounding rock at the tunnel arch. However, in actual construction, arch deformation and collapse still occur due to insufficient support strength or untimely support. Therefore, studying the stability of the tunnel arch in weak and fractured strata, analyzing the arch effect of the surrounding rock, and proposing appropriate support measures have always been key concerns in hydraulic rock engineering.

[0003] Existing technologies typically employ numerical methods, model tests, and physical tests. Numerical methods quantify the influence of lithology, geostress, and rock mass joints on the location and shape of the pressure arch. Model tests investigate the sand arching effect on the top arch of shield tunnels. Physical tests study the correlation between the failure depth of the surrounding rock in ultra-large cross-section tunnels and the range of the arching effect.

[0004] However, all of the above methods require model building and experimentation, which are slow and costly in the analysis process, and pose corresponding implementation difficulties for engineering applications. Summary of the Invention

[0005] This invention proposes a method for calculating the collapse depth of the surrounding rock of the arch considering the redistribution of excavation unloading stress, in order to solve the technical problems of slow speed, high cost and difficult implementation of the existing technology.

[0006] To address the aforementioned technical problems, this invention provides a method for calculating the collapse depth of the surrounding rock of the arch considering the redistribution of excavation unloading stress, comprising the following steps:

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

[0008] Step S2: Collect tunnel radius, surrounding rock unit weight, cohesion, and internal friction angle;

[0009] Step S3: After excavation, perform stress decomposition and stress redistribution analysis to determine the collapse depth of the surrounding rock of the arch.

[0010] Preferably, step S3 includes:

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

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

[0013] Step S33: The tangential and radial stresses after excavation are obtained by integrating and then taking the mean value. The self-stabilizing height is obtained by using the iterative method to calculate the collapse depth.

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

[0015]

[0016] In the formula, F1 is the frictional force of the surrounding rock on the detached body within the self-stabilizing height, F2 is the pressure of the surrounding rock on the detached body within the self-stabilizing height, and G is the self-weight of the rock mass within the self-stabilizing height.

[0017] Preferably, in step S32, the surrounding rock friction force F1 experienced by the detached body within the self-stabilizing height is analyzed as follows:

[0018]

[0019] In the formula, h′ represents the collapse depth, σ θ and σ r These represent the tangential and radial stresses after excavation, respectively, where c is the rock mass cohesion. The friction angle within the rock mass is denoted as .

[0020] Preferably, in step S32, the surrounding rock pressure F2 of the detached body within the self-stabilizing height is analyzed as follows:

[0021]

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

[0023]

[0024] In the formula, γ is the unit weight of the rock mass.

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

[0026]

[0027] In the formula, r is the radius vector and p is the support force acting on the excavation face of the surrounding rock.

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

[0029]

[0030] In the formula, R represents the radius of the tunnel before excavation. and The stress is the combined tangential and radial stress of the surrounding rock within the self-stabilizing height h′.

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

[0032]

[0033] In the formula, h represents the collapse depth of the arch top before excavation.

[0034] Preferably, the collapse volume V can also be obtained using the following formula:

[0035]

[0036] The beneficial effects of this invention include at least the following: as a method parallel to numerical simulation and physical simulation, the method of this invention has the advantages of fast analysis speed, low cost, and ease of engineering application. Based on a systematic review of the arch effect in underground caverns, this 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 projects, accurately deriving the collapse depth. This provides a simple and reliable analytical approach for the arch support design of tunnels in weak surrounding rock. Attached Figure Description

[0037] Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention;

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

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

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

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

[0042] Figure 6 This is a schematic diagram showing the solution results of the top arch collapse depth in an embodiment of the present invention. Detailed Implementation

[0043] 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.

[0044] The surrounding rock of the tunnel arch can loosen under excavation disturbance, leading to collapse of the rock mass within a certain range without support. Simultaneously, the unloading during deep tunnel excavation causes stress redistribution in the surrounding rock, creating a secondary stress field that acts as a clamping force on the arch surrounding rock. This force can resist the self-weight load within a certain range, preventing an increase in collapse height. Therefore, within the collapse arch range, there exists a critical height where the rock mass within this height range is in a critical equilibrium under the clamping force of self-weight and surrounding rock stress. Based on the foregoing analysis, existing formulas for predicting collapse arch height rarely consider the influence of the secondary stress field of the surrounding rock. Therefore, this invention provides a method for calculating the collapse depth of the arch surrounding rock considering the stress redistribution during excavation unloading, and a method for calculating the tunnel collapse depth considering the influence of stress redistribution during excavation unloading, such as... Figure 1 As shown, it includes the following steps:

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

[0046] like Figure 2 As shown, when the collapsed arch is triangular, H is the height of the collapsed arch calculated using the triangle formula, considering only its own weight, and h is the collapse depth at the top of the arch before excavation. The self-stabilizing height h′ and collapse depth L to be determined are also marked in the figure.

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

[0048] Step S2: Collect tunnel radius, surrounding rock unit weight, cohesion, and internal friction angle.

[0049] Step S3: After excavation, perform stress decomposition and stress redistribution analysis to determine the collapse depth of the surrounding rock of the arch.

[0050] Specifically, such as Figure 3 As shown, a force analysis is performed on the semi-detached body, and the equilibrium equation in the vertical direction is:

[0051]

[0052] In the formula, F1 is the frictional force of the surrounding rock on the detached body within the self-stabilizing height, F2 is the pressure of the surrounding rock on the detached body within the self-stabilizing height, and G is the self-weight 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 excavation of the tunnel are used to analyze each force in the equilibrium equation, and the results are obtained respectively.

[0054]

[0055]

[0056] In the formula, c represents the cohesion of the rock mass. γ is the internal friction angle of the rock mass (in radians), γ is the unit weight of the rock mass, and σ is the internal friction angle of the rock mass. θ and σ r These represent the tangential stress and radial stress after the excavation of the tunnel.

[0057] A secondary stress field analysis was conducted. After the excavation of the deep-buried tunnel, a secondary stress field was formed around the tunnel chamber due to the unloading effect of the surrounding rock. Based on the MC rock strength criterion and combined with elastoplastic mechanics analysis, the secondary stress distribution diagram after the excavation of the circular tunnel chamber 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 face of the surrounding rock.

[0060] According to equations (9) and (10), the radial and tangential stress distributions of the surrounding rock vary with the radius r. The combined tangential and radial stresses of the surrounding rock within the self-stabilizing height h′ are obtained by first integrating and then taking the average. and have:

[0061]

[0062] Then, by combining equations (6) to (12), we obtain:

[0063]

[0064]

[0065] In the formula: L is the collapse depth, and V is the collapse volume. Figure 2 The shaded area in the diagram, R represents the radius of the cavern before excavation. and The stress 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 obtain an equation with the self-stabilizing height h′ as the only unknown. Solving by iterative method, we can obtain the self-stabilizing height h′, and then substitute it 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 and unloading.

[0067] The following explanation uses a water conveyance tunnel of a water diversion project as an example, hereinafter referred to as Project A. It traverses a fault fracture zone, where the tectonic rock consists of fragmented and fractured rock. The tunnel section is approximately 750m deep. Initial geostress field analysis of similar tunnel sections indicates that the horizontal lateral pressure coefficient of this section is close to 1.0. The crown arch has steeply angled, long fissures, with generally rough and uneven surfaces. After excavation and unloading, these fissures often open up and are mostly filled with 0.2–1cm of clay. The hanging wall rock mass of the fault zone is relatively fractured to broken, generally exhibiting a fractured to thin-layered structure. During excavation, continuous rockfalls occurred in the crown arch, damaging two steel arch frames and extending towards the tunnel face. Ultimately, a cavity with an arc length of approximately 6.5m, extending 3.2m along the tunnel axis, and a depth of approximately 3m was formed in the arch. Figure 5 As shown.

[0068] Based on on-site investigation and preliminary survey and design data, the excavation of this tunnel section revealed that the surrounding rock was within a fault fracture zone. Significant fault compression was observed at the interface between the fault zone and the hanging wall and footwall strata, resulting in a localized distribution of siltstone of considerable thickness. Simultaneously, the excavation revealed that the hanging wall rock mass was fractured, with a fragmented-thin-layer structure. Due to the poor integrity of the rock mass within the fault zone, once an open face is formed after excavation, the surrounding rock at the top of the arch lacks self-stabilizing capacity under gravity. Furthermore, due to insufficient initial support strength and a lack of other effective support measures, significant loosening and deformation occur immediately, further inducing surrounding rock collapse and instability, leading to deformation and collapse failure of the surrounding rock.

[0069] Based on design data and engineering geological conditions, the tunnel radius is 5m, and the unit weight of the surrounding rock in the fault zone is 21kN / m³. 3 The cohesion is 0.1 MPa, and the internal friction angle is approximately 18°. Substituting these parameters into equations (11) to (13) and using an iterative method, the collapse cavity depth can be calculated to be 3.2 m. Subsequently, the self-stabilizing height of 4.63 m and the unit width collapse volume of 20.74 m³ are calculated using equations (14) and (15). 3 The combined radial and tangential stresses of the surrounding rock within the self-stabilizing height can be calculated as 0.39 MPa and 0.99 MPa using equations (14) and (15), respectively. The calculation results are as follows: Figure 6As shown, without considering the stress redistribution during excavation, the collapse depth of the crown arch reaches 7.83m. After considering the stress redistribution, the collapse depth decreases to 3.2m, very close to the actual collapse depth of 3m, indicating that this method can more accurately predict the collapse range. Therefore, the required support force per unit width should be no less than 435.5kN. It is evident that without considering the stress redistribution during excavation, the required support force will significantly increase, leading to higher support costs and reduced economic efficiency of the engineering measures.

[0070] In summary, by employing the method of this invention, based on the triangular collapse arch assumption and introducing the concept of self-stabilizing height, and using analytical solutions of the radial and tangential stress distribution of the surrounding rock, formulas for the collapse cavity depth and collapse volume considering the influence of the redistribution of unloading stress in the surrounding rock can be derived, thereby obtaining the self-stabilizing height. Case studies show that the proposed formula can more accurately predict the collapse cavity depth of the surrounding rock in the tunnel arch and determine the surrounding rock support force, providing a reasonable dynamic design basis for tunnel construction traversing fault fracture zones.

[0071] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described; only preferred embodiments of the present invention are illustrated. The descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the present invention. As long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification.

[0072] It should be noted that those skilled in the art can make various modifications and improvements without departing from the inventive concept, and these all fall within the scope of protection of this invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A method for calculating the depth of crown rock collapse considering the redistribution of unloading stress during excavation, characterized in that: The method comprises the following steps: Step S1: the height of the collapse arch before excavation is calculated by using a triangular formula; Step S2: the tunnel radius, the surrounding rock bulk density, the cohesion and the internal friction angle are collected; Step S3: stress decomposition and stress redistribution analysis are carried out after excavation, and the collapse depth of the top arch surrounding rock is obtained; Step S3 comprises: Step S31: stress analysis is carried out on the semi-detached body, and a vertical balance equation is constructed; Step S32: the self-stable height is taken as an unknown variable, and each stress in the balance equation is analyzed by using the tangential stress and the radial stress after the tunnel excavation, so that the expression of the self-stable height is obtained; Step S33: the tangential comprehensive stress and the radial comprehensive stress after excavation are obtained by using the method of first integration and then averaging, and the self-stable height is solved by using the iterative method, so that the collapse depth is calculated; The expression of the balance equation in step S31 is: ； In the formula, F1 is the friction force of the self-stable height on the semi-detached body, F2 is the surrounding rock pressure of the self-stable height on the semi-detached body, G is the self-weight of the self-stable height, φ is the internal friction angle of the rock mass; In step S32, the friction force F1 of the self-stable height on the semi-detached body is analyzed as: ； ； ； wherein represents the self-stable height, and respectively represent the tangential stress and the radial stress after excavation, and c is the rock mass cohesion. In step S32, the surrounding rock pressure F2 of the self-stable height on the semi-detached body is analyzed as: ； In step S32, the self-weight G of the self-stable height on the semi-detached body is analyzed as: ； In the formula, γ is the bulk density of the rock mass; tangential stress and radial stress The expression for the tangential stress ； ； ； ； In the formula, r is the vector radius, p is the supporting force acting on the surrounding rock excavation surface, and R represents the radius of the tunnel before excavation; the self-stable height and the expression of the collapse depth L is: ； ； wherein and is the self-stabilizing height the tangential and radial combined stresses of the surrounding rock within the range The integrated value of tangential stress after excavation The integrated value of radial stress The expression is: ； ； In the formula, h represents the collapse depth of the arch top part before excavation.

2. The method according to claim 1, wherein the method is characterized in that: The collapse volume V can also be obtained by the following formula: 。

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