Quantitative characterization method and device for underground cavern excavation surrounding rock damage failure stress driving

Abstract

The invention discloses a quantitative characterization method and device for underground cavern excavation surrounding rock damage failure stress driving, and belongs to the technical field of rock mechanics and underground engineering. The method comprises the steps of firstly calculating first principal stress and third principal stress distribution of cavern surrounding rock based on an elastic theory; furthermore, a stress driving index (SDI) is innovatively defined to quantify the driving effect of stress on damage, and a relative shear strength index (RSSI) is defined to represent the shear strength of the rock mass. Curves of SDI and RSSI changing along with the distance are drawn in the same coordinate system, the intersection point A of the two curves serves as a critical judgment point, the area between the point A and the free face of the cavern is a damage area with the stress driving effect exceeding the rock mass strength, and the point A is a stable area with the depth. The method is clear in concept and easy and convenient to calculate, the surrounding rock damage range can be rapidly and quantitatively determined without complex numerical simulation, and an efficient and reliable theoretical tool is provided for stability evaluation and support design of underground engineering.

Description

Technical Field

[0001] This invention relates to the fields of rock mechanics and underground engineering, and in particular to a method and apparatus for quantitatively characterizing the extent of damage to surrounding rock after excavation of underground caverns. Background Technology

[0002] After the excavation of underground caverns (such as tunnels, roadways, and underground storage facilities), the original stress equilibrium is disrupted, leading to a redistribution of stress in the surrounding rock and the formation of a certain range of damaged zones around the cavern, namely plastic zones or loosened zones. Accurately predicting and quantitatively characterizing the extent of this damaged zone is of paramount importance for evaluating cavern stability, optimizing support design, and ensuring construction safety.

[0003] Currently, there are three main types of methods for characterizing the damaged zone of surrounding rock: First, field measurement methods, such as borehole photography and sonic testing. These methods provide intuitive results but are costly, time-consuming, and have a time lag, making them unsuitable for early design and prediction. Second, numerical simulation methods, such as finite element method and discrete element method. These methods can consider complex geological conditions, but the calculation process is complex, model establishment relies on experience, and the accuracy of the results is affected by various parameters. Third, theoretical analytical methods, such as formulas for calculating the radius of the plastic zone based on the Mohr-Coulomb or Hawke-Brown strength criteria. These methods are simple and quick, but traditional formulas are usually based on a single strength criterion and fail to clearly reveal the "driving" mechanism of stress on damage. Furthermore, they have poor applicability to non-circular caverns.

[0004] Therefore, there is an urgent need in this field for a new method that is conceptually clear, computationally simple, physically meaningful, and applicable to the quantitative characterization of surrounding rock damage and failure in caverns with different cross-sectional shapes. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a method and apparatus for quantitative characterization of surrounding rock damage and failure in underground cavern excavation based on the stress-driven concept. This method, by introducing a "stress-driven index" and a "relative shear strength index," intuitively reveals the mechanical mechanism of surrounding rock damage and quickly and accurately determines the extent of the damage zone.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A quantitative characterization method for stress-driven damage and failure of surrounding rock during underground cavern excavation includes the following steps:

[0008] Step 1: Obtain engineering geological parameters, including the uniaxial compressive strength of the rock mass. The equivalent radius R of the cavern and the initial stress in the far field. and ;

[0009] Step 2: Based on the theory of elasticity and the equivalent radius R of the cavity and the initial stress in the far field obtained in Step 1. and Calculate the first principal stress σ1(r) and the third principal stress σ3(r) at different locations in the surrounding rock;

[0010] Step 3: Based on σ1(r) calculated in Step 2 and the uniaxial compressive strength of the rock mass obtained in Step 1... Calculate the stress driving index (SDI) at different locations in the surrounding rock;

[0011] Step 4: Based on the σ3(r) calculated in Step 2 and the uniaxial compressive strength of the rock mass obtained in Step 1... Calculate the relative shear strength index (RSSI) at different locations in the surrounding rock;

[0012] Step 5: Plot the curves of the stress driving index SDI and the relative shear strength index RSSI obtained in Step 3 and Step 4 as a function of distance r in the same coordinate system, and determine the intersection point A of the two curves; take point A as the critical point, and determine the area between point A and the free face of the cavern as the damaged zone, and the area from point A into the depth of the surrounding rock as the undamaged zone.

[0013] Furthermore, in step 2, for a circular cross-section cavity, the first principal stress σ1(r) and the third principal stress σ3(r) are calculated using the following formulas:

[0014] (1+ );

[0015] (1- );

[0016] Where r is the distance from a point in the surrounding rock to the center of the cavern.

[0017] Furthermore, in step 1, for non-circular cross-section caverns, the equivalent radius is calculated using the principle of area equivalence:

[0018] ;

[0019] Where A is the cross-sectional excavation area of ​​the non-circular cavern.

[0020] Furthermore, the formula for calculating the stress-driven index SDI in step 3 is as follows:

[0021] .

[0022] Furthermore, the formula for calculating the relative shear strength index (RSSI) in step 4 is as follows:

[0023] ;

[0024] in , It is used to characterize the relative shear strength of rock mass under this stress state.

[0025] A device for analyzing damage and failure of surrounding rock in underground caverns includes:

[0026] The parameter acquisition module is used to acquire engineering geological parameters, including the uniaxial compressive strength of the rock mass. The equivalent radius R of the cavern and the initial stress in the far field. and ;

[0027] The stress calculation module is used to calculate the equivalent radius R of the chamber and the initial stress in the far field based on elasticity theory and the parameter acquisition module. and Calculate the first principal stress σ1(r) and the third principal stress σ3(r) at different locations in the surrounding rock;

[0028] The SDI calculation module is used to calculate σ1(r) from the stress calculation module and the uniaxial compressive strength of the rock mass obtained from the parameter acquisition module. Calculate the stress driving index (SDI) at different locations in the surrounding rock;

[0029] The RSSI calculation module is used to calculate σ3(r) based on step 2 and the uniaxial compressive strength of the rock mass obtained by the parameter acquisition module. Calculate the relative shear strength index (RSSI) at different locations in the surrounding rock;

[0030] The damage zone determination module is used to plot the curves of the stress driving index SDI and the relative shear strength index RSSI obtained in steps 3 and 4 as a function of distance r in the same coordinate system, and determine the intersection point A of the two curves; taking point A as the critical point, the area between point A and the free surface of the cavern is determined as the damage zone, and the area from point A into the depth of the surrounding rock is determined as the undamaged zone.

[0031] Furthermore, the stress calculation module, for a circular cross-section cavity, uses the following formula to calculate the first principal stress σ1(r) and the third principal stress σ3(r):

[0032] (1+ );

[0033] (1- );

[0034] Where r is the distance from a point in the surrounding rock to the center of the cavern.

[0035] Furthermore, the parameter acquisition module calculates the equivalent radius for non-circular cross-section caverns using the principle of area equivalence:

[0036] ;

[0037] Where A is the cross-sectional excavation area of ​​the non-circular cavern.

[0038] Furthermore, the formula for calculating the stress-driven index SDI by the SDI calculation module is as follows:

[0039] .

[0040] Furthermore, the formula for calculating the relative shear strength index (RSSI) by the RSSI calculation module is as follows:

[0041] ;

[0042] in , It is used to characterize the relative shear strength of rock mass under this stress state.

[0043] The beneficial effects of this invention are reflected in the following aspects:

[0044] (1) The concept is novel and the mechanism is clear. By introducing the "stress-driven index" and the "relative shear strength index", the complex rock mass damage problem is transformed into a comparison of two intuitive mechanical indicators, which profoundly reveals the stress-driven nature of surrounding rock damage.

[0045] (2) The calculation is simple and the application is very practical. This method is mainly based on analytical formulas and does not require complex numerical simulation software. It is fast and very suitable for rapid evaluation and preliminary design in engineering sites.

[0046] (3) Wide applicability. By applying the principle of area equivalence, the method can be conveniently applied to various non-circular cross-section caverns, breaking through the limitations of traditional analytical methods on cross-sectional shape.

[0047] (4) The results are clear. By graphically displaying two exponential curves, the extent of the damage area is clearly visible, making it easy for engineering technicians to understand and apply. Attached Figure Description

[0048] Figure 1 This is a flowchart illustrating a quantitative characterization method for stress-driven damage and failure of surrounding rock during underground cavern excavation, according to an embodiment of the present invention.

[0049] Figure 2 This is a schematic diagram of the stress distribution in the surrounding rock of a circular cavern.

[0050] Figure 3This is a graph showing the stress-driven index (SDI) and relative shear strength index (RSSI) as a function of distance r in an embodiment of the present invention, where the intersection point A determines the extent of the damage zone. Detailed Implementation

[0051] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, 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 scope of protection of the present invention.

[0052] Please see Figure 1 This invention provides a quantitative characterization method for stress-driven damage and failure of surrounding rock during underground cavern excavation, comprising the following steps:

[0053] Step 1: Quantitative calculation of stress distribution in surrounding rock.

[0054] Obtain basic engineering geological and design parameters: uniaxial compressive strength of rock mass Equivalent radius R of the cavern, initial stress and ;

[0055] Calculation of the first principal stress of the surrounding rock of the cavern based on elasticity theory With the third principal stress For a circular cross-section cavern (as shown in Figure 2), the stress at any point in the surrounding rock is calculated using the Kirch solution in elasticity, according to the following formula:

[0056] (1+ );

[0057] (1- );

[0058] Where r is the distance from a point in the surrounding rock to the center of the cavern.

[0059] For non-circular cross-section caverns (such as city gate-shaped or rectangular caverns), the principle of area equivalence is applied, and they are calculated as equivalent to circular caverns. The formula for calculating the equivalent radius is: , where A is the actual cross-sectional excavation area of ​​the cavern.

[0060] Step 2: Calculate the Stress Driven Index (SDI). To quantitatively characterize the driving effect of surrounding rock stress on damage and failure, the Stress Driven Index (SDI) is defined, and its calculation formula is as follows:

[0061]

[0062] The physical meaning of this index is: the first principal stress. (Typically the maximum principal stress) and the uniaxial compressive strength of rock The ratio of SDI to rock density. The larger the SDI value, the stronger the stress-driven effect on rock compression failure.

[0063] Step 3: Calculate the Relative Shear Strength Index (RSSI)

[0064] To characterize the shear failure resistance of rock mass under specific stress states, the Relative Shear Strength Index (RSSI) is defined, and its calculation formula is as follows:

[0065] This formula originates from the basic idea of ​​the Mohr-Coulomb strength theory and reflects the third principal stress. (Usually the minimum principal stress) for rock mass shear strength The strengthening effect. In the formula, "1" represents the benchmark value of the relative shear strength of the rock under no confining pressure.

[0066] Step 4: Determine the extent of damage to the surrounding rock.

[0067] In the same graph, two curves are plotted with distance r on the x-axis and the values ​​of SDI and RSSI on the y-axis. The SDI curve typically starts from its maximum value at the cavern wall (r=R), gradually decreasing and approaching 0 as r increases. The RSSI curve starts from its minimum value (usually 1) at the cavern wall (r=R), gradually increasing and approaching ( ). The two curves must intersect at a point, denoted as point A.

[0068] Mechanical Interpretation and Damage Zone Determination: At point A, SDI = RSSI, meaning that the stress-driven force and the shear strength of the rock mass have reached a critical equilibrium. In the region from point A to the free face of the cavern, SDI > RSSI, indicating that the stress-driven force exceeds the shear strength of the rock mass, and the rock mass in this region will yield or fail, which is the damage zone quantitatively characterized by this invention. In the direction from point A towards the depth of the surrounding rock, SDI < RSSI, indicating that the rock mass strength is sufficient to resist the stress-driven force, and the rock mass in this region is in an elastically stable state, which is the undamaged zone. Therefore, the radial coordinate of point A is the boundary of the damage zone.

[0069] Implementation Case: Taking a circular cavern project as an example, the basic parameters are as follows:

[0070] Far-field initial stress

[0071] Uniaxial compressive strength of rock

[0072] tunnel radius

[0073] Triaxial test friction angle

[0074] Step 1. Stress distribution calculation:

[0075] Select a calculation range from r = 5m to r = 20m, and use the formula to calculate the values ​​at each point. and For example, at r=5m:

[0076] Step 2. Calculate SDI:

[0077] At r=5m, Calculate the SDI corresponding to a series of r values ​​accordingly.

[0078] Step 3. Calculate RSSI:

[0079] At r=5m, .

[0080] Calculate the RSSI corresponding to a series of r values ​​in this way.

[0081] Step 4. Determine the extent of the damage / collapse zone:

[0082] Plot the curves of SDI and RSSI as a function of r. For example... Figure 3 As shown, assume the two curves are in The two points intersect at point A. Therefore, the annular area from the tunnel wall (r=5m) to r=7.5m is determined to be the damage zone caused by this excavation, with a thickness of 2.5m. This area should be given priority consideration in the support design.

[0083] The beneficial effects of this invention are specifically reflected in the following aspects:

[0084] 1. Clear Mechanism, Intuitive Judgment: By innovatively defining the "Stress Driven Index (SDI)" and the "Relative Shear Strength Index (RSSI)," the complex problem of surrounding rock damage is transformed into a comparison and intersection judgment of two mechanical indicators with clear physical meaning (intersection point A). This profoundly reveals the essential mechanism that damage is "stress-driven" rather than "rock mass resistance," making the criteria for judging the damage zone intuitive and clear.

[0085] 2. High computational efficiency and strong practicality: The core steps of the method (stress calculation, SDI / RSSI calculation, and plotting judgment) are all based on analytical formulas, eliminating the need for complex and time-consuming numerical simulation software and modeling processes. This makes it particularly suitable for early-stage engineering design, rapid on-site assessment, and preliminary stability evaluation, significantly improving efficiency.

[0086] 3. Wide applicability and breakthrough in shape limitations: By introducing the "area equivalence principle" to treat non-circular caverns as equivalent to circular ones, the analytical method based on the elastic stress solution of circular caverns can be flexibly applied to caverns with various cross-sectional shapes (such as city gate-shaped and rectangular ones), thus expanding the scope of engineering applications of the method.

[0087] 4. Quantitative results with strong guidance: The method ultimately provides a quantitative graphical representation of the boundary of the damaged area (radial coordinates of intersection point A). The results are clear, directly indicating the extent and thickness of the damaged area, and providing a clear quantitative basis for key areas of support design.

[0088] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A quantitative characterization method for stress-driven damage and failure of surrounding rock during underground cavern excavation, characterized in that, Includes the following steps: Step 1: Obtain engineering geological parameters, including the uniaxial compressive strength of the rock mass. The equivalent radius R of the cavern and the initial stress in the far field. and ; Step 2: Based on the theory of elasticity and the equivalent radius R of the chamber and the initial stress in the far field obtained in Step 1. and Calculate the first principal stress σ1(r) and the third principal stress σ3(r) at different locations in the surrounding rock; Step 3: Based on σ1(r) calculated in Step 2 and the uniaxial compressive strength of the rock mass obtained in Step 1... Calculate the stress driving index (SDI) at different locations in the surrounding rock; Step 4: Based on the σ3(r) calculated in Step 2 and the uniaxial compressive strength of the rock mass obtained in Step 1... Calculate the relative shear strength index (RSSI) at different locations in the surrounding rock; Step 5: Plot the curves of the stress driving index SDI and the relative shear strength index RSSI obtained in Step 3 and Step 4 as a function of distance r in the same coordinate system, and determine the intersection point A of the two curves; Using point A as the critical point, the area between point A and the free face of the cavern is defined as the damaged zone, and the area from point A into the depth of the surrounding rock is defined as the undamaged zone.

2. The method according to claim 1, characterized in that, In step 2, for a circular cross-section cavity, the first principal stress σ1(r) and the third principal stress σ3(r) are calculated using the following formulas: （1+ ）； （1- ）； Where r is the distance from a point in the surrounding rock to the center of the cavern.

3. The method according to claim 1, characterized in that, In step 1, for non-circular cross-section caverns, the equivalent radius is calculated using the principle of area equivalence: ； Where A is the cross-sectional excavation area of ​​the non-circular cavern.

4. The method according to claim 1, characterized in that, The formula for calculating the stress-driven index (SDI) in step 3 is as follows: 。 5. The method according to claim 1, characterized in that, The formula for calculating the relative shear strength index (RSSI) in step 4 is as follows: ； in , It is used to characterize the relative shear strength of rock mass under this stress state.

6. A device for analyzing damage and failure of surrounding rock in underground caverns, characterized in that, include: The parameter acquisition module is used to acquire engineering geological parameters, including the uniaxial compressive strength of the rock mass. The equivalent radius R of the cavern and the initial stress in the far field. and ; The stress calculation module is used to calculate the equivalent radius R of the chamber and the initial stress in the far field based on elasticity theory and the parameter acquisition module. and Calculate the first principal stress σ1(r) and the third principal stress σ3(r) at different locations in the surrounding rock; The SDI calculation module is used to calculate σ1(r) from the stress calculation module and the uniaxial compressive strength of the rock mass obtained from the parameter acquisition module. Calculate the stress driving index (SDI) at different locations in the surrounding rock; The RSSI calculation module is used to calculate σ3(r) based on step 2 and the uniaxial compressive strength of the rock mass obtained by the parameter acquisition module. Calculate the relative shear strength index (RSSI) at different locations in the surrounding rock; The damage zone determination module is used to plot the curves of the stress driving index SDI and the relative shear strength index RSSI obtained in steps 3 and 4 as a function of distance r in the same coordinate system, and to determine the intersection point A of the two curves. Using point A as the critical point, the area between point A and the free face of the cavern is defined as the damaged zone, and the area from point A into the depth of the surrounding rock is defined as the undamaged zone.

7. The apparatus according to claim 6, characterized in that, The stress calculation module calculates the first principal stress σ1(r) and the third principal stress σ3(r) for a circular cross-section cavity using the following formula: （1+ ）； （1- ）； Where r is the distance from a point in the surrounding rock to the center of the cavern.

8. The apparatus according to claim 6, characterized in that, The parameter acquisition module calculates the equivalent radius for non-circular cross-section caverns using the principle of area equivalence. ； Where A is the cross-sectional excavation area of ​​the non-circular cavern.

9. The apparatus according to claim 6, characterized in that, The formula for calculating the stress-driven index SDI by the SDI calculation module is as follows: 。 10. The apparatus according to claim 6, characterized in that, The formula for calculating the relative shear strength index (RSSI) by the RSSI calculation module is as follows: ； in , It is used to characterize the relative shear strength of rock mass under this stress state.

Images