A method for predicting the stability of a rock slope with a trailing edge crack under the action of blasting excavation

Abstract

The application provides a method for predicting the stability of a rock slope with a trailing edge crack under the action of blasting excavation, uses the fracture mechanics theory, gives a calculation formula of the stress intensity factor of the crack tip of the trailing edge of the slope under the action of blasting excavation, considers the extension length of the branch crack, constructs a mechanical model of crack extension and penetration of the rock mass of the slope, and establishes a calculation method of the stability coefficient of the slope, thereby improving the scientificity and accuracy of the calculation of the stability of the slope, and the calculation method is simple and fast, and has important engineering application value. The method comprises the following steps: step 1, generalization of a geological model; step 2, solution of the stress intensity factor of the crack tip of the trailing edge under the action of excavation unloading; step 3, solution of the stress intensity factor of the crack tip of the trailing edge under the action of blasting; step 4, solution of the stress intensity factor of the crack tip of the trailing edge under the action of blasting excavation; step 5, calculation of the extension length of the crack of the trailing edge of the slope under the action of blasting excavation; and step 6, derivation of the safety coefficient of the slope with the trailing edge crack under the action of blasting excavation.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of slope stability research, and particularly relates to a method for predicting the stability of a rock slope with a trailing edge crack under the action of blasting excavation. BACKGROUND

[0002] Under the action of external loads such as blasting excavation, a certain scale of tensile cracks will be formed on the top of the slope and the top of the local platform in the metal open-pit mine slope, which is relatively common in actual engineering. The adjustment stress and unloading disturbance caused by further rock excavation will continuously expand these tensile cracks, and then lead to sudden instability of the slope, which will cause great threat to the life and property of the surrounding personnel. The characteristics of such rock slope are that there is a near-horizontal or gently inclined slope outside structural plane (usually bedding plane or weak interlayer) in the front edge of the slope, and there is a tensile crack in the trailing edge. The area between the gently inclined structural plane in the front edge and the trailing edge crack plays a controlling role in the stability of the slope. At present, the stability of the rock slope with trailing edge crack is usually evaluated by indoor model test and numerical simulation method, such as the literature "Locking segment failure mode and evolution mechanism of three-section rock landslide. Rock and Soil Mechanics, 2018, 40(9): 1601-1609" and the literature "Anti-sliding stability of locking segment of "retaining wall buckling" landslide. Rock and Soil Mechanics, 2016, 38(9): 1734-1740". However, the numerical simulation modeling is complex, the calculation time is long, and the parameters are difficult to determine, which leads to the difficulty in engineering application, and there is a lack of theoretical research on the rock slope with trailing edge crack under the action of blasting excavation.

[0003] To solve the above problems, a simple prediction method for the stability of the rock slope with trailing edge crack under the action of blasting and excavation unloading is needed. SUMMARY

[0004] In order to solve the technical problems proposed in the background art, the present application provides a method for predicting the stability of a rock slope with trailing edge crack under the action of blasting excavation. The present application gives a formula for calculating the stress intensity factor at the tip of the trailing edge crack of the slope under the action of blasting excavation by using the theory of fracture mechanics, considers the extension length of the branch crack, constructs a mechanical model for the extension and penetration of the crack in the rock mass of the slope, and establishes a calculation method for the stability coefficient of the slope, thereby improving the scientificity and accuracy of the calculation of the stability of such slope, and the calculation method is simple and fast, which has important engineering application value.

[0005] In order to achieve the above purpose, the present application adopts the following technical scheme:

[0006] A method for predicting the stability of a rock slope with trailing edge crack under the action of blasting excavation, comprising the following steps:

[0007] Step 1: geological model generalization, establishing the slope sliding mechanics model; determining the relevant parameters, including the angle α of the rear edge crack and the horizontal direction, the angle β of the lower crack and the horizontal direction, the weight W of the sliding body, the force W of the sliding body in the direction parallel to the lower crack t , the force W of the sliding body in the direction perpendicular to the lower crack n , the tangential force W of the rear edge crack τ , the normal force W of the rear edge crack σ , γ is the bulk density of the rock mass, V is the volume of the sliding body, T is the excavation unloading tensile stress;

[0008] Step 2: solving the stress intensity factor of the rear edge crack tip under the action of excavation unloading; including:

[0009] 1) establishing the generalization model of the rear edge crack propagation of the slope, determining the relevant parameters, including the average height h of the rock mass not penetrated by the rear edge crack and the upper rock mass thereof, the vertical height z of the crack, the horizontal distance a of the sliding body gravity center to the crack tip, the vertical distance b of the sliding body gravity center to the crack tip, and the bending moment M generated by the sliding body and the unloading tensile stress to the crack tip;

[0010] 2) solving the tensile stress intensity factor, shear stress intensity factor and bending moment at the rear edge crack tip stress intensity factor K Ι1 , K Ι2 and K ΙΙ3 ;

[0011] 3) solving the I-type stress intensity factor and II-type stress intensity factor K Ι卸 and K ΙΙ卸 at the rear edge crack tip under the action of excavation unloading;

[0012] Step 3: solving the I-type stress intensity factor and II-type stress intensity factor K Ι动 (t) and K II动 (t) at the rear edge crack tip under the action of blasting;

[0013] Step 4: solving the stress intensity factor at the rear edge crack tip under the action of blasting excavation; according to the stress intensity factor superposition principle, the results of step 2 and step 3 are added to obtain the stress intensity factor at the rear edge crack tip under the action of blasting excavation;

[0014] Step 5: calculating the propagation length of the rear edge crack of the blasting excavation slope; under the action of the self-weight stress of the sliding body, the blasting load and the unloading tensile stress, the stress intensity factor K I (l) at the branch crack tip increases with the increase of the crack length, when K I (l) = K ΙC , the branch crack unstably expands; with the adjustment of the stress field in the slope rock mass, when K I (l) < KΙC When the crack stops expanding; K ΙC is the fracture toughness of the rock mass, and the length of the branching crack is l;

[0015] Step 6: Derivation of the safety factor of the slope with the trailing edge crack under the action of blasting excavation; determine the relevant parameters, including the cohesion c and the internal friction angle of the rock mass the cohesion c of the extended crack surface i and the internal friction angle the cohesion c on the lower crack surface j and the internal friction angle The weight of the sliding body W along the sliding surface is calculated using the limit equilibrium principle T and F T , W T is the component of the weight of the sliding body W along the sliding surface and perpendicular to the sliding surface, F T is the maximum shear force that the sliding surface AD can withstand under the action of gravity, then the expression of the safety factor K of the slope with the crack expansion length under the action of blasting excavation is K = F T / W T ; when K > 1, the slope is in a stable state; when K < 1, the slope is in an unstable state; when K = 1, the slope is in a limit equilibrium state.

[0016] Further, in step 1, a slope sliding mechanics model is established, as the normal stress on the excavated rock surface unloads to 0, the differential rebound deformation of the rock mass is generated, this deformation generates an excavation unloading tensile stress T pointing to the excavation surface in the slope, under the combined action of the excavation unloading tensile stress T and the self-weight stress of the sliding body, the trailing edge crack expands;

[0017] W t represents the force of the sliding body in the direction parallel to the lower crack, W n represents the force of the sliding body perpendicular to the direction of the lower crack, which is decomposed into the tangential and normal forces of the slope trailing edge crack as follows:

[0018] W t = W sin β (1)

[0019] W n = W cos β (2)

[0020] W τ = W t cos(α-β) + W n sin(α-β) (3)

[0021] W σ = W t sin(α-β) - W n cos(α-β) (4)

[0022] W = γV (5)

[0023] The solution method of the excavation unloading tensile stress T is:

[0024] The value of the excavation unloading tensile stress T is obtained by the indoor true triaxial unloading test, the field fracture sample is loaded to the original rock stress state, the lateral unloading is started, with the continuous unloading, the excavation unloading tensile stress T is constantly changed, and the formula T = σ0- σ t is obtained, wherein σ0 is the horizontal stress value at the starting unloading moment, σ t is the horizontal stress value corresponding to the fracture starting moment recorded by the high-speed photography in the test process.

[0025] Further, in the step 2, the slope rear edge fracture propagation generalization model is established, according to the stress intensity factor superposition principle, the stress intensity factor at the rear edge fracture tip under the action of the upper sliding body self-weight and the unloading tensile stress can be decomposed into the tensile stress, the shear stress and the bending moment, and the fracture tip stress intensity factors K Ι1 , K Ι2 and K ΙΙ3 are respectively:

[0026]

[0027]

[0028]

[0029] σ = W σ sinα / h + Tsinα (9)

[0030] τ = W τ sinα / h + Tcosα (10)

[0031] σ max = 6M / h 2 (11)

[0032] In the above formula, σ is the tensile stress on the fracture surface; τ is the shear stress on the fracture surface; σ max is the maximum tensile stress; M = Wa;

[0033] Therefore, the I-type stress intensity factor and the II-type stress intensity factor K Ι卸 and K ΙΙ卸 at the rear edge fracture tip of the slope under the excavation unloading condition are:

[0034]

[0035] The results of the above formula are substituted into formula (12) to obtain the I-type stress intensity factor and the II-type stress intensity factor K Ι卸 and K ΙΙ卸 are:

[0036]

[0037] Further, in step 3, in actual blasting engineering site, the explosive stress wave is usually a cylindrical wave, and the problem is simplified to a plane wave for practical application, and the propagation of the explosive stress wave in the rock mass includes elastic P wave and SV wave; when the P wave and SV wave reach the surface of the rock mass crack, not only the I-type dynamic stress intensity factor is generated at the crack tip, but also the II-type dynamic stress intensity factor is generated;

[0038] The shear failure of the explosive stress wave on the crack surface is discussed, and the shear failure is mainly controlled by the II-type stress intensity factor at the crack tip, and the II-type stress intensity factor generated by the SV wave is the largest under the same intensity, so the SV wave is mainly studied below; here, let:

[0039] m = ω / c (14)

[0040] In the formula, ω represents the circular frequency of the SV wave, Hz; c represents the wave speed, m / s; and m represents the wave number, which has the dimension of 1 / length;

[0041] The stress intensity factor generated by the blasting stress wave-SV wave at the crack tip is:

[0042]

[0043] wherein

[0044] τ m = μm 2 ψ0 (16)

[0045] In the formula, μ is the Lame constant; τ m is the maximum shear stress of the SV wave on the crack surface; and ψ0 is a general constant; and are the I-type and II-type dynamic stress intensity factors with the dimension of 1, respectively; and are the phase angles of the I-type and II-type, respectively; K Ι动 (t) and K ΙΙ动 (t) are the I-type stress intensity factor and the II-type stress intensity factor at the crack tip of the rear edge under the blasting action, respectively.

[0046] Further, in step 4, according to the stress intensity factor superposition principle, the formula (13) and (15) are added to obtain the stress intensity factor at the crack tip of the rear edge under the blasting excavation:

[0047]

[0048] K I and K II are the stress intensity factors of type I and II at the crack tip of the back crack under the action of blasting excavation, respectively.

[0049] Further, in step 5, the back crack of the slope rock mass expands in a tensile-shear manner, and the stress intensity factor K Ι (l) at the branch crack tip under the action of tensile-shear stress is:

[0050]

[0051] wherein, l is the length of the branch crack expansion.

[0052] The stress intensity factor at the branch crack tip is increased by the action of unloading tensile stress and blasting load; under the action of the self-weight stress of the sliding body, the blasting load and the unloading tensile stress, the stress intensity factor K I (l) at the branch crack tip is increased with the increase of the crack length, and when K I (l) = K ΙC , the branch crack will expand unstably; when the stress intensity factor K I (l) at the branch crack tip is less than K ΙC , the crack stops expanding; thus, the length l of the branch crack expansion is:

[0053]

[0054] Further, in step 6, the back crack will expand through in the direction of the lower crack approximately, the height of the slope is H, the sliding surface inclination angle is β, and the length of the branch crack expansion is l.

[0055] The components of the weight W of the sliding body along the sliding surface and perpendicular to the sliding surface are:

[0056] W T = W sin β, W N = W cos β (20)

[0057] The average normal stress on the sliding surface AD is:

[0058]

[0059] Under the action of the self-weight, the maximum shear force F T that can be borne on the sliding surface AD is:

[0060]

[0061] The expression of the slope safety factor K of the crack propagation length under unloading is:

[0062]

[0063] Compared with the prior art, the present application has the beneficial effects that:

[0064] The present application provides a kind of prediction method of the stability of rock slope containing trailing edge crack under blasting excavation, its fundamental feature is based on fracture mechanics theory and limit equilibrium principle, comprehensively consider the effect of blasting load, slope self weight and excavation unloading, etc. External load, the calculation formula of stress intensity factor of crack tip of trailing edge of slope is given, the branch crack propagation length is considered, the crack propagation through mechanical model of slope rock mass is constructed, and the calculation method of slope stability coefficient is established, with high scientificity and accuracy.The present application method solves the problem that previous single limit equilibrium method cannot be applied to the stability evaluation of slope under blasting excavation, and the calculation method is simple and fast, which provides practical and feasible theoretical support for engineering design. BRIEF DESCRIPTION OF DRAWINGS

[0065] Figure 1 It is the slope sliding mechanics model diagram of the present application.

[0066] Figure 2 It is the slope trailing edge crack propagation generalization model diagram of the present application.

[0067] Figure 3 It is the superposition principle diagram of stress intensity factor of crack tip of trailing edge of slope of the present application.

[0068] Figure 4 It is the slope trailing edge crack propagation through schematic diagram of the present application.

[0069] Figure 5 It is the slope sliding surface penetration stress schematic diagram of the present application.

[0070] Figure 6 It is the geological profile and generalization mechanics model diagram of east slope of some iron mine of the embodiment of the present application. DETAILED DESCRIPTION

[0071] The specific embodiment provided by the present application is described in detail below in combination with the drawings.

[0072] A prediction method of the stability of rock slope containing trailing edge crack under blasting excavation, comprising the following steps:

[0073] Step 1: geological model generalization, establish the slope sliding mechanics model; determine the relevant parameters, the relevant parameters include the angle α of trailing edge crack and horizontal direction, the angle β of lower crack and horizontal direction, the weight W of sliding body, the force W of sliding body in parallel to the direction of lower crack tThe force W of the sliding body perpendicular to the lower crack direction n , Tangential force W of the trailing edge crack τ The normal force W of the trailing edge crack σ γ is the unit weight of the rock mass, V is the volume of the landslide body, and T is the tensile stress during excavation unloading;

[0074] Step 2: Solving for the stress intensity factor at the tip of the trailing edge crack under excavation unloading; including:

[0075] 1) Establish a generalized model of crack propagation at the rear edge of the slope and determine relevant parameters. The relevant parameters include the average height h of the rock mass that the crack does not penetrate and the rock mass above it, the vertical height z of the crack, the horizontal distance a from the center of mass of the sliding body to the crack tip, the vertical distance b from the center of mass of the sliding body to the crack tip, and the bending moment M generated by the sliding body and unloading tensile stress on the crack tip.

[0076] 2) Solve for the tensile stress intensity factor, shear stress intensity factor, and bending moment stress intensity factor K at the trailing edge crack tip. Ι1 K Ι2 and K ΙΙ3 ;

[0077] 3) Solve for the Type I and Type II stress intensity factors at the tip of the trailing crack under excavation unloading. Ι卸 and K ΙΙ卸 ;

[0078] Step 3: Solve for the Type I and Type II stress intensity factors K at the tip of the trailing edge fracture under blasting action. Ι动 (t) and K II动 (t);

[0079] Step 4: Solve for the stress intensity factor at the tip of the trailing edge fracture under blasting excavation; According to the principle of superposition of stress intensity factors, the stress intensity factor at the tip of the trailing edge fracture under blasting excavation can be obtained by adding the results of Step 2 and Step 3.

[0080] Step 5: Calculation of crack propagation length at the rear edge of the blasted excavation slope; Under the action of the landslide body's self-weight stress, blasting load, and unloading tensile stress, the stress intensity factor K at the tip of the branch crack. I (l) It increases with the increase of the crack length, when it increases to K I (l)=K ΙC At that time, the branch fracture expands unstablely; as the stress field within the slope rock mass adjusts, when the stress intensity factor K at the tip of the branch fracture... I (l) < K ΙC At that time, the crack stopped propagating; K ΙC Given the fracture toughness of the rock mass, the length of the branch fracture propagation is obtained as l;

[0081] Step 6: Derivation of the safety factor of the slope with the rear edge crack under the action of blasting excavation; determining the relevant parameters, including the cohesion c and internal friction angle of the rock mass Cohesion c of the extended crack surface i and internal friction angle Cohesion c on the lower crack surface j and internal friction angle The force W of the sliding body weight W along the sliding surface is calculated using the limit equilibrium principle T and F T , W T is the component of the sliding body weight G along the sliding surface and perpendicular to the sliding surface, F T is the maximum shear force that the sliding surface AD can withstand under the action of gravity, then the expression of the safety factor K of the slope considering the crack extension length under the action of blasting excavation is K = F T / W T ; when K > 1, the slope is in a stable state; when K < 1, the slope is in an unstable state; when K = 1, the slope is in a limit equilibrium state.

[0082] Further, in step 1, a mechanical model as shown in Figure 1 is established, as the normal stress on the excavated rock surface is unloaded to 0, and the unloading will cause differential rebound deformation of the rock mass, which will generate tensile stress T pointing to the excavation surface in the slope body, under the combined action of tensile stress T and the self-weight stress of the sliding body, the rear edge crack will initiate and expand.

[0083] Figure 1 A is the rear edge crack tip, O is the center of gravity position of the sliding body, W t represents the force of the sliding body in the direction parallel to the lower crack, W n represents the force of the sliding body in the direction perpendicular to the lower crack, which is decomposed into the tangential and normal forces of the rear edge crack of the slope as follows:

[0084] W t = W sin β (1)

[0085] W n = W cos β (2)

[0086] W τ = W t cos (α - β) + W n sin (α - β) (3)

[0087] W σ = W t sin (α - β) - W n cos (α - β) (4)

[0088] W = γV (5)

[0089] The solution method of the excavation unloading tensile stress T is as follows:

[0090] The value of the excavation unloading tensile stress T is obtained by a laboratory true triaxial unloading test, i.e., a field fissure sample is loaded to the original rock stress state, lateral unloading is started, and the excavation unloading tensile stress T is constantly changed with the continuous unloading, and the value of the excavation unloading tensile stress T is obtained by the formula T = σ0- σ t , wherein σ0 is the horizontal stress value at the moment when unloading is started, and σ t is the horizontal stress value corresponding to the moment when the fissure is initiated, which is recorded by high-speed photography during the test.

[0091] Further, in step 2, a slope rear edge fissure propagation generalization model as shown in FIG. 2 is established, according to the stress intensity factor superposition principle, the stress intensity factor at the rear edge fissure tip under the action of the self-weight of the upper sliding body and the unloading tensile stress can be decomposed as shown in FIG. 3, wherein ①-③ are the tensile stress, shear stress and bending moment, respectively, and the stress intensity factor at the fissure tip is: Figure 2 Figure 3

[0092]

[0093]

[0094]

[0095] σ = W σ sinα / h + T sinα (9)

[0096] τ = W τ sinα / h + T cosα (10)

[0097] σ max = 6M / h 2 (11)

[0098] In the above formulae, σ is the tensile stress on the fissure surface; τ is the shear stress on the fissure surface; σ max is the maximum tensile stress; and M = Wa.

[0099] Therefore, the I-type stress intensity factor and the II-type stress intensity factor K Ι卸 and K ΙΙ卸 at the rear edge fissure tip of the slope under the excavation unloading condition are as follows:

[0100]

[0101] The calculation results of the above formulae are substituted into formula (12) to obtain the I-type stress intensity factor and the II-type stress intensity factor K Ι卸 and K ΙΙ卸 at the rear edge fissure tip of the slope under the excavation unloading condition.​​

[0102]

[0103] Further, in step 3, in the actual blasting engineering site, the explosion stress wave is usually a cylindrical wave, and the problem is simplified as a plane wave for practical application, and the main elastic P wave and SV wave are generated in the rock mass propagation of the explosion stress wave. When P wave and SV wave reach the surface of the rock mass crack, not only I type dynamic stress intensity factor is generated at the crack tip, but also II type dynamic stress intensity factor is generated.

[0104] The present application mainly discusses the shear failure of the explosion stress wave on the crack surface, and the shear failure is mainly controlled by the II type stress intensity factor at the crack tip. The II type stress intensity factor generated by the SV wave is the largest under the same intensity, and therefore, the SV wave is mainly studied below. Herein, let:

[0105] m = ω / c (14)

[0106] In the formula, ω represents the circular frequency of the SV wave, Hz; c represents the wave speed, m / s; and m represents the wave number, which has the dimension of 1 / length.

[0107] The stress intensity factor generated by the blasting stress wave-SV wave at the crack tip is:

[0108]

[0109] wherein

[0110] τ m = μm 2 ψ0 (16)

[0111] In the formula, μ is the Lame constant; τ m is the maximum shear stress of the SV wave on the crack surface, MPa; and ψ0 is a general constant (having the dimension of length square). and are I and II type dynamic stress intensity factors (dynamic stress intensity factor divided by the corresponding static value at ω = 0) respectively, which have the dimension of 1; and are the phase angles of I and II types, (°); K Ι动 (t) and K ΙΙ动 (t) are I and II type stress intensity factors generated by the blasting stress wave-SV wave at the crack tip, MPa·m 1 / 2 .

[0112] Further, in step 4, according to the stress intensity factor superposition principle, the stress intensity factor at the trailing edge crack tip under the action of blasting excavation can be obtained by adding (13) and (15).

[0113]

[0114] In the above formula: K I and K II These are the Type I and Type II stress intensity factors at the tip of the trailing edge crack under blasting excavation, respectively.

[0115] Furthermore, in step 5, the slope rock mass forms, under the influence of initial geological tectonic activity and external load disturbance, as follows: Figure 4 The trailing edge fissure OA, as shown, continuously expands under the action of slope blasting excavation, eventually connecting with the underlying fissure and causing a landslide. During the first slope blasting excavation, when the stress intensity factor at the tip of the trailing edge fissure exceeds the fracture toughness of the rock mass under the combined action of the landslide body's self-weight stress, blasting load, and unloading tensile stress, the fissure initiates and expands to a certain length AB at the initiation angle θ0. Subsequently, the slope stress field adjustment ends, the rock mass as a whole is in equilibrium, and the fissure stops expanding. During the second blasting excavation, under the action of the stress field within the slope rock mass, the fissure initiates and expands again to a certain length BC based on the initial equivalent length OB. Thus, with each excavation of the slope rock mass, the fissure expands once, and the expansion length continuously accumulates until it eventually connects with the underlying fissure.

[0116] The propagation of fractures at the rear edge of the slope rock mass is a tensile-shear propagation, and the stress intensity factor K at the tip of the branch fracture under tensile-shear stress is... Ι (l) is

[0117]

[0118] In the formula: l is the branch crack propagation length.

[0119] The effects of unloading tensile stress and blasting load increase the stress intensity factor at the branch fracture tip. Under the action of the sliding body's self-weight stress, blasting load, and unloading tensile stress, the stress intensity factor K at the branch fracture tip... I (l) It increases with the increase of the crack length, when it increases to K I (l)=K ΙC At this time, the branch fracture will propagate unstablely. As the stress field within the slope rock mass adjusts, when the stress intensity factor K at the tip of the branch fracture... I (l) < K ΙC At this point, the crack stops propagating. Therefore, the length of the branched crack propagation can be obtained as:

[0120]

[0121] Furthermore, in step 6, step 5 calculated the branch crack propagation length when the slope rock mass was damaged and failed under blasting excavation, and step 6 further derives the solution for the slope safety factor from a macroscopic perspective. For example... Figure 5As shown, the trailing edge fracture will extend and penetrate along the direction of the approximately lower fracture, with a slope height of H, a slip surface dip angle of β, and a branch fracture extension length of l.

[0122] The components of the sliding body weight W along the sliding surface and perpendicular to the sliding surface are:

[0123] W T =Wsinβ, W N =Wcosβ (20)

[0124] The average normal stress on the sliding surface AD ​​is:

[0125]

[0126] Under its own weight, the maximum shear force F that the sliding surface AD ​​can withstand is T for:

[0127]

[0128] The expression for the slope safety factor K, considering the crack propagation length under unloading, is:

[0129] Specific Implementation

[0131] Step 1: Geological model generalization, as follows Figure 6 As shown, the volume V of the landslide mass on this slope is approximately 4.4 × 10³ m³. 3 The lower fracture dip angle is approximately 38°. A tensile fracture, approximately 460m long and 13m deep, with a nearly vertical direction, exists at the rear edge. The unloading tensile stress was approximated using a true triaxial unloading test conducted indoors. The fractured sample was loaded to the original rock stress state, and lateral unloading began. As unloading continued, the horizontal tensile stress T reached 0.5MPa, and the rock mass unit weight was 26KN / m³. 3 .

[0132] Step 2: According to the geological model, the average height is 86m, and the horizontal distance a from the center of gravity to the fracture tip is 0.8m. Substituting the parameters determined in Steps 1 and 2 into formulas (1)-(13) in sequence, the stress intensity factor K at the fracture tip under excavation unloading can be obtained. Ι卸 and K ΙΙ卸 .

[0133] Step 3: The frequency of the on-site blasting stress wave is 300Hz, and the wave velocity is 300m / s. The disturbance effect of the blasting stress wave on the fracture is calculated based on the maximum. Take 1, Take 2. Substituting the determined parameters into formula (15), the stress intensity factor K at the tip of the trailing edge fracture under blasting action can be obtained. Ι动 (t) and KII动 (t).

[0134] Step 4: The stress intensity factor of the crack tip at the back edge under the action of blasting excavation is obtained by adding the results obtained in steps 2 and 3.

[0135] Step 5: The fracture toughness of the slope rock mass is taken as 1.2 MPa.m 1 / 2 The length of the crack at the back edge under the action of blasting excavation is obtained by substituting the parameters involved in steps 1-3 into formula (19).

[0136] Step 6: The in-situ rock parameters of the slope are shown in Table 1, and the safety factor K of the slope with the crack at the back edge under the action of blasting excavation is obtained by substituting the relevant parameters into formula (19). The specific calculation results are shown in Table 2.

[0137] Table 1 Physical and mechanical parameters of rock mass

[0138]

[0139] Table 2 Calculation results table

[0140]

[0141] Those skilled in the art will understand that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROMs, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of the present application can be implemented in various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0142] The present application is described with reference to flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and the combination of the flows and / or blocks in the flowcharts and / or block diagrams can be implemented by computer program instructions. These computer program instructions can be provided to a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing apparatus to produce a machine, so that the instructions executed by the computer or other programmable data processing apparatus produce a device that implements the functions specified in the flowcharts and / or block diagrams. Figure 1 The functions specified in a flow or multiple flows and / or blocks Figure 1 The device that implements the functions specified in a flow or multiple flows and / or blocks.

[0143] These computer program instructions can also be stored in a computer readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer readable memory produce an article of manufacture including instructions which implement the Figure 1 function specified in the flow or flows and / or blocks Figure 1 of the block or blocks.

[0144] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions that are executed on the computer or other programmable apparatus provide steps for implementing the Figure 1 function specified in the flow or flows and / or blocks Figure 1 of the block or blocks.

[0145] Although preferred embodiments of the application have been described herein, substitutions and alterations are possible in view of the disclosure of this application without departing from the spirit and scope of the present application. Therefore, it is intended that the appended claims be interpreted as including all such alternatives and modifications as fall within the true spirit and scope of the present application.

[0146] It will be apparent to those skilled in the art that various modifications and variations can be made to the present application without departing from the spirit or scope of the application. Thus, it is intended that the present application cover modifications and variations of this application provided they come within the scope of the appended claims and their equivalents.

Claims

1. A method for predicting the stability of a rock slope with trailing edge fractures under blasting excavation, characterized in that, Includes the following steps: Step 1: Geological model generalization, establishing a slope sliding dynamic model; determining relevant parameters, including the angle between the trailing edge fracture and the horizontal direction. The angle between the lower crack and the horizontal direction Weight of the sliding body Force on the sliding body parallel to the direction of the lower crack Force on the sliding body perpendicular to the lower crack direction Tangential force of trailing edge crack Normal force of trailing edge crack , For the density of rock mass, Let T be the volume of the sliding body and T be the tensile stress during excavation unloading. Step 2: Solving for the stress intensity factor at the tip of the trailing edge crack under excavation unloading; including: 1) Establish a generalized model of the propagation of the crack at the rear edge of the slope and determine the relevant parameters. The relevant parameters include the average height h of the rock mass that the crack does not penetrate and the rock mass above it, the vertical height z of the crack, the horizontal distance a from the center of mass of the sliding body to the crack tip, the vertical distance b from the center of mass of the sliding body to the crack tip, and the bending moment M generated by the sliding body and the unloading tensile stress on the crack tip. 2) Solve for the tensile stress intensity factor, shear stress intensity factor, and bending moment stress intensity factor at the trailing edge crack tip. , and ; 3) Solving for the Type I and Type II stress intensity factors at the tip of the trailing edge crack under excavation unloading. and ; Step 3: Solve for the Type I and Type II stress intensity factors at the tip of the trailing edge fracture under blasting action. and ; Step 4: Solve for the stress intensity factor at the tip of the trailing edge fracture under blasting excavation; According to the principle of superposition of stress intensity factors, the stress intensity factor at the tip of the trailing edge fracture under blasting excavation can be obtained by adding the results of Step 2 and Step 3. Step 5: Calculation of crack propagation length at the rear edge of the blasted excavation slope; stress intensity factor at the tip of the branch crack under the action of the landslide body's self-weight stress, blasting load, and unloading tensile stress. It increases with increasing crack length, and when it increases to = At that time, the branch fractures propagate unstablely; as the stress field within the slope rock mass adjusts, the stress intensity factor at the tip of the branch fracture increases. < At that time, the crack stopped expanding; Given the fracture toughness of the rock mass, the length of the branch fracture propagation is obtained as l; Step 6: Derivation of the safety factor for a slope with trailing fractures under blasting excavation; determination of relevant parameters, including the cohesion of the rock mass. and internal friction angle and Cohesion of the extended fracture surface and internal friction angle and Cohesion on the lower fracture surface and internal friction angle and The force along the sliding surface caused by the weight W of the sliding body is calculated using the principle of limit equilibrium. and , Let W be the component of the weight of the sliding body along the sliding surface and perpendicular to the sliding surface. To determine the maximum shear force that the slope can withstand on the sliding surface AD ​​under its own weight, the expression for the slope safety factor K, considering the crack propagation length under blasting excavation, is as follows: When K > 1, the slope is in a stable state; when K < 1, the slope is in an unstable state; when K = 1, the slope is in a state of limit equilibrium.

2. The method for predicting the stability of a rock slope with trailing edge fractures under blasting excavation as described in claim 1, characterized in that, In step 1, a slope sliding dynamics model is established. As the normal stress on the surface of the excavated rock mass is unloaded to 0, the unloading causes differential rebound deformation of the rock mass. This deformation causes the excavation unloading tensile stress T in the slope body to be directed towards the excavation face. Under the combined action of the excavation unloading tensile stress T and the self-weight stress of the sliding body, the rear edge cracks are initiated and propagated. W t W represents the force exerted on the sliding body in a direction parallel to the lower crack. n The force representing the sliding body perpendicular to the lower crack direction is decomposed into forces along the tangential and normal directions of the crack at the rear edge of the slope, respectively: （1） （2） （3） （4） （5） The method for solving the excavation unloading tensile stress T is as follows: The value of the excavation unloading tensile stress T was approximately obtained through indoor true triaxial unloading tests. The field-grown fractured specimens were loaded to the original rock stress state, and lateral unloading began. As unloading continued, the excavation unloading tensile stress T changed continuously. This change was determined using the formula... The result is obtained, where σ0 is the horizontal stress value at the start of unloading, and σ t To record the horizontal stress value corresponding to the moment the crack initiation during the experiment using high-speed photography.

3. The method for predicting the stability of a rock slope with trailing edge fractures under blasting excavation as described in claim 1, characterized in that, In step 2, a generalized model of crack propagation at the rear edge of the slope is established. Based on the principle of stress intensity factor superposition, the stress intensity factor at the crack tip under the action of the upper sliding body's self-weight and unloading tensile stress can be decomposed into tensile stress, shear stress, and bending moment. Their stress intensity factors at the crack tip... , and They are respectively: （6） （7） （8） （9） （10） （11） In the above formula: This represents the tensile stress on the crack surface; This represents the shear stress on the crack surface; This represents the maximum tensile stress. ; Therefore, under excavation unloading conditions, the Type I and Type II stress intensity factors at the tip of the crack at the rear edge of the slope are... and for: （12） Substituting the calculation results of the above formulas into equation (12), we can obtain the Type I stress intensity factor and Type II stress intensity factor at the tip of the crack at the rear edge of the slope under excavation and unloading conditions. and for: （13）。 4. The method for predicting the stability of a rock slope with trailing edge fractures under blasting excavation as described in claim 1, characterized in that, In step 3, in actual blasting engineering sites, the explosive stress wave is usually a cylindrical wave. For practical application, the problem is simplified to a plane wave. The explosive stress wave propagates in the rock mass, including elastic P-waves and SV-waves. When the P-waves and SV-waves reach the surface of the rock mass fractures, they not only generate a type I dynamic stress intensity factor at the fracture tip, but also generate a type II dynamic stress intensity factor. This study investigates the shear failure induced by explosive stress waves on the fracture surface. Shear failure is primarily controlled by the Type II stress intensity factor at the fracture tip. The Type II stress intensity factor generated by the SV wave is the largest under the same stress, therefore, the study mainly focuses on the SV wave. Here, we set: （14） In the formula: The angular frequency of the SV wave, expressed in Hz; Wave speed is expressed in m / s; It represents the wave number and has the dimension of 1 / length; The stress intensity factor generated at the fracture tip by the blast stress wave - SV wave is: （15） in （16） In the above formula: μ is Lamé's constant; This represents the maximum shear stress of the SV wave on the fracture surface. These are general constants; and These are the dimensionless type I and type II dynamic stress intensity factors, respectively. and For phase angles of types I and II; and These are the Type I and Type II stress intensity factors at the tip of the trailing edge crack under blasting action, respectively.

5. The method for predicting the stability of a rock slope with trailing edge fractures under blasting excavation as described in claim 4, characterized in that, In step 4, according to the principle of stress intensity factor superposition, formulas (13) and (15) are added together to obtain the stress intensity factor at the tip of the rear edge crack under blasting excavation: （17） In the above formula: K I and K II These are the Type I and Type II stress intensity factors at the tip of the trailing edge crack under blasting excavation, respectively.

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