Method for analyzing rock slope excavation unloading failure path based on crack propagation

Abstract

The application discloses a kind of based on fissure expansion's rock slope excavation unloading failure path analysis method, belong to slope stability analysis technical field, including the following steps: S1, fissure equivalent simulation;S2, stress intensity factor calculation and expansion type judgment;S3, fissure cracking judgment;S4, fissure expansion calculation;S5, fissure expansion section generation.The fissure expansion's rock slope excavation unloading failure path analysis method in the application, by the originally complex fissure expansion environment is divided into multiple sub fissure dynamic expansion model, then single sub fissure expansion model is analyzed one by one, then the fissure expansion situation of single sub fissure expansion model is combined with other sub fissure expansion model and is analyzed, such as step by step calculation, obtain the fissure expansion situation of rock slope under overall complex environment, overall calculation logic is clear, avoid complex redundant calculation, improve fissure expansion situation analysis efficiency.

Description

Technical Field

[0001] This invention belongs to the field of slope stability analysis technology, specifically relating to a method for analyzing the failure path of rock slopes under excavation unloading based on crack propagation. Background Technology

[0002] Fissures are widely present in rock slopes and play an important role in the deformation and failure of slopes during excavation and unloading. The deformation and failure of fissure rock slopes are closely related to the fracturing evolution of the slope fissures. The failure process is transformed into the tension and slippage of fissures, and the initiation, expansion and eventual formation of a through-type fracture surface within the rock bridge.

[0003] Early studies on fractured rock slopes played a crucial role in revealing slope failure mechanisms, but certain limitations remain. Drawing on solid fracture mechanics, this study applies fracture mechanics to the stability of fractured rock slopes, further elucidating the mechanisms of fracture propagation and connection under typical fracture distribution conditions in rock slopes. However, because slope fracture propagation is a complex dynamic process, the interaction between the fracture network and rock bridges, and fracture propagation and convergence are comprehensive issues. Under the combined effects of unloading stress conditions, stratigraphic lithology, and fracture network, the mechanisms of slope fracture propagation and connection, and the resulting slope rupture paths, cannot yet be directly obtained through calculation. Summary of the Invention

[0004] In view of one or more of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a method for analyzing the excavation unloading failure path of rock slopes based on crack propagation, so as to simulate the excavation unloading failure path of rock slopes.

[0005] To achieve the above objectives, this invention provides a method for analyzing the failure path of rock slopes during excavation based on fracture propagation, comprising the following steps:

[0006] S1. Equivalent simulation of cracks: The overall dynamic crack propagation model is equivalently simulated into multiple sub-crack dynamic propagation models;

[0007] S2. Stress Intensity Factor Calculation and Expansion Type Determination: The stress extrapolation method is used to calculate the Type I and Type II stress intensity factors at the fracture tip in the sub-fracture dynamic expansion model. I and II. Determine the extension type based on the stress intensity factor;

[0008] S3. Crack initiation judgment: Determine the crack initiation and propagation type at the crack tip based on the propagation type, which includes tension-type crack initiation and propagation and shear-type crack initiation and propagation.

[0009] S4. Crack propagation calculation: Calculate the crack initiation angle based on the crack initiation and propagation type at the crack tip. and extended distance ;

[0010] S5: Crack propagation segment generation: Generate a crack propagation segment based on the crack initiation angle and propagation distance. Fit the generated crack propagation segment to other sub-crack dynamic propagation models. Determine the propagation direction after cracks converge based on the fitting results.

[0011] As a further improvement of the present invention, in step S5, the direction of crack propagation after convergence is determined based on the fitting results:

[0012] The stress intensity factor at the crack tip along different directions of the crack propagation segment is calculated, with the crack propagation direction being the direction that extends the furthest beyond the envelope.

[0013] As a further improvement of the present invention, step S6 is also included:

[0014] In step S5, the direction of expansion after the fracture convergence is determined based on the fitting results, and a new sub-fracture dynamic expansion model is generated. Steps S2, S3, S4, and S5 are repeated.

[0015] As a further improvement to the present invention, the Type I and Type II stress intensity factors at the crack tip in step S2... I and The calculation of II specifically includes:

[0016] Boundary conditions and material parameters are set to generate initial joints and fractures. Material parameters for the joints and fractures are then set to obtain displacement, strain, and stress. Based on these displacement, strain, and stress, Type I and Type II stress intensity factors at the fracture tip are calculated. I and II.

[0017] As a further improvement of the present invention, the determination of the tensile crack initiation and propagation type in step S3 specifically includes:

[0018] S301. Obtain the envelope of the crack tip when tensile propagation occurs based on calculations;

[0019] S302. Obtain the envelope of the crack tip when shear propagation occurs based on calculations;

[0020] S303. Obtain the intersection point of the envelope based on the tension-type extended envelope and the shear-type extended envelope;

[0021] S304. Establish a coordinate system. Divide the coordinate quadrant into several regions using the origin coordinates, the tension-type expansion envelope, the shear-type expansion envelope, and the intersection of the envelopes. Then, define the Type I and Type II stress intensity factors at the crack tip. I and II. Substitute the coordinates into the equations and determine the extension type.

[0022] As a further improvement of the present invention, the several regions divided in step S304 include a region where the crack tip does not propagate, a region where the crack tip undergoes shear-type propagation but not tensile-type propagation, a region where the crack tip undergoes tensile-type propagation but not shear-type propagation, and a region where the crack tip undergoes both tensile-type and shear-type propagation.

[0023] The aforementioned improved technical features can be combined with each other as long as they do not conflict with each other.

[0024] In summary, the beneficial effects of the above-described technical solutions conceived by this invention compared with the prior art include:

[0025] (1) The rock slope excavation unloading failure path analysis method based on crack propagation of the present invention develops the fracture propagation criterion of cracks under complex stress environment into numerical simulation, realizing the analysis of the influence law of excavation unloading on crack initiation and propagation from the mechanical perspective of crack propagation. It divides the originally complex crack propagation environment into multiple sub-crack dynamic propagation models, analyzes each sub-crack propagation model one by one, and then combines the crack propagation of the individual sub-crack propagation models with other sub-crack propagation models for analysis. In this way, the crack propagation of the rock slope under the overall complex environment is obtained step by step. The overall calculation logic is clear, avoiding complex and redundant calculations and improving the efficiency of crack propagation analysis. Attached Figure Description

[0026] Figure 1 This is a schematic diagram of the simulation process of the rock slope excavation unloading failure path analysis method based on crack propagation in an embodiment of the present invention;

[0027] Figure 2 This is a schematic diagram illustrating the crack tension-shear expansion determination in an embodiment of the present invention;

[0028] Figure 3 This is a schematic diagram of the equivalent and dynamic propagation of cracks in an embodiment of the present invention;

[0029] Figure 4 This is a schematic diagram of the stress distribution at the crack tip and the value points obtained by extrapolation in an embodiment of the present invention;

[0030] Figure 5 This is a schematic diagram of crack convergence and crack propagation in an embodiment of the present invention;

[0031] Figure 6 This is a schematic diagram of uniaxial compression simulation of a double-fractured rock sample in an embodiment of the present invention;

[0032] Figure 7 This is a schematic diagram of stress hardening evolution and propagation pattern recognition at the crack tip in an embodiment of the present invention;

[0033] Figure 8 This is a geological overview diagram of the slope engineering in an embodiment of the present invention. Detailed Implementation

[0034] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0035] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," and "circumferential" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0036] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0037] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components, unless otherwise explicitly limited. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0038] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can mean that the first feature is in direct contact with the second feature, or that the first feature is in indirect contact with the second feature through an intermediate medium. Furthermore, "above," "over," and "on top" of the second feature can mean that the first feature is directly above or diagonally above the second feature, or simply that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature can mean that the first feature is directly below or diagonally below the second feature, or simply that the first feature is at a lower horizontal level than the second feature.

[0039] Example:

[0040] Please see Figures 1-8 The preferred embodiment of the present invention provides a method for analyzing the unloading failure path of rock slope excavation based on crack propagation, which includes the following steps:

[0041] S1. Equivalent simulation of cracks: The overall dynamic crack propagation model is equivalently simulated into multiple sub-crack dynamic propagation models;

[0042] S2. Stress Intensity Factor Calculation and Expansion Type Determination: The stress extrapolation method is used to calculate the Type I and Type II stress intensity factors at the fracture tip in the sub-fracture dynamic expansion model. I and II. Determine the extension type based on the stress intensity factor;

[0043] S3. Crack initiation judgment: Determine the crack initiation and propagation type at the crack tip based on the propagation type, which includes tension-type crack initiation and propagation and shear-type crack initiation and propagation.

[0044] S4. Crack propagation calculation: Calculate the crack initiation angle and propagation distance l based on the crack initiation and propagation type at the crack tip;

[0045] S5. Crack propagation segment generation: Generate crack propagation segments based on crack initiation angle and propagation distance. Fit the generated crack propagation segments with other sub-crack dynamic propagation models. Determine the propagation direction after crack convergence based on the fitting results.

[0046] Furthermore, steps S1 to S5 above mainly concern the dynamic propagation model of a single sub-crack and the propagation situation after the dynamic propagation model of a single sub-crack intersects with other dynamic propagation models of sub-cracks. In practice, a single dynamic propagation model of a single sub-crack will generate a new dynamic propagation model of a sub-crack. Therefore, the propagation model of the crack is a continuous iterative development process until the crack stops propagating.

[0047] Therefore, this application also includes step S6: generating a new sub-fracture dynamic propagation model based on the propagation direction determined by the fitting in step S5 after the fracture convergence, and then simulating the new sub-fracture dynamic propagation model, repeating steps S2, S3, S4, and S5, as detailed below. Figure 1 As shown.

[0048] Furthermore, as a preferred embodiment of the present invention, the determination of the tensile crack initiation and propagation type in step S3 of this application specifically includes:

[0049] S301. Obtain the envelope of the crack tip when tensile propagation occurs based on calculations;

[0050] S302. Obtain the envelope of the crack tip when shear propagation occurs based on calculations;

[0051] S303. Obtain the intersection point of the envelope based on the tension-type extended envelope and the shear-type extended envelope;

[0052] S304. Establish a coordinate system. Divide the coordinate quadrant into several regions using the origin coordinates, the tension-type expansion envelope, the shear-type expansion envelope, and the intersection of the envelopes. Then, define the Type I and Type II stress intensity factors at the crack tip. I and II. Substitute the coordinates into the equations and determine the extension type.

[0053] Optionally, the envelope of the crack tip during tensile propagation in step S301 above is:

[0054] (Formula 1)

[0055] in I This refers to the fracture toughness of a material under pure tensile conditions, which can be selected according to the material type.

[0056] Specifically, under linear elastic conditions, the I / II mixed stress field at the crack tip can be represented in polar coordinates by type I and type II stress intensity factors ( I and II) indicates, see Formula 2.

[0057] (Formula 2)

[0058] In the above scheme, cracks mainly propagate in two types under complex stress conditions: tensile and shear. The maximum circumferential tensile stress theory (MHSC) is used as the criterion for tensile propagation. It is assumed that when the material fails under tensile stress, the initial propagation direction of the crack is the direction of the maximum circumferential tensile stress at the crack tip. According to the analytical expression of the stress field at the crack tip, the direction of the maximum circumferential tensile stress satisfies Equation 3. Substituting Equation 2 into Equation 3, we obtain Equation 4 for the direction of the maximum circumferential tensile stress. Finally, substituting the direction of the maximum circumferential tensile stress into Equation 2 yields the crack tip direction when the tensile propagation occurs. I and The envelope of II.

[0059] Specifically, the direction of maximum circumferential tensile stress satisfies the following formula:

[0060] (Formula 3)

[0061] Specifically, the direction of maximum circumferential tensile stress is as follows:

[0062] (Formula 4)

[0063] Optionally, the envelope of the crack tip when shear-type propagation occurs in step S302 above is:

[0064] (Formula 5)

[0065] In the above scheme, the maximum shear stress criterion (MSSC) is used to determine shear-type propagation. It is assumed that when the material experiences shear-type failure, the initial propagation direction of the crack is the direction of maximum shear stress at the crack tip. According to the analytical expression of the stress field at the crack tip, the direction of maximum shear stress satisfies Equation 6. Substituting Equation 2 into Equation 6, let... = tan 1 ( I / II Solving for the maximum shear stress direction yields Formula 7. Substituting Formula 7 into Formula 2, we obtain the crack tip direction when shear propagation occurs. I and The envelope of II, Equation 5. Wherein, and These are the critical tensile and critical shear stresses of the material, respectively. / The value ranges from 0.5 to 1.0, corresponding to different types of materials from ductile to brittle.

[0066] Specifically, the direction of maximum shear stress satisfies the following formula:

[0067] (Formula 6)

[0068] Specifically, the direction of maximum shear stress is as follows:

[0069] (Formula 7)

[0070] Further, in step S303 above, the intersection point of the tension-type extended envelope and the shear-type extended envelope 1 is determined. By combining formula 1 and formula 5, the intersection point expression is obtained:

[0071] (Formula 8)

[0072] Furthermore, the specific division method in step S304 above is as follows: using the crack propagation type judgment method under composite stress state, the envelope lines of Formula 1 and Formula 5 are simultaneously drawn on... I- In the II coordinate system, the initiation and propagation types of cracks are identified based on the distribution of the stress state at the crack tip within this coordinate system, such as... Figure 2 As shown, when the stress at the crack tip is in regions a and b, the crack does not propagate; when it is in region c, the crack tip undergoes shear propagation but not tensile propagation; when it is in region d, the crack tip undergoes tensile propagation but not shear propagation; when it is in regions e and f, both tensile and shear propagation may occur at the crack tip, but tensile propagation is dominant in region e and shear propagation is dominant in region f.

[0073] In the above scheme, a method of weakening local solid elements is used to equivalently create the initial crack and simulate crack propagation. First, the spatial distribution of the initial crack is determined, such as... Figure 3 (a); Secondly, based on the spatial distribution of the cracks, an equivalent initial crack is created by weakening the material strength and stiffness of the local solid units around the cracks, such as... Figure 3 (b) The equivalent simulation of the crack propagation process is similar to the initial crack creation direction. That is: first, the crack initiation angle and propagation distance are calculated, such as... Figure 3 (c) Determine the distribution location of the crack tip propagation segment, and then generate new crack propagation segments around it using local solid element material weakening based on the distribution location of the propagation segment, and update the crack tip position, such as... Figure 3 (d).

[0074] In the above scheme, the stress intensity factor at the crack tip, calculated using the extrapolation method based on element stress, is used as the crack propagation factor, as shown in Formula 9. The calculation principle is as follows: Figure 4As shown in Equation 9, A1, A2, B1, and B2 are the parameters for linear fitting. When r approaches 0, the intercepts B1 and B2 in Equation 9 correspond to the Type I and Type II stress intensity factors at the fracture tip, respectively. By substituting the distance near the fracture tip and its corresponding stress intensity factor into Equation 9, as shown in (… , I )and( , II The stress intensity factor at the crack tip can be extrapolated. I and II. According to the linear regression method, the stress intensity factor at the crack tip is shown in Equation 10.

[0075] Specifically, the above extrapolation method based on element stress is as follows:

[0076] (Formula 9)

[0077] Specifically, the stress intensity factor at the crack tip is as follows:

[0078] (Formula 10)

[0079] Furthermore, in step S4 above, the crack initiation angle is calculated based on the crack initiation and propagation type at the crack tip. and extended distance The result is obtained by calculating using formula 2 above, where r is the extended distance. The crack angle is formed at the crack.

[0080] (Formula 2)

[0081] Furthermore, the specific principle behind the generation of the crack propagation segment in step S5 above is as follows: Figure 5 Before the fractures converge, the extending fracture and an existing fracture are at a certain distance, such as... Figure 5 (a); When the tip of the propagating crack is close to an existing crack, calculations are used to determine whether the propagating crack will intersect with the existing crack in the non-propagating calculation. If they intersect, the location of the intersection point is determined, such as... Figure 5 (b) and extend the tip of the expanding crack to the junction point to complete the crack junction calculation, such as... Figure 5 (c) After the fractures converge, the tip of the propagating fracture adjusts. This invention assumes that there are three potential propagation directions after the fractures converge, namely: propagation along any end of the existing fracture, such as... Figure 5 (d) and Figure 5(e), and propagation along the original direction of the propagating crack, such as Figure 5 (f).

[0082] Furthermore, from the three potential propagation directions mentioned above, the most likely propagation direction is selected as the propagation direction after the fractures converge. Figure 5 (d) Figure 5 (e) and Figure 5 (f). The judgment method is as follows: calculate the stress intensity factor at the crack tip along different directions and its value in... Figure 2 The distance from the middle envelope line indicates that the crack propagates in the direction of maximum distance beyond the envelope line.

[0083] The following section verifies the multi-stage rock slope excavation unloading failure path analysis method based on fracture propagation in this application:

[0084] To verify the rationality and applicability of this scheme, two typical double-fractured rock samples were selected for uniaxial compression simulation. Figure 6 The calculation conditions were as follows: the rock was modeled using a linear elasticity, with an elastic modulus of 20 GPa, a Poisson's ratio of 0.25, and a type I fracture toughness of 2.0 MPa. m0.5; Considering the characteristics of no interaction at the interface under tension but friction at the interface under compression and shear, the crack is simulated using the Mohr-Coulomb model with the parameters set as follows: cohesion and tensile strength are both 0, and the internal friction angle is 30°; The vertical load on the specimen starts from 0 and is applied at a rate of 0.1 MPa per step until the crack starts to crack, at which point the load increase is stopped and the crack propagation calculation begins. Figure 7 The dynamic propagation process of the crack is demonstrated. Comparison with the crack propagation test results of the corresponding double-cracked specimen under uniaxial compression shows that... Figure 7 The calculated final crack propagation path agrees well with the experimental results, thus demonstrating the rationality of the crack propagation equivalent simulation method proposed in this invention in crack propagation path analysis.

[0085] The stress intensity factor at the fracture tip before propagation is extracted and placed into the envelope diagram to analyze the fracture propagation mode (see...). Figure 7 , Figure 8 During uniaxial loading, the stress states at points A, B, and D at the crack tip are as follows: I- In coordinate system II, the fracture evolves along paths ①, ②, and ④ respectively, ultimately reaching the MHSC envelope and undergoing tensile propagation; while the stress state at point C at the fracture tip... I- The crack propagation occurs along path ③ in coordinate system II, eventually reaching the MSSC envelope and undergoing shear-type propagation. The crack propagation mode analyzed in this invention is the same as the propagation mode of the corresponding uniaxial compression test of the double-cracked specimen, that is, tensile propagation occurs at points A, B, and D of the crack tip, and shear propagation occurs at point C, thus demonstrating the rationality of the crack propagation simulation method proposed in this invention in crack propagation mode analysis.

[0086] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for analyzing the failure path of rock slopes during excavation and unloading based on fracture propagation, characterized in that, Includes the following steps: S1. Equivalent simulation of cracks: The overall dynamic crack propagation model is equivalently simulated into multiple sub-crack dynamic propagation models; S2. Stress Intensity Factor Calculation and Expansion Type Determination: The stress extrapolation method is used to calculate the Type I and Type II stress intensity factors at the fracture tip in the sub-fracture dynamic expansion model. I and II. Determine the extension type based on the stress intensity factor; S3. Crack Initiation Judgment: Based on the calculation, obtain the tensile-type expansion envelope and the shear-type expansion envelope, and obtain the intersection point of the two envelopes. Establish a coordinate system, and divide the coordinate quadrant into several regions using the origin coordinates, the tensile-type expansion envelope, the shear-type expansion envelope, and the intersection point of the envelopes. Substitute the type I and type II stress intensity factors KI and KII at the crack tip into the coordinate system to determine the crack initiation and expansion type at the crack tip. The crack initiation and expansion types include tensile-type crack initiation and expansion and shear-type crack initiation and expansion. S4. Crack propagation calculation: Calculate the crack initiation angle based on the crack initiation and propagation type at the crack tip. and extended distance ; S5. Crack propagation segment generation: Generate a crack propagation segment based on the crack initiation angle and propagation distance. Fit the generated crack propagation segment to other sub-crack dynamic propagation models. Determine the propagation direction after cracks converge based on the fitting results. Among them, the direction of crack propagation after crack convergence is determined based on the fitting results: the stress intensity factor of the crack tip along different directions of the crack propagation segment is calculated respectively, and the direction of crack propagation is the direction of propagation with the largest distance beyond the envelope. S6. Repeat steps S2, S3, S4, and S5 until the crack stops propagating.

2. The method for analyzing the unloading failure path of rock slope excavation based on fracture propagation according to claim 1, characterized in that, Type I and Type II stress intensity factors at the crack tip in step S2 I and The calculation of II specifically includes: Boundary conditions and material parameters are set to generate initial joints and fractures. Material parameters for the joints and fractures are then set to obtain displacement, strain, and stress. Based on these displacement, strain, and stress, Type I and Type II stress intensity factors at the fracture tip are calculated. I and II.

3. The method for analyzing the unloading failure path of rock slope excavation based on fracture propagation according to claim 1, characterized in that, The several regions divided in step S3 include the region where the crack tip does not propagate, the region where the crack tip undergoes shear-type propagation but not tensile-type propagation, the region where the crack tip undergoes tensile-type propagation but not shear-type propagation, and the region where the crack tip undergoes both tensile-type and shear-type propagation.

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