A method for constructing a rock multi-scale fracture evaluation index

Abstract

This invention discloses a method for constructing a multi-scale fracture assessment index for rocks under true three-dimensional stress, comprising the following steps: S1, establishing a yield function F based on the Mogi-Coulomb three-dimensional strength criterion; S2, constructing a formula for assessing the degree of multi-scale fracture of rocks based on the strength envelope of the three-dimensional strength criterion and the geometric relationship between the yield surface and the stress point; S3, assessing the degree of rock mass fracture based on the range of the multi-scale fracture assessment index. This invention proposes a method for constructing a multi-scale fracture assessment index for rocks, providing a theoretical basis for safety evaluation and stability analysis of high-stress deep rock engineering.

Description

Technical Field

[0001] This invention relates to the field of rock mechanical properties and engineering research, specifically to a method for constructing an evaluation index for the degree of multi-scale fracture of rocks. Background Technology

[0002] Numerical analysis software provides crucial reference for engineering stability analysis and optimized excavation and support design. However, typical numerical analysis software often only provides results for the plastic zone or safety factor. The plastic zone indicates the area where rock undergoes plastic deformation, but cannot assess the degree of rock fracture; the safety factor only assesses the overall safety of the rock engineering project, failing to evaluate the progressive damage and failure process of the rock or the specific location of localized risk zones. Due to the lack of multi-scale evaluation indicators such as rock damage under true three-dimensional stress state and micro-fracture to fracture, numerical calculation results cannot further assess the fracture evolution behavior, degree of rock fracture, and location and extent of key risk zones in rock engineering excavation.

[0003] Therefore, this invention proposes a method for constructing a multi-scale rock fracture degree assessment index, which is of great significance for studying the excavation response analysis of high-stress deep engineering, the evolution of rock failure zones, and safety evaluation. Summary of the Invention

[0004] The purpose of this invention is to provide a method for constructing a multi-scale rock fracture degree assessment index, which can intuitively and quantitatively characterize the fracture location, range and degree of damage of rocks under true three-dimensional stress, and provide a theoretical basis for safety evaluation and stability analysis of high-stress deep rock engineering.

[0005] To achieve the above technical objectives, this invention provides a method for constructing a multi-scale rock fracture degree assessment index, the steps of which include:

[0006] S1. Based on the Mogi-Coulomb three-dimensional strength criterion, establish the multi-scale yield function F of rock;

[0007] S2. Based on the geometric relationship between the strength envelope and the yield surface and stress point of the three-dimensional strength criterion, construct a formula for evaluating the degree of multi-scale fracture of rocks;

[0008] S3. Based on the range of rock multi-scale fracture degree assessment indexes, assess the degree of rock mass fracture by region.

[0009] In step S1, the Mogi-Coulomb criterion is used to establish the three-dimensional rock multi-scale yield function F. The method is as follows:

[0010] The effective average stress σ is established based on the Mogi-Coulomb criterion. m,2 and octahedral shear stress τ oct The relationship is:

[0011] τ oct =a+bσ m, twenty one)

[0012]

[0013]

[0014] Where σ1, σ2, and σ3 are the maximum principal stress, intermediate principal stress, and minimum principal stress, respectively, and c and These are cohesion and internal friction angle, respectively.

[0015] The principal stress formulas in three-dimensional stress space are as follows:

[0016]

[0017] Where q, p and θ σ These are equivalent shear stress, mean stress, and Lode angle, respectively.

[0018]

[0019]

[0020]

[0021] The three-dimensional rock multi-scale yield function F equation, established based on the relationship between the Mogi-Coulomb criterion and the spatial principal stress formula (4), is as follows:

[0022]

[0023]

[0024] In step S2, based on the rock multi-scale yield function F, the strength envelope and yield surface of the yield function are drawn. Point P(p,q) is the stress point on the meridional plane of the average stress p and the equivalent shear stress q, and point B(p,q') is located on the yield surface.

[0025] On the π plane, point B is located on the yield surface, so the coordinates of point B satisfy the yield function (8);

[0026]

[0027]

[0028] When the stress point P is within the yield surface (F<0), the rock multi-scale fracture degree assessment index RMFD is:

[0029]

[0030] When the stress point P is on the yield surface (F=0), the equivalent plastic strain ε after yielding is... s p Define the multi-scale fracture degree assessment index (RMFD) for rocks:

[0031]

[0032]

[0033] in, For equivalent plastic strain The extreme values, and These represent the maximum plastic principal strain, the intermediate plastic principal strain, and the minimum plastic principal strain, respectively.

[0034] In step S3, a true triaxial compression test is performed on the rock sample to obtain the characteristic stress of the rock under the true triaxial stress level: the stress σ corresponding to the stable propagation initiation point of the internal crack in the rock. ci The stress σ corresponding to the initiation point of unstable crack propagation inside the rock cd Peak intensity σ p and residual strength σ r ;

[0035] The rock mass fracture degree is assessed based on RMFD range zoning as follows:

[0036]

[0037] Among them, RMFD ci and RMFD cd These are the stresses σ corresponding to the stable propagation initiation point of internal cracks in rocks under true triaxial stress. ci The stress σ corresponding to the initiation point of unstable crack propagation inside the rock cd The corresponding RMFD value;

[0038] When RMFD <RMFD ci At that time, the σ corresponding to the total stress-strain curve of the rock under true triaxial compression ci In the previous stage, the rock mass was in an elastic state and was defined as the undisturbed zone;

[0039] When RMFD is in RMFD ci ~RMFD cd Within the range, σ corresponds to the total stress-strain curve of rock under true triaxial compression. ci With σ cd The phases between these points are defined as the disturbance zone;

[0040] When RMFD is in RMFD cdWhen the value is in the range of ~1.0, the σ value corresponds to the full stress-strain curve of the rock under true triaxial compression. cd With σ p The phases between these phases are defined as the damage zone;

[0041] When RMFD is in the range of 1.0 to 2.0, the corresponding σ of the rock under true triaxial compression full stress-strain curve is... p With σ r The stage is defined as the fracture zone;

[0042] When RMFD ≥ 2, let its value be 2, which corresponds to σ in the full stress-strain curve of rock under true triaxial compression. r The subsequent stage is defined as the fully fractured zone.

[0043] The beneficial effects of this invention are as follows:

[0044] 1. The index proposed in this invention can be used to assess the degree of rock fracture under true three-dimensional stress.

[0045] 2. The indicators proposed in this invention can be used to assess the process, location, extent, and severity of disasters in deep rock engineering. Attached Figure Description

[0046] Figure 1 This is a flowchart illustrating the construction process of the multi-scale rock fracture assessment index of the present invention.

[0047] Figure 2 The geometric relationship between the meridian of the three-dimensional strength criterion envelope and the stress point;

[0048] Figure 3 This represents the relationship between the stress point and the yield surface on the π-plane.

[0049] Figure 4 The RMFD evolution process and values ​​of true triaxial compression rock failure;

[0050] Figure 5 This is an RMFD cloud map of the chamber after its phased excavation. Detailed Implementation

[0051] The specific embodiments of the present invention are described below with reference to the accompanying drawings, but the present invention is not limited to the scope of the specific embodiments. It should be noted that any creation based on or dependent on the present invention is within the protection scope of the present invention.

[0052] This embodiment uses numerical simulation to model the excavation response of deep underground engineering, and constructs and verifies the applicability and reliability of the multi-scale rock fracture degree assessment index.

[0053] refer to Figure 1 , Figure 1A flowchart illustrating the construction process of multi-scale rock fracture assessment indices is shown, such as... Figure 1 As shown, the method includes steps S1 to S3.

[0054] In step S1, a three-dimensional rock multi-scale yield function F is established based on the Mogi-Coulomb criterion:

[0055]

[0056]

[0057] Where q, p and θ σ These represent the equivalent shear stress, mean stress, and Lode angle, respectively; the cohesion c is 32 MPa; and the internal friction angle is... It is 45°.

[0058] In step S2, based on the meridian of the strength envelope of the yield function, the geometric relationship between the yield surface in three-dimensional stress space and the π plane and the stress point, and the magnitude of the equivalent plastic strain after yielding, the multi-scale fracture degree assessment index RMFD of rocks is constructed:

[0059] Based on the multi-scale yield function F of rock, the strength envelope and yield surface of the yield function are plotted. Point P(p,q) is the stress point on the meridional plane of the mean stress p and equivalent shear stress q, and point B(p,q') lies on the yield surface. The perpendiculars from points P and C to the yield surface are both located in the same meridional plane, and the feet of the perpendiculars E and D, as well as point B, are all located on the meridional line. Figure 2 As shown; on the π plane, point B lies on the yield surface, and the coordinates of point B satisfy the yield function F = 0, as... Figure 3 As shown;

[0060]

[0061]

[0062] The most dangerous stress path is along line PE from point P. ΔPBE and ΔCBD are similar triangles, as shown below. Figure 2 As shown; based on the geometric relationship between the yield surface and the stress point, the RMFD formula for assessing the degree of rock fracture at stress point P within the yield surface is constructed:

[0063]

[0064] When the stress point P is on the yield surface (F=0), the rock fracture degree assessment index RMFD is:

[0065]

[0066] In summary, the multi-scale fracture assessment index (RMFD) for rocks is:

[0067]

[0068] In step S3, a true triaxial compression test is performed on the marble to determine the stress σ corresponding to the stable propagation initiation point of the internal cracks in the rock. ci The stress σ corresponding to the initiation point of unstable crack propagation inside the rock is 110 MPa. cd 227 MPa, peak strength σ p For 315 MPa and residual strength σ r The maximum equivalent plastic strain is 86 MPa. The RMFD evolution process and zonal values ​​of true triaxial compression rock failure are as follows: 0.6%; Figure 4 As shown;

[0069] The rock mass fracture degree is assessed based on RMFD range zoning as follows:

[0070]

[0071] A schematic diagram of the multi-scale rock fracturing index (RMFD) after the step-by-step excavation of the pilot tunnel, side walls, and lower floor slab in a deep engineering chamber according to an embodiment of the present invention is shown below. Figure 5 As shown; Figure 5 (a), (b), and (c) are RMFD cloud maps after the excavation of the central tunnel, the two side walls, and the lower floor slab, respectively.

[0072] This invention uses the Mogi-Coulomb criterion to establish a multi-scale yield function F for rocks. Based on the three-dimensional strength criterion's strength envelope and the geometric relationship between the yield surface and stress points, a formula for evaluating the degree of multi-scale rock fracture is constructed. The degree of rock fracture is then assessed by region based on the stress-strain curves from true triaxial compression tests. The schematic diagram of the RMFD (Real-Scale Fragmentation Function for Rocks) allows for a direct and quantitative determination of the location, extent, and degree of rock fracture. This is of significant importance for studying the excavation response analysis of high-stress deep engineering projects, the evolution of rock failure zones, and safety assessment.

[0073] Finally, it should be noted that the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of protection of the present invention.

Claims

1. A method for constructing a multi-scale rock fracture degree assessment index, comprising the following steps: S1. Based on the Mogi-Coulomb three-dimensional strength criterion, establish the multi-scale yield function F of rock; S2. Based on the geometric relationship between the strength envelope and the yield surface and stress point of the three-dimensional strength criterion, construct a formula for evaluating the degree of multi-scale fracture of rocks; Based on the multi-scale yield function F of rock, the strength envelope and yield surface of the yield function are plotted. Point P(p, q) is the stress point on the meridional plane of the mean stress p and the equivalent shear stress q, and point B(p, It lies on the yield surface; On the π plane, point B lies on the yield surface, so the coordinates of point B satisfy the yield function F=0; Where c and φ are the cohesive force and the internal friction angle, respectively, and θ σ For Cape Lord; When the stress point P is within the yield surface, F < 0, and the rock multi-scale fracture degree assessment index RMFD is: When the stress point P is on the yield surface, F=0, and the rock multi-scale fracture degree assessment index RMFD is: in, For equivalent plastic strain The extreme values, , and These represent the maximum plastic principal strain, the intermediate plastic principal strain, and the minimum plastic principal strain, respectively. S3. Based on the range of rock multi-scale fracture degree assessment indexes, assess the degree of rock mass fracture in different zones; True triaxial compression tests were conducted on rock samples to obtain the characteristic stresses of the rock under true triaxial stress levels: the stress σ corresponding to the stable propagation initiation point of internal cracks in the rock. ci The stress σ corresponding to the initiation point of unstable crack propagation inside the rock cd Peak intensity σ p and residual strength σ r ; The rock mass fracture degree is assessed based on RMFD range zoning as follows: Among them, RMFD ci and RMFD cd These are the stresses σ corresponding to the stable propagation initiation point of internal cracks in rocks under true triaxial stress. ci The stress σ corresponding to the initiation point of unstable crack propagation inside the rock cd The corresponding RMFD value; When RMFD < RMFD ci At that time, the σ corresponding to the total stress-strain curve of the rock under true triaxial compression ci In the previous stage, the rock mass was in an elastic state and was defined as the undisturbed zone; When RMFD is in RMFD ci ~RMFD cd Within the range, σ corresponds to the total stress-strain curve of rock under true triaxial compression. ci With σ cd The phases between these points are defined as the disturbance zone; When RMFD is in RMFD cd When the value is in the range of ~1.0, the σ value corresponds to the full stress-strain curve of the rock under true triaxial compression. cd With σ p The phases between these phases are defined as the damage zone; When RMFD is in the range of 1.0 to 2.0, the corresponding σ of the rock under true triaxial compression full stress-strain curve is... p With σ r The stage is defined as the fracture zone; When RMFD ≥ 2, let its value be 2, which corresponds to σ in the full stress-strain curve of rock under true triaxial compression. r The subsequent stage is defined as the fully fractured zone.

2. The method for constructing a multi-scale rock fracture degree assessment index according to claim 1, characterized in that, In step S1, the Mogi-Coulomb criterion is used to establish the three-dimensional rock multi-scale yield function F. The method is as follows: The effective average stress σ is established based on the Mogi-Coulomb criterion. m,2 and octahedral shear stress τ oct The relationship is: Where σ1, σ2 and σ3 are the maximum principal stress, intermediate principal stress and minimum principal stress, respectively, and c and φ are the cohesion and internal friction angle, respectively. The principal stress formulas in three-dimensional stress space are as follows: Where q, p and θ σ These are equivalent shear stress, mean stress, and Lodé angle, respectively. The three-dimensional rock multi-scale yield function F equation, established based on the relationship between the Mogi-Coulomb criterion and the spatial principal stress formula, is as follows: 。

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