Method for constructing wave velocity anisotropy model of stochastic fractured rock considering confining pressure effect

Abstract

The application discloses a method for constructing a random fissure rock wave velocity anisotropy model considering the confining pressure effect, relates to the technical field of rock fissure wave velocity, and comprises the following steps: S1, equivalent of the randomly distributed microfissure in the rock to a two-dimensional elliptical fissure; S2, establishment of a geometric relationship between the apparent wave velocity and the detour path length based on the diffraction path of ultrasonic wave propagation along the rock matrix around the fissure; S3, introduction of the compression effect of the confining pressure on the short axis half length of the elliptical fissure, and establishment of a quantitative expression of the short axis half length under the action of the confining pressure; S4, prediction of the rock apparent wave velocity under different propagation directions based on the geometric relationship of the diffraction path and the short axis half length after compression of the confining pressure b The method can quickly and non-destructively identify the dominant extension direction of the main fissure of the rock mass, further identify the dominant direction of the maximum principal stress release, and provide a simple and effective detection means for the damage of the complex fissure rock mass and the evaluation of the stress direction in the underground rock engineering.

Description

Technical Field

[0001] This invention relates to the field of rock fracture wave velocity technology, and in particular to a method for constructing a random fracture rock wave velocity anisotropy model that takes into account the confining pressure effect. Background Technology

[0002] The development characteristics of natural random fractures and the complexity of their impact on surrounding rock stability have attracted widespread attention. However, most studies focus on the mechanical characteristics and fracture mechanisms of regularly developed fractures, while systematic research on the wave velocity evolution and failure prediction methods of heterogeneous fractured limestone under different confining pressures remains lacking. Particularly for heterogeneous rocks containing primary fractures, the combined effect of the internal random fracture structure and stress conditions causes wave velocities to exhibit directional and complex variations. Especially under confining pressure, the fracture closure and propagation processes further influence wave velocity propagation characteristics, thus increasing the complexity of failure prediction. Traditional wave velocity models simply calculate wave velocity characteristics by passing through rock fractures, simplifying many key parameters and resulting in ideal results that differ significantly from reality. Therefore, this invention takes heterogeneous fractured limestone as the research object and establishes a circumferential wave velocity theoretical prediction model considering the influence of confining pressure to predict and characterize the failure behavior of randomly fractured limestone. Summary of the Invention

[0003] The purpose of this invention is to provide a method for constructing a wave velocity anisotropy model of stochastic fractured rocks that takes into account the confining pressure effect. A wave velocity anisotropy model of rock fractures based on elliptical fractures is established, revealing the influence of confining pressure and fracture direction on wave velocity.

[0004] To achieve the above objectives, this invention provides a method for constructing a stochastic fractured rock wave velocity anisotropy model considering confining pressure effects, comprising the following steps: S1. The randomly distributed micro-fractures inside the rock are equivalent to two-dimensional elliptical fractures, which have a major axis. and short axis ; S2. Based on the diffraction path of ultrasonic waves propagating along the rock matrix around the fracture, establish the apparent wave velocity. The geometric relationship between apparent wave velocity and the length of the bypass path is that apparent wave velocity is the ratio of the straight-line distance between the probes to the actual bypass propagation time of the ultrasonic wave. S3, Introducing confining pressure For the minor axis of the elliptical crack The compression effect establishes the semi-length of the minor axis under confining pressure. Quantitative expression; S4. Based on the geometric relationship of the diffraction path and the semi-length of the minor axis after confining pressure. The apparent wave velocity of rocks under different propagation directions was predicted, and the direction of the maximum wave velocity was determined to be the direction of the long axis of the fracture, and the direction of the minimum wave velocity was determined to be the direction of the short axis of the fracture.

[0005] Preferably, the apparent wave velocity in S2 is: In the formula, The diameter of the rock. The speed at which ultrasound propagates in the rock matrix. Let AC be the length of line segment AC. Let the length of line segment BC be , For testing angles; and Represented as: In the formula, It is the angle between the point on the crack surface that is furthest from the straight-line propagation and the minor axis of the crack.

[0006] Preferably, the compressed short axis half-length in S3 for: In the formula, Poisson's ratio, This represents the elastic modulus of the rock.

[0007] Preferably, the confining pressure in S3 When applied along the minor axis of the fracture, a normal closing pressure is applied to the fracture, causing it to contract and close. The compressive response is as follows: In the formula, For surface normal stiffness.

[0008] Preferably, the confining pressure in S3 Applying a reverse Mode-I load to the crack reduces its stress intensity factor (SIF), causing the elliptical crack to exhibit higher stress in the far field. With confining pressure Under the combined effect, its Type I SIF is written as: In the formula, It is a geometric correction function; Mode-I opening displacement satisfies: In the formula, For opening displacement, Poisson's ratio, It is the major axis of the elliptical crack.

[0009] Preferably, in S4, the compression amplitude of the minor axis increases linearly with the increase of confining pressure, until the confining pressure reaches a level that makes... As the value approaches zero, the crack tends to close.

[0010] Preferably, the major axis of the elliptical crack in S4 Sensitivity to adjusting wave velocity anisotropy, aspect ratio The larger the wave velocity, the more sensitive it is to changes in direction.

[0011] Therefore, this invention employs the aforementioned method for constructing anisotropic wave velocity models of stochastic fractured rocks that consider confining pressure effects. It reveals the influence of confining pressure and fracture direction on wave velocity. Wave velocity exhibits anisotropic variation with propagation direction. When the propagation direction aligns with the fracture extension direction, a waveguide channel forms at the fracture interface, maximizing wave velocity. Conversely, when the propagation direction is perpendicular to the fracture, the wave must traverse the fracture interface, leading to enhanced scattering and energy loss, thus reducing wave velocity. This method allows for rapid and non-destructive identification of the dominant extension direction of main rock fractures and the dominant direction of stress release, providing a simple and effective detection method for evaluating structural surfaces in rock engineering. It also provides a crucial mechanical theoretical foundation for real-time monitoring of rock mass mechanical state and identification of potential failure precursors in slope engineering, tunnel excavation, and rockburst prediction.

[0012] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0013] Figure 1 This is a flowchart illustrating the method for constructing a stochastic fractured rock wave velocity anisotropy model considering confining pressure effects, as described in this invention. Figure 2 The figure shows the theoretical calculation results of wave velocity in fractured limestone according to the present invention. (a) shows the confining pressure and b Value relationship, (b) is the confining pressure and b The relationship between the reduction rate of the value, (c) is the major axis of the same crack. a Value theory is used to calculate wave velocity characteristics; Figure 3 This is a ripple propagation diagram of the present invention. Detailed Implementation

[0014] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0015] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0016] Example Please see Figures 1-3 This invention provides a method for constructing a stochastic fractured rock wave velocity anisotropy model considering confining pressure effects, comprising the following steps: S1. The directionally distributed micro-fractures inside the rock are equivalent to two-dimensional elliptical fractures, with the major axis being... and short axis .

[0017] S2. Based on the diffraction path of ultrasonic waves propagating along the rock matrix around the fracture, establish the apparent wave velocity. The geometric relationship between apparent wave velocity and the length of the bypass path is that apparent wave velocity is the ratio of the straight-line distance between the probes to the actual bypass propagation time of the ultrasonic wave.

[0018] Elliptical fractures can both describe the typical aspect ratio characteristics of natural fractures and ensure consistency between the stress singularity at the crack tip and fracture mechanics. Based on wave velocity... As can be seen from the test principle, the wave velocity is equal to the diameter of the rock specimen. With the time of transmission The diameter of the rock specimen It is a fixed value. Therefore, the only factor affecting wave speed is propagation time. The propagation time is related to the propagation path of the ultrasound.

[0019] In the formula, For wave speed, The diameter of the rock specimen is _____. For the duration of transmission.

[0020] Under normal propagation conditions, waves do not traverse the fissure but propagate along the matrix around it, with the propagation time controlled by the path length. Therefore, the wave velocity depends on the path length rather than the difference in wave velocity between media. Due to the presence of the fissure, the wave propagation path changes from straight-line propagation to diffraction, making the actual propagation path length greater than the geometric distance between probes. The wave velocity obtained in ultrasonic testing is the apparent wave velocity calculated based on the straight-line distance between probes; therefore, its value is lower than the intrinsic wave velocity of the material and is affected by the geometric characteristics of the fissure and the propagation angle.

[0021] Assume the cross section of the rock specimen has a diameter of The circle, while the major axis of the elliptical statistical crack at the center of the cross-section is... The minor axis is Establish a rectangular coordinate system with the major and minor axes of the ellipse, such as Figure 3 As shown. Points A and B are the test endpoints. This represents the test angle. There are many propagation paths, including two special paths: linear propagation (path ADEB) and propagation around the hole (path ACB). Point C is the point on the statistical crack surface farthest from the linear propagation path (path ADEB), and the angle between point C and the minor axis of the statistical crack is denoted as . Assuming diameter It is 50mm long axis It is 5mm long and has a short shaft. It is 0.5mm. The wave velocity is 5000 m / s (limestone wave velocity), and the wave velocity calculated by the borehole model is consistent with the actual measured wave velocity-microcrack relationship.

[0022] The apparent wave velocity in rock fissures can be represented by the propagation velocity along a curved path equivalent to a straight distance. From geometric relationships, the apparent wave velocity along the propagation path around the hole can be obtained as follows: In the formula, For apparent wave velocity, The diameter of the rock. The speed at which ultrasound propagates in the rock matrix. Let AC be the length of line segment AC. Let the length of line segment BC be , For testing angles; and Represented as: In the formula, Let AC be the length of line segment AC. Let the length of line segment BC be , For testing angles, The diameter of the rock specimen is _____. The major axis of the elliptical crack, The minor axis of the elliptical crack. It is the angle between the point on the crack surface that is furthest from the straight-line propagation and the minor axis of the crack.

[0023] S3, Introducing confining pressure For the minor axis of the elliptical crack The compression effect establishes the semi-length of the minor axis under confining pressure. The quantitative expression for .

[0024] When confining pressure When acting along the minor axis of the fracture, it is equivalent to applying a normal closing pressure to the fracture, causing it to contract and close. Treating the elliptical fracture as an equivalent elliptical cavity, its compressive response can be described as follows: In the formula, To compress the response, For confining pressure, For surface normal stiffness.

[0025] Therefore, the compressed minor axis is: In the formula, For the short axis half length, The minor axis of the elliptical crack. For confining pressure, It is related to the crack roughness, contact condition, and rock elastic modulus. In the case of elasticity It can be approximated as: In the formula, For surface normal stiffness, For the elastic modulus of rock, Poisson's ratio, This refers to the characteristic aperture of a crack under a certain condition.

[0026] therefore: In the formula, For the short axis half length, The minor axis of the elliptical crack. For confining pressure, Poisson's ratio, For the elastic modulus of rock, This refers to the characteristic aperture of a crack under a certain condition.

[0027] when (At the initial fracture aperture): In the formula, For the short axis half length, The minor axis of the elliptical crack. For confining pressure, Poisson's ratio, This represents the elastic modulus of the rock.

[0028] This expression indicates that increased confining pressure will lead to short-axis linear contraction, the magnitude of which is affected by the rock's elastic modulus. Poisson's ratio and the short axis of the fracture b Control.

[0029] Confining pressure Applying a reverse Mode-I load to the crack reduces its stress intensity factor (SIF). Elliptical cracks under far-field stress... With confining pressure Under the combined effect, its Type I SIF is written as: In the formula, This is a geometric correction function.

[0030] Mode-I opening displacement satisfies: In the formula, For the crack opening displacement, Poisson's ratio, For the elastic modulus of rock, It is the major axis of the elliptical crack.

[0031] An increase in confining pressure will lead to and The minor axis is reduced proportionally, thus reducing the length of the minor axis. The equivalent opening in the direction tends to converge. In summary, whether from the perspective of elastic contact model or fracture mechanics, confining pressure reduces the opening capacity of the elliptical crack, causing the minor axis to... It continues to compress as the confining pressure increases. When the confining pressure reaches a sufficiently high level, the short axis of the fracture can approach a closed state.

[0032] S4. Based on the geometric relationship of the diffraction path and the semi-length of the minor axis after confining pressure. The apparent wave velocity of rock under different propagation directions was predicted, and the direction of the maximum wave velocity was determined to be the direction of the fracture's long axis, and the direction of the minimum wave velocity was determined to be the direction of the fracture's short axis. The compression amplitude of the short axis increased linearly with increasing confining pressure, and the compression amplitude reached a certain value when the confining pressure reached a certain level. As the value approaches zero, the fracture tends to close. (Major axis of the elliptical fracture) Sensitivity to adjusting wave velocity anisotropy, aspect ratio The larger the wave velocity, the more sensitive it is to changes in direction.

[0033] Assuming the elastic modulus of limestone is 40 GPa and the Poisson's ratio is 0.25, theoretical results are obtained for different confining pressures and initial conditions. Compression characteristics such as Figure 2 As shown, it can be observed that as the confining pressure increases... The value decreases linearly. The reduction rate also increases linearly. Since the major axis has a greater impact on the propagation distance around the hole, it is the one that significantly affects the propagation distance. Furthermore, it demonstrated Different times value The theoretical calculation of wave velocity considering confining pressure, a Changes in [the wave velocity] will affect the wave velocity value, but will have little effect on the direction of the maximum and minimum values. The most sensitive, Minimal sensitivity, i.e. The larger the wave size, the greater the impact on wave velocity. Figure 3 This diagram shows the relationship between theoretical predictions and the actual crack long axis direction. The red arrows point in the direction of the crack long axis. Direction, along the long axis of the crack High directional wave velocity, conversely, short axis of crack. The directional wave velocity is small. It can be seen that the direction of the maximum wave velocity obtained theoretically is basically consistent with the direction of the actual fracture long axis, that is, the results are consistent.

[0034] It should be noted that in actual rock masses, the fracture interface usually exhibits contact and closure effects, which alters the wave propagation mechanism and may cause the extreme wave velocity direction to deviate from theoretical predictions. Wave velocity varies anisotropically with the propagation direction. When the propagation direction is consistent with the fracture extension direction, the fracture interface forms a wave-guiding channel, maximizing the wave velocity. However, when the propagation direction is perpendicular to the fracture, the wave must pass through the fracture interface, leading to increased scattering and energy loss, thus reducing the wave velocity.

[0035] Therefore, this invention employs the aforementioned method for constructing a random fractured rock wave velocity anisotropy model considering confining pressure effects. It clarifies the differences in sensitivity of fractures of different scales to wave velocity magnitude and extreme direction, providing a quantitative indicator for inverting the geometric morphology of internal rock fractures using acoustic wave test data, thus improving the accuracy of geological exploration interpretation. It indicates that the direction of the maximum wave velocity corresponds to the long axis extension direction of the fracture, and the direction of the minimum wave velocity corresponds to the short axis (opening) direction of the fracture. This allows for rapid and non-destructive identification of the dominant extension direction of the main rock fracture and the dominant direction of stress release, providing a simple and effective detection method for evaluating structural surfaces in rock engineering. This model can be used to establish a quantitative relationship between the rate of change of wave velocity anisotropy and the change of confining pressure, providing a crucial mechanical theoretical foundation for real-time monitoring of the rock mass mechanical state and identification of precursors of failure in slope engineering, tunnel excavation, and rockburst prediction. When an abnormal turning point occurs in wave velocity anisotropy, it can be used to infer the abrupt change in the closure-opening state of the fracture, providing early warning of rock mass instability risks.

[0036] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for constructing a stochastic fractured rock wave velocity anisotropy model considering confining pressure effects, characterized in that, Includes the following steps: S1. The randomly distributed micro-fractures inside the rock are equivalent to two-dimensional elliptical fractures, which have a major axis. and short axis ; S2. Based on the diffraction path of ultrasonic waves propagating along the rock matrix around the fracture, establish the apparent wave velocity. The geometric relationship between apparent wave velocity and the length of the bypass path is that apparent wave velocity is the ratio of the straight-line distance between the probes to the actual bypass propagation time of the ultrasonic wave. S3, Introducing confining pressure For the minor axis of the elliptical crack The compression effect establishes the semi-length of the minor axis under confining pressure. Quantitative expression; S4. Based on the geometric relationship of the diffraction path and the semi-length of the minor axis after confining pressure. b The apparent wave velocity of rocks under different propagation directions and confining pressures was predicted, and the direction of the maximum wave velocity was determined to be the long axis of the fracture, and the direction of the minimum wave velocity was determined to be the short axis of the fracture.

2. The method for constructing a stochastic fractured rock wave velocity anisotropy model considering confining pressure effect according to claim 1, characterized in that: The apparent wave velocity in S2 is: In the formula, The diameter of the rock. The speed at which ultrasound propagates in the rock matrix. Let AC be the length of line segment AC. Let the length of line segment BC be , For testing angles; and Represented as: In the formula, It is the angle between the point on the crack surface that is furthest from the straight-line propagation and the minor axis of the crack.

3. The method for constructing a stochastic fractured rock wave velocity anisotropy model considering confining pressure effects according to claim 2, characterized in that: The compressed short axis semi-length in S3 for: In the formula, Poisson's ratio, This represents the elastic modulus of the rock.

4. The method for constructing a stochastic fractured rock wave velocity anisotropy model considering confining pressure effect according to claim 3, characterized in that: S3 medium pressure When applied along the minor axis of the fracture, a normal closing pressure is applied to the fracture, causing it to contract and close. The compressive response is as follows: In the formula, For surface normal stiffness.

5. The method for constructing a stochastic fractured rock wave velocity anisotropy model considering confining pressure effects according to claim 4, characterized in that: S3 medium pressure Applying a reverse Mode-I load to the crack reduces its stress intensity factor (SIF), causing the elliptical crack to exhibit higher stress in the far field. With confining pressure Under the combined effect, its Type I SIF is written as: In the formula, It is a geometric correction function; Mode-I opening displacement satisfies: In the formula, For opening displacement, Poisson's ratio, It is the major axis of the elliptical crack.

6. The method for constructing a stochastic fractured rock wave velocity anisotropy model considering confining pressure effect according to claim 5, characterized in that: In S4, the compression amplitude of the minor axis increases linearly with increasing confining pressure, until the confining pressure reaches a point where... As the value approaches zero, the crack tends to close.

7. The method for constructing a stochastic fractured rock wave velocity anisotropy model considering confining pressure effects according to claim 6, characterized in that: The major axis of the elliptical crack in S4 a Sensitivity to adjusting wave velocity anisotropy, aspect ratio a / b The larger the wave velocity, the more sensitive it is to changes in direction.

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