阅读说明：本技术 危岩裂缝水深度测量方法、危岩崩塌预警方法与系统 (Dangerous rock crack water depth measurement method, dangerous rock collapse early warning method and system ) 是由 王林峰 张继旭 唐宁 冉楗 于 2021-08-23 设计创作，主要内容包括：本发明涉及危岩崩塌预警技术领域,公开了危岩裂缝水深度测量方法、危岩崩塌预警方法与系统,本发明通过超声脉冲平测法可以实现对危岩裂缝深度的实时监测,基于横波和纵波在水中传播的特性可以测量出危岩主控结构面裂缝水深度,克服目前工程上采用经验估计而无法准确得出裂缝水深度导致的缺陷。基于危岩裂缝水深度和裂缝张开角度的监测,采用断裂力学COD准则、最大周向应力准则等其他相关理论对危岩主控结构面的扩展进行分析,建立基于断裂力学的危岩稳定性判别公式,实现对危岩体的崩塌预警。(The invention relates to the technical field of dangerous rock collapse early warning, and discloses a dangerous rock fracture water depth measuring method, a dangerous rock collapse early warning method and a dangerous rock fracture water depth early warning system. Based on monitoring of the water depth and the crack opening angle of the dangerous rock cracks, the expansion of the main control structural plane of the dangerous rock is analyzed by adopting other relevant theories such as a fracture mechanics COD (chemical oxygen demand) criterion and a maximum circumferential stress criterion, a dangerous rock stability discrimination formula based on fracture mechanics is established, and collapse early warning of dangerous rock bodies is realized.)

1. A fracture water depth measurement method is characterized by comprising the following steps:

arranging an ultrasonic transducer: the two sides of the central transducer are respectively provided with a gap-crossing transducer and a gap-not-crossing transducer at equal intervals; the central transducer and the non-seam-crossing transducer are both positioned on the top surface of the mother rock, and the seam-crossing transducer is positioned on the top surface of the dangerous rock mass; the central transducer can respectively transmit and receive ultrasonic waves with the gap-crossing transducer and the gap-non-crossing transducer;

measuring the crack depth h by adopting a transverse wave method in an ultrasonic pulse leveling method:

measuring the depth h from the water surface to the end face of the crack opening end by adopting a longitudinal wave method in an ultrasonic pulse leveling method₁：

In the formula, t₀When the sound is measured by the non-slit-crossing leveling between the central transducer and the non-slit-crossing transducer; t is the time of the seam crossing leveling sound between the central transducer and the seam crossing transducer; l is the distance measurement between the central transducer and the slit-crossing transducer, L ═ L '+ a, and L' is the distance between the central transducer and the slit-crossing transducer, i.e. the distance of the inner edge; a is the intercept of a pre-calibrated time-distance graph, the time-distance graph is a scatter diagram formed by taking the sound time of each measuring point without crossing a seam as a horizontal coordinate and taking distance measurement as a vertical coordinate, and finally the intercept a is calculated according to a linear regression method;

calculating the depth h of the fracture water₂：h₂＝h-h₁。

2. The method for measuring the water depth of the crack as claimed in claim 1, wherein the non-seam crossing transducers are arranged on the measuring points with different distances from the central transducer in advance, and the sound time value and the distance measurement on each measuring point are respectively read, so that a time-distance graph is drawn according to the sound time value and the distance measurement.

3. A dangerous rock collapse early warning method is characterized by comprising the following steps: the fracture water depth measurement method is adopted to measure the fracture water depth in real time, so that the fracture water depth is monitored; the method comprises the following steps:

monitoring the crack opening angle by using a dial angle measuring instrument: inserting a dial type angle measuring instrument on the top surface of the dangerous rock mass in a direction parallel to the initial unopened crack, keeping the dial type angle measuring instrument and the dangerous rock mass to integrally move along with the continuous opening of the crack, keeping a gravity pointer of the dial type angle measuring instrument vertical all the time under the action of gravity, enabling a reading alpha of the gravity pointer to be an included angle between the dangerous rock mass and the vertical direction after displacement, enabling 90-alpha-beta to be an opened angle value of the crack, and enabling beta to be an initial included angle between the crack and a horizontal plane when the crack is unopened;

calculating the fracture opening V according to the fracture depth h and the fracture opening angle:

calculating fracture opening displacement delta according to the fracture opening degree V:

in the formula, H is the thickness of the dangerous rock mass, r is a rotation factor, and the value of the rotation factor is 0.3-0.5;

the crack opening displacement delta of the calculated critical rock main control structure surface and the crack critical opening displacement delta measured by performing a three-point bending test on the critical rock sample_cComparing if delta is larger than or equal to delta_cThe crack is shown to be expanded, and the dangerous rock has the possibility of unstable collapse;

when delta is larger than or equal to delta_cAnd then, calculating a dangerous rock stability coefficient Fs, and judging whether the dangerous rock is stable according to the dangerous rock stability coefficient Fs, wherein the method comprises the following steps:

according to the stress characteristics of the dumping type dangerous rock, the influence of earthquake force is not considered, and under the action of dead weight and fracture water pressure, the load applied to the fracture tip of the main control structural plane of the dangerous rock is decomposed into a load from sigma_max、τ_maxAnd σ_M(ii) a Under the condition of independent action of three loads, the fracture mode is decomposed into three modes of tension I-type fracture, shear II-type fracture and bending I-type fracture;

according to the depth h of the fracture water₂Critical depth h of crack propagation with main control structure surface₀Calculating the load sigma_maxAccording to the critical depth h of crack propagation of the main control structure surface₀Calculating the load τ_maxAnd σ_M(ii) a When delta is equal to delta_cThe measured crack depth is the critical depth h of the crack propagation of the main control structure surface₀。

Analyzing each fracture mode independently, calculating a stress intensity factor under each condition mode according to corresponding load, combining and superposing according to a superposition principle to obtain I-type and II-type stress intensity factors of the dangerous rock fracture tip, and calculating a combined stress intensity factor Ke of a dangerous rock main control structural plane according to the I-type and II-type stress intensity factors of the dangerous rock fracture tip;

calculating a dangerous rock stability coefficient Fs: f_s＝K_C/K_e(ii) a Wherein the fracture toughness K of the complete rock of the dangerous rock_CMeasured by fracture mechanics tests;

if F_sIf the critical rock mass is more than or equal to 1, judging that the dangerous rock mass is stable, F_s<And 1, judging that the dangerous rock mass is going to collapse unstably.

4. The dangerous rock collapse early warning method according to claim 3, wherein: load sigma_maxThe calculation formula of (a) is as follows:

σ_max＝γ_wh₂-γ_sh₀cos(90°-α)；

load τ_maxThe calculation formula of (a) is as follows:

τ_max＝γ_sh₀sin(90°-α)

load sigma_MThe calculation formula of (a) is as follows:

in the formula, gamma_wIs the severity of the fracture water; gamma ray_sThe severity of the dangerous rock mass; w is dead weight of the dangerous rock mass; m is a bending moment generated by dead weight of the dangerous rock; b is the horizontal distance from the center of gravity of the dangerous rock to the tip of the fracture.

5. The dangerous rock collapse early warning method according to claim 4, wherein: for tension I-type fracture, the fracture surface of the main control structure surface is subjected to linear load, and the stress intensity factor handbook is combined to obtain the tension I-type fracture stress intensity factor which is as follows:

for the II-type fracture under shear, the crack surface of the main control structure surface is subjected to linear load, and the stress intensity factor handbook is combined to obtain the stress intensity factor for the II-type fracture under shear as follows:

for flexural I-type fracture, combining a stress intensity factor manual to obtain the stress intensity factor of the flexural I-type fracture as follows:

wherein H is the thickness of the dangerous rock mass, H₀The critical depth of crack propagation of the main control structure surface.

6. The dangerous rock collapse early warning method according to claim 5, wherein: calculating the type I and type II stress intensity factors of the tip of the dangerous rock crack according to the superposition principle of the stress intensity factors:

K_Ⅰ＝K_Ⅰ1+K_Ⅰ2

K_Ⅱ＝K_Ⅱ1

in the formula, K_ⅠType I stress intensity factor, K, for the tip of a dangerous rock fracture_ⅡIs the type II stress intensity factor of the tip of the dangerous rock crack.

7. The dangerous rock collapse early warning method according to claim 6, wherein: main control structural surfaceJoint stress intensity factor K of fracture tip_e：

In the formula, theta₀Representing the fracture angle of the fractures of the critical rock.

8. A dangerous rock collapse early warning system applying the dangerous rock collapse early warning method according to claim 3, characterized in that: the crack water depth monitoring device comprises a crack water depth monitoring device, a crack opening angle monitoring device, a remote communication device, a power supply device, a host and an early warning module;

the fracture water depth monitoring device is used for monitoring the fracture water depth and comprises the following ultrasonic transducers: the two sides of the central transducer are respectively provided with a gap-crossing transducer and a gap-not-crossing transducer at equal intervals; the crack opening angle monitoring device is used for monitoring the crack opening angle and comprises a dial angle measuring instrument and a pointer instrument reading device; the pointer instrument reading device is used for automatically reading the reading of the dial angle measuring instrument;

the crack water depth monitoring device and the crack opening angle monitoring device send monitoring data to the host through the remote communication device;

the host is used for calculating the dangerous rock stability coefficient Fs according to the monitoring data and sending the calculation result to the early warning module;

the early warning module is used for judging whether the dangerous rock mass is stable according to the dangerous rock stability coefficient, and when the dangerous rock mass is judged to collapse in a destabilizing mode, an early warning signal is sent out.

9. The dangerous rock collapse early warning system according to claim 8, wherein: the remote communication module is a 5G communication module; the power supply device is a solar power supply device.

10. The dangerous rock collapse early warning system according to claim 8, wherein: the central transducer, the seam crossing transducer and the non-seam crossing transducer are all in close contact with the surface of the rock body through the paste couplant.

Technical Field

The invention relates to the technical field of dangerous rock collapse early warning.

Background

The dangerous rocks are generally rock blocks which are located on a cliff and cut by a rock mass structural plane and can be collapsed at any time, and the dangerous rocks can be classified into sliding type dangerous rocks, dumping type dangerous rocks and falling type dangerous rocks according to a destabilization mode. Dangerous rock collapse is a common geological disaster in mountainous areas, has large impact energy and strong formed damage, and brings serious threat to human production and life. The unstable destruction of the dangerous rock is mainly a process of crack expansion and penetration of a main control structure surface of the dangerous rock under the action of dead weight of the dangerous rock and external load (mainly considering crack water pressure and not considering earthquake force).

The opening angle of the cracks on the main control structural plane of the dangerous rock has great influence on the stability of the dangerous rock, the opening angle of the cracks of the dangerous rock body is gradually increased under the action of self weight and external load, the overall stability of the dangerous rock is adversely affected, and the opening displacement can be calculated according to the opening angle of the measured cracks, so that whether the cracks are expanded or not is judged. Under the rainfall condition, the crack water can be gathered in the critical rock main control structure surface, the crack water depth is obtained according to experience at present, 1/3 of the length of the crack through section is taken under the natural working condition, and 1/2-2/3 of the length of the crack through section is taken under the rainstorm working condition. The depth of the crack water of the critical rock main control structure surface can not be accurately measured, so that the crack water pressure value of the critical rock is not accurately calculated, and a reasonable stability state of the critical rock can not be obtained.

Disclosure of Invention

Aiming at the defects of the prior art, the invention provides a dangerous rock fracture water depth monitoring device, which solves the technical problem that the fracture water depth depends on experience value in the prior art.

In order to solve the technical problems, the invention adopts the following technical scheme: a fracture water depth measurement method comprises the following steps:

arranging an ultrasonic transducer: the two sides of the central transducer are respectively provided with a gap-crossing transducer and a gap-not-crossing transducer at equal intervals; the central transducer and the non-seam-crossing transducer are both positioned on the top surface of the mother rock, and the seam-crossing transducer is positioned on the top surface of the dangerous rock mass; the central transducer can respectively transmit and receive ultrasonic waves with the gap-crossing transducer and the gap-non-crossing transducer;

measuring the crack depth h by adopting a transverse wave method in an ultrasonic pulse leveling method:

measuring the depth h from the water surface to the end face of the crack opening end by adopting a longitudinal wave method in an ultrasonic pulse leveling method₁：

In the formula, t₀When the sound is measured by the non-slit-crossing leveling between the central transducer and the non-slit-crossing transducer; t is the time of the seam crossing leveling sound between the central transducer and the seam crossing transducer; l is the distance measurement between the central transducer and the slit-crossing transducer, L ═ L '+ a, and L' is the distance between the central transducer and the slit-crossing transducer, i.e. the distance of the inner edge; a is the intercept of a pre-calibrated time-distance graph, the time-distance graph is a scatter diagram formed by taking the sound time of each measuring point without crossing a seam as a horizontal coordinate and taking distance measurement as a vertical coordinate, and finally the intercept a is calculated according to a linear regression method;

calculating the depth h of the fracture water₂：h₂＝h-h₁。

The invention also provides a dangerous rock collapse early warning method, namely a dangerous rock collapse early warning method, the fracture water depth is measured in real time by adopting the fracture water depth measuring method, so that the fracture water depth is monitored; the method comprises the following steps:

monitoring the crack opening angle by using a dial angle measuring instrument: inserting a dial type angle measuring instrument on the top surface of the dangerous rock mass in a direction parallel to the initial unopened crack, keeping the dial type angle measuring instrument and the dangerous rock mass to integrally move along with the continuous opening of the crack, keeping a gravity pointer of the dial type angle measuring instrument vertical all the time under the action of gravity, enabling a reading alpha of the gravity pointer to be an included angle between the dangerous rock mass and the vertical direction after displacement, enabling 90-alpha-beta to be an opened angle value of the crack, and enabling beta to be an initial included angle between the crack and a horizontal plane when the crack is unopened;

calculating the fracture opening V according to the fracture depth h and the fracture opening angle:

calculating fracture opening displacement delta according to the fracture opening degree V:

in the formula, H is the thickness of the dangerous rock mass, r is a rotation factor, and the value of the rotation factor is 0.3-0.5;

the crack opening displacement delta of the calculated critical rock main control structure surface and the crack critical opening displacement delta measured by performing a three-point bending test on the critical rock sample_cComparing if delta is larger than or equal to delta_cThe crack is shown to be expanded, and the dangerous rock has the possibility of unstable collapse;

when delta is larger than or equal to delta_cAnd then, calculating a dangerous rock stability coefficient Fs, and judging whether the dangerous rock is stable according to the dangerous rock stability coefficient Fs, wherein the method comprises the following steps:

according to the stress characteristics of the dumping type dangerous rock, the influence of earthquake force is not considered, and under the action of dead weight and fracture water pressure, the load applied to the fracture tip of the main control structural plane of the dangerous rock is decomposed into a load from sigma_max、τ_maxAnd σ_M(ii) a Under the condition of independent action of three loads, the fracture mode is decomposed into three modes of tension I-type fracture, shear II-type fracture and bending I-type fracture;

according to the depth h of the fracture water₂Critical depth h of crack propagation with main control structure surface₀Calculating the load sigma_maxAccording to the critical depth h of crack propagation of the main control structure surface₀Calculating the load τ_maxAnd σ_M(ii) a When delta is equal to delta_cThe measured crack depth is the critical depth h of the crack propagation of the main control structure surface₀。

Analyzing each fracture mode independently, calculating a stress intensity factor under each condition mode according to corresponding load, combining and superposing according to a superposition principle to obtain I-type and II-type stress intensity factors of the dangerous rock fracture tip, and calculating a combined stress intensity factor Ke of a dangerous rock main control structural plane according to the I-type and II-type stress intensity factors of the dangerous rock fracture tip;

calculating a dangerous rock stability coefficient Fs: f_s＝K_C/K_e(ii) a Wherein the fracture toughness K of the complete rock of the dangerous rock_CMeasured by fracture mechanics tests;

if F_sIf the critical rock mass is more than or equal to 1, judging that the dangerous rock mass is stable, F_s<And 1, judging that the dangerous rock mass is going to collapse unstably.

The invention also provides a dangerous rock collapse early warning system applying the rock collapse early warning method, which comprises a crack water depth monitoring device, a crack opening angle monitoring device, a remote communication device, a power supply device, a host and an early warning module;

the crack water depth monitoring device is used for monitoring the crack water depth and comprises a center transducer, wherein two sides of the center transducer are respectively provided with a cross-crack transducer and a non-cross-crack transducer at equal intervals; the crack opening angle monitoring device is used for monitoring the crack opening angle and comprises a dial angle measuring instrument;

the crack water depth monitoring device and the crack opening angle monitoring device send monitoring data to the host through the remote communication device;

the host is used for calculating the dangerous rock stability coefficient Fs according to the monitoring data and sending the calculation result to the early warning module;

the early warning module is used for judging whether the dangerous rock mass is stable according to the dangerous rock stability coefficient, and when the dangerous rock mass is judged to collapse in a destabilizing mode, an early warning signal is sent out.

Compared with the prior art, the invention has the following beneficial effects:

1. according to the invention, real-time monitoring of the depth of the cracks of the dangerous rock can be realized by an ultrasonic pulse planimetry method, the depth of the cracks of the main control structural surface of the dangerous rock can be measured based on the characteristics of propagation of transverse waves and longitudinal waves in water, and the defect that the depth of the cracks cannot be accurately obtained due to empirical estimation in the existing engineering is overcome.

2. According to the invention, the opening angle of the crack of the dumping type dangerous rock main control structure surface can be monitored in real time through the dangerous rock inclination angle measuring device, the opening degree of the crack can be calculated through the monitored angle, and accurate parameters are provided for the subsequent calculation of the crack opening displacement delta.

3. The invention is based on the fracture mechanics COD criterion according to the geometryCalculating the opening displacement delta of the crack of the main control structural plane of the dangerous rock according to the relation, and finally calculating the critical opening displacement delta of the crack of the dangerous rock_cComparing, judging whether the displacement crack can be further expanded or not, and measuring the critical crack depth h during expansion₀。

4. The method is based on the theory of maximum circumferential stress of fracture mechanics, and the fracture angle theta of the dangerous rock fracture during expansion is calculated₀And joint stress intensity factor K of fracture tip_e. By analyzing the stress condition of the dumping type dangerous rock under the action of dead weight and fracture water pressure, the dumping type dangerous rock fracture mode is decomposed into three conditions of tension I-type fracture, shear II-type fracture and bending I-type fracture. Firstly, analyzing each fracture mode independently, calculating the stress intensity factor under each condition, and finally carrying out combined superposition according to the superposition principle to obtain the stress intensity factor of the critical rock main control structural surface. And finally, establishing a dangerous rock stability calculation formula based on fracture mechanics, substituting data measured by the measuring system into a specific formula for calculation, and finally obtaining the dangerous rock stability state after crack propagation.

5. According to the invention, the crack generation and expansion are taken as the premise of the instability of the dangerous rock mass, the natural process of dangerous rock collapse is met, the dangerous rock collapse can be more accurately early-warned, the false alarm and missing report rate is reduced, the calculated amount is reduced, and the direct calculation of the stability coefficient of the dangerous rock is avoided.

Drawings

Fig. 1 is a schematic structural diagram of a dangerous rock collapse early warning system in this embodiment;

FIG. 2 is a schematic diagram of the principle of ultrasonic pulse leveling method in case of no crack water;

FIG. 3 is a schematic diagram of the principle of ultrasonic pulse leveling method in the case of water containing cracks;

FIG. 4 is a schematic view of fracture characteristic parameters;

FIG. 5 is a schematic diagram of the force of a dumping type dangerous rock;

fig. 6 is an exploded view of a fracture mode of a top end of a critical rock main control structural plane.

Description of reference numerals: 1. a dangerous rock main control structural plane; 2. a dial angle gauge; 3. a gravity pointer; 4. a T transducer; 5. an R transducer; 6. a 5G communication module; 7. a power supply device; 8. a signal receiving module; 9. a host; 10. a wireless transmission module; 11. an early warning module; 12. an image recognition device.

Detailed Description

In order to realize the dangerous rock collapse early warning method, firstly, a dangerous rock collapse early warning system is installed, and the system comprises a crack water depth monitoring device, a crack opening angle monitoring device, a remote communication device, a power supply device, a host and an early warning module.

The fracture water depth monitoring device is used for monitoring the fracture water depth and comprises the following ultrasonic transducers: the two sides of the central transducer are respectively provided with a gap-crossing transducer and a gap-not-crossing transducer at equal intervals; the crack opening angle monitoring device is used for monitoring the crack opening angle and comprises a dial angle measuring instrument and a pointer instrument reading device; the pointer instrument reading device is used for automatically reading the reading of the dial angle measuring instrument. The reading device of the pointer instrument adopts the prior art, such as a reading method and a reading device of the pointer instrument in Chinese patent (CN 111382738A).

The crack water depth monitoring device and the crack opening angle monitoring device send monitoring data to the host through the remote communication device.

The host computer is used for calculating the dangerous rock stability coefficient Fs according to the monitoring data and sending the calculation result to the early warning module.

The early warning module is used for judging whether the dangerous rock mass is stable according to the dangerous rock stability coefficient, and when the dangerous rock mass is judged to collapse in a destabilizing mode, an early warning signal is sent out.

The remote communication module is a 5G communication module, data (sound time and pointer reading) measured by the measuring system are transmitted to the signal receiving module of the host computer in a 5G cloud mode based on 5G signal transmission, the host computer performs a series of operations to obtain specific calculation results, and then the calculation results are transmitted to the early warning module through the wireless transmission module, so that the real-time early warning function of dangerous rock instability and collapse is realized.

The method for pre-warning of dangerous rock collapse based on the system is specifically described below.

(1) Crack opening angle monitoring

And inserting the dial plate type angle measuring instrument into the dangerous rock mass, keeping the inserting direction parallel to the initial unopened crack, and measuring the initial inclination angle. The dip angle measuring system and the dangerous rock mass keep moving integrally with the crack, a gravity pointer of the dial angle measuring instrument keeps vertical all the time under the action of gravity, the reading alpha of the gravity pointer on the angle measuring dial is the included angle between the shifted dangerous rock mass and the vertical direction, 90-alpha-beta is the crack opening angle value, beta is the initial included angle between the crack and the horizontal plane when the crack is not opened, and the initial included angle beta can be obtained by subtracting the initial dip angle from 90 degrees.

(2) Crack water depth monitoring

The two sides of the central transducer, the seam crossing transducer and the non-seam crossing transducer are respectively provided with the seam crossing transducer and the non-seam crossing transducer at equal intervals; the central transducer and the non-seam-crossing transducer are both positioned on the top surface of the mother rock, and the seam-crossing transducer is positioned on the top surface of the dangerous rock mass; the central transducer can respectively transmit and receive ultrasonic waves with the gap-crossing transducer and the gap-non-crossing transducer; in this embodiment, the central transducer is a T transducer for transmitting ultrasonic waves, and the slit-crossing transducer and the non-slit-crossing transducer are both R transducers for receiving ultrasonic waves.

The central transducer, the seam crossing transducer and the non-seam crossing transducer are all in close contact with the surface of the rock body through the paste couplant. The function of the ultrasonic transducer is to convert the input electric power into mechanical power (i.e. ultrasonic waves) and then transmit the mechanical power. As shown in fig. 2, when the central transducer and the cross-slit transducer are respectively arranged at two sides of a crack of the main control structural plane, a part of ultrasonic waves emitted by the central transducer (point a) are transmitted along the surface, and cannot directly reach the cross-slit transducer (point C) due to the reflection of the crack, but the other part of ultrasonic waves pass through the crack through the point B in the rock body and reach the cross-slit transducer (point C), and when the cross-slit horizontal sound measurement is measured, t, the crack depth h is obtained according to the side length relation of the triangle.

In the formula, t₀When the sound is measured without crossing the seam; t is when the sound is measured across the seam; l is transducer range, L '+ a, L' is the ultrasonic transducer inner edge distance, and a is the intercept of the "time-distance graph".

Time t of sound measurement without crossing seam₀The ultrasonic wave transmitted by the T transducer propagates along the surface of the rock mass, and the propagation time of the ultrasonic wave is measured when no crack exists in the rock mass. The measurement of the sound needs to arrange an R transducer on the side of the T transducer far away from the crack, three transducers are required to be arranged at equal intervals (namely AD (AC)), and the time of ultrasonic wave propagation between the two transducers which do not cross the crack is measured when the sound does not cross the crack₀。

The time-distance diagram is a scatter diagram formed by taking the sound time of each measuring point without crossing a seam as a horizontal coordinate and taking distance measurement as a vertical coordinate, and finally, the intercept a is calculated according to a linear regression method. The T and R transducers are placed on the surface of a representative rock mass with uniform quality near a dangerous rock crack, the transducers cannot cross the crack, and the distance L between the inner edges of the two transducers_i' equal to 100mm, 150mm, 200m, 250mm, 300mm, 350mm respectively reads each sound time value t_iAnd drawing a time-distance graph, wherein the points are approximately on a straight line, the slope of the straight line is the propagation speed of the rock mass ultrasonic wave, and the intercept of the straight line is the value a.

The ultrasonic pulse leveling method is divided into a transverse wave method and a longitudinal wave method, wherein the transverse wave belongs to shear waves and cannot be transmitted in water, and the longitudinal wave can be directly transmitted through the water surface and cannot pass through the bottom of a crack when water exists in the crack. Therefore, a transverse wave method is adopted when the crack depth is measured, transverse waves cannot propagate in the crack water by emitting the transverse waves and only can reach the R transducer by bypassing the bottom of the crack, and the measured depth is the crack depth h. When the depth of the crack water is measured, a longitudinal wave method is adopted, and by transmitting the longitudinal wave, the longitudinal wave propagates in the water and reaches the R transducer (shown in figure 3) from the surface of the crack water, and the measured depth is h₁。

The values of t when the sound is measured by the transverse wave method and the longitudinal wave method and the sound is measured by the transverse wave method and the longitudinal wave method, the values of t are different when the sound is measured by the transverse wave method and the transverse wave method are different.

Subtracting the depth h measured by longitudinal wave method from the depth h measured by transverse wave method₁The filling height h of the crack water is₂I.e. crack water filling height h₂＝h-h₁。

(3) Judging whether the crack will be expanded or not

According to the data of the crack opening angle and the crack depth of the main control structure surface obtained by the measuring system, the opening degree V and the crack opening displacement delta of the crack are calculated according to the schematic diagram of fig. 4 according to the following formula, the dotted line part of fig. 4 represents an imaginary crack tip, and the actual crack tip cannot be carved into a specific position relation because the actual crack tip has small opening displacement.

In the formula, V is the crack opening of the dangerous rock; h is the crack depth of the dangerous rock; h is the thickness of the dangerous rock mass, r is a rotation factor, the value of the rotation factor is stabilized between 0.3 and 0.5, and r can be 0.45 obtained by a large amount of actual measurement and theoretical analysis of a slip line field; alpha is the reading of the gravity pointer; beta is the initial angle from the horizontal when the fracture is not opened.

The crack opening displacement delta of the calculated critical rock main control structure surface and the crack critical opening displacement delta measured by performing a three-point bending test on the critical rock sample_cComparing if delta is larger than or equal to delta_cThe crack is shown to be expanded, the early warning module can be triggered at the moment, and the dangerous rock has the possibility of unstable collapse.

(4) Judging the stability of dangerous rock mass

When the cracks of the dangerous rock mass are expanded, the dangerous rock forms a stress concentration area at the tip of the main control structural surface under the action of self weight and water pressure of cracks, and when the stress is increased enough to overcome the breaking strength of the rock mass, the stress concentration area is mainly formedControlling the tip of the structural surface along a certain angle theta₀Cracking, based on the maximum circumferential stress theory in fracture mechanics, calculating the fracture angle theta of the dangerous rock fracture₀And joint stress intensity factor K of fracture tip_e. The main control structure surface belongs to the problem of composite fracture expansion under the action of the tensile stress generated by the bending moment generated by dead weight of a dangerous rock body and the water pressure of a crack (without considering earthquake load). For the plane composite fracture problem under I and II type loading, the solution can be carried out according to the maximum circumferential stress theory. The stress component expression (polar coordinate form) of the crack tip region of the plane composite loaded main control structure surface is as follows:

in the formula, K_ⅠIs type I stress intensity factorK_ⅡIs type II stress intensity factorAnd r and theta are respectively a polar coordinate radius and an inclination angle expression form of any point in the crack tip region of the critical rock main control structure surface.

The principal control structure face crack propagation is along the principal maximum circumferential tensile stress σ_θmaxThe included angle between the cross section and the original crack line of the main control structure surface is called the fracture angle theta of the main control structure surface₀. Fracture angle theta of dangerous rock main control structural surface₀The solution can be performed according to the following two methods:

the value of θ satisfying the above formula is the fracture angle.

At the same time let tau_rθWhen the value is 0, the obtained value of θ is also the fracture angle because the shear stress in the section is zero and belongs to the principal plane. Finally obtaining the fracture angle theta₀：

So far, the fracture angle cannot be directly calculated, and I-type and II-type stress intensity factors of the tip of the dangerous rock fracture need to be calculated firstly. According to the stress condition of the tip of the toppling type dangerous rock main control structure surface (as shown in figure 5), the load applied to the crack tip of the dangerous rock main control structure surface is decomposed into a load from sigma_max、τ_maxAnd σ_M(ii) a Under the condition of three loads acting alone, the fracture mode is decomposed into three conditions of tension type I fracture, shear type II fracture and bending type I fracture (as shown in figure 6). Firstly, analyzing each fracture mode independently, calculating the stress intensity factor under each condition, and finally carrying out combined superposition according to the superposition principle to obtain the stress intensity factor of the critical rock main control structural surface.

For tension I-type fracture, the crack surface of the main control structure surface is subjected to linear load, and the stress intensity factor handbook is combined, so that the stress intensity factor of the tension I-type fracture is obtained as follows:

for the II-type fracture under shear, the crack surface of the main control structure surface is subjected to linear load, and the stress intensity factor handbook is combined, so that the stress intensity factor of the II-type fracture under shear is obtained as follows:

for flexural I-type fracture, combining with a handbook of stress intensity factors, the stress intensity factors for flexural I-type fracture can be obtained as follows:

in the formula, h₀To control the critical depth of crack propagation in the structural plane, when delta is delta_cThe measured crack depth is the critical depth h of the crack propagation of the main control structure surface₀The critical depth is the depth at which the crack is about to propagate, and is the necessary course for the crack to propagate.

According to the stress characteristics of the dumping type dangerous rock, the influence of seismic force is not considered, and under the action of dead weight and fracture water pressure, the stress condition of the main control structural surface (as shown in figure 5) is as follows:

σ_max＝γ_wh₂-γ_sh₀ cos(90°-α)

τ_max＝γ_sh₀ sin(90°-α)

in the formula, gamma_wIs the severity of the fracture water (kN/m)³)；γ_sIs in danger of the severe degree (kN/m) of rock mass³) (ii) a W is the dead weight (kN) of the dangerous rock mass; m is bending moment (kN.m) generated by dead weight of the dangerous rock; b is the horizontal distance (m) from the center of gravity of the dangerous rock to the tip of the fracture.

According to the analysis, the fracture stress intensity factor K under three conditions of tension type I fracture, shear type II fracture and bending type I fracture can be calculated_Ⅰ1、K_Ⅱ1、K_Ⅰ2And then calculating according to the superposition principle of the stress intensity factorsType I and type II stress intensity factors of the tip of a dangerous rock fracture.

K_Ⅰ＝K_Ⅰ1+K_Ⅰ2；K_Ⅱ＝K_Ⅱ1

Therefore, K is_Ⅰ、K_ⅡSubstituting into the fracture angle calculation formula to calculate the fracture angle theta of the dangerous rock fracture expansion₀. Meanwhile, the joint stress intensity factor K of the crack tip of the main control structural surface_e：

Optionally, based on the joint stress intensity factor K of the main control structural surface_eAnd fracture toughness K of complete rock of dangerous rock_CThe stability factor F of the dangerous rock can be established_sFracture mechanics expression of (a): f_s＝K_C/K_e. If F_sNot less than 1, the dangerous rock mass is stable, F_s<1, the dangerous rock mass is unstable and collapses. Fracture toughness K of complete rock of dangerous rock_CAs determined by fracture mechanics testing. Therefore, a calculation result of the stability of the dangerous rock after the crack of the main control structural plane of the dangerous rock is expanded is obtained, and the calculation result is transmitted to the early warning module, so that the real-time early warning function is realized.