CN113050169A - Rock mass anisotropy coefficient probability analysis method based on Monte Carlo sampling - Google Patents

Rock mass anisotropy coefficient probability analysis method based on Monte Carlo sampling Download PDF

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CN113050169A
CN113050169A CN202110291115.0A CN202110291115A CN113050169A CN 113050169 A CN113050169 A CN 113050169A CN 202110291115 A CN202110291115 A CN 202110291115A CN 113050169 A CN113050169 A CN 113050169A
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rock mass
hole
wave velocity
longitudinal wave
anisotropy
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CN113050169B (en
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高启栋
周海孝
王亚琼
冷振东
张士朝
王志丰
任锐
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Changan University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
    • G01V1/28—Processing seismic data, e.g. analysis, for interpretation, for correction
    • G01V1/30—Analysis
    • G01V1/306—Analysis for determining physical properties of the subsurface, e.g. impedance, porosity or attenuation profiles
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
    • G01N29/04—Analysing solids
    • G01N29/07—Analysing solids by measuring propagation velocity or propagation time of acoustic waves
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
    • G01N29/44—Processing the detected response signal, e.g. electronic circuits specially adapted therefor
    • G01N29/449—Statistical methods not provided for in G01N29/4409, e.g. averaging, smoothing and interpolation
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
    • G01V1/16—Receiving elements for seismic signals; Arrangements or adaptations of receiving elements
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
    • G01V1/28—Processing seismic data, e.g. analysis, for interpretation, for correction
    • G01V1/30—Analysis
    • G01V1/303—Analysis for determining velocity profiles or travel times

Abstract

The invention discloses a rock mass anisotropy coefficient probability analysis method based on Monte Carlo sampling, which comprises the following steps: three test holes are arranged on the vertical bedding surface of the rock mass, and the test holes are distributed in an equilateral triangle; obtaining the axial longitudinal wave velocity and the radial longitudinal wave velocity of each test hole by adopting a single-hole test method and a cross-hole combination method; calculating the standard deviation and the average value of the axial longitudinal wave velocity and the radial longitudinal wave velocity by using a Monte Carlo random sampling method, and randomly generating N variable samples of the axial longitudinal wave velocity and the N radial longitudinal wave velocities; determining N rock mass anisotropy coefficients according to the concept of the rock mass anisotropy coefficients; counting the transcendental probability that the anisotropy coefficients of the N rock masses are larger than a certain determined anisotropy coefficient; and changing a certain determined anisotropy coefficient, drawing a change curve of the transcendental probability along with the certain determined anisotropy coefficient, and determining the anisotropy coefficient of the rock mass. Compared with the traditional method, the method of the invention is simpler and more convenient to operate, and the measurement result is more real and reliable.

Description

Rock mass anisotropy coefficient probability analysis method based on Monte Carlo sampling
Technical Field
The invention relates to the technical field of rock mass engineering, in particular to a rock mass anisotropy coefficient probability analysis method based on Monte Carlo sampling.
Background
High-quality geological exploration is an important guarantee for engineering safety and smooth construction. In the long geological history process, the rock mass is destroyed and transformed by various internal and external force geological actions such as structural change, weathering action, unloading action and the like, and complex physical and mechanical properties are formed. The elasticity modulus, the Poisson ratio, the tensile strength and the compressive strength of a rock mass in an actual stratum are often distributed unevenly in space, and the accurate recognition of the uneven anisotropy of the rock mass has important significance for safe and efficient construction of engineering.
The existing rock mass anisotropy measurement method is generally obtained by adopting an indoor test or an on-site measurement device. The indoor test mode is adopted, a large number of core samples need to be drilled and prepared, the consumed time is long, the cost is high, and the ground stress environment caused by the in-situ engineering rock mass cannot be fully reflected. The anisotropy of the rock mass can be measured in an in-situ state by a field device testing mode, but the testing device is high in manufacturing cost and complex in operation and is not suitable for projects with complex geological conditions. However, the elastic wave velocity detection method of rock mass is a commonly used method for nondestructive testing of rock mass quality, and converts an electric signal into a sound wave signal through a sound wave transmitting system, the sound wave signal propagates inside the rock mass, the sound wave signal is converted into the electric signal through a sound wave receiving system, and then the electric signal is processed by a data processing system to obtain usable sound wave data. According to the displayed sound wave data, the propagation time and propagation speed of the ultrasonic wave in the rock mass can be obtained, and further the relaxation characteristics and integrity of the rock mass are reflected.
The physical and mechanical properties of engineering rock masses in all directions are different, uncertain factors are more, and the engineering rock masses have certain randomness, while the existing rock mass anisotropy measurement method usually provides one or more determined values, which only can represent the anisotropy of the rock masses at the measuring point positions, cannot represent the anisotropy condition of the rock masses in the whole area, and has certain limitation.
Disclosure of Invention
The embodiment of the invention provides a method for rapidly determining the anisotropy of a rock mass by utilizing a single-hole and cross-hole sound wave combined detection mode based on Monte Carlo analysis, and aims to solve the problems of high cost, complex operation and inaccurate detection result in the conventional rock mass anisotropy determination method.
The embodiment of the invention provides a rock mass anisotropy coefficient probability analysis method based on Monte Carlo sampling, which comprises the following steps:
three test holes are arranged on the vertical bedding surface of the rock mass, and the test holes are distributed in an equilateral triangle; wherein the three test wells comprise: the test hole A, the test hole B and the test hole C;
obtaining the axial longitudinal wave velocity of each test hole by adopting a single-hole test method; and adopting a cross-hole combination method to obtain the radial longitudinal wave velocity of each test hole;
calculating the standard deviation and the average value of the wave velocity of the axial longitudinal wave by using a Monte Carlo random sampling method, and randomly generating N variable samples of the wave velocity of the axial longitudinal wave; calculating the standard deviation and the average value of the radial longitudinal wave velocity by using a Monte Carlo random sampling method, and randomly generating N variable samples of the radial longitudinal wave velocity;
determining N rock mass anisotropy coefficients by combining N variable samples of axial longitudinal wave velocity and N variable samples of radial longitudinal wave velocity according to the concept of rock mass anisotropy coefficients;
counting the transcendental probability that the anisotropy coefficients of the N rock masses are larger than a certain determined anisotropy coefficient; and changing a certain determined anisotropy coefficient, drawing a change curve of the transcendental probability along with the certain determined anisotropy coefficient, and determining the anisotropy coefficient of the rock mass.
Further, the air conditioner is provided with a fan,
the radius of the test hole is 1.5-2.0 times larger than the maximum radius of a measuring probe of the ultrasonic instrument;
the side length of the equilateral triangle is 1.0-1.5 m.
Further, a single-hole testing method is adopted to obtain the axial longitudinal wave velocity of the testing hole A, and the method specifically comprises the following steps:
injecting water into the test hole A until water flows out of the orifice of the test hole A;
placing an ultrasonic transmitting probe at the bottom of the hole A of the test hole, placing a first ultrasonic receiving probe at a position above the bottom of the hole A of the test hole, and operating a sound wave instrument to test;
collecting and storing data in a display of the acoustic wave instrument, measuring and reading three times for each pair, wherein the difference of the maximum reading is not more than 3%, and recording the wave velocity at the moment as the axial longitudinal wave velocity C of the test hole AAZ。
Further, a cross-hole combination method is adopted to obtain the radial longitudinal wave velocity of the test hole A, and the method specifically comprises the following steps:
placing an ultrasonic transmitting probe at the bottom of a test hole A, placing a second ultrasonic receiving probe at the bottom of a test hole B and placing a third ultrasonic receiving probe at the bottom of a test hole C, and operating a sound wave instrument to carry out testing;
collecting and storing data in the display of the sound wave instrument, and reading three times for each pair of measurement, wherein the difference of the maximum reading is not more than 3%, and recording the wave velocity C at the momentA→B；
Placing an ultrasonic transmitting probe at the bottom of the hole B of the test hole, placing a second ultrasonic receiving probe at the bottom of the hole A of the test hole, placing a third ultrasonic receiving probe at the bottom of the hole C of the test hole, and operating a sound wave instrument to carry out testing;
collecting and storing data in the display of the sound wave instrument, and reading three times for each pair of measurement, wherein the difference of the maximum reading is not more than 3%, and recording the wave velocity C at the momentB→A；
Convection velocity CA→BSum wave velocity CB→AAnd (3) averaging, and determining the radial longitudinal wave velocity:
Figure BDA0002982742320000031
wherein beta is the included angle between the isotropic face of the rock mass and the horizontal plane.
Further, determining N rock mass anisotropy coefficients by combining N variable samples of axial longitudinal wave velocity and N variable samples of radial longitudinal wave velocity according to the concept of rock mass anisotropy coefficients; the method specifically comprises the following steps:
anisotropy coefficient eta of rock massdDynamic modulus of elasticity E in the axial directiondzDynamic elastic modulus E in the direction of the specific vertical axisdxDetermined as follows:
Figure BDA0002982742320000032
dynamic modulus of elasticity E of rock massdThe following formula:
Figure BDA0002982742320000033
in the formula, rho is rock mass density; ν is the poisson ratio; vpThe longitudinal wave velocity of the rock mass;
according to the two expressions, the anisotropy coefficient expression of the rock mass is determined:
Figure BDA0002982742320000041
substituting the variable samples of N axial longitudinal wave velocities and the variable samples of N radial longitudinal wave velocities into the formula to obtain N rock mass anisotropy coefficients etad；CizThe wave velocity of the randomly generated axial longitudinal wave; cixIs the wave velocity of the radial longitudinal wave generated randomly.
Further, the counting of the transcendental probability that the anisotropy coefficients of the N rock masses are greater than a certain determined anisotropy coefficient specifically includes:
counting the number n of samples greater than a certain determined anisotropy coefficient eta, and then the transcendental probability greater than the certain determined anisotropy coefficient eta of the rock mass is:
Figure BDA0002982742320000042
and increasing the value of the total number N of the samples until the transcendental probability P is not changed along with the increase of N, wherein the transcendental probability P is the transcendental probability which is larger than the anisotropy coefficient eta of a certain rock mass.
The embodiment of the invention provides a rock mass anisotropy coefficient probability analysis method based on Monte Carlo sampling, and compared with the prior art, the rock mass anisotropy coefficient probability analysis method has the following beneficial effects:
the invention relates to a method for measuring in-situ rock mass anisotropy, in particular to a method for rapidly determining a rock mass anisotropy coefficient by using a single-hole and cross-hole sound wave combined detection mode based on a Monte Carlo analysis method. The Monte Carlo analysis method is a calculation method for estimating results by random sampling statistics, and the Monte Carlo analysis method is used for processing data, so that the probability of being greater than a certain determined anisotropy value can be calculated, the value range of the anisotropy value of the engineering rock mass is obtained, the method is closer to the actual situation of an engineering site, and the reliability of the calculation results is improved. The method is suitable for reasonable and efficient measurement of the anisotropy of the rock mass in engineering construction, is simpler and more convenient to operate than the traditional method, and is more real and reliable in measurement result.
Drawings
FIG. 1 is a plan view of a test well arrangement provided by an embodiment of the present invention;
FIG. 2 is a cross-sectional view of a test well arrangement provided by an embodiment of the present invention;
FIG. 3 is a flow chart of a rock mass anisotropy coefficient probability analysis method based on Monte Carlo sampling according to an embodiment of the present invention;
fig. 4 is a variation rule of the transcendental probability P with the anisotropy value η according to the embodiment of the present invention.
Reference numerals:
1-a first ultrasonic signal receiving probe; 2-ultrasonic signal emission probe; 3-a second ultrasonic signal receiving probe; 4-a third ultrasonic signal receiving probe; 5-test well A; 6-test well B; 7-test well C; 8-bedding rock mass.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The embodiment of the invention provides a rock mass anisotropy coefficient probability analysis method based on Monte Carlo sampling, which comprises the following steps:
step 1: three test holes are arranged on the vertical bedding surface of the rock mass, and the test holes are distributed in an equilateral triangle; wherein the three test wells comprise: test hole A, test hole B, test hole C.
Step 2: obtaining the axial longitudinal wave velocity of each test hole by adopting a single-hole test method; and obtaining the radial longitudinal wave velocity of each test hole by adopting a cross-hole combination method.
And step 3: calculating the standard deviation and the average value of the wave velocity of the axial longitudinal wave by using a Monte Carlo random sampling method, and randomly generating N variable samples of the wave velocity of the axial longitudinal wave; and calculating the standard deviation and the average value of the radial longitudinal wave velocity by using a Monte Carlo random sampling method, and randomly generating N variable samples of the radial longitudinal wave velocity.
And 4, step 4: and determining N rock mass anisotropy coefficients by combining the N variable samples of the axial longitudinal wave velocity and the N variable samples of the radial longitudinal wave velocity according to the rock mass anisotropy coefficient concept.
And 5: counting the transcendental probability that the anisotropy coefficients of the N rock masses are larger than a certain determined anisotropy coefficient; and changing a certain determined anisotropy coefficient, drawing a change curve of the transcendental probability along with the certain determined anisotropy coefficient, and determining the anisotropy coefficient of the rock mass.
The main principle of the invention is as follows:
(1) the anisotropy coefficient of the rock mass can be determined from the dynamic elastic modulus in the axial direction to the radial direction, as shown in equation (1)
Figure BDA0002982742320000061
And the dynamic elastic modulus E of rock massdMay be represented by formula (2):
Figure BDA0002982742320000062
in the formula, rho is rock mass density; ν is the poisson ratio; cpIs the longitudinal wave velocity of the rock mass.
(2) Let η be a certain parameter of anisotropy of the rock mass, where Ciz，CixThe longitudinal wave velocity in the axial direction and the radial direction is the C, because of the complexity of the physical and mechanical properties of the rock bodyiz，CixConsidered as random variables that obey a normal distribution. Let alpha be eta-etadWhen is alpha<0 indicates a random variable Ciz，CixCalculated anisotropy parameter eta of rock massdIs larger than the determined anisotropy parameter eta of the rock mass. Assume that the total number of samples of the random variable is N, where the calculation result of N samples is less than 0, i.e. alpha<0, then
Figure BDA0002982742320000063
To ensure that the probability P has sufficient accuracy, the number of total number of samples N is increased until the probability P is no longer sensitive to an increase in N, at which point P is the probability of exceeding the determined anisotropy value η. Similarly, by changing the value of η, the probability of exceeding different anisotropy values can be obtained.
The specific description of the steps 1 to 5 is as follows:
(1) three test holes are drilled on the vertical bedding surface of the face-hollow wall surface of the engineering rock body to be tested, and are respectively marked as a test hole A, a test hole B and a test hole C. The connecting lines of the central points of the orifices of the three measuring holes form an equilateral triangle, the side length is generally 1.0-1.5 m, and the radius of the measuring hole is generally 1.5-2.0 times larger than the maximum radius of a measuring probe of an ultrasonic instrument, as shown in fig. 1 and fig. 2.
(2) Obtaining the longitudinal wave velocity of each measuring hole in the axial direction by using a single-hole testing method, and respectively recording the longitudinal wave velocity as CAZ、CBZ、CCZAnd calculating the average value M of the longitudinal wave velocity of each measuring hole in the axial directionzAnd standard deviation σz. Obtaining the longitudinal wave velocity of the rock mass between the measuring hole A and the measuring hole B, between the measuring hole B and the measuring hole C and between the measuring hole C and the measuring hole A by using a space penetration test method, and respectively recording the longitudinal wave velocity as CAX、CBX、CCXAnd calculating the average value M of the longitudinal wave velocities in each horizontal directionxAnd standard deviation σx。
(3) Assume random variables (C)iz，Cix) Following normal distribution, according to the average value M of the longitudinal wave velocity of each measuring hole in the axial directionzAnd standard deviation σzRandomly generating N variable samples of longitudinal wave velocity in axial direction, and similarly, according to average value M of longitudinal wave velocity in each radial directionxAnd standard deviation σxAnd randomly generating N radial variable samples of the wave speed of the longitudinal wave. The random variable samples are generated in a normal distribution manner, and are not limited to the normal distribution, but may be other distribution functions, such as a weber distribution.
(4) Substituting N variable samples into formula (2) to obtain N anisotropic values, and taking the calculated anisotropic values into formula (3) to count alpha<A sample number n of 0, the probability of exceeding a certain anisotropy value can be obtained
Figure BDA0002982742320000071
And increasing the number of the total number N of the samples until the probability P is not changed along with the increase of N, wherein the probability that P exceeds the determined anisotropy value eta is marked as the transcendental probability.
Figure BDA0002982742320000072
In the formula: η is a certain anisotropy value; etadCalculating the anisotropy value; cizThe wave velocity of the randomly generated axial longitudinal wave; cixIs the wave velocity of the radial longitudinal wave generated randomly.
(5) Changing the value of eta to obtain the transcendental probability P exceeding different anisotropy values, drawing a curve of the transcendental probability changing along with the anisotropy values by taking the different anisotropy values as a horizontal axis and the transcendental probability P as a vertical axis, and obtaining the anisotropy value of the rock mass smaller than a certain probability according to the change curve, referring to the graph 4.
Example analysis:
the invention is further illustrated below with reference to specific examples, which specifically comprise the following steps:
(1) the included angle beta between the isotropic face of the bedding rock mass and the horizontal plane is determined through a protractor or a compass, the central point positions of three measuring holes, namely a measuring hole A5, a measuring hole B6 and a measuring hole C7, are marked on the wall surface of the bedding rock mass 8, the vertical distance between the measuring holes is 1.0-1.5 m, and the connecting lines of the central points of the three measuring holes form an equilateral triangle, so that ultrasonic signals can be clearly identified by a signal receiving system when cross-hole testing is carried out. And drilling a hole A5, a hole B6 and a hole C7 by utilizing a drilling machine vertical bedding surface according to the position of the marked central point, wherein the drilling depth is set to be 5 m.
(2) And (3) injecting water into the hole A5 until water flows out of the hole opening, and if the hole wall has a water leakage phenomenon, continuously injecting water in the test process to ensure that the ultrasonic receiving probe 3 and the ultrasonic receiving probe 4 are always immersed by the water in the subsequent test. Slowly arranging the ultrasonic transmitting probe 2 at the bottom of a test hole, arranging the ultrasonic receiving probe 1 at a certain position above the hole bottom, operating the sonic apparatus to test, collecting and storing data after stable and clear waveforms appear in a display of the sonic apparatus, reading three times for each pair of measurements, wherein the difference of the maximum readings is not more than 3%, and recording the longitudinal wave velocity at the moment as CAZ. Similarly, the axial longitudinal wave velocities in the hole 6B and the hole 7C are measured respectively and recorded as CBZ、CCZ。
(3) The ultrasonic transmitting probe 2 is arranged on the A sideThe hole 5 is at the bottom of the hole, the ultrasonic receiving probe 3 and the ultrasonic receiving probe 4 are respectively arranged at the bottom of the hole B6 and the hole C7, the sound wave instrument is operated to test, when stable and clear waveforms appear in a display of the sound wave instrument, data are collected and stored, each pair of measurements should be read for three times, the difference of the maximum readings is not more than 3%, and the longitudinal wave velocity is recorded as CA→B. Similarly, the position of the transmitting probe 2 is changed to be positioned at the hole B and the hole C, and the hole C is measuredB→A、CB→C、CC→A、CC→B. To improve the accuracy of the measurement, considering the complex geological conditions in the field, C is takenA→B、CB→AThe radial longitudinal wave velocity can be expressed as
Figure BDA0002982742320000081
Get CB→C、CC→BThe radial longitudinal wave velocity can be expressed as
Figure BDA0002982742320000082
Get CC→A、CA→CThe radial longitudinal wave velocity can be expressed as
Figure BDA0002982742320000083
(4) The average value M and the standard deviation σ of each radial longitudinal wave velocity and axial longitudinal wave velocity obtained by field test are respectively calculated, and the specific values are shown in table 1. Randomly generating 20 groups of sample data according to the standard deviation sigma and the average value M obtained by calculation and normal distribution, substituting the sample data into an equation (2) and calculating etad。
TABLE 1 on-site actual measurement of longitudinal wave velocity
Figure BDA0002982742320000091
(5) Let η equal to 1.4, let ηdEta is substituted for formula (3), statistics of alpha<0 sample number. From Table 2, it can be seen that<If the number of samples of 0 is 11 and the total number of samples is 20, then P is 11/20 is 0.55. Since the total number of samples is small, Pn at this time isInstead of a constant value, the total number of samples is increased and the value of P is calculated until the value of P approaches a plateau, where the value of P is calculated for a total number of samples of 20, 100, 500, 1000, 5000, 10000, see table 3. As shown in Table 3, when the total number of random samples is large enough, the P value is close to 0.376, so the probability that the anisotropy value is greater than 1.4 is 0.376. The probability of exceeding different anisotropy values eta can be obtained by changing the eta value, and a curve of the transcendental probability P along with the change of the anisotropy value eta is drawn by taking eta as a horizontal coordinate and the transcendental probability P exceeding the eta value as a vertical coordinate, as shown in the attached figure 3. As shown in fig. 3, the overrun probability P gradually decreases with the increase of η, and when η is 1.28, the overrun probability P is 1, and when η is greater than 1.52, the overrun probability P is 0.01, and in sum, the anisotropy value of the engineered rock mass is considered to be between 1.28 and 1.52.
TABLE 2 sample data generated randomly
Figure BDA0002982742320000092
Figure BDA0002982742320000101
TABLE 3 overrun probabilities P for different sample sizes
Figure BDA0002982742320000102
Although the embodiments of the present invention have been disclosed in the foregoing for illustrative purposes, those skilled in the art will appreciate that various modifications, additions and substitutions are possible, without departing from the scope and spirit of the invention as disclosed in the accompanying drawings.

Claims (6)

1. A rock mass anisotropy coefficient probability analysis method based on Monte Carlo sampling is characterized by comprising the following steps:
three test holes are arranged on the vertical bedding surface of the rock mass, and the test holes are distributed in an equilateral triangle; wherein the three test wells comprise: the test hole A, the test hole B and the test hole C;
obtaining the axial longitudinal wave velocity of each test hole by adopting a single-hole test method; and adopting a cross-hole combination method to obtain the radial longitudinal wave velocity of each test hole;
calculating the standard deviation and the average value of the wave velocity of the axial longitudinal wave by using a Monte Carlo random sampling method, and randomly generating N variable samples of the wave velocity of the axial longitudinal wave; calculating the standard deviation and the average value of the radial longitudinal wave velocity by using a Monte Carlo random sampling method, and randomly generating N variable samples of the radial longitudinal wave velocity;
determining N rock mass anisotropy coefficients by combining N variable samples of axial longitudinal wave velocity and N variable samples of radial longitudinal wave velocity according to the concept of rock mass anisotropy coefficients;
counting the transcendental probability that the anisotropy coefficients of the N rock masses are larger than a certain determined anisotropy coefficient; and changing a certain determined anisotropy coefficient, drawing a change curve of the transcendental probability along with the certain determined anisotropy coefficient, and determining the anisotropy coefficient of the rock mass.
2. The method of probabilistic analysis of rock mass anisotropy coefficient based on Monte Carlo sampling according to claim 1,
the radius of the test hole is 1.5-2.0 times larger than the maximum radius of a measuring probe of the ultrasonic instrument;
the side length of the equilateral triangle is 1.0-1.5 m.
3. The method for probability analysis of the rock mass anisotropy coefficient based on monte carlo sampling according to claim 1, wherein a single-hole testing method is adopted to obtain the axial longitudinal wave velocity of the testing hole a, and the method specifically comprises the following steps:
injecting water into the test hole A until water flows out of the orifice of the test hole A;
placing an ultrasonic transmitting probe at the bottom of the hole A of the test hole, placing a first ultrasonic receiving probe at a position above the bottom of the hole A of the test hole, and operating a sound wave instrument to test;
collecting and storing data in a display of the acoustic wave instrument, measuring and reading three times for each pair, wherein the difference of the maximum reading is not more than 3%, and recording the wave velocity at the moment as the axial longitudinal wave velocity C of the test hole AAZ。
4. The method for probability analysis of the rock mass anisotropy coefficient based on monte carlo sampling according to claim 1, wherein a cross-hole combination method is adopted to obtain the radial longitudinal wave velocity of the test hole a, and the method specifically comprises the following steps:
placing an ultrasonic transmitting probe at the bottom of a test hole A, placing a second ultrasonic receiving probe at the bottom of a test hole B and placing a third ultrasonic receiving probe at the bottom of a test hole C, and operating a sound wave instrument to carry out testing;
collecting and storing data in the display of the sound wave instrument, and reading three times for each pair of measurement, wherein the difference of the maximum reading is not more than 3%, and recording the wave velocity C at the momentA→B；
Placing an ultrasonic transmitting probe at the bottom of the hole B of the test hole, placing a second ultrasonic receiving probe at the bottom of the hole A of the test hole, placing a third ultrasonic receiving probe at the bottom of the hole C of the test hole, and operating a sound wave instrument to carry out testing;
collecting and storing data in the display of the sound wave instrument, and reading three times for each pair of measurement, wherein the difference of the maximum reading is not more than 3%, and recording the wave velocity C at the momentB→A；
Convection velocity CA→BSum wave velocity CB→AAnd (3) averaging, and determining the radial longitudinal wave velocity:
Figure FDA0002982742310000021
wherein beta is the included angle between the isotropic face of the rock mass and the horizontal plane.
5. The Monte Carlo sampling-based probability analysis method for rock mass anisotropy coefficients as claimed in claim 1, wherein the N rock mass anisotropy coefficients are determined by combining N variable samples of axial longitudinal wave velocity and N variable samples of radial longitudinal wave velocity according to the concept of rock mass anisotropy coefficients; the method specifically comprises the following steps:
anisotropy coefficient eta of rock massdDynamic modulus of elasticity E in the axial directiondzDynamic elastic modulus E in the direction of the specific vertical axisdxDetermined as follows:
Figure FDA0002982742310000022
dynamic modulus of elasticity E of rock massdThe following formula:
Figure FDA0002982742310000023
in the formula, rho is rock mass density; ν is the poisson ratio; vpThe longitudinal wave velocity of the rock mass;
according to the two expressions, the anisotropy coefficient expression of the rock mass is determined:
Figure FDA0002982742310000031
substituting the variable samples of N axial longitudinal wave velocities and the variable samples of N radial longitudinal wave velocities into the formula to obtain N rock mass anisotropy coefficients etad；CizThe wave velocity of the randomly generated axial longitudinal wave; cixIs the wave velocity of the radial longitudinal wave generated randomly.
6. The method for analyzing the probability of the rock mass anisotropy coefficient based on the monte carlo sampling as claimed in claim 1, wherein the statistics of the transcendence probability that the N rock mass anisotropy coefficients are larger than a certain determined anisotropy coefficient specifically comprises:
counting the number n of samples greater than a certain determined anisotropy coefficient eta, and then the transcendental probability greater than the certain determined anisotropy coefficient eta of the rock mass is:
Figure FDA0002982742310000032
and increasing the value of the total number N of the samples until the transcendental probability P is not changed along with the increase of N, wherein the transcendental probability P is the transcendental probability which is larger than the anisotropy coefficient eta of a certain rock mass.
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