CN107145633B - A kind of Forecasting Methodology of rock fracture network occurrence three-dimensional statistical distribution - Google Patents
A kind of Forecasting Methodology of rock fracture network occurrence three-dimensional statistical distribution Download PDFInfo
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- CN107145633B CN107145633B CN201710224352.9A CN201710224352A CN107145633B CN 107145633 B CN107145633 B CN 107145633B CN 201710224352 A CN201710224352 A CN 201710224352A CN 107145633 B CN107145633 B CN 107145633B
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Abstract
The present invention provides a kind of Forecasting Methodology of rock fracture network occurrence three-dimensional statistical distribution, comprises the following steps：Arrange the survey line of field inspection rock, gather the crack intersected with survey line, measure tendency, inclination angle and the size in these cracks, and calculate the average value of the size in crack, the sample size at statistics tendency and inclination angle；Measure pitching to, angle of pitch and width for the survey line；Judge the crack tendency and inclination angle whether in probability space random distribution；Judge whether the order of magnitude of the width of the survey line is less than the order of magnitude of the average value of the size in crack；Projection transform is penetrated into limit by pole in the tendency in the crack and inclination angle, obtain the observed frequency of each limit；Calculate the sine value at meet angle；Calculate the deviation compensation coefficient of the observed frequency of limit；The initial predicted frequency of limit is calculated, the initial predicted frequency is obtained into the prediction frequency of limit by the method for round.The present invention is capable of the three-dimensional statistical distribution of Accurate Prediction crack occurrence.
Description
Technical field
The present invention relates to rock mechanics and geological technique field, more particularly to a kind of three-dimensional statistics of rock fracture network occurrence
The Forecasting Methodology of distribution.
Background technology
Rock fracture includes the notable plane of fracture of joint plane, bed plane and other negligible tensile strengths, it is in the earth's crust
A kind of dielectric interface of generally existing, the geometry character of the network being made of each crack element, particularly its network, control
The behaviors such as kinematics, mechanics and the waterpower of rock medium, geometry character available size, position and the occurrence of Fracture Networks etc. one
The statistical distribution of group three dimensional physical amount carrys out quantitative description.
Survey line technology is a kind of common geometry character field inspection technology, and this technology only collects splitting of intersecting with survey line
Gap, its observation sample reflection is one-dimensional crack geological information, can not represent three-dimensional statistic.Forefathers develop it is a variety of by
The method of three-dimensional statistical distribution, including Fisher methods, Tokhmchi are predicted in one-dimensional observed quantity that this observation technology obtains
Method, Williams-Stroud methods, Zazoun methods, Follin methods, Berrone methods, Zaree methods, Terzaghi
There is following deficiency in formula and Terzaghi improved methods, these Forecasting Methodologies：
(1) these Forecasting Methodologies need the measurement of other survey information such as infiltration coefficients, add actual measurement workload, and
Need to set some parameters during prediction, prediction result is to these additional survey informations and sets possible sensitivity, so as to draw
Play the uncertainty and inaccuracy of prediction result.
(2) one or more theoretical occurrence distribution patterns must be defined, and they may not meet real distributed in three dimensions,
Meanwhile practical method not can be used to identify optimal distribution pattern now.
(3) some samples in itself and do not meet theoretical distribution, so, define theoretical distribution type in additive manner by force and seem
It is and unreasonable.
The Fouch é methods of latest developments are relatively advanced methods, and Fouch é methods carry out gridding to projection net, will
Projection net counts the frequency for falling into each grid after being divided into structured grid, is added by corresponding deviation compensation formula
Power, Fouch é methods consider sample size effect so that precision of prediction is improved.But it has some shortcomings at the same time, than
As observation error not being completely eliminated, for approximately parallel crack such as bed plane, prediction result and three-dimensional true distribution are poor
Away from smaller, it can reflect three-dimensional statistical distribution, but for nonparallel situation such as joint plane, the residual error after prediction also compares
Substantially, and prediction result is caused to also have certain gap from three-dimensional true distribution, it is impossible to effectively to represent three-dimensional statistical distribution.Therefore,
Obtain accurate prediction result, it is necessary to which Fouch é methods are improved.
The content of the invention
In view of this, the present invention provides a kind of rock fracture net for being capable of Accurate Prediction crack occurrence three-dimensional statistical distribution
The Forecasting Methodology of network occurrence three-dimensional statistical distribution.
The present invention provides a kind of Forecasting Methodology of rock fracture network occurrence three-dimensional statistical distribution, comprises the following steps：
Arrange the survey line of field inspection rock, gather the crack intersected with the survey line, these are measured using circumferentor
The tendency in crack and inclination angle, using the size in these cracks of tape measuring, and calculate the average value of the size in the crack, so
The sample size at the tendency and inclination angle is counted afterwards；
Using circumferentor measure the survey line pitch to and angle of pitch, using the width of survey line described in kind of calliper；
Judge the crack tendency and inclination angle whether in probability space random distribution；
Judge whether the order of magnitude of the width of the survey line is less than the order of magnitude of the average value of the size in crack；
Split if the order of magnitude of the tendency in the crack and the inclination angle width of random distribution and survey line in probability space is less than
The order of magnitude of the average value of the size of gap, then penetrate projection transform into limit by pole with inclination angle by the tendency in the crack, obtain
It is projected on the observed frequency of each limit；
Obtain the survey line and be projected on the meet angle in the crack of each limit, calculate the sine value at the meet angle；
The deviation compensation coefficient of the observed frequency of limit is calculated according to the sine value at the meet angle；
The initial predicted frequency of limit is calculated according to the deviation compensation coefficient and observed frequency of the observed frequency of the limit,
The initial predicted frequency is obtained into the prediction frequency of limit by the method for round.
Further, the tendency for judging crack and inclination angle whether in probability space random distribution specific steps
For：Examined by geological analysis, if the crack of research is in homogeneous geological environment and is subjected to identical historic geology
During effect, illustrate tendency and the inclination angle random distribution in probability space in crack；If the crack of research is in different geology
Environment is subjected to different historic geology effects, then is regarded as counting heterogeneous area, the tendency in crack and inclination angle are in probability
Random distribution is unsatisfactory in space.
Further, the acquisition is projected on concretely comprising the following steps for the observed frequency of each limit：Statistics is projected on each
The crack quantity of limit, these crack quantity are the observed frequency of each limit obtained using one-dimensional survey line observation method.
Further, the calculation formula of the sine value at the meet angle is：
Sin θ=| sin β cos ζ cos (α-ψ)-cos β sin ζ |
In formula, θ is survey line and is projected on the meet angle in the crack of each limit, and α is the tendency in crack, and β is inclining for crack
Angle, ψ are that survey line pitches to ζ is the angle of pitch of survey line.
Further, the calculation formula of the deviation compensation coefficient of the observed frequency of the limit is：
In formula, δ (θ, n) is the deviation compensation coefficient of the observed frequency of limit, and n is the sample size at tendency and inclination angle,It is less than being equal toMaximum integer.
Further, the calculation formula of the initial predicted frequency of the limit is：
Pc=Po·δ(θ,n)
In formula, PcIt is the initial predicted frequency of limit, PoIt is the observed frequency of limit.
Compared with prior art, the beneficial effect that technical solution provided by the invention is brought is：
1. the frequency number data that the Forecasting Methodology for passing through the present invention obtains can not only be converted into the directly perceived of tendency and inclination angle
Expression-form, such as pole graph and isodensity map, can also be conveniently used for calculating the distributed constant at tendency and inclination angle, including average
Occurrence and Fisher constants, have extensive engineering application value.
2. the Forecasting Methodology Simple And Practical of the present invention, can effectively reduce actual measurement workload, project inputs, the present invention are reduced
Forecasting Methodology needed for parameter it is less, reduce influence of the parameter to prediction result, effectively reduce the uncertain of prediction result
Property, adds the stability of prediction result, Forecasting Methodology of the invention without considering sampling instrument dimensional effect, and can by because
Without considering error constraints caused by this simplification of sampling instrument dimensional effect in an extremely small level, so as to effectively carry
The high precision of prediction result.
3. for three classes situation, including：(a) it is parallel to each other or the approximate crack being parallel to each other, and in measurement process
Intersect with survey line in wide-angle；(b) be parallel to each other or the approximate crack being parallel to each other, and in measurement process with survey line in small
Angle of intersection；(c) mutually nonparallel crack, and intersecting in measurement process with survey line in wide-angle, it is provided by the invention
The result that Forecasting Methodology obtains is more accurate.
Brief description of the drawings
Fig. 1 is a kind of flow diagram of the Forecasting Methodology of rock fracture network occurrence three-dimensional statistical distribution of the present invention.
Fig. 2 is the schematic diagram of rock fracture in one embodiment of the invention.
Fig. 3 is the schematic diagram at the tendency of rock fracture and inclination angle in one embodiment of the invention.
Fig. 4 is that rock survey line pitches to the schematic diagram with angle of pitch in one embodiment of the invention.
Embodiment
To make the object, technical solutions and advantages of the present invention clearer, below in conjunction with attached drawing to embodiment party of the present invention
Formula is further described.
Please refer to Fig.1 to Fig. 4, the embodiment provides a kind of rock fracture network occurrence three-dimensional statistical distribution
Forecasting Methodology, comprises the following steps：
Step S101, arranges the survey line 3 of field inspection rock, gathers the crack 2 intersected with survey line 3, utilizes circumferentor
The tendency α and angle of inclination beta in these cracks 2 are measured, usually represents state and orientation of the crack in space with the occurrence of rock fracture, its
Including tendency and inclination angle, the tendency of rock fracture is the azimuth that the normal of rock fracture plane projects in the horizontal plane, rock
The inclination angle in crack is the complementary angle of the normal angle with horizontal plane of rock fracture plane, using the size in these cracks 2 of tape measuring,
And the average value of the size in crack 2 is calculated, then statistics is inclined to α and the sample size n of angle of inclination beta.
Step S102, using pitching to ψ and angle of pitch ζ for circumferentor measurement survey line 3, survey line pitches to being that survey line refers to
The azimuth projected in the horizontal plane to underground direction, angle of pitch are that survey line projects angle with the survey line in the horizontal plane, i.e.,
The angle of the survey line and horizontal plane in vertical plane where survey line, where being also equal to survey line in vertical plane the normal of the survey line with
The complementary angle of the angle of horizontal plane, using the width of kind of calliper survey line 3.
Referring to figs. 2 to Fig. 4, cube 1 represents rock, and oblique line represents survey line 3,1 surface of cube it is of different shapes straight
Line represents that crack 2,21 represents the normal vector in a certain crack 2, the tendency α in the crack 2 for normal vector 21 in the horizontal plane
The angle of projection 22 and projection 23 of the normal vector 21 in North and South direction, the angle of inclination beta in the crack 2 is normal vector 21 and normal direction
The angle of the projection 24 of vectorial 21 in the vertical directions；31 represent surveys line 3 direction vector, survey line 3 pitch to ψ for direction to
The angle of 31 projection 32 in the horizontal plane and projection 33 of the direction vector 31 in North and South direction is measured, the angle of pitch ζ of survey line 3 is
Direction vector 31 and the angle of the projection 32 of direction vector 31 in the horizontal plane.
Step S103, judge crack tendency α and angle of inclination beta whether in probability space random distribution：
If the tendency α and angle of inclination beta in the crack random distribution in probability space, to step S104；
If the tendency α and angle of inclination beta in crack are unsatisfactory for random distribution in probability space, to step S109.
Judge crack tendency α and angle of inclination beta whether in probability space random distribution concretely comprises the following steps：
For the crack formed in homogeneous geological environment and geology process, it is inclined to and random point of the approximate obedience in inclination angle
Cloth, the geologic province of tendency and inclination angle of the definition with random distribution is statistics homogeneous area, therefore, when crack is in homogeneous ground
Matter environment and when being subjected to identical geologic process, can be regarded as statistics homogeneous area, be examined by geological analysis, if research
When crack is in homogeneous geological environment and is subjected to identical historic geology effect, then statistics homogeneous area is regarded as, is split
The tendency of gap and the inclination angle random distribution in probability space；If the crack of research is in different geological environments or is subjected to not
With historic geology effect, then be regarded as counting heterogeneous area, the tendency in crack and inclination angle be unsatisfactory in probability space with
Machine is distributed.
Step S104, judges whether the order of magnitude of the width of survey line is less than the order of magnitude of the average value of the size in crack：If
The order of magnitude of the width of survey line is less than the order of magnitude of the average value of the size in crack, to step S105；
If the order of magnitude of the width of survey line is greater than or equal to the order of magnitude of the average value of the size in crack, to step S109.
Step S105, if the order of magnitude of tendency α and the angle of inclination beta width of random distribution and survey line in probability space in crack
Less than the order of magnitude of the average value of the size in crack, then the tendency α in crack and angle of inclination beta are penetrated into projection transform into limit by pole,
Obtain the observed frequency P for being projected on each limito。
Obtain the observed frequency P for being projected on each limitoConcretely comprise the following steps：Statistics is projected on the crack number of each limit
Amount, these crack quantity are the observed frequency P of each limit obtained using one-dimensional survey line observation methodo。
Step S106, obtains survey line and is projected on the meet angle θ in the crack of each limit, meet angle is crack plane with surveying
The angle of line, calculates the sine value of meet angle θ.
The calculation formula of the sine value of meet angle θ is：
Sin θ=| sin β cos ζ cos (α-ψ)-cos β sin ζ |
In formula, θ is survey line and is projected on the meet angle in the crack of limit, and α is the tendency in crack, and β is the inclination angle in crack, ψ
It is that survey line pitches to ζ is the angle of pitch of survey line.
Step S107, the deviation compensation coefficient δ (θ, n) of the observed frequency of limit is calculated according to the sine value of meet angle θ.
The calculation formula of the deviation compensation coefficient δ (θ, n) of the observed frequency of limit is：
In formula, n is the sample size at tendency and inclination angle,It is less than being equal toMaximum integer.
Step S108, according to the deviation compensation coefficient δ (θ, n) and observed frequency P of the observed frequency of limitoCalculate limit
Initial predicted frequency Pc, by initial predicted frequency PcThe prediction frequency of limit is obtained by the method for round, limit
Prediction frequency can to accurately represent in three dimensions in rock fissare tendency α and angle of inclination beta probability distribution.
The initial predicted frequency P of limitcCalculation formula be：
Pc=Po·δ(θ,n)
In formula, PoIt is the observed frequency of limit.
Step S109, terminates to calculate.
The prediction frequency number data obtained by the Forecasting Methodology of the present invention, which can be not only converted into, is inclined to α and angle of inclination beta
Expression-form directly perceived, such as pole graph and isodensity map, can also be conveniently used for calculating tendency α and the distributed constant of angle of inclination beta, bag
Average occurrence and Fisher constants are included, there is extensive engineering application value；The Forecasting Methodology Simple And Practical of the present invention, Neng Gouyou
Effect reduces actual measurement workload, reduces project inputs, and parameter needed for Forecasting Methodology of the invention is less, reduces parameter and prediction is tied
The influence of fruit, effectively reduces the uncertainty of prediction result, adds the stability of prediction result, Forecasting Methodology of the invention
Without considering sampling instrument dimensional effect, and can will because caused by without considering this simplification of sampling instrument dimensional effect error
An extremely small level is constrained in, so as to effectively increase the precision of prediction result；For three classes situation, including：(a) phase
The mutual parallel or approximate crack being parallel to each other, and intersect in measurement process with survey line in wide-angle；(b) it is parallel to each other or closely
The crack being seemingly parallel to each other, and intersect in measurement process with survey line in low-angle；(c) mutual nonparallel crack, and
Intersect in measurement process with survey line in wide-angle, the result that Forecasting Methodology provided by the invention obtains is more accurate.
In the case where there is no conflict, the feature in embodiment and embodiment herein-above set forth can be combined with each other.
The foregoing is merely presently preferred embodiments of the present invention, is not intended to limit the invention, it is all the present invention spirit and
Within principle, any modification, equivalent replacement, improvement and so on, should all be included in the protection scope of the present invention.
Claims (6)
1. a kind of Forecasting Methodology of rock fracture network occurrence three-dimensional statistical distribution, it is characterised in that comprise the following steps：
Arrange the survey line of field inspection rock, gather the crack intersected with the survey line, these cracks are measured using circumferentor
Tendency and inclination angle, using the size in these cracks of tape measuring, and calculate the average value of the size in the crack, Ran Houtong
Count the sample size at the tendency and inclination angle；
Using circumferentor measure the survey line pitch to and angle of pitch, using the width of survey line described in kind of calliper；
Judge the crack tendency and inclination angle whether in probability space random distribution；
Judge whether the order of magnitude of the width of the survey line is less than the order of magnitude of the average value of the size in crack；
If the order of magnitude of the tendency in the crack and the inclination angle width of random distribution and survey line in probability space is less than crack
The order of magnitude of the average value of size, then penetrate projection transform into limit by pole with inclination angle by the tendency in the crack, obtain projection
In the observed frequency of each limit；
Obtain the survey line and be projected on the meet angle in the crack of each limit, calculate the sine value at the meet angle；
The deviation compensation coefficient of the observed frequency of limit is calculated according to the sine value at the meet angle；
The initial predicted frequency of limit is calculated according to the deviation compensation coefficient and observed frequency of the observed frequency of the limit, by institute
State initial predicted frequency and the prediction frequency of limit is obtained by the method for round.
2. the Forecasting Methodology of rock fracture network occurrence three-dimensional statistical distribution as claimed in claim 1, it is characterised in that：It is described
Judge crack tendency and inclination angle whether in probability space random distribution concretely comprises the following steps：Examined by geological analysis, such as
When the crack of fruit research is in homogeneous geological environment and is subjected to identical historic geology effect, illustrate crack tendency and
Inclination angle random distribution in probability space；If the crack of research is in different geological environments or with being subjected to different history
Matter acts on, then is regarded as counting heterogeneous area, the tendency in crack and inclination angle are unsatisfactory for random distribution in probability space.
3. the Forecasting Methodology of rock fracture network occurrence three-dimensional statistical distribution as claimed in claim 1, it is characterised in that：It is described
Acquisition is projected on concretely comprising the following steps for the observed frequency of each limit：Statistics is projected on the crack quantity of each limit, these split
Gap quantity is the observed frequency of each limit obtained using one-dimensional survey line observation method.
4. the Forecasting Methodology of rock fracture network occurrence three-dimensional statistical distribution as claimed in claim 1, it is characterised in that：It is described
The calculation formula of the sine value at meet angle is：
Sin θ=| sin β cos ζ cos (α-ψ)-cos β sin ζ |
In formula, θ is survey line and is projected on the meet angle in the crack of each limit, and α is the tendency in crack, and β is the inclination angle in crack, ψ
It is that survey line pitches to ζ is the angle of pitch of survey line.
5. the Forecasting Methodology of rock fracture network occurrence three-dimensional statistical distribution as claimed in claim 1, it is characterised in that：It is described
The calculation formula of the deviation compensation coefficient of the observed frequency of limit is：
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<mi>&delta;</mi>
<mrow>
<mo>(</mo>
<mi>&theta;</mi>
<mo>,</mo>
<mi>n</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mo><</mo>
<mfrac>
<mrow>
<mi>n</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mrow>
<mi>s</mi>
<mi>i</mi>
<mi>n</mi>
<mi>&theta;</mi>
</mrow>
</mfrac>
<mo>|</mo>
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</mrow>
In formula, δ (θ, n) is the deviation compensation coefficient of the observed frequency of limit, and n is the sample size at tendency and inclination angle,
It is less than being equal toMaximum integer.
6. the Forecasting Methodology of rock fracture network occurrence three-dimensional statistical distribution as claimed in claim 5, it is characterised in that：It is described
The calculation formula of the initial predicted frequency of limit is：
Pc=Po·δ(θ,n)
In formula, PcIt is the initial predicted frequency of limit, PoIt is the observed frequency of limit.
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| CN111222094B (en) * | 2019-10-24 | 2021-08-27 | 中国地质大学（武汉） | Evaluation method of residual error after application of Fouche fracture occurrence probability distribution calculation method |
| CN110826215A (en) * | 2019-10-31 | 2020-02-21 | 中国地质大学（武汉） | Minimum included angle and minimum sample capacity algorithm for realizing high-precision occurrence distribution estimation |
| CN110806406A (en) * | 2019-10-31 | 2020-02-18 | 中国地质大学（武汉） | Minimum intersection angle and sample capacity prediction method for realizing high-precision occurrence distribution estimation |
| CN113468639A (en) * | 2021-06-23 | 2021-10-01 | 西南交通大学 | Method for establishing fracture network three-dimensional visualization model based on occurrence state |
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| CN101738639B (en) * | 2008-11-24 | 2012-05-30 | 中国石油天然气集团公司 | Method for improving computing precision of rock fracture parameters |
| CN105093352A (en) * | 2015-08-11 | 2015-11-25 | 武汉迈格睿地质环境科技有限公司 | Method for measuring and calculating rock mass fracture rate in field |
| CN105319603B (en) * | 2015-11-06 | 2018-04-17 | 中国石油大学(华东) | The Forecasting Methodology of tight sandstone reservoir complexity chicken-wire cracking |
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