CN104881564B - The construction method of structural plane roughness coefficient dimensional effect probability density estimation - Google Patents

The construction method of structural plane roughness coefficient dimensional effect probability density estimation Download PDF

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CN104881564B
CN104881564B CN201510101573.8A CN201510101573A CN104881564B CN 104881564 B CN104881564 B CN 104881564B CN 201510101573 A CN201510101573 A CN 201510101573A CN 104881564 B CN104881564 B CN 104881564B
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structural plane
probability density
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roughness coefficient
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CN104881564A (en
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杜时贵
雍睿
黄曼
刘育明
夏才初
刘文连
任伟中
李长宏
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University of Shaoxing
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Abstract

A kind of construction method of structural plane roughness coefficient dimensional effect probability density estimation, comprises the following steps:According to structural plane contour line orientation measurement, the drawing of interrecord structure facial contour line is scanned using large scale scanner, and be converted into picture format text;According to the surface coordinate information of structural fece sample, the roughness value that the concise formula of Barton straight flanges method calculates Series of Samples is adopted;Based on only as and significance test, respectively to the overall distribution progress Weibull probability density functions fitting (1) of each size sample data;Weibull distribution mesoscale parameters a, form parameter b and specimen size l functional relation are explored, and then structural plane roughness coefficient dimensional effect probability density estimation (2) can be built.It is of the invention can influence of the accurate description dimensional effect to structural plane roughness coefficient statistical law, so as to easily and quickly estimate the shearing strength of array of sizes structural plane.

Description

The construction method of structural plane roughness coefficient dimensional effect probability density estimation
Technical field
The present invention relates to a kind of structural plane roughness coefficient probability statistics model, specifically, the invention provides one kind Consider the construction method of the sample roughness value probability density estimation of structural plane dimensional effect.Suitable for according to roughness Coefficient measures Statistical Analysis, estimates the occasion of array of sizes structural face shear strength.
Background technology
Before the present invention makes, at present still not on structural plane roughness coefficient dimensional effect probability density function mould The report of type.Structural face shear strength is the key parameter of engineering rock mass stability analysis and consolidation process design.It is indoor and existing Field direct shear test is to determine the basic skills of this parameter, but the structural plane experiment for carrying out various sizes is often less feasible. Early in the eighties in last century, the scholar such as N.Barton is shown by the direct shear test research of structural face shear strength, structural plane Wall rock intensity and surface undulation form are the principal elements for determining shearing strength, and propose famous JRC-JCS empirical estimatings Model, this method has that cost is low, speed is fast, the remarkable advantage such as simple and easy to do.Because rock mass discontinuity configuration of surface has respectively The features such as the matter opposite sex, anisotropy and heterogencity.In structural plane surface roughness values orientation survey, the knot of each measuring section There is also difference for structure face configuration of surface.Therefore, how estimation is carried out to structural plane roughness coefficient under the conditions of array of sizes to seem It is particularly important.Before making the present invention, researchers have carried out desk study to structural plane roughness coefficient probability statistical analysis, have The representative studies achievement for closing structural plane roughness coefficient statistical measurement is as follows:
(1) 2004 year, Publication No. CN 1779414A Chinese patent application《Rock structural plane roughness coefficient is determined Method》In, it is proposed that it is specific that exposure rock is tested using contourgraph about the Statistical Determination of rock structural plane roughness coefficient Body structural plane length surface 10cm multiple surveys section, determines that structural plane is coarse according to the roughness value statistical law of each survey section Spend the mathematic expectaion of coefficient.
(2) 2006 years, Publication No. CN 1779458A Chinese patent application《Rock mass structural plane shearing strength experience is estimated Calculation method》In, it is proposed that the different roughness value of section, meter are surveyed for 10cm, 30cm according to each structural plane surface area length Calculate the structural plane roughness coefficient of correspondence length.
(3) 2013 years, it is valued for when Huang Man, Luo comrade-in-arms, Du《The sample representation experimental study of petrophysical model structural plane》One Wen Zhong, to measurement and statistical analysis of the sampling size for 10cm 18 groups of rock structural face roughness values (JRC), is somebody's turn to do Structural plane roughness coefficient probability density function of the size based on normal distribution law.
Research shows that the structural face shear strength roughness value regularity of distribution is related to structural plane sampling size:Sample chi Very little smaller, the otherness of sample shearing strength is more notable;Roughness value average value subtracts with the increase of sample sampling length It is small.However, the studies above work only considered the probability statistics rule of structural plane roughness coefficient under a certain size, do not build The functional relation of vertical structural plane roughness coefficient probability statistics rule and sampling size, does not more propose to consider the knot of dimensional effect Structure surface roughness coefficient probability density estimation.Therefore, there is limitation in existing structural plane roughness coefficient statistical model, It cannot be directly used to the estimation of array of sizes structural face shear strength.
The content of the invention
Array of sizes structural plane shearing resistance is cannot be directly used in order to overcome existing structure surface roughness coefficients statistics model The deficiency of the estimation of intensity, the present invention provides a kind of structure of structural plane roughness coefficient dimensional effect probability density estimation Method, can influence of the accurate description dimensional effect to structural plane roughness coefficient statistical law, so as to easily and quickly Estimate the shearing strength of array of sizes structural plane.
The technical solution adopted for the present invention to solve the technical problems is:
A kind of construction method of structural plane roughness coefficient dimensional effect probability density estimation, comprises the following steps:
1) according to structural plane contour line orientation measurement, using large scale scanner by the drawing of interrecord structure facial contour line It is scanned, and is converted into picture format text;
2) according to the surface coordinate information of structural fece sample, adopt the concise formula of Barton straight flanges method and calculate the thick of Series of Samples Roughness coefficient;
3) it is general to the overall distribution progress Weibull of each size sample data respectively based on only as and significance test Rate density function is fitted:
Wherein, f (x | a, b) is Weibull probability density functions, and a is the scale parameter during Weibull is distributed, and b is Form parameter in Weibull distributions, x is one-dimensional real random variable;
4) Weibull distribution mesoscale parameters a, form parameter b and specimen size l functional relation are explored, and then can structure Build structural plane roughness coefficient dimensional effect probability density estimation:
L ∈ [universe] (2);
Wherein, f (x | a (l), b (l)) is structural plane roughness coefficient dimensional effect probability density function, and a (l) is yardstick Functions of the parameter a on specimen size l, b (l) is functions of the form parameter b on specimen size l.
Further, the construction method also comprises the following steps:
5) according to structural plane roughness coefficient dimensional effect probability density function, probability density function maximum is taken to be used as this Structural plane roughness estimate JRC under size conditionn
6) array of sizes structural plane roughness estimate is brought into structural face shear strength experience estimation formulas (3), you can Calculate array of sizes structural face shear strength estimates of parameters τp
Wherein, σnTo act on the normal stress of structural plane, φbFor structural plane basal farmland dependency, JRCnIt is for sample length LnStructural plane roughness coefficient, JCSnIt is L for sample lengthnWall rock intensity.
Beneficial effects of the present invention are mainly manifested in:Can accurate description dimensional effect to structural plane roughness coefficient count The influence of rule, so as to easily and quickly estimate the shearing strength of array of sizes structural plane.
Brief description of the drawings:
Fig. 1 is Weibull distribution mesoscale parameter a and specimen size l function relation figure.
Fig. 2 is the function relation figure of form parameter b and specimen size l in Weibull distributions.
Embodiment
The invention will be further described below.
A kind of construction method of structural plane roughness coefficient dimensional effect probability density estimation, comprises the following steps:
1) according to structural plane contour line orientation measurement, using large scale scanner by the drawing of interrecord structure facial contour line It is scanned, and is converted into picture format text;
2) according to the surface coordinate information of structural fece sample, adopt the concise formula of Barton straight flanges method and calculate the thick of Series of Samples Roughness coefficient;
3) it is general to the overall distribution progress Weibull of each size sample data respectively based on only as and significance test Rate density function is fitted:
Wherein, f (x | a, b) is Weibull probability density functions, and a is the scale parameter during Weibull is distributed, and b is Form parameter in Weibull distributions, x is one-dimensional real random variable;
4) Weibull distribution mesoscale parameters a, form parameter b and specimen size l functional relation are explored, and then can structure Build structural plane roughness coefficient dimensional effect probability density estimation:
L ∈ [universe] (2);
Wherein, f (x | a (l), b (l)) is structural plane roughness coefficient dimensional effect probability density function, and a (l) is yardstick Parameter a and specimen size l function, b (l) is form parameter b and specimen size l function.
Further, the construction method also comprises the following steps:
5) according to structural plane roughness coefficient dimensional effect probability density function, probability density function maximum is taken to be used as this Structural plane roughness estimate JRC under size conditionn
6) array of sizes structural plane roughness estimate is brought into structural face shear strength experience estimation formulas (3), you can Calculate array of sizes structural face shear strength estimates of parameters τp
Wherein, σnTo act on the normal stress of structural plane, φbFor structural plane basal farmland dependency, JRCnIt is for sample length LnStructural plane roughness coefficient, JCSnIt is L for sample lengthnWall rock intensity.
The present embodiment chooses the good typical slate structural plane of Changshan County, Zhejiang Province exposure condition as research object, series The measurement process of the shearing strength in dimensional structure face is as follows:
1) using the structural plane contour line of profilograph orientation survey 100cm size ranges;
2) drawing of interrecord structure facial contour line is scanned using large scale scanner, and is converted into picture format text This;
3) structural plane contour scanning map is extracted and handled by gray value using Matlab softwares, extract series Dimensional structure interviews the surface coordinate information of sample;
4) according to the surface coordinate information of structural fece sample, Series of Samples is calculated using the concise formula of Barton straight flanges method Roughness value;
5) based on only as learn and significance test, respectively to size be 10cm, 20cm, 30cm, 40cm, 50cm, 60cm, The overall distribution of 70cm, 80cm, 90cm sample data carries out Weibull probability density function fittings, the statistical result such as institute of table 1 Show.
Table 1
6) analysis Weibull distribution mesoscale parameters a, form parameter b and specimen size l functional relation, as shown in Figure 1, Figure 2 It is shown, and then functional relation a (l), form parameter and the examination of scale parameter and specimen size can be obtained by Function Fitting respectively The functional relation b (l) of sample ruler cun.Build structural plane roughness coefficient dimensional effect probability density estimation:
L ∈ [universe]
7) according to structural plane roughness coefficient dimensional effect probability density function, structural fece sample research size l is substituted into*, Probability density function maximum is calculated, as structural plane roughness estimate JRC under the size conditionn
8) array of sizes structural plane roughness estimate is brought into structural face shear strength experience estimation formulas, you can calculate Array of sizes structural face shear strength estimates of parameters.

Claims (2)

1. a kind of construction method of structural plane roughness coefficient dimensional effect probability density estimation, it is characterised in that:It is described Construction method comprises the following steps:
1) according to structural plane contour line orientation measurement, the drawing of interrecord structure facial contour line is carried out using large scale scanner Scanning, and it is converted into picture format text;
2) according to the surface coordinate information of structural fece sample, the coarse of Series of Samples is calculated using the concise formula of Barton straight flanges method Spend coefficient;
3) it is close to the overall distribution progress Weibull probability of each size sample data respectively based on only as and significance test Spend Function Fitting:
<mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>|</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mi>b</mi> <mi>a</mi> </mfrac> <msup> <mrow> <mo>(</mo> <mfrac> <mi>x</mi> <mi>a</mi> </mfrac> <mo>)</mo> </mrow> <mrow> <mi>b</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msup> <mi>e</mi> <mrow> <mo>-</mo> <msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>/</mo> <mi>a</mi> <mo>)</mo> </mrow> <mi>b</mi> </msup> </mrow> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
Wherein, f (x | a, b) is Weibull probability density functions, and a is the scale parameter during Weibull is distributed, and b is Weibull Form parameter in distribution, x is one-dimensional real random variable;
4) Weibull distribution mesoscale parameters a, form parameter b and specimen size l functional relation are explored, and then knot can be built Structure surface roughness coefficient dimensional effect probability density estimation:
Wherein, f (x | a (l), b (l)) is structural plane roughness coefficient dimensional effect probability density function, and a (l) is scale parameter a On specimen size l function, b (l) is functions of the form parameter b on specimen size l.
2. a kind of structure side of structural plane roughness coefficient dimensional effect probability density estimation as claimed in claim 1 Method, it is characterised in that:The construction method also comprises the following steps:
5) according to structural plane roughness coefficient dimensional effect probability density function, probability density function maximum is taken to be grown as sampling Spend for LnStructural plane roughness coefficient estimate JRCn
6) array of sizes structural plane roughness estimate is brought into structural face shear strength experience estimation formulas (3), you can calculate Array of sizes structural face shear strength estimates of parameters τp
<mrow> <msub> <mi>&amp;tau;</mi> <mi>p</mi> </msub> <mo>=</mo> <msub> <mi>&amp;sigma;</mi> <mi>n</mi> </msub> <mi>t</mi> <mi>a</mi> <mi>n</mi> <mo>&amp;lsqb;</mo> <msub> <mi>&amp;phi;</mi> <mi>b</mi> </msub> <mo>+</mo> <msub> <mi>JRC</mi> <mi>n</mi> </msub> <mi>lg</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>JCS</mi> <mi>n</mi> </msub> </mrow> <msub> <mi>&amp;sigma;</mi> <mi>n</mi> </msub> </mfrac> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
Wherein, σnTo act on the normal stress of structural plane, φbFor structural plane basal farmland dependency, JRCnIt is L for sample lengthn's Structural plane roughness coefficient estimate, JCSnIt is L for sample lengthnWall rock intensity.
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CN106570338B (en) * 2016-11-14 2020-05-08 绍兴文理学院 Method for determining sampling precision of contour line in roughness size effect of rock mass structural plane
CN109099880B (en) * 2018-07-12 2020-08-11 宁波大学 Rock mass structural plane roughness coefficient global search measuring method
CN109029334B (en) * 2018-07-12 2020-06-02 宁波大学 Rock mass structural plane roughness coefficient size effect global search measurement method

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