CN113049326B - Sample preparation method with quantitatively controllable structural surface shape and spectrum components - Google Patents
Sample preparation method with quantitatively controllable structural surface shape and spectrum components Download PDFInfo
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Abstract
A sample preparation method with quantitatively controllable structural surface shape and spectrum components comprises the following steps: s1, acquiring a three-dimensional morphology model of a structural surface consistent with the actual shearing state of the structural surface of a rock mass; s2, determining a distribution function of the mean square value of the fluctuation height of the structural surface in a frequency range based on the two-dimensional power spectral density; s3, taking turning points of the function diagram as limit frequencies f of high-frequency and low-frequency components tc The method comprises the steps of carrying out a first treatment on the surface of the S4, quantitatively controlling the content ratio gamma of the high-frequency component and the low-frequency component by adjusting the content of the high-frequency component 0 Calculating the upper frequency limit f of the high-frequency component u The method comprises the steps of carrying out a first treatment on the surface of the S5, according to f tc Or f u Extracting frequency components of a rock mass structural plane, and establishing a structural plane three-dimensional morphology model with different content ratios of the frequency components; s6, engraving the rock mass structural surface sample with the quantitative controllable undulating component content proportion by adopting a rock engraving machine. The invention solves the problem that the content ratio of high-frequency fluctuation and low-frequency fluctuation components in the shape of the rock mass structural surface can not be quantitatively controlled for sample preparation.
Description
Technical Field
The invention relates to the technical field of geotechnical engineering, in particular to a sample preparation method with quantitatively controllable spectrum components of structural surface shape and appearance.
Background
The structural surface of the side slope rock mass is acted by the combined action of the geological and geological forces inside and outside the earth, the mechanical property of the side slope rock mass is far lower than that of the rock mass, the integrity and the overall strength of the rock mass are reduced, and the side slope rock mass is easy to slide and unstably along the controllable structural surface. Considering that the three-dimensional shape of the natural structural surface has certain frequency spectrum characteristics and is composed of fluctuation components with different frequency characteristics, the abrasion evolution characteristics of the different fluctuation components in the shearing process have great difference on the shearing mechanism and shearing strength influence of the structural surface. Therefore, it is necessary to manufacture a structural surface sample with quantitatively controllable content ratio of high-frequency fluctuation and low-frequency fluctuation components, and a foundation is laid for quantitatively researching the abrasion evolution rule of different frequency components in the shearing process.
Du Shigui and the like divide the surface morphology of the rock mass structural plane into three-level factors of macroscopic geometric outline, surface relief morphology and microscopic roughness, and researches show that the contribution of different frequency components or relief morphology factors to the structural plane shear strength is obviously different in the shearing process. The macroscopic geometrical outline of the structural surface is the geometrical outline of the largest level of the surface of the structural surface, reflects the macroscopic overall undulating shape of the surface of the structural surface, and is characterized by the path (surface) of the peaks Gu Bao of the morphological elements (namely, the surface undulating shape) of the smaller level; the surface relief form is a common relief form of the surface of the structural surface, and forms a peak-valley relief contour of the surface of the structural surface on a visible scale; the microscopic roughness is the rough relief form of the minimum level of the surface of the rock mass structural plane, reflects the tiny geometric relief of the surface relief form peak Gu Pomian, and reflects the distribution and arrangement characteristics of mineral particles or tiny crystals on the surface of the structural plane. For the surface relief form and the micro roughness in the three-level elements of the surface form of the structural surface, scholars describe and divide the relief characteristics of the structural surface by adopting names or modes such as first-order relief and second-order relief, large-scale ripple component and small-scale irregular component, ripple component and random irregularity component. In practice, the topography of the surface relief with small relief frequency but higher relief height ("first order relief" or "large scale ripple component" or "waviness component") is attributed to the low frequency relief component, while the microroughness with large relief frequency but lower relief height ("second order relief" or "small scale irregularity component" or "random irregularity component") is attributed to the high frequency relief component. In the three-level elements of structural surface topography described above, the surface relief morphology of the structural surface is often the determining factor affecting structural surface mechanical properties and shear behavior. Although the macroscopic geometry of the structured surface can be directly obtained from the peak-to-valley envelope of the surface relief, there is no obvious boundary between the structured surface relief and the microroughness, which is difficult to quantitatively divide intuitively.
The prior scholars usually adopt methods such as Fourier series, gaussian filtering, wavelet transformation, different sampling precision and the like to artificially control or separate different fluctuation components in the structural surface morphology. For example, xia Cai initially extracts ripple and irregular components through a moving data window and least squares smoothing; yang et al Tang Zhicheng and Liu Quansheng represent first and second order undulating elements with different fourier series of section lines; jiang and the like filter the morphology of the structure surface before and after shearing by adopting a cut-off wavelength of a Gaussian filter of 2.5mm, and extract the first-order fluctuation and the second-order fluctuation of the structure surface; extracting first-order relief by a fourth layer of a two-dimensional section line of the structural surface approximately represented by wavelet analysis; liu et al, using standard section lines drawn at large sampling intervals as first-order fluctuation components, and using the rest components as second-order fluctuation components; zhu Xiaoming et al and Liu et al, the first and second order relief of the structural plane is represented by triangular protrusions of two relief heights; sun Cheng, huang Man, etc. divide the first and second order undulations according to the rate of change of the morphology area for different mesh sizes. However, the different relief components constituting the structural surface generally vary continuously in macroscopic size, and the relief components decomposed by different students using gaussian filtering or wavelet analysis methods based on the macroscopic size difference are often not uniform.
The two-dimensional power spectral density function can effectively analyze the spectral characteristics of the structural surface morphology, describe the distribution condition of the fluctuation heights of different fluctuation components of the structural surface morphology in different frequency ranges, can effectively solve the problem that the frequency limit between different fluctuation components of the structural surface on a macroscopic scale cannot be quantitatively identified, and further can finish the quantitative decomposition of the high-frequency fluctuation component and the low-frequency fluctuation component in the three-dimensional morphology of the structural surface. Based on the fluctuation components obtained by quantitative decomposition, according to the content proportion of the specified high-frequency fluctuation components and low-frequency fluctuation components, the structural surface shape model which has different content proportions of the high-frequency fluctuation components and the low-frequency fluctuation components and can be controlled quantitatively can be completed by adopting inverse Fourier transform.
Disclosure of Invention
The invention provides a sample preparation method with quantitatively controllable spectrum components of a structural surface shape, which aims to solve the problems that the limit of high-frequency fluctuation components and low-frequency fluctuation components in the structural surface shape of the existing rock mass cannot be quantitatively determined and the content ratio of the high-frequency fluctuation components and the low-frequency fluctuation components is difficult to quantitatively control.
The technical scheme adopted for solving the technical problems is as follows:
a method for quantitatively controllable sampling of spectral components of structural surface morphology, the method comprising the steps of:
s1, acquiring a three-dimensional morphology model of a structural surface consistent with the actual shearing state of the structural surface of a rock mass;
s2, determining a distribution function of the mean square value of the three-dimensional topography fluctuation height of the rock mass structural plane in a frequency range based on the two-dimensional power spectral density, wherein the calculation formula is shown in the following formula (1):
wherein P is 3D Is a high mean square value, PSD (f x ,f y ) Two-dimensional power spectral density, f, of structural surface morphology x And f y The spatial frequencies of structural surface shape frequency components in the directions of the x axis and the y axis are respectively f t Is a frequency threshold, f max Is the maximum frequency value;
s3, drawing three-dimensional topography fluctuation of rock mass structural surfaceThe distribution function image with the height mean square value in the frequency range takes the frequency corresponding to the turning point of the function chart as the limit frequency f of the high-frequency component and the low-frequency component of the structural surface morphology tc ；
S4, keeping the content of the low-frequency fluctuation component in the rock mass structural plane unchanged, and quantitatively controlling the content ratio gamma of the high-frequency fluctuation component and the low-frequency fluctuation component of the rock mass structural plane by adjusting the content of the high-frequency fluctuation component 0 Then the ratio of the components to the content gamma 0 The upper frequency limit f of the corresponding high-frequency fluctuation component u The calculation formula of (2) is as follows:
s5, according to the determined limit frequency f tc Or upper frequency limit f of high-frequency fluctuation component u Extracting fluctuation components of different frequencies of the three-dimensional morphology of the rock mass structural surface, and establishing a structural surface three-dimensional morphology model with different content ratios of high-frequency fluctuation components and low-frequency fluctuation components;
s6, carving by a rock carving machine according to the quantitatively established three-dimensional shape model of the structural surface with different content ratios of the high-frequency fluctuation component and the low-frequency fluctuation component, so as to manufacture a rock structural surface sample with quantitatively controllable high-frequency fluctuation component and low-frequency fluctuation component.
Further, the step S1 includes:
s11, acquiring three-dimensional morphology discrete coordinate data of a rock mass structural surface along a shearing direction, taking an included angle between a coordinate data least square fitting plane and a coordinate plane as a trend direction of the three-dimensional morphology of the structural surface, and reversely rotating the structural surface morphology data along the trend direction to ensure that the trend direction of the three-dimensional morphology of the structural surface after rotation is in a horizontal state;
s12, translating the rotated three-dimensional shape data of the structural surface to enable the average plane of the undulating height to coincide with the coordinate plane, and establishing a three-dimensional shape model of the structural surface.
Preferably, in the step S2, the rock mass structural surface shape two-dimensional power spectral density PSD (f x ，f y ) The calculation formula of (2) is as follows:
wherein L is x And L y To be the length of the three-dimensional shape of the rock mass structural plane in the directions of the x axis and the y axis, Z (f) x ,f y ) Two-dimensional Fourier transform of three-dimensional morphology z (x, y) of structural plane in space frequency domain, j 2 ＝-1。
Preferably, the process of step S5 is as follows:
if a three-dimensional structural surface shape model only containing high-frequency fluctuation components and having zero low-frequency fluctuation component content is established, the three-dimensional structural surface shape model can be based on the two-dimensional Fourier transform of the three-dimensional structural surface shape in the frequency domain space, and the three-dimensional structural surface shape model is smaller than the limit frequency f tc Setting the frequency component of (2) to be zero, and then obtaining a three-dimensional morphology model of the structural surface only containing the high-frequency fluctuation component through inverse Fourier transform, wherein the calculation formula is as follows (4):
if the content of the low-frequency fluctuation component is kept unchanged, a three-dimensional structural surface shape model with different content ratios of the high-frequency fluctuation component and the low-frequency fluctuation component is established, and the frequency upper limit f larger than the high-frequency fluctuation component can be obtained based on the two-dimensional Fourier transform of the three-dimensional structural surface shape in the frequency domain space u Setting the frequency component of (2) to be zero, and obtaining the content ratio of the high-frequency fluctuation component and the low-frequency fluctuation component to be gamma by inverse Fourier transform 0 Is calculated according to the following formula (5):
the beneficial effects of the invention are mainly shown in the following steps: the method comprises the steps of taking the characteristic that the fluctuation height of a high-frequency fluctuation component in the three-dimensional appearance of a structural surface is obviously lower than that of a low-frequency fluctuation component as an entry point, deeply researching the change characteristic that the mean square value of the three-dimensional appearance fluctuation height of the structural surface gradually increases along with the frequency value based on the distribution function of the mean square value of the three-dimensional appearance fluctuation height of the structural surface in a frequency range, finding the turning point of the fluctuation height of the low-frequency component and the high-frequency component of the three-dimensional appearance of the structural surface, quantitatively dividing the frequency limit between the high-frequency fluctuation component and the low-frequency fluctuation component, determining the upper frequency limit of the high-frequency fluctuation component corresponding to the content ratio of the high-frequency fluctuation component and the low-frequency fluctuation component of the structural surface of a rock mass, solving the problem that the frequency limit between different fluctuation components of the structural surface on a macroscopic size cannot be quantitatively identified, further completing the quantitative generation of the structural surface appearance containing different high-frequency fluctuation components and the low-frequency fluctuation components, and quantitatively controllable structural surface samples.
Drawings
FIG. 1 is a three-dimensional topographical model of an example natural sandstone structure surface;
FIG. 2 is a graph of a distribution function of the relief height mean square value of an example natural sandstone structure surface profile over a range of frequencies;
FIG. 3 is a morphology model containing only high frequency undulating elements;
FIG. 4 shows the content ratio gamma of the high-frequency fluctuation component and the low-frequency fluctuation component 0 Morphology model=0;
FIG. 5 shows the content ratio gamma of the high-frequency fluctuation component and the low-frequency fluctuation component 0 Morphology model of=1.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Referring to fig. 1 to 5, a method for quantitatively controlling spectral components of structural surface morphology, the method comprising the steps of:
s1, acquiring a three-dimensional morphology model of a structural surface consistent with the actual shearing state of the structural surface of a rock mass;
s2, determining a distribution function of the mean square value of the three-dimensional topography fluctuation height of the rock mass structural plane in a frequency range based on the two-dimensional power spectral density, wherein the calculation formula is shown in the following formula (1):
wherein the method comprises the steps of，P 3D Is a high mean square value, PSD (f x ,f y ) Two-dimensional power spectral density, f, of structural surface morphology x And f y The spatial frequencies of structural surface shape frequency components in the directions of the x axis and the y axis are respectively f t Is a frequency threshold, f max Is the maximum frequency value;
specifically, as can be seen from the equation (1), the frequency f follows the threshold value t Is increased by the root mean square value P3 of the undulating height of the structural surface D Gradually increase, when f t When the maximum frequency value is increased, the mean square value of the fluctuation height of the whole three-dimensional shape of the structural surface can be obtained;
s3, drawing a distribution function image of the three-dimensional morphology fluctuation height mean square value of the rock mass structural plane in a frequency range, and taking the frequency corresponding to the turning point of the function image as the limit frequency f of the high-frequency component and the low-frequency component of the three-dimensional morphology of the structural plane tc ；
Specifically, the relief height of the high-frequency relief component in the three-dimensional shape of the structural surface is obviously lower than that of the low-frequency relief component, and when f t The value is smaller than the limit frequency f tc When the threshold frequency is increased, the mean square value of the three-dimensional morphology fluctuation height of the structural surface increases faster, and the threshold frequency is still in a low-frequency component area; when f t The value is greater than the limit frequency f tc In the process, the mean square value increasing rate of the three-dimensional topography fluctuation height of the structural surface is slowed along with the increase of the threshold frequency, so that the high-frequency component and the low-frequency component limit frequency f of the three-dimensional topography of the structural surface can be quantitatively determined according to turning points of the function image of (1) tc Is a value of (2);
s4, keeping the content of the low-frequency fluctuation component in the rock mass structural plane unchanged, and quantitatively controlling the content ratio gamma of the high-frequency fluctuation component and the low-frequency fluctuation component of the rock mass structural plane by reducing the content of the high-frequency fluctuation component 0 Then the ratio of the components to the content gamma 0 The upper frequency limit f of the corresponding high-frequency fluctuation component u The calculation formula of (2) is as follows:
specifically, the ratio of the high-frequency fluctuation component content to the low-frequency fluctuation component content of the structural surface morphology can be determined by the ratio of the high-frequency fluctuation frequency range to the low-frequency fluctuation frequency range;
s5, according to the determined limit frequency f tc Or upper frequency limit f of high-frequency fluctuation component u Extracting fluctuation components of different frequencies of the three-dimensional morphology of the rock mass structural surface, and establishing a structural surface three-dimensional morphology model with different content ratios of high-frequency fluctuation components and low-frequency fluctuation components;
s6, carving by a rock carving machine according to the quantitatively established three-dimensional shape model of the structural surface with different content ratios of the high-frequency fluctuation component and the low-frequency fluctuation component, so as to manufacture a rock structural surface test with quantitatively controllable high-frequency fluctuation component and low-frequency fluctuation component.
The step S1 includes:
s11, acquiring three-dimensional morphology discrete coordinate data of a rock mass structural surface along a shearing direction, taking an included angle between a coordinate data least square fitting straight line and a coordinate axis as a trend direction of the three-dimensional morphology of the structural surface, and reversely rotating the structural surface morphology data along the trend direction to ensure that the trend direction of the three-dimensional morphology of the structural surface after rotation is in a horizontal state;
s12, translating the rotated three-dimensional shape data of the structural surface to enable the average straight line of the fluctuation height to coincide with the coordinate transverse axis, and establishing a three-dimensional shape model of the structural surface.
In particular, when testing the shear strength of a structural face of a rock mass in an indoor or in-situ test, the structural face shear face should be maintained perpendicular to the applied normal stress, excluding shear strengths that increase in the overall trend of the structural face upward or shear strengths that decrease in the overall trend downward. Therefore, the influence of the overall trend direction of the structural surface should be excluded when describing the relief features or calculating the roughness of the structural surface topography. In addition, the influence of the direct current component of the structural surface appearance can be removed by translating the removal trend to the influenced structural surface coordinate data, so that the average straight line of the fluctuation height coincides with the coordinate axis, and the fluctuation characteristics of the structural surface in different frequency ranges can be reflected more clearly by the distribution function of the three-dimensional appearance fluctuation height mean square value of the structural surface in the frequency range, which is calculated in the subsequent step.
In the step S2, the three-dimensional morphology single-side power spectrum density PSD of the rock mass structural plane * The calculation formula of (2) is as follows:
wherein L is x And L y To be the length of the three-dimensional shape of the rock mass structural plane in the directions of the x axis and the y axis, Z (f) x ,f y ) Two-dimensional Fourier transform of three-dimensional morphology z (x, y) of structural plane in space frequency domain, j 2 ＝-1。
The process of the step S5 is as follows:
if a three-dimensional structural surface shape model only containing high-frequency fluctuation components and having zero low-frequency fluctuation component content is established, the three-dimensional structural surface shape model can be based on the two-dimensional Fourier transform of the three-dimensional structural surface shape in the frequency domain space, and the three-dimensional structural surface shape model is smaller than the limit frequency f tc Setting the frequency component of (2) to be zero, and then obtaining a three-dimensional morphology model of the structural surface only containing the high-frequency fluctuation component through inverse Fourier transform, wherein the calculation formula is as follows (4):
if the content of the low-frequency fluctuation component is kept unchanged, a three-dimensional structural surface shape model with different content ratios of the high-frequency fluctuation component and the low-frequency fluctuation component is established, and the frequency upper limit f larger than the high-frequency fluctuation component can be obtained based on the two-dimensional Fourier transform of the three-dimensional structural surface shape in the frequency domain space u Setting the frequency component of (2) to be zero, and obtaining the content ratio of the high-frequency fluctuation component and the low-frequency fluctuation component to be gamma by inverse Fourier transform 0 Is calculated according to the following formula (5):
examples: a rock mass structural surface sample preparation method with quantitative controllable content ratio of high-frequency fluctuation and low-frequency fluctuation components comprises the following steps:
firstly, selecting a sandstone structural surface in a landslide area of Zhenma Jiangkui in Hubei province as a research object, collecting morphology discrete coordinate data of a natural sandstone structural surface along a shearing direction by adopting a sampling interval of 0.4mm, taking an included angle between a coordinate data least square fitting plane and a coordinate axis as trend direction of a three-dimensional morphology of the structural surface, rotating the structural surface morphology data in a reverse direction along the trend direction, ensuring that the trend direction of the three-dimensional morphology of the structural surface after rotation is in a horizontal state, translating the three-dimensional morphology data after rotation so that an undulating height average plane coincides with the coordinate plane, and establishing a three-dimensional morphology model of the structural surface, as shown in fig. 1;
then, calculating the distribution function of the mean square value of the three-dimensional topography relief height of the structural surface in the frequency range according to the formulas (1) and (3), drawing a distribution function image of the mean square value of the three-dimensional topography relief height of the structural surface in the frequency range, and taking the frequency corresponding to the turning point of the function image as the limit frequency f of the high-frequency component and the low-frequency component of the three-dimensional topography of the structural surface as shown in fig. 2 tc I.e. f tc ＝0.1/mm；
Further, a three-dimensional morphology model of the structural surface containing only the high-frequency fluctuation component is built according to the formula (4), as shown in fig. 3; establishing the content proportion gamma of the high-frequency fluctuation component and the low-frequency fluctuation component according to the formula (5) 0 Three-dimensional morphology models of 0 and 1, respectively, are shown in fig. 4 and 5, respectively.
Finally, according to the three-dimensional morphological model figures 3-5 of the structural surface with different content ratios of the high-frequency fluctuation component and the low-frequency fluctuation component, a rock carving machine is adopted to carve the rock test block to obtain the required high-frequency fluctuation and low-frequency fluctuation ratio gamma 0 Is a rock mass structural plane sample.
The embodiments described in this specification are merely illustrative of the manner in which the inventive concepts may be implemented. The scope of the present invention should not be construed as being limited to the specific forms set forth in the embodiments, but the scope of the present invention and the equivalents thereof as would occur to one skilled in the art based on the inventive concept.
Claims (3)
1. A sample preparation method with quantitatively controllable structural surface shape spectrum components, which is characterized by comprising the following steps:
s1, acquiring a three-dimensional morphology model of a structural surface consistent with the actual shearing state of the structural surface of a rock mass;
s2, determining a distribution function of the mean square value of the three-dimensional topography fluctuation height of the rock mass structural plane in a frequency range based on the two-dimensional power spectral density, wherein the calculation formula is shown in the following formula (1):
wherein P is 3D Is a high mean square value, PSD (f x ,f y ) Two-dimensional power spectral density, f, of structural surface morphology x And f y The spatial frequencies of structural surface shape frequency components in the directions of the x axis and the y axis are respectively f t Is a frequency threshold, f max Is the maximum frequency value;
s3, drawing a distribution function image of the three-dimensional topography relief height mean square value of the rock mass structural plane in a frequency range, and taking the frequency corresponding to the turning point of the function image as the limit frequency f of the structural plane topography high-frequency component and the structural plane topography low-frequency component tc ；
S4, keeping the content of the low-frequency fluctuation component in the rock mass structural plane unchanged, and quantitatively controlling the content ratio gamma of the high-frequency fluctuation component and the low-frequency fluctuation component of the rock mass structural plane by adjusting the content of the high-frequency fluctuation component 0 Then the ratio of the components to the content gamma 0 The upper frequency limit f of the corresponding high-frequency fluctuation component u The calculation formula of (2) is as follows:
s5, according to the determined limit frequency f tc Or upper frequency limit f of high-frequency fluctuation component u Extracting fluctuation components of different frequencies of three-dimensional morphology of rock mass structural surface, and establishing the three-dimensional morphology of the structural surface with different content ratios of high-frequency fluctuation components and low-frequency fluctuation componentsA model;
the process of the step S5 is as follows:
if a three-dimensional structural surface shape model only containing high-frequency fluctuation components and having zero low-frequency fluctuation component content is established, the three-dimensional structural surface shape model is smaller than the limit frequency f based on the two-dimensional Fourier transform of the three-dimensional structural surface shape in the frequency domain space tc Setting the frequency component of (2) to be zero, and then obtaining a three-dimensional morphology model of the structural surface only containing the high-frequency fluctuation component through inverse Fourier transform, wherein the calculation formula is as follows (4):
if the content of the low-frequency fluctuation component is kept unchanged, a three-dimensional structural surface shape model with different content ratios of the high-frequency fluctuation component and the low-frequency fluctuation component is established, and the frequency upper limit f larger than the high-frequency fluctuation component is set based on the two-dimensional Fourier transform of the three-dimensional structural surface shape in the frequency domain space u Setting the frequency component of (2) to be zero, and obtaining the content ratio of the high-frequency fluctuation component and the low-frequency fluctuation component to be gamma by inverse Fourier transform 0 Is calculated according to the following formula (5):
wherein Z (f) x ,f y ) Two-dimensional Fourier transform of three-dimensional morphology z (x, y) of structural plane in space frequency domain, j 2 ＝-1；
S6, carving by a rock carving machine according to the quantitatively established three-dimensional shape model of the structural surface with different content ratios of the high-frequency fluctuation component and the low-frequency fluctuation component, so as to manufacture a rock structural surface sample with quantitatively controllable high-frequency fluctuation component and low-frequency fluctuation component.
2. The method for quantitatively controlling spectral components of structural surface topography according to claim 1, wherein the step S1 comprises:
s11, acquiring three-dimensional morphology discrete coordinate data of a rock mass structural surface along a shearing direction, taking an included angle between a coordinate data least square fitting plane and a coordinate plane as a trend direction of the three-dimensional morphology of the structural surface, and reversely rotating the structural surface morphology data along the trend direction to ensure that the trend direction of the three-dimensional morphology of the structural surface after rotation is in a horizontal state;
s12, translating the rotated three-dimensional shape data of the structural surface to enable the average plane of the undulating height to coincide with the coordinate plane, and establishing a three-dimensional shape model of the structural surface.
3. The method for quantitatively controllable sampling of spectral components of structural surface topography according to claim 1 or 2, wherein in step S2, the two-dimensional power spectral density PSD (f x ,f y ) The calculation formula of (2) is as follows:
wherein L is x And L y To be the length of the three-dimensional shape of the rock mass structural plane in the directions of the x axis and the y axis, Z (f) x ,f y ) Two-dimensional Fourier transform of three-dimensional morphology z (x, y) of structural plane in space frequency domain, j 2 ＝-1。
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