Facade projection net measuring method for measuring true spacing of rock mass structural plane

Abstract

The embodiment of the invention provides a facade projection net measuring method for measuring the true spacing of a rock mass structural plane. According to the corresponding technical scheme, the method is composed of five steps. The method comprises the following steps: firstly, selecting a relatively flat outcrop which tends to a free face, determining a representative occurrence of a to-be-measured structural plane, then moving to a virtual facade measuring net along the outcrop face, projecting to the outcrop face, drawing a projection measuring net, and further measuring the visual spacing of the structural plane in the projection measuring net along a horizontal projection measuring line and a vertical projection measuring line respectively; and then the true spacing of the structural surface along the normal direction is converted by a mathematical formula deduced and constructed by the method, and finally reliability analysis is carried out on a measurement result, so that the value of the true spacing is completed, and a final result is described. The method has the advantages of being clear in theory and convenient to apply, deep mining of structural plane information from a two-dimensional outcrop to a three-dimensional space can be effectively achieved, the involved mathematical formula has general applicability, and a final result contains reliability feedback.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of engineering geological survey, and particularly relates to a vertical projection measuring network method for measuring true spacing of rock mass structural plane. BACKGROUND

[0002] Rock mass is a part of geological body related to human engineering activities which is divided by structural plane under certain stress state. In the human engineering scene such as slope and tunnel involving rock mass excavation, structural plane directly affects the safety and stability of engineering rock mass and the parameter value of engineering design. Therefore, it is of great significance to quantitatively analyze the basic indexes of rock mass structural plane in engineering geological survey.

[0003] The true spacing of rock mass structural plane refers to the spacing distance of two adjacent structural planes of the same group along the normal direction of the structural plane, which directly affects the rock mass quality classification and the value of mechanical parameters. However, the current spacing measurement methods used in many engineering practices and even textbooks can only measure the apparent spacing of structural plane on the outcrop surface. Although the importance of true spacing measurement of rock mass structural plane is emphasized in the “Engineering Rock Mass Classification Standard” (GB / T 50218-2014), and the idea of measuring along the horizontal line is proposed, the true spacing of structural plane can only be obtained from the single direction of outcrop strike, which cannot meet the needs of checking and verifying the true spacing measurement results of structural plane. SUMMARY

[0004] In order to meet the above needs, the present application provides a vertical projection measuring network method for measuring the true spacing of rock mass structural plane, which aims to measure the true spacing of the same group of structural planes along the normal direction from different spatial directions, and then realize the checking and reliability analysis of the measurement results.

[0005] The technical solution of the present application consists of five steps, specifically including: ①, selecting a suitable rock outcrop and measuring its occurrence (outcrop strike ö and outcrop dip β ), recording the occurrence of the outcrop rock mass and the surrounding structural plane, and determining the representative occurrence of the group of structural planes to be measured (structural plane strike ö J and structural plane dip β J ); ②, virtually measuring the vertical network along the strike direction of the outcrop surface (including horizontal and vertical measuring lines which are perpendicular to each other), and projecting it to the rock outcrop plane in the opposite direction of the outcrop strike to obtain the projection measuring network (including horizontal and vertical projection measuring lines which are perpendicular to each other); ③, in the projection measuring network of the outcrop, the apparent spacing of the adjacent two structural planes of the same group of structural planes along the measuring line direction is measured according to the apparent spacing measurement rule, and the apparent spacing d i x′(in, i =1, 2, 3, … , n and the distance between sight lines along the vertical projection line. d j z′ (in, j =1, 2, 3, … , m ); ④ Based on the three-dimensional spatial relationship between the orientation of the structural surfaces and the survey lines, mathematical formulas are established through theoretical derivation to obtain the true spacing of the same set of structural surfaces along their normal directions, calculated from two different spatial directions (horizontal projection survey line direction and vertical projection survey line direction). D x′ and D z′ ⑤ Compare and verify the true spacing of the two structural surfaces calculated from different spatial directions, perform reliability analysis on the calculation results, and finally obtain and state the final calculation results according to the rules for taking the true spacing of the structural surfaces.

[0006] The "suitable rock outcrop" mentioned in step ① requires that the outcrop surface be relatively flat and inclined towards the air.

[0007] The "facade surveying grid" mentioned in step ② must be an upright rectangular surveying grid parallel to the orientation of the outcrop (the normal direction of the grid surface is consistent with the dip direction of the outcrop), with both horizontal width and vertical height being [missing information]. a The value can be adjusted and optimized based on the estimated apparent spacing of the structural surfaces on site. Generally, it is recommended to... a The value is 1 m; within the vertical survey network, intervals of 0.1 m are made along both the horizontal and vertical directions. a Set up a survey line to form 9 vertical survey lines (numbered from left to right). z 1 , z 2 , z 3 , z 4 , z 5 , z 6 , z 7 , z 8 and z 9 ) and 9 horizontal survey lines (numbered from bottom to top) x 1 , x 2 , x 3 , x 4 ,x 5 , x 6 , x 7 , x 8 and x 9 ).

[0008] The projection rule that must be followed in step ② is: project the elevation survey mesh onto the outcrop surface in the opposite direction of the outcrop surface's inclination to obtain the projected survey mesh.

[0009] The "projection survey network" located on the rock outcrop plane described in step ② is characterized by the following: vertical projection survey lines are obtained by projecting vertical survey lines, and the spacing between adjacent survey lines remains at 0.1. a Numbered from left to right z′ 1 , z′ 2 , z′ 3 , z′ 4 , z′ 5 , z′ 6 , z′ 7 , z′ 8 and z′ 9 The horizontal projection survey lines are obtained by projecting the horizontal survey lines, and remain orthogonal to the vertical projection survey network. The spacing between adjacent survey lines is transformed to 0.1 through projection. a / sin β Numbered from bottom to top x′ 1 , x′ 2 , x′ 3 , x′ 4 , x′ 5 , x′ 6 , x′ 7 , x′ 8 and x′ 9 .

[0010] The "sight distance measurement rule" mentioned in step ③ is specifically described as follows: on the horizontal projection survey line... x′ 1 Above, from left to right, check all intersections of its trace with the surface of the structure to be measured, and determine the intersections of all adjacent pairs of intersections.x′ 1 The spacing along the survey line yields multiple sight distance data; similarly, the spacing along the horizontal projection survey line is obtained. x′ 2 , x′ 3 , x′ 4 , x′ 5 , x′ 6 , x′ 7 , x′ 8 and x′ 9 Measure all available sight distance data until a total of [data] is accumulated along the horizontal projection survey line. m First, the stadia spacing data. Then, following the same stadia spacing measurement rules along the vertical projection survey line, a total of [number] stadia spacing data were accumulated. n Individual view distance data.

[0011] The “mathematical formula” mentioned in step ④ aims to construct a functional expression through mathematical theoretical derivation to quantify the true spacing and apparent spacing of structural surfaces. d i x′ or d j z′ ), structural tendencies ö J Structural surface inclination angle β J Tendency to emerge ö and the angle of emergence β The universal quantitative relationship of the parameters is used to convert the true spacing of the structural surface from the horizontal projection survey line direction and the vertical projection survey line direction respectively. The relevant mathematical formulas are specifically expressed as Equation (1) and Equation (2).

[0012] (1) (2) in, D x′ and D z′ These are the true spacings of the structural surfaces calculated along the horizontal and vertical projection survey lines, respectively.

[0013] The "reliability analysis" described in step ⑤ is specifically performed as follows: The difference between the true distances of the structural surfaces measured from two different spatial directions is calculated, and the absolute value is taken. This difference is then divided by the larger of the two values ​​to obtain the calculation error. Finally, the calculation error is subtracted from 1 to obtain the calculated reliability. RThe calculation method is expressed as shown in equation (3).

[0014] (3) The "value selection rule" mentioned in step ⑤ is: if the calculated reliability is ≥95%, then the true spacing is... D The final value is D x′ and D z′ The arithmetic mean; if the reliability of the measurement is <95%, then the true spacing D The final value is D x′ .

[0015] The "final calculation result" mentioned in step ⑤ is specifically described as follows: the representative occurrence is... ö ∠ β The true spacing between the structural surfaces along their normal direction is D (The calculated reliability is) R ).

[0016] The beneficial effects of this invention are as follows: The elevation projection measurement network method of the present invention has the characteristics of clear theory and easy application. It can effectively realize the in-depth mining of rock mass structural surface information from two-dimensional outcrops to three-dimensional space. The mathematical formulas involved have universal applicability. The measurement results are presented as the true spacing of the rock mass structural surface along its normal direction, and include the measurement reliability feedback. Attached Figure Description

[0017] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments conforming to the present invention and, together with the description, serve to explain the technical solutions of the invention. Obviously, the drawings described below are merely some embodiments of the present invention, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0018] The flowcharts shown in the accompanying drawings are merely illustrative and do not necessarily include all content and operations / steps, nor do they necessarily have to be performed in the described order. For example, some operations / steps can be broken down, while others can be combined or partially combined; therefore, the actual execution order may change depending on the specific circumstances.

[0019] Figure 1 This is a three-dimensional schematic diagram of the present invention; Figure 2 This is the front view of the elevation survey grid; Figure 3 Nine horizontal survey lines are formed within the facade survey network; Figure 4 Nine vertical survey lines are formed within the facade survey network. Figure 5 Nine horizontal projection lines are located within the projection network. Figure 6 Nine vertical projection lines are formed within the projection network; Figure 7 The results of the visual distance measurement on the horizontal projection line in this embodiment of the invention; Figure 8 The results of the visual distance measurement on the vertical projection survey line in an embodiment of the present invention are shown. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the specific technical solutions of the present invention will be further described in detail below with reference to the accompanying drawings of the embodiments of the present invention. The following embodiments are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0021] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein is for the purpose of describing embodiments of the invention only and is not intended to limit the invention.

[0022] In the following description, references to "some embodiments," "this embodiment," "inventory embodiments," and examples, etc., describe a subset of all possible embodiments. However, it is understood that "some embodiments" may be the same subset or different subsets of all possible embodiments and may be combined with each other without conflict.

[0023] If the application documents contain similar descriptions such as "first / second", the following explanation shall be added: In the following description, the terms "first / second / third" are used only to distinguish similar objects and do not represent a specific order of objects. It is understood that "first / second / third" may be interchanged in a specific order or sequence where permitted, so that the embodiments of the present invention described herein can be implemented in an order other than that illustrated or described herein.

[0024] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the application of the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the scope defined and determined by the appended claims, all inventions utilizing the concept of the present invention are protected.

[0025] The technical solution described in this invention consists of five steps, specifically including: ① Selecting a suitable rock outcrop and determining its attitude (outcrop dip). ö and the angle of emergence βThe attitude of the outcrop rock mass and surrounding structural planes is recorded, and the representative attitude of the set of structural planes for which the true spacing is to be measured (the dip of the structural planes) is determined. ö J and structural surface dip angle β J ); ②, A virtual elevation survey network (including mutually orthogonal horizontal and vertical survey lines) is constructed along the strike direction of the outcrop and projected onto the outcrop plane in the opposite direction of the outcrop's dip to obtain a projection survey network (including mutually orthogonal horizontal and vertical projection survey lines); ③, Within the projection survey network of the outcrop, the apparent distance between two adjacent structural surfaces in the same group along the survey line direction is measured according to the rules for measuring apparent distance, and the apparent distance along the horizontal projection survey line direction is obtained respectively. d i x′ (in, i =1, 2, 3, … , n and the distance between sight lines along the vertical projection line. d j z′ (in, j =1, 2, 3, … , m ); ④ Based on the three-dimensional spatial relationship between the orientation of the structural surfaces and the survey lines, mathematical formulas are established through theoretical derivation to obtain the true spacing of the same set of structural surfaces along their normal directions, calculated from two different spatial directions (horizontal projection survey line direction and vertical projection survey line direction). D x′ and D z′ ⑤ Compare and verify the true spacing of the two structural surfaces calculated from different spatial directions, perform reliability analysis on the calculation results, and finally obtain and state the final calculation results according to the rules for taking the true spacing of the structural surfaces.

[0026] The "suitable rock outcrop" mentioned in step ① requires that the outcrop surface be relatively flat and inclined towards the air.

[0027] The "facade surveying grid" mentioned in step ② must be an upright rectangular surveying grid parallel to the orientation of the outcrop (the normal direction of the grid surface is consistent with the dip direction of the outcrop), with both horizontal width and vertical height being [missing information]. a The value can be adjusted and optimized based on the estimated apparent spacing of the structural surfaces on site. Generally, it is recommended to... a The value is 1 m; within the vertical survey network, intervals of 0.1 m are made along both the horizontal and vertical directions. a Set up a survey line to form 9 vertical survey lines (numbered from left to right). z 1 , z 2 , z3 , z 4 , z 5 , z 6 , z 7 , z 8 and z 9 ) and 9 horizontal survey lines (numbered from bottom to top) x 1 , x 2 , x 3 , x 4 , x 5 , x 6 , x 7 , x 8 and x 9 ).

[0028] The projection rule that must be followed in step ② is: project the elevation survey mesh onto the outcrop surface in the opposite direction of the outcrop surface's inclination to obtain the projected survey mesh.

[0029] The "projection survey network" located on the rock outcrop plane described in step ② is characterized by the following: vertical projection survey lines are obtained by projecting vertical survey lines, and the spacing between adjacent survey lines remains at 0.1. a Numbered from left to right z′ 1 , z′ 2 , z′ 3 , z′ 4 , z′ 5 , z′ 6 , z′ 7 , z′ 8 and z′ 9 The horizontal projection survey lines are obtained by projecting the horizontal survey lines, and remain orthogonal to the vertical projection survey network. The spacing between adjacent survey lines is transformed to 0.1 through projection. a / sin β Numbered from bottom to top x′ 1 , x′ 2 ,x′ 3 , x′ 4 , x′ 5 , x′ 6 , x′ 7 , x′ 8 and x′ 9 .

[0030] The "sight distance measurement rule" mentioned in step ③ is specifically described as follows: on the horizontal projection survey line... x′ 1 Above, from left to right, check all intersections of its trace with the surface of the structure to be measured, and determine the intersections of all adjacent pairs of intersections. x′ 1 The spacing along the survey line yields multiple sight distance data; similarly, the spacing along the horizontal projection survey line is obtained. x′ 2 , x′ 3 , x′ 4 , x′ 5 , x′ 6 , x′ 7 , x′ 8 and x′ 9 Measure all available sight distance data until a total of [data] is accumulated along the horizontal projection survey line. m First, the stadia spacing data. Then, following the same stadia spacing measurement rules along the vertical projection survey line, a total of [number] stadia spacing data were accumulated. n Individual view distance data.

[0031] The “mathematical formula” mentioned in step ④ aims to construct a functional expression through mathematical theoretical derivation to quantify the true spacing and apparent spacing of structural surfaces. d i x′ or d j z′ ), structural tendencies ö J Structural surface inclination angle β J Tendency to emerge ö and the angle of emergence β The universal quantitative relationship of the parameters is used to convert the true spacing of the structural surface from the horizontal projection survey line direction and the vertical projection survey line direction respectively. The relevant mathematical formulas are specifically expressed as Equation (1) and Equation (2).

[0032] (1) (2) in, D x′ and D z′ These are the true spacings of the structural surfaces calculated along the horizontal and vertical projection survey lines, respectively.

[0033] The "reliability analysis" described in step ⑤ is specifically performed as follows: The difference between the true distances of the structural surfaces measured from two different spatial directions is calculated, and the absolute value is taken. This difference is then divided by the larger of the two values ​​to obtain the calculation error. Finally, the calculation error is subtracted from 1 to obtain the calculated reliability. R The calculation method is expressed as shown in equation (3).

[0034] (3) The "value selection rule" mentioned in step ⑤ is: if the calculated reliability is ≥95%, then the true spacing is... D The final value is D x′ and D z′ The arithmetic mean; if the reliability of the measurement is <95%, then the true spacing D The final value is D x’ .

[0035] The "final calculation result" mentioned in step ⑤ is specifically described as follows: the representative occurrence is... ö ∠ β The true spacing between the structural surfaces along their normal direction is D (The calculated reliability is) R ).

[0036] For example, a three-dimensional schematic diagram of the present invention is shown below. Figure 1 As shown, for the rock outcrop of a certain engineering slope, the true spacing of the structural planes was calculated. The front view of the elevation survey network is shown below. Figure 2 As shown, the nine horizontal survey lines inside the facade survey network are as follows: Figure 3 As shown, the nine vertical survey lines inside the facade survey network are as follows: Figure 4 As shown, the nine horizontal projection lines within the projection network are as follows: Figure 5 The nine vertical projection lines inside the projection network are as follows: Figure 6 As shown; the measurement results of the apparent distance on the horizontal projection survey line in this embodiment of the invention are as follows. Figure 7 As shown; the measurement results of the apparent distance on the vertical projection survey line in this embodiment of the invention are as follows. Figure 8 As shown.

[0037] The beneficial effects of this invention are as follows: The elevation projection measurement network method of the present invention has the characteristics of clear theory and easy application. It can effectively realize the in-depth mining of rock mass structural surface information from two-dimensional outcrops to three-dimensional space. The mathematical formulas involved have universal applicability. The measurement results are presented as the true spacing of the rock mass structural surface along its normal direction, and include the measurement reliability feedback.

[0038] For example, refer to Figure 1 For an outcrop of rock mass on a certain engineering slope, the true spacing of structural surfaces was calculated. Following the standards described in step ①, a suitable outcrop surface was selected, and its attitude was determined to be 262∠60°. The representative attitude of a certain group of structural surfaces for which the true spacing was to be measured was 102∠76°. The research object was treated as a general case, and the size parameters of the measurement network were set. a The value is 1 m. Based on the survey network layout method and projection principles described in step ②, refer to... Figure 5 A projection grid was drawn on the outcrop surface of the slope. The spacing of the vertical projection lines on the outcrop surface was 0.1 m, and the spacing of the horizontal projection lines on the outcrop surface was calculated to be 0.115 m. To ensure the accurate horizontal distribution of the horizontal projection lines within the grid, the geological compass was deployed along the planned horizontal projection lines, and the compass bubble was centered by adjusting the direction of the planned horizontal projection lines. Furthermore, a right-angled triangle was used to ensure that the vertical and horizontal projection lines were orthogonal within the outcrop surface. The distance measurement rules were followed according to step ③, referring to… Figure 7 The distances between sights along the horizontal projection survey lines were measured as follows: d 1 x′ =0.393m d 2 x′ =0.436m d 3 x′ =0.435m d 4 x′ =0.444m d 5 x′ =0.384m d 6 x′ =0.394m d 7 x′ =0.392m d 8 x′ =0.394m d 9 x′ =0.379m d 10 x′=0.380m d 11 x′ =0.380m d 12 x′ =0.393m and d 13 x′ =0.386m, reference Figure 8 The distances between sights along the vertical projection survey line were measured as follows: d 1 z′ =0.408m d 2 z′ =0.447m d 3 z′ =0.416m d 4 z′ =0.445m d 5 z′ =0.409m d 6 z′ =0.447m d 7 z′ =0.416m d 8 z′ =0.453m d 9 z′ =0.411m、 d 10 z′ =0.409m d 11 z′ =0.447m d 12 z′ =0.408m d 13 z′ =0.409m d 14 z′ =0.408m d 15 z′ =0.401m d 16 z′ =0.407m d 17 z′ =0.399 m、d 18 z′ =0.408m d 19 z′ =0.391m d 20 z′ =0.409m d 21 z′ =0.416m d 22 z′ =0.395m and d 23 z′ =0.423m. Calculations were performed using the mathematical formula described in step ④ to obtain the true spacing between structural surfaces measured along the horizontal and vertical projection survey lines, respectively. D x′ =0.132m and D z′ =0.135m. The reliability of the results obtained from the above calculations is assessed according to step ⑤. R =98.4%, therefore, the final calculated result is taken as 98.4%. D x′ and D z′ The arithmetic mean is expressed as follows: the true spacing of the structural plane with a representative attitude of 102∠76 along its normal direction is 0.134 meters (the reliability of the calculation is 98.4%).

[0039] The methods disclosed in the several method embodiments provided in this invention can be arbitrarily combined without conflict to obtain new method embodiments.

[0040] The features disclosed in the several product embodiments provided in this invention can be arbitrarily combined without conflict to obtain new product embodiments.

[0041] The features disclosed in the several method or device embodiments provided in this invention can be arbitrarily combined without conflict to obtain new method or device embodiments.

[0042] The above description is merely an embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the protection scope of the present invention. Therefore, the protection scope of the present invention should be determined by the protection scope of the claims.

Claims

1. A method for determining the true spacing of rock mass structural surfaces using elevation projection grids, characterized in that, The method includes: ① Select a relatively flat outcrop that tends towards the free surface and determine the representative attitude of the structural surface where the true spacing to be measured is to be determined; ② A virtual elevation survey network is constructed along the direction of the outcrop (the direction of the network normal is consistent with the outcrop dip). This elevation survey network is then projected onto the outcrop plane in the opposite direction of the outcrop dip to obtain the projected survey network. ③ Within the projection grid on the outcrop plane, measure the stadia spacing along the horizontal projection lines. d i x′ (where i = 1, 2, 3, … , n) and the distance between sight lines along the vertical projection line. d j z′ (Where, j = 1, 2, 3, … , m); ④ Using the mathematical formulas constructed based on the spatial relationships of geometric objects in this invention, the true spacing of structural surfaces obtained from two different directions (horizontal projection survey line direction and vertical projection survey line direction) is converted. D x′ and D z′ ) ; ⑤ Compare and verify the true spacing of the two structural surfaces calculated from different directions, analyze the reliability R of the calculation results, and finally obtain and state the final calculation results according to the rules for taking the true spacing of the structural surfaces.

2. The method according to claim 1, characterized in that, The method further includes: 1) The horizontal width and vertical height of the elevation survey network are both [missing information]. a Within the survey network, intervals of 0.1 are observed along both the horizontal and vertical directions. a Set up a survey line to form 9 vertical survey lines and 9 horizontal survey lines; 2) When the projection survey network is located on the outcrop surface, the lengths of the horizontal and vertical projection survey lines are respectively... a and a / sinβ The nine vertical projection lines within it are spaced 0.1 apart. a The interval between the nine horizontal projection lines is 0.

1. a / sinβ; 3) For the results of the distance measurement along the horizontal projection survey line ( d i x′ ), used to convert the corresponding true spacing of structural surfaces ( D x′ The mathematical formula for ) is: （1） in, ө J For structural surface tendency, β J For the inclination angle of the structural surface, ө It tends to emerge; 4) For the results of the distance measurement along the vertical projection survey line ( d j z′ ), used to convert the corresponding true spacing of structural surfaces ( D z′ The mathematical formula for ) is: （2） Where β is the outcrop inclination angle, and the other parameters are as described above; 5) The reliability R of the measurement results is calculated as follows: （3） 6) If the calculated reliability is ≥95%, then the final value of the true spacing D is... D x′ and D z′ The arithmetic mean; if the calculated reliability is <95%, then the final value of the true spacing D is... D x′； 7) The final calculation result is specifically stated as follows: Representative occurrence is... ө ∠ β The true spacing between the structural surfaces along their normal direction is D (the calculated reliability is...). R ).

3. The method according to claim 1 or 2, characterized in that, The method further includes: 1) First, determine the attitude of the outcrop surface and the attitude of the structural planes on the selected suitable outcrop surface, and determine the dimensional parameters based on the estimated apparent spacing of the structural planes on site. a The value of (generally it is recommended to) a (Value is 1 m). 2) Then, use chalk to draw the projection grid on the outcrop of the slope. During this process, let the geological compass spread out along the direction of the horizontal projection line to be drawn. Use the center of the bubble of the geological compass to ensure that the horizontal projection line is accurately spread horizontally. In addition, use a right triangle to ensure that the vertical projection line is orthogonal to the horizontal projection line in the outcrop. 3) Finally, measure separately d i x′ (where i = 1, 2, 3, … , n) and d j z′ (Where j = 1, 2, 3, … ,m), converted from mathematical formulas. D x′ , D z′ and R After completing the data processing, the final calculation results are given.

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