CN109918846B - Method for positioning center of karst depression excavation by utilizing concentric circles - Google Patents
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Abstract
The invention discloses a method for positioning the center of excavation of a karst depression by using concentric circles, which comprises the following steps: 1) selecting a mechanism to excavate a central candidate area; 2) determining factors influencing excavation center positioning; 3) primarily selecting and determining a plane coordinate of a better excavation central point; 4) determining an optimal elevation plane; 5) and accurately positioning in the optimal elevation plane to obtain an optimal mechanism excavation center. According to the method, different positions of the spherical crown type structure excavation center in the large-scale karst depression are simulated, the position of the spherical crown type mechanism center in the large-scale karst depression is solved by taking the total engineering cost as a constraint condition, the optimized output and the accurate positioning of the spherical crown type mechanism excavation center in the large-scale karst depression are realized, and a scientific and reasonable reference method is provided for the positioning of the spherical crown type mechanism excavation center in the large-scale karst depression.
Description
Technical Field
The invention relates to a method for positioning the center of excavation of a karst depression by using concentric circles.
Background
Karst depressions are a kind of negative topography formed by erosion in carbonate areas, and the topography at the bottom of the depressions is flat, and the diameter of the depressions is generally from hundreds of meters to thousands of meters. The method is particularly suitable for building spherical crown type structures in large karst depressions, particularly large circular karst depressions. However, the excavation center positions of different spherical crown structures will produce different excavation effects, such as different excavation amounts, different geological hazard treatment workload, and the like. In a word, the excavation effect is to meet the installation requirement of the spherical crown type structure on the premise of ensuring the safety of the spherical crown type structure, and meanwhile, the overall construction cost of the spherical crown type structure is considered, so that the excavation engineering quantity is reduced to the maximum extent. Therefore, how to position the optimal excavation center of the spherical-crown structure and realize reasonable excavation of the large-scale karst-hole land is a problem which needs to be considered when the spherical-crown mechanism of the large-scale karst-hole land is built.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method for positioning the excavation center of the concentric karst-hole land is provided, and aims to solve the problems that in a large-scale karst-hole land excavation project, due to the fact that different spherical crown type structures have different excavation effects due to the fact that the center positions of the different spherical crown type structures need to be positioned, the optimal excavation center of the spherical crown type structures needs to be positioned, and the large-scale karst-hole land is optimized and reasonably excavated.
The technical scheme adopted by the invention is as follows: a concentric circle karst depression excavation center positioning method comprises the following steps:
1) selecting a spherical crown structure in a set range from the center of the bottom of the large-scale karst depression to excavate a central candidate area;
2) determining influence factors influencing the positioning of an excavation center, wherein the influence factors comprise earth and rockfill excavation engineering, collapse huge rock mixture treatment engineering, dangerous rock treatment engineering, side slope engineering, drainage engineering and spherical crown structure construction cost;
3) primary selection is carried out to determine the plane coordinates of the better excavation central points: taking the earth and stone excavation project with the maximum influence factor as a calculation object in the candidate area, calculating the earth and stone excavation project amount when the excavation center depth is a set value through an interactive integral algorithm to obtain an excavation project amount contour map, and preliminarily determining the central point of the excavation amount contour map as a better excavation central point;
4) determining an optimal elevation plane: in each elevation plane, taking the coordinate of a better excavation center plane as an assumed excavation center, calculating the total construction cost of the engineering corresponding to the elevation plane by calculating the construction cost corresponding to each influence factor, and determining the optimal elevation plane by taking the elevation as the horizontal coordinate and the total construction cost as the vertical coordinate;
5) accurate positioning in the optimal elevation plane: in an optimal elevation plane, a preferred excavation central point is taken as an origin, an area in a set range is further selected, the optimal area is determined by utilizing a multi-factor decision-making base number method of concentric circle point selection, namely, a representative point is selected on a concentric circle, a comprehensive score of each point is calculated by utilizing the multi-factor decision-making base number method, and an optimal area is selected, and the specific steps are as follows:
A. selecting representative points to establish constraint set
Two concentric circles with a small circle radius of 5 meters and a large circle radius of 10 meters are drawn by taking the optimal excavation central point as the center of the circle. Selecting representative points, and selecting 17 points in total, wherein the points are respectively 0 point, N1 point, N2 point, NE1 point, NE2 point, E1 point, E2 point, ES1 point, ES2 point, S1 point, S2 point, SW1 point, SW2 point, W1 point, W2 point, WN1 point and WN2 point;
the 0 point is a better excavation central point 1, the N1 point represents that the O point translates to the positive north for 5 meters, and the NE1 point represents that the N1 rotates clockwise for 45 degrees by taking the O point as the center of a circle;
the point N2 represents that the point O translates 10 meters to the positive north, and the point NE2 represents that the point N2 rotates 45 degrees clockwise by taking the point O as the center;
point E1 indicates that N1 is rotated 90 ° clockwise around point O, and point E2 indicates that N2 is rotated 90 ° clockwise around point O;
point ES1 indicates N1 is rotated clockwise by 135 ° around point O, and point ES2 indicates N2 is rotated clockwise by 135 ° around point O;
a point S1 shows that N1 rotates 180 degrees clockwise around the O point, and a point S2 shows that N2 rotates 180 degrees clockwise around the O point;
point SW1 shows N1 rotated clockwise by 225 ° around point O, and point SW2 shows N2 rotated clockwise by 225 ° around point O;
point W1 indicates that N1 rotates clockwise 270 ° around point O, and point W2 indicates that N2 rotates clockwise 270 ° around point O;
WN1 point represents N1 rotated clockwise 315 degrees around O point, WN2 point represents N2 rotated clockwise 315 degrees around O point, the constraint set of the problem is:
X＝{x1,x2,x3，…，x16,x17}
B. establishing a multi-factor decision model
Let x be a decision variable, then A1(x)，A2(x)，A3(x)，A4(x)，A5(x) In turn is a soil stoneThe method comprises the following steps of square excavation engineering, collapse huge rock mixture treatment engineering, dangerous rock treatment engineering, side slope engineering and drainage engineering, wherein a multi-factor decision model is as follows:
MinA1(x)，A4(x)
MaxA2(x)，A3(x)
OptA5(x)
in the formula, the earth and stone excavation engineering quantity A1Removing coefficient of collapse dissolving huge stone mixture A2Critical rock removal coefficient A3Engineering quantity of side slope A4All can be obtained by quantitative calculation; the drainage engineering firstly carries out qualitative judgment and then quantifies the qualitative problem;
C. setting earthwork excavation work amount A1Removing coefficient of collapse dissolving huge stone mixture A2Critical rock removal coefficient A3Engineering quantity of side slope A4And the problem attributes of the drainage engineering and the quantification and the qualitative determination of the attributes in the constraint set of the problem, as shown in the table:
for quantitative class attributes a1, a2, A3, a4, let:
for qualitative class attributes, set as scores, we can translate into:
the problem quantitative numerical matrix is then obtained, for a total of 5 rows, 17 columns:
D. solving the number of merit bases on attributes for 17 points
a. For A1, A4 for minimal attributes and A5 for optimal attributes, it is calculated as follows:
b. for A solving maximum attribute2、A3Calculated as follows:
obtaining a good radix matrix of the problem, wherein the number of the good radix matrix is 5 rows and 17 columns, and obtaining good base points of 17 points through the good radix matrix;
E. determining a weight coefficient
Excavation project A for earth and stone1(x) Collapse dissolving huge stone mixture treatment engineering A2(x) Dangerous rock treatment project A3(x) Slope engineering A4(x) Drainage engineering A5(x) These 5 attributes are weighted as shown in the table:
F. weighting and summing the priority numbers, and sequencing, thereby obtaining 17 points of scores on the preferred elevations to obtain the direction in which the optimized area is located;
G. according to the direction in which the optimized area is located, in the optimized area, an optimal area with a set size is further selected according to the engineering total cost contour map by using the distance with the set size and the engineering total cost contour map distribution map, points in the area are encrypted, the set size value is used as the distance, the engineering total cost corresponding to each encryption point is calculated, and the coordinates of the encryption points in the optimal area and the corresponding engineering total cost table are obtained;
6) selecting a fitting function, performing three-dimensional space surface fitting on the coordinates of the encrypted points in the optimal area and the construction value in the corresponding total construction cost table, taking coordinate points x and y as independent variables, selecting the total construction cost as a dependent variable Z, constructing a binary function, solving the minimum value of the function, assuming the shape of the function as a paraboloid, and constructing the binary function about x, y and Z by applying an undetermined coefficient method in the following manner:
Z＝Ax2+Bx+Cy2+Dy+Exy+F
wherein A, B, C, D, E and F are binary function coefficients, the binary function coefficients are fitted to obtain a function shown as the following formula, and the correlation coefficient r2＝0.9786：
Z＝90.484x2+459.859x+56.120y2+8.522y-87.460xy+9836.042
In the formula: x and y are horizontal directions, Z is a vertical direction, and the minimum value point obtained by the binary function is the optimal mechanism excavation center.
The invention has the beneficial effects that: compared with the prior art, the method has the advantages that different positions of the spherical crown type structure excavation center in the large-scale karst depression are simulated, multiple influence factors of earth and rocky excavation engineering, collapse boulder mixture body treatment engineering, dangerous rock treatment engineering, side slope engineering, drainage engineering and spherical crown structure construction cost are comprehensively considered, the total engineering cost calculated by the multiple influence factors is taken as a constraint condition, the position of the spherical crown type mechanism center in the large-scale karst depression is solved, the optimal output and accurate positioning of the spherical crown type mechanism excavation center in the large-scale karst depression are realized, and a scientific and reasonable reference method is provided for the positioning of the spherical crown type mechanism excavation center in the large-scale karst depression.
Drawings
FIG. 1 is a flow chart of the present invention.
FIG. 2 is a distribution diagram of the contour line of the excavation engineering quantity during initial selection.
FIG. 3 is a diagram of a total construction cost curve (including cost for each impact factor) for determining an optimal elevation.
The concentric circles of fig. 4 represent dot distribution plots.
The concentric circles of fig. 5 represent point scores.
FIG. 6 is a contour map of total construction cost of excavation projects when accurate positioning is performed in the optimal elevation plane.
Fig. 7 is a diagram of the finally solved excavation center point positions.
Detailed Description
The invention is further described with reference to the accompanying drawings and specific embodiments.
Example 1: as shown in fig. 1-7, a method for excavating a center using concentric karst-depression includes the following steps:
1) a 100 m x 100 m square area was selected at the center of the bottom of the depression: a spherical crown structure is constructed in a large karst depression, and therefore a candidate area of 100 m multiplied by 100 m is selected in the bottom center area of the depression and is used as an area where the center of the spherical crown structure can move randomly. The lowest elevation of the original ground at the bottom of the depression is 841 meters, and the excavation depth principle is determined through qualitative analysis as follows: the lower limit of the excavation center depth is 13 meters, namely 828 meters; the upper limit of the excavation center depth is 5 meters, i.e., 836 meters.
2) Analyzing and determining the influence factors: selecting factors influencing the center selection of the spherical crown structure, wherein the factors comprise earth and stone excavation engineering, collapse huge rock mixture treatment engineering, dangerous rock treatment engineering, side slope engineering, drainage engineering and the construction cost of the spherical crown structure.
3) Primary selection is carried out to determine the plane coordinates of the better excavation central points: in 1) the earth and stone excavation project with the maximum influence factor in the 100 m × 100 m candidate area is taken as a calculation object, the earth and stone excavation project amount when the excavation center depth is 13 m is calculated through an interactive integral algorithm, an excavation project amount contour map is obtained, and a central point of the excavation amount contour map is preliminarily determined to be a better excavation central point 1 as shown in an attached figure 2.
4) Determining an optimal elevation: in a height plane of 828-836 m, a better excavation central point 1 is taken as an optimization origin, and all influence factors, namely the construction cost increment of an earth and rockfill excavation project, a collapse huge rock mixture management project, a dangerous rock management project, a side slope project, a drainage project and a spherical crown structure are considered. And calculating the engineering cost corresponding to each influence factor to obtain the total engineering cost. The method specifically comprises the following steps: the total construction cost of the excavation project corresponding to the optimal excavation central point 2 in the elevation of 828 m to 836 m is respectively calculated by taking 1 m as a step and gradually raising the position of the excavation central point 1, and a total construction cost curve chart (comprising construction costs of various influence factors) is obtained, and is shown in an attached figure 3. As can be seen from FIG. 3, when the elevation is 834 m, the total construction cost is the lowest, so the optimum elevation is 834 m.
5) Accurate positioning in the optimal elevation plane: within 834 m of the optimal elevation, a 20 m × 20 m area 2 is selected by taking the optimal excavation central point 1 as an origin, and the optimal area is determined by using a multi-factor decision-making base number type method utilizing concentric circle point selection. Namely, representative points are selected on a concentric circle, comprehensive scores of all points are calculated by a multi-factor decision-making base number method, and an optimization area is selected. The method comprises the following specific steps:
A. selecting representative points to establish constraint set
Two concentric circles with a small circle radius of 5 meters and a large circle radius of 10 meters are drawn by taking the optimal excavation central point 1 as the center of the circle. Selecting representative points, and selecting 17 points which are respectively 0 point (preferably excavating a central point 1), N1, N2, NE1, NE2, E1, E2, ES1, ES2, S1, S2, SW1, SW2, W1, W2, WN1 and WN 2. The numbering and positioning of the points in the figure are shown in fig. 4, and as point N1 indicates that point O is translated by 5 meters in the positive north direction, point NE1 indicates that point N1 is rotated by 45 degrees clockwise around point O, the constraint set of the problem is:
X＝{x1,x2,x3，…，x16,x17}
B. establishing a multi-factor decision model
Among the influencing factors, in the same elevation plane, the smaller the excavation engineering quantity of earth and stone is, the better the excavation engineering quantity of the earth and stone is, the more the removal of the collapse rock mixture is, the better the removal of the dangerous rock treatment is, the less the slope engineering is, the better the drainage is, and the more favorable the drainage is. Let x be a decision variable, then A1(x)，A2(x)，A3(x)，A4(x)，A5(x) The method sequentially comprises an earth and stone excavation project, a collapse huge rock mixture treatment project, a dangerous rock treatment project, a side slope project and a drainage project. The multi-factor decision model is:
MinA1(x)，A4(x)
MaxA2(x)，A3(x)
OptA5(x)
in the formula, the earth and stone excavation engineering quantity A1Removing coefficient of collapse dissolving huge stone mixture A2Critical rock removal coefficient A3Engineering quantity of side slope A4All can be obtained by quantitative calculation; the drainage engineering firstly carries out qualitative judgment and then quantifies qualitative problems.
C. Setting problem attributes and quantifying attributes
For quantitative class attributes a1, a2, A3, a4, let:
for qualitative class attributes, we can translate into:
the problem quantitative numerical matrix is then obtained, for a total of 5 rows, 17 columns:
D. solving the number of merit bases on attributes for 17 points
a. For A1, A4 for minimal attributes and A5 for optimal attributes, it is calculated as follows:
the calculation result is as follows:
b. for A solving maximum attribute2、A3Calculated as follows:
in the formula, m represents the number of attributes, which is 5 attribute numbers of influence factors, s represents the number of optimization schemes, which is 17, and the calculation result is:
the problem of the optimal radix matrix is obtained, 5 rows and 17 columns are used:
the excellent base points for 17 points were found to be:
E. determining a weight coefficient
Excavation project A for earth and stone1(x) Collapse dissolving huge stone mixture treatment engineering A2(x) Dangerous rock treatment project A3(x) Slope engineering A4(x) Drainage engineering A5(x) These 5 attributes are weighted as shown in the table:
F. and (4) weighting, summing and sorting the priority numbers, and calculating:
u1＝0.7720×0.30+0.2237×0.25+0.2244×0.15+0.8089×0.25+0.3509×0.05＝0.5410u2＝0.7528×0.30+0.1466×0.25+0.1470×0.15+0.8071×0.25+0.2729×0.05＝0.5000
……
u17figure 5 shows the score of 17 points at 834 m elevation from 0.7299 × 0.30+0.2315 × 0.25+0.2322 × 0.15+0.7714 × 0.25+0.1949 × 0.05-0.5220. As can be seen from the figure: the score of the SW1 point is obviously higher than that of other areas, and the optimization area is known to be positioned in the southwest direction;
G. from the above step, the optimized area is located in the southwest direction, so that the total construction cost can be calculated only in the optimized area with 2 meters as the distance, and the contour distribution map of the total construction cost is obtained, as shown in fig. 6. According to the contour map of the total construction cost of the project, an optimal area 3 with the size of 4 meters multiplied by 5 meters is further selected, points in the area are encrypted, 1 meter is taken as an interval, and the total construction cost corresponding to each encryption point is calculated, as shown in a table 1.
Table 1 encryption point coordinates in optimal area 3 and corresponding total construction cost table
6) And selecting a fitting function, and performing three-dimensional space surface fitting on the engineering value in the table 1. In table 1, since x and y are independent variables, the total construction cost is selected as a dependent variable Z, a binary function is constructed, and the minimum value of the function is obtained. Assuming that the function shape is a paraboloid, a binary function form about x, y and Z is constructed by applying a undetermined coefficient method as follows:
Z＝Ax2+Bx+Cy2+Dy+Exy+F
by fitting, a function is obtained as shown below (correlation coefficient r)2＝0.9786)：
Z＝90.484x2+459.859x+56.120y2+8.522y-87.460xy+9836.042
In the formula: x and y are horizontal directions, and Z is a vertical direction.
And (3) solving the minimum value of the curved surface according to the formula, and solving the optimal coordinate value (-4.1349, -3.2866), wherein the optimal coordinate value is the optimal excavation central point 4, and the height is 834 m, as shown in the attached figure 7.
The above description is only an embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of changes or substitutions within the technical scope of the present invention, and therefore, the scope of the present invention should be determined by the scope of the claims.
Claims (1)
1. A concentric circle karst depression excavation center positioning method is characterized by comprising the following steps: the method comprises the following steps:
1) selecting a spherical crown structure in a set range from the center of the bottom of the large-scale karst depression to excavate a central candidate area;
2) determining influence factors influencing the positioning of an excavation center, wherein the influence factors comprise earth and rockfill excavation engineering, collapse huge rock mixture treatment engineering, dangerous rock treatment engineering, side slope engineering, drainage engineering and spherical crown structure construction cost;
3) primary selection is carried out to determine the plane coordinates of the better excavation central points: taking the earth and stone excavation project with the maximum influence factor as a calculation object in the candidate area, calculating the earth and stone excavation project amount when the excavation center depth is a set value through an interactive integral algorithm to obtain an excavation project amount contour map, and preliminarily determining the central point of the excavation amount contour map as a better excavation central point;
4) determining an optimal elevation plane: in each elevation plane, taking the coordinate of a better excavation center plane as an assumed excavation center, calculating the total construction cost of the engineering corresponding to the elevation plane by calculating the construction cost corresponding to each influence factor, and determining the optimal elevation plane by taking the elevation as the horizontal coordinate and the total construction cost as the vertical coordinate;
5) accurate positioning in the optimal elevation plane: in an optimal elevation plane, a preferred excavation central point is taken as an origin, an area in a set range is further selected, the optimal area is determined by utilizing a multi-factor decision-making base number method of concentric circle point selection, namely, a representative point is selected on a concentric circle, a comprehensive score of each point is calculated by utilizing the multi-factor decision-making base number method, and an optimal area is selected, and the specific steps are as follows:
A. selecting representative points to establish constraint set
Drawing two concentric circles with a small circle radius of 5 meters and a large circle radius of 10 meters by taking the optimal excavation central point as the center of the circle; selecting representative points, and selecting 17 points in total, wherein the points are respectively 0 point, N1, N2, NE1, NE2, E1, E2, ES1, ES2, S1, S2, SW1, SW2, W1, W2, WN1 and WN2:
the 0 point is a better excavation central point 1, the N1 point represents that the O point translates to the positive north for 5 meters, and the NE1 point represents that the N1 rotates clockwise for 45 degrees by taking the O point as the center of a circle;
the point N2 represents that the point O translates 10 meters to the positive north, and the point NE2 represents that the point N2 rotates 45 degrees clockwise by taking the point O as the center;
point E1 indicates that N1 is rotated 90 ° clockwise around point O, and point E2 indicates that N2 is rotated 90 ° clockwise around point O;
point ES1 indicates N1 is rotated clockwise by 135 ° around point O, and point ES2 indicates N2 is rotated clockwise by 135 ° around point O;
a point S1 shows that N1 rotates 180 degrees clockwise around the O point, and a point S2 shows that N2 rotates 180 degrees clockwise around the O point;
point SW1 shows N1 rotated clockwise by 225 ° around point O, and point SW2 shows N2 rotated clockwise by 225 ° around point O;
point W1 indicates that N1 rotates clockwise 270 ° around point O, and point W2 indicates that N2 rotates clockwise 270 ° around point O;
WN1 point represents N1 rotated clockwise 315 degrees around O point, WN2 point represents N2 rotated clockwise 315 degrees around O point, the constraint set of the problem is:
X＝{x1,x2,x3，…，x16,x17}
B. establishing a multi-factor decision model
Let x be a decision variable, then A1(x)，A2(x)，A3(x)，A4(x)，A5(x) The method sequentially comprises an earth and rock excavation project, a collapse huge rock mixture treatment project, a dangerous rock treatment project, a side slope project and a drainage project, wherein the multi-factor decision model is as follows:
Min A1(x)，A4(x)
Max A2(x)，A3(x)
OptA5(x)
in the formula, the earth and stone excavation engineering quantity A1Removing coefficient of collapse dissolving huge stone mixture A2Critical rock removal coefficient A3Engineering quantity of side slope A4All can be obtained by quantitative calculation; the drainage engineering firstly carries out qualitative judgment and then quantifies the qualitative problem;
C. setting earthwork excavation work amount A1Removing coefficient of collapse dissolving huge stone mixture A2Critical rock removal coefficient A3Engineering quantity of side slope A4And the problem attributes of the drainage engineering and the quantification and the qualitative determination of the attributes in the constraint set of the problem, as shown in the table:
for quantitative class attributes a1, a2, A3, a4, let:
for qualitative class attributes, set as scores, convert to:
the problem quantitative numerical matrix is then obtained, for a total of 5 rows, 17 columns:
D. solving the number of merit bases on attributes for 17 points
a. For A1, A4 for minimal attributes and A5 for optimal attributes, it is calculated as follows:
in the formula, m represents the number of attributes and is 5 influence factor attributes, and s represents the number of optimization schemes and is 17;
b. for A solving maximum attribute2、A3Calculated as follows:
in the formula, m represents the number of attributes and is 5 influence factor attributes, and s represents the number of optimization schemes and is 17;
obtaining a good radix matrix of the problem, wherein the number of the good radix matrix is 5 rows and 17 columns, and obtaining good base points of 17 points through the good radix matrix;
E. determining a weight coefficient
Excavation project A for earth and stone1(x) Collapse dissolving huge stone mixture treatment engineering A2(x) Dangerous rock treatment project A3(x) Slope engineering A4(x) Drainage engineering A5(x) These 5 attributes take weight coefficients, as shown in the table;
F. Weighting and summing the priority numbers, and sequencing, thereby obtaining 17 points of scores on the preferred elevations to obtain the direction in which the optimized area is located;
G. according to the direction in which the optimized area is located, in the optimized area, an optimal area with a set size is further selected according to the engineering total cost contour map by using the distance with the set size and the engineering total cost contour map distribution map, points in the area are encrypted, the set size value is used as the distance, the engineering total cost corresponding to each encryption point is calculated, and the coordinates of the encryption points in the optimal area and the corresponding engineering total cost table are obtained;
6) selecting a fitting function, performing three-dimensional space surface fitting on the coordinates of the encrypted points in the optimal area and the construction value in the corresponding total construction cost table, taking coordinate points x and y as independent variables, selecting the total construction cost as a dependent variable Z, constructing a binary function, solving the minimum value of the function, assuming the shape of the function as a paraboloid, and constructing the binary function about x, y and Z by applying an undetermined coefficient method in the following manner:
Z＝Ax2+Bx+Cy2+Dy+Exy+F
wherein A, B, C, D, E and F are binary function coefficients, the binary function coefficients are fitted to obtain a function shown as the following formula, and the correlation coefficient r2＝0.9786：
Z＝90.484x2+459.859x+56.120y2+8.522y-87.460xy+9836.042
In the formula: x and y are horizontal directions, Z is a vertical direction, and the minimum value point obtained by the binary function is the optimal mechanism excavation center.
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