CN113761638A - Method for designing arch dam body - Google Patents
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- CN113761638A CN113761638A CN202111128519.4A CN202111128519A CN113761638A CN 113761638 A CN113761638 A CN 113761638A CN 202111128519 A CN202111128519 A CN 202111128519A CN 113761638 A CN113761638 A CN 113761638A
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Abstract
The invention relates to a method for designing an arch dam body, which belongs to the technical field of arch dam engineering and comprises the steps of firstly establishing a coordinate system, then establishing a base plane for a selected arch dam, selecting 4 individual designed control elevation sub-arch rings, drawing up 4 design parameters of the control elevation sub-arch rings, then drawing up the drawing up 4 design parameters of the control elevation sub-arch rings to be a curve equation for 3 times, obtaining the design parameters of other elevation sub-arch rings through calculation, and finally calculating the curvature radius and the central angle of each elevation sub-arch ring to finish the body design of the arch dam. The method for designing the arch dam body shape only needs to determine 16 parameters to describe the arch dam body shape, reduces the number of body shape adjusting parameters, obviously improves the efficiency of body shape design, and adopts the method of reversely calculating the curvature radius and the central angle of a sub-arch ring curve by the central coordinate of the arch end, so that the position of the arch end is not changed in the body shape adjusting process, the body shape adjustment is carried out on the selected arch dam building base surface, and the effectiveness of the body shape design of the arch dam is ensured.
Description
Technical Field
The invention relates to a method for designing an arch dam body, belonging to the technical field of arch dam engineering.
Background
The arch dam body design is the core content of the arch dam design, and the existing design process is as follows: determining the axial line position of the arch dam, determining the center line position of the arch dam, determining the embedding depth of the arch end, and then carrying out body shape layout design. The arch dam axis and the arch dam central line play roles of arch dam body skeleton and positioning control, and the arch dam body design process is to continuously adjust the shape of an arch crown beam and adjust the curvature radius and the thickness of each height sub-arch ring until the body design requirements are met. For the project with complicated geological conditions, the range of available rock mass of a dam foundation is not large, the position of a reasonable foundation surface is determined by demonstration, and little adjustment is needed. In addition, in the existing arch dam body design process, the parameters which need to be adjusted during body shape design are more, taking an arch dam divided into 10 layers of arch rings as an example, the axis of the arch ring adopts a parabolic line shape, after the position of the building base surface of the arch dam is determined, 3 parameters are needed to describe the shape of the upstream surface of the arch crown beam, 4 parameters are needed to describe the thickness of the arch crown beam, 20 curvature radiuses and 20 arch end thicknesses, that is, 47 parameters are needed to describe the body shape of the arch dam in total, and the 47 parameters need to be adjusted continuously in the body shape design process, so that the designed body shape meets the relevant requirements.
Disclosure of Invention
The invention aims to provide a method for designing an arch dam body with higher efficiency.
The technical scheme adopted by the invention for solving the technical problems is as follows: a method for designing an arch dam body, wherein the arch ring axis line of the arch dam is parabolic, and is characterized in that: the method comprises the following steps:
a. determining the position of the center line of the arch dam, and establishing a coordinate system of the arch dam body design;
b. dividing an arch ring of the arch dam into a plurality of sequentially connected sub-arch rings from bottom to top along the height direction of the dam, wherein the sub-arch ring with the largest elevation is a top arch ring, and the sub-arch ring with the smallest elevation is a bottom arch ring;
c. establishing a base plane for the selected arch dam, and determining the center coordinates of the arch ends of the left bank and the right bank corresponding to all the sub-arch rings;
d. selecting a control elevation sub-arch ring designed in a body shape, wherein the control elevation sub-arch ring is a bottom arch ring, a top arch ring and any other 2 sub-arch rings;
e. d, drawing up the arch crown beam thickness TCi, the left arch end thickness TLi, the right arch end thickness TRi and the distance Li from the arch ring axis to the coordinate origin corresponding to the 4 control elevation sub-arch rings in the step d as design parameters;
f. according to the 4 design parameters of the control elevation sub-arch ring drawn up in the step e, respectively fitting the corresponding arch crown beam thickness TCi, the left arch end thickness TLi, the right arch end thickness TRi and the distance Li between the arch ring axis at the arch crown and the coordinate origin into a 3-time curve equation to obtain undetermined coefficients of the 3-time curve equation;
g. according to the determined curve equation of 3 times, calculating the arch crown beam thickness TCi, the left arch end thickness TLi, the right arch end thickness TRi and the distance Li from the arch ring axis at the arch to the coordinate origin corresponding to other elevation sub-arch rings;
h. calculating the curvature radius and the center angle of each elevation sub-arch ring according to the distance Li from the arch ring axis at the arch crown of each elevation sub-arch ring to the coordinate origin and the center coordinates of the arch end of the left bank and the center coordinates of the arch end of the right bank determined in the step c;
wherein i is a numerical value corresponding to a certain elevation sub-arch ring, the numerical values corresponding to the sub-arch rings are sequentially increased from top to bottom along the direction of the dam height, the numerical value corresponding to the top arch ring is 1, and i is a positive integer.
Further, in the step a, the determined center line of the arch dam is taken as a Y axis, the positive direction of the Y axis is taken as an upstream direction, the cross river direction is taken as an X axis, the positive direction of the X axis is directed to a right bank, the negative direction of the X axis is directed to a left bank, and the vertical direction is taken as a Z axis.
Further, in step c, the arch end center coordinate of the left bank is (XL)i，YLi，Zi) And the center coordinates of the arch end of the right bank are expressed as (XR)i，YRi，Zi)。
Further, in step f:
the 3-order curve equation of the arched crown beam thickness fitting is as follows: TCi ═ b0+b1(Hi/H)+b2(Hi/H)2+b3(Hi/H)3；
The 3-degree curve equation fitted to the left arch thickness is: TLi ═ c0+c1(Hi/H)+c2(Hi/H)2+c3(Hi/H)3；
The 3-degree curve equation fitted to the right arch thickness is: TRi ═ d0+d1(Hi/H)+d2(Hi/H)2+d3Hi/H)3；
The 3-order curve equation of the distance fit between the arch ring axis at the arch crown and the coordinate origin is as follows: li ═ a0+a1(Hi/H)+a2(Hi/H)2+a3(Hi/H)3；
Wherein, a0, a1, a2 and a 3; b0, b1, b2, b 3; c0, c1, c2, c 3; d0, d1, d2 and d3 are coefficients to be determined, H is the maximum dam height, and Hi is the relative dam height corresponding to a certain arch centering;
further, in step h: dividing each elevation sub-arch ring into a left part and a right part by taking the center line of the arch dam as a boundary line, connecting the left sub-arch ring with the left bank dam foundation to form the left sub-arch ring, and connecting the right sub-arch ring with the right bank dam foundation to form the right sub-arch ring, wherein the curvature radius of the left sub-arch ring at a certain elevation is RLi：RLi＝|XLi 2/(2(YLi-Li) Is RR, the radius of curvature of the right-side arch segment at a certain elevation is RRi：RRi＝|XRi 2/ (2(YRi-Li))|；
The central angle of the left arch-dividing ring at a certain elevation is phi Li：φLi＝|arctan(XLi/RLi) The central angle of the right sub-arch ring at a certain elevation is phi Ri＝|arctan(XRi/RRi)|。
The invention has the beneficial effects that: firstly, an arch ring of the arch dam is divided into a plurality of sequentially connected sub-arch rings from bottom to top along the dam height direction by establishing a coordinate system, then a base surface is established for the selected arch dam, the center coordinates of the left bank arch end and the center coordinates of the right bank arch end corresponding to all the sub-arch rings are determined, then 4 individual design control elevation sub-arch rings are selected, the design parameters of the 4 control elevation sub-arch rings are drawn up, the design parameters of the 4 drawn up control elevation sub-arch rings are drawn up to be a curve equation for 3 times, the design parameters of other elevation sub-arch rings are obtained by calculation, and finally the curvature radius and the center angle of each elevation sub-arch ring are calculated by the distance Li from the arch ring axis at the arch crown to the coordinate origin, the determined center coordinates of the left bank arch end and the center coordinates of the right bank arch end, so that the design of the arch dam is completed. Therefore, after determining the arch dam building base surface and determining the center coordinates of the left bank arch end and the right bank arch end corresponding to all the sub-arch rings, the method only needs to determine 16 parameters to describe the arch dam body shape, reduces the number of body shape adjustment parameters, and obviously improves the efficiency of body shape design.
Drawings
FIG. 1 is a schematic illustration of a certain elevation sub-arch and arch dam design coordinate system;
parts, positions and numbers in the drawings: the system comprises a left arch division ring curvature radius RL, a right arch division ring curvature radius RR, a left bank arch end center DL, a right bank arch end center DR, an arch dam coordinate system origin O and a distance L from an arch ring axis at an arch crown to a coordinate origin.
Detailed Description
The invention will be further explained with reference to the drawings.
A method for designing an arch dam body, wherein the arch ring axis line of the arch dam is parabolic, and the method comprises the following steps:
a. determining the position of the center line of the arch dam, establishing a coordinate system designed in the shape of the arch dam, and taking the determined center line of the arch dam as a Y axis, the positive direction of the Y axis as the upstream direction, the cross river direction as an X axis, the positive direction of the X axis pointing to the right bank, the negative direction of the X axis pointing to the left bank, and the vertical direction as a Z axis as shown in figure 1.
b. The method comprises the steps of dividing an arch ring of the arch dam into a plurality of sequentially connected sub-arch rings from bottom to top along the height direction of the dam, wherein the sub-arch ring with the maximum height is a top arch ring, the sub-arch ring with the minimum height is a bottom arch ring, thinning the arch rings, and then respectively designing the thinned sub-arch rings into a body shape, so that the body shape of the arch dam is smooth, the center of the arch end of each sub-arch ring is located on an expected arch dam building base surface, an initial body shape design result of the arch dam is obtained, and the difficulty of body shape design is reduced.
c. B, establishing a base plane for the selected arch dam, determining the center coordinates of the arch ends of the left bank and the right bank corresponding to all the sub-arch rings, and designing a coordinate system according to the arch dam body shape established in the step a, wherein the center coordinate of the arch end of the left bank is (XL)i，YLi，Zi) And the center coordinates of the arch end of the right bank are expressed as (XR)i，YRi，Zi)。
d. Selecting a control elevation sub-arch ring designed in a body shape, wherein the control elevation sub-arch ring is a bottom arch ring, a top arch ring and any other 2 sub-arch rings;
e. d, drawing up the arch crown beam thickness TCi, the left arch end thickness TLi, the right arch end thickness TRi and the distance Li from the arch ring axis to the coordinate origin corresponding to the 4 control elevation sub-arch rings in the step d as design parameters;
f. according to the 4 design parameters of the elevation control sub-arch ring drawn up in the step e, respectively fitting the corresponding arch crown beam thickness TCi, the left arch end thickness TLi, the right arch end thickness TRi and the distance Li between the arch ring axis at the arch crown and the coordinate origin into a curve equation for 3 times to obtain a curve equation for 3 timesUndetermined coefficients of the curve equation are as follows: the 3-order curve equation of the arched crown beam thickness fitting is as follows: TCi ═ b0+b1(Hi/H)+b2(Hi/H)2+b3(Hi/H)3(ii) a The 3-degree curve equation fitted to the left arch thickness is: TLi ═ c0+c1(Hi/H)+c2(Hi/H)2+c3(Hi/H)3(ii) a The 3-degree curve equation fitted to the right arch thickness is: TRi ═ d0+d1(Hi/H)+d2(Hi/H)2+d3Hi/H)3(ii) a The 3-order curve equation of the distance fit between the arch ring axis at the arch crown and the coordinate origin is as follows: li ═ a0+a1(Hi/H)+a2(Hi/H)2+a3(Hi/H)3(ii) a Wherein, a0, a1, a2 and a 3; b0, b1, b2, b 3; c0, c1, c2, c 3; d0, d1, d2 and d3 are waiting coefficients, H is the maximum dam height, Hi is the relative dam height corresponding to a certain sub-arch ring, and the waiting coefficients a0, a1, a2 and a3 can be obtained by respectively substituting the designed parameters of 4 control elevation sub-arch rings into the fitted 3-time curve equation; b0, b1, b2, b 3; c0, c1, c2, c 3; d0, d1, d2, d 3. Through fitting into a curve equation of 3 times, the parameters of other elevations are calculated, firstly, the design parameters can be reduced, and secondly, the whole body shape is smooth and does not have mutation when the body shape parameters are adjusted.
g. According to the determined 3-time curve equation and the relative dam height Hi corresponding to each elevation sub-arch ring, substituting Hi/H into the 3-time curve equation to calculate the arch crown beam thickness TCi, the left arch end thickness TLi, the right arch end thickness TRi and the distance Li from the arch ring axis at the arch to the coordinate origin corresponding to other elevation sub-arch rings;
h. calculating the curvature radius and the center angle of each elevation sub-arch ring according to the distance Li from the arch ring axis at the arch crown of each elevation sub-arch ring to the coordinate origin and the center coordinates of the arch end of the left bank and the center coordinates of the arch end of the right bank determined in the step c; in particular, the parabolic equation y + x2the/2R is 0 and is expressed by the arch crown being positioned on the x axis, and in a coordinate system for establishing the arch dam body shape design, the parabolic equation is (y-L) + x2The curvature radius R of the parabola at the arch crown is | x2L (2(y-L)) |, left and rightThe arch axis passes through a left bank arch end center DL and a right bank arch end center DR, and takes an arch dam center line as a boundary line, each elevation sub-arch ring is divided into a left part and a right part, the left sub-arch ring is connected with a left bank dam foundation, and the right sub-arch ring is connected with a right bank dam foundation, so that the curvature radius of the left sub-arch ring at a certain elevation is RLi: RLi ═ XLi2(2(YLi-Li)) |, the radius of curvature of a certain elevation right-hand sub-arch is RRi: RRi ═ XRi2(2(YRi-Li)) |, and setting the center coordinate of the left bank arch end corresponding to each elevation sub-arch ring as (XL)i，YLi，Zi) And the center coordinates of the arch end of the right bank are expressed as (XR)i，YRi，Zi) And substituting the distance Li between the axis of the arch ring at the arch crown and the origin of coordinates into an equation to obtain the curvature radius of each elevation left sub-arch ring and each elevation right sub-arch ring. According to the parabolic equation y + x2/2R＝0，y＝-x2And 2R, the tangential slope of any point on the parabola is Y' — X/R, and the included angle between the tangent slope and the Y axis is | arctan (X/R) |, so that the central angle of the left sub-arch ring at a certain elevation is phi Li：φLi＝|arctan(XLi/RLi) The central angle of the right sub-arch ring at a certain elevation is phi Ri＝|arctan (XRi/RRi) The center coordinate of the left bank arch end corresponding to each elevation sub-arch ring is (XL)i，YLi，Zi) And the center coordinates of the arch end of the right bank are expressed as (XR)i，YRi，Zi) And substituting the corresponding curvature radius into an equation to obtain the central angle of each elevation left sub-arch ring and each elevation right sub-arch ring.
Wherein i is a numerical value corresponding to a certain elevation sub-arch ring, the numerical values corresponding to the sub-arch rings are sequentially increased from top to bottom along the direction of the dam height, the numerical value corresponding to the top arch ring is 1, and i is a positive integer.
In summary, after determining the arch dam building base surface and determining the center coordinates of the left bank arch end and the right bank arch end corresponding to all the sub-arch rings, the method for designing the arch dam body shape only needs to determine 16 parameters to describe the arch dam body shape, reduces the number of body shape adjustment parameters, and obviously improves the efficiency of body shape design.
Example 1
The method for designing the arch dam body shape comprises the following steps of:
a. determining the position of the center line of the arch dam, establishing a coordinate system designed in the shape of the arch dam, and taking the determined center line of the arch dam as a Y axis, the positive direction of the Y axis as the upstream direction, the cross river direction as an X axis, the positive direction of the X axis pointing to the right bank, the negative direction of the X axis pointing to the left bank, and the vertical direction as a Z axis as shown in figure 1.
b. And dividing the arch ring of the arch dam into 10 sequentially connected sub-arch rings from bottom to top along the height direction of the dam, wherein the sub-arch ring with the maximum elevation is a top arch ring, and the sub-arch ring with the minimum elevation is a bottom arch ring.
c. B, designing a selected arch dam building base surface according to the initial body shape, determining the center coordinates of the arch ends of the left bank and the right bank corresponding to all the sub-arch rings, and according to the coordinate system of the arch dam body shape design established in the step a, the center coordinates of the arch ends of the left bank are (XL)i， YLi，Zi) And the center coordinates of the arch end of the right bank are expressed as (XR)i，YRi，Zi). The center coordinates of the arch end of the left bank and the center coordinates of the arch end of the right bank are shown in a table I:
watch 1
d. The method comprises the following steps of selecting a bottom arch ring, a top arch ring, a 4 th elevation sub-arch ring and a 7 th elevation sub-arch ring as a control elevation sub-arch ring designed in a body shape, wherein the top arch ring is also the 1 st elevation sub-arch ring, and the bottom arch ring is also the 10 th elevation sub-arch ring.
e. D, drawing up the arch crown beam thickness TCi, the left arch end thickness TLi, the right arch end thickness TRi and the distance Li from the arch ring axis to the coordinate origin corresponding to the 4 control elevation sub-arch rings in the step d as design parameters, wherein the specific parameters are shown in the table II:
watch two
f. According to the 4 design parameters of the control elevation sub-arch ring drawn up in the step e, respectively fitting the corresponding arch crown beam thickness TCi, the left arch end thickness TLi, the right arch end thickness TRi and the distance Li between the arch ring axis at the arch crown and the coordinate origin into a 3-time curve equation to obtain undetermined coefficients of the 3-time curve equation; specifically, the method comprises the following steps: the 3-order curve equation of the arched crown beam thickness fitting is as follows: TCi ═ b0+b1(Hi/H)+b2(Hi/H)2+b3(Hi/H)3(ii) a The 3-degree curve equation fitted to the left arch thickness is: TLi ═ c0+c1(Hi/H)+c2(Hi/H)2+c3(Hi/H)3(ii) a The 3-degree curve equation fitted to the right arch thickness is: TRi ═ d0+d1(Hi/H)+d2(Hi/H)2+d3Hi/H)3(ii) a The 3-order curve equation of the distance fit between the arch ring axis at the arch crown and the coordinate origin is as follows: li ═ a0+a1(Hi/H)+a2(Hi/H)2+a3(Hi/H)3(ii) a Respectively substituting the designed 4 design parameters for controlling the elevation sublevel arch ring into the fitted 3-time curve equation to obtain undetermined coefficients a0, a1, a2 and a 3; b0, b1, b2, b 3; c0, c1, c2, c 3; the values of d0, d1, d2, d3 are shown in table three:
| coefficient of performance | Li | TCi | TLi | TRi |
| Cubic term | a3＝-46.18512 | b3＝72.328228 | c3＝15.963228 | d3＝75.04886 |
| Second order term | a2＝-7.62091 | b2＝-137.1057 | c2＝-80.17724 | d2＝-199.6863 |
| Item of one time | a1＝62.306033 | b1＝111.77746 | c1＝111.71401 | d1＝171.1374 |
| Constant term | a0＝292 | b0＝16 | c0＝18.5 | d0＝18 |
Watch III
g. According to the determined curve equation for 3 times and the relative dam height Hi corresponding to each elevation sub-arch ring, substituting Hi/H into the curve equation for 3 times to calculate the arch crown beam thickness TCi, the left arch end thickness TLi, the right arch end thickness TRi and the distance Li from the arch ring axis at the arch to the coordinate origin corresponding to other elevation sub-arch rings, wherein the obtained specific parameters are as shown in the fourth table:
| arc dividing ring i | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Elevation Zi (m) | 1885 | 1870 | 1830 | 1790 | 1750 | 1710 | 1670 | 1630 | 1600 | 1580 |
| Hi/H | 0 | 0.049180 | 0.180327 | 0.311475 | 0.442623 | 0.573770 | 0.704918 | 0.836065 | 0.934426 | 1 |
| Li(m) | 292 | 295.0403 | 302.7169 | 309.2718 | 314.0800 | 316.5164 | 315.9560 | 311.7736 | 305.8839 | 300.5 |
| TLi(m) | 18.5 | 23.8021 | 36.1315 | 46.0000 | 53.6235 | 59.2182 | 63.0000 | 65.1850 | 65.9059 | 66 |
| TCi(m) | 16 | 21.1742 | 32.1223 | 39.7000 | 44.8862 | 48.6599 | 52.0000 | 55.8853 | 59.7460 | 63 |
| TRi(m) | 18 | 25.9425 | 42.8075 | 54.2000 | 61.1358 | 64.6305 | 65.7000 | 65.3599 | 64.7908 | 64.5 |
Watch four
h. Calculating the curvature radius and the center angle of each elevation sub-arch ring according to the distance Li from the arch ring axis at the arch crown of each elevation sub-arch ring to the coordinate origin and the center coordinates of the arch end of the left bank and the center coordinates of the arch end of the right bank determined in the step c; the curvature radius of the left arc of a certain elevation is RLi: RLi ═ XLi2(2(YLi-Li)) |, the radius of curvature of a certain elevation right-hand sub-arch is RRi: RRi ═ XRi2/
(2(YRi-Li)) |, the central angle of the left sub-arch ring at a certain elevation is phi Li：φLi＝|arctan(XLi/RLi) The central angle of the right sub-arch ring at a certain elevation is phi Ri＝|arctan(XRi/RRi) The resulting radius of curvature is shown in table five and the resulting central angle is shown in table six:
| arch ring i | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Elevation Zi (m) | 1885 | 1870 | 1830 | 1790 | 1750 | 1710 | 1670 | 1630 | 1600 | 1580 |
| Hi/H | 0 | 0.0491803 | 0.1803279 | 0.3114754 | 0.442623 | 0.5737705 | 0.704918 | 0.8360656 | 0.9344262 | 1 |
| XLi(m) | -247.4 | -241.75 | -226.31 | -208.83 | -185.17 | -153.95 | -119.2 | -85.88 | -59.13 | -28.83 |
| YLi(m) | 173.37 | 176.5 | 185.54 | 197.18 | 214.13 | 235.91 | 256.75 | 273.76 | 285.32 | 295.5 |
| XRi(m) | 235.41 | 218.55 | 186.6 | 166.41 | 153.86 | 142.18 | 130.36 | 104.36 | 78.97 | 15.16 |
| YRi(m) | 172.56 | 185.65 | 208.86 | 223.92 | 233.41 | 242.31 | 250.04 | 265.63 | 277.54 | 299.27 |
| RLi(m) | 257.9734 | 246.5114 | 218.5423 | 194.5279 | 171.5254 | 147.0143 | 119.9932 | 97.0096 | 85.0120 | 83.1169 |
| RRi(m) | 231.9904 | 218.3196 | 185.4929 | 162.2244 | 146.7268 | 136.2089 | 128.9044 | 118.0121 | 110.0106 | 93.4250 |
Watch five
| Arch ring i | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Elevation Zi (m) | 1885 | 1870 | 1830 | 1790 | 1750 | 1710 | 1670 | 1630 | 1600 | 1580 |
| Hi/H | 0 | 0.0491803 | 0.1803279 | 0.3114754 | 0.442623 | 0.5737705 | 0.704918 | 0.8360656 | 0.9344262 | 1 |
| XLi(m) | -247.4 | -241.75 | -226.31 | -208.83 | -185.17 | -153.95 | -119.2 | -85.88 | -59.13 | -28.83 |
| YLi(m) | 173.37 | 176.5 | 185.54 | 197.18 | 214.13 | 235.91 | 256.75 | 273.76 | 285.32 | 295.5 |
| XRi(m) | 235.41 | 218.55 | 186.6 | 166.41 | 153.86 | 142.18 | 130.36 | 104.36 | 78.97 | 15.16 |
| YRi(m) | 172.56 | 185.65 | 208.86 | 223.92 | 233.41 | 242.31 | 250.04 | 265.63 | 277.54 | 299.27 |
| RLi(m) | 257.9734 | 246.5114 | 218.5423 | 194.5279 | 171.5254 | 147.0143 | 119.9932 | 97.0096 | 85.0120 | 83.1169 |
| RRi(m) | 231.9904 | 218.3196 | 185.4929 | 162.2244 | 146.7268 | 136.2089 | 128.9044 | 118.0121 | 110.0106 | 93.4250 |
| φLi(°) | 43.8014 | 44.4413 | 46.0004 | 47.0307 | 47.1907 | 46.3201 | 44.8100 | 41.5176 | 34.8205 | 19.1297 |
| φRi(°) | 45.4192 | 45.0302 | 45.1705 | 45.7297 | 46.3594 | 46.2287 | 45.3217 | 41.4868 | 35.6723 | 9.2170 |
Table six.
Claims (5)
1. A method for designing an arch dam body, wherein the arch ring axis line of the arch dam is parabolic, and is characterized in that: the method comprises the following steps:
a. determining the position of the center line of the arch dam, and establishing a coordinate system of the arch dam body design;
b. dividing an arch ring of the arch dam into a plurality of sequentially connected sub-arch rings from bottom to top along the height direction of the dam, wherein the sub-arch ring with the largest elevation is a top arch ring, and the sub-arch ring with the smallest elevation is a bottom arch ring;
c. establishing a base plane for the selected arch dam, and determining the center coordinates of the arch ends of the left bank and the right bank corresponding to all the sub-arch rings;
d. selecting a control elevation sub-arch ring designed in a body shape, wherein the control elevation sub-arch ring is a bottom arch ring, a top arch ring and any other 2 sub-arch rings;
e. d, drawing up the arch crown beam thickness TCi, the left arch end thickness TLi, the right arch end thickness TRi and the distance Li from the arch ring axis to the coordinate origin corresponding to the 4 control elevation sub-arch rings in the step d as design parameters;
f. according to the 4 design parameters of the control elevation sub-arch ring drawn up in the step e, respectively fitting the corresponding arch crown beam thickness TCi, the left arch end thickness TLi, the right arch end thickness TRi and the distance Li between the arch ring axis at the arch crown and the coordinate origin into a 3-time curve equation to obtain undetermined coefficients of the 3-time curve equation;
g. according to the determined curve equation of 3 times, calculating the arch crown beam thickness TCi, the left arch end thickness TLi, the right arch end thickness TRi and the distance Li from the arch ring axis at the arch to the coordinate origin corresponding to other elevation sub-arch rings;
h. calculating the curvature radius and the center angle of each elevation sub-arch ring according to the distance Li from the arch ring axis at the arch crown of each elevation sub-arch ring to the coordinate origin and the center coordinates of the arch end of the left bank and the center coordinates of the arch end of the right bank determined in the step c;
wherein i is a numerical value corresponding to a certain elevation sub-arch ring, the numerical values corresponding to the sub-arch rings are sequentially increased from top to bottom along the direction of the dam height, the numerical value corresponding to the top arch ring is 1, and i is a positive integer.
2. A method of designing an arch dam according to claim 1, wherein: in the step a, the determined center line of the arch dam is taken as a Y axis, the positive direction of the Y axis is taken as an upstream direction, the transverse river direction is taken as an X axis, the positive direction of the X axis is directed to the right bank, the negative direction of the X axis is directed to the left bank, and the vertical direction is taken as a Z axis.
3. As claimed in claim 2The method for designing the arch dam body is characterized by comprising the following steps: in step c, the arch end center coordinate of the left bank is (XL)i，YLi，Zi) And the center coordinates of the arch end of the right bank are expressed as (XR)i，YRi，Zi)。
4. A method of designing an arch dam according to claim 3, wherein: in step f:
the 3-order curve equation of the arched crown beam thickness fitting is as follows: TCi ═ b0+b1(Hi/H)+b2(Hi/H)2+b3(Hi/H)3；
The 3-degree curve equation fitted to the left arch thickness is: TLi ═ c0+c1(Hi/H)+c2(Hi/H)2+c3(Hi/H)3；
The 3-degree curve equation fitted to the right arch thickness is: TRi ═ d0+d1(Hi/H)+d2(Hi/H)2+d3 Hi/H)3；
The 3-order curve equation of the distance fit between the arch ring axis at the arch crown and the coordinate origin is as follows: li ═ a0+a1(Hi/H)+a2(Hi/H)2+a3(Hi/H)3；
Wherein, a0, a1, a2 and a 3; b0, b1, b2, b 3; c0, c1, c2, c 3; d0, d1, d2 and d3 are coefficients to be determined, H is the maximum dam height, and Hi is the relative dam height corresponding to a certain arch centering.
5. A method of designing an arch dam according to claim 4, wherein: in step h: dividing each elevation sub-arch ring into a left part and a right part by taking the center line of the arch dam as a boundary line, connecting the left sub-arch ring with the left bank dam foundation to form the left sub-arch ring, and connecting the right sub-arch ring with the right bank dam foundation to form the right sub-arch ring, wherein the curvature radius of the left sub-arch ring at a certain elevation is RLi：RLi＝|XLi 2/(2(YLi-Li) Is RR, the radius of curvature of the right-side arch segment at a certain elevation is RRi：RRi＝|XRi 2/(2(YRi-Li))|；
The central angle of the left arch-dividing ring at a certain elevation is phi Li：φLi＝|arctan(XLi/RLi) The central angle of the right sub-arch ring at a certain elevation is phi Ri＝|arctan(XRi/RRi)|。
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| CN107133383A (en) * | 2017-04-05 | 2017-09-05 | 中国电建集团贵阳勘测设计研究院有限公司 | Parabola hyperbolic arch dam arch ring weaving and drawing method |
| CN110284465A (en) * | 2019-06-28 | 2019-09-27 | 中国电建集团成都勘测设计研究院有限公司 | Arch dam pour construction control method |
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| CN107133383A (en) * | 2017-04-05 | 2017-09-05 | 中国电建集团贵阳勘测设计研究院有限公司 | Parabola hyperbolic arch dam arch ring weaving and drawing method |
| CN110284465A (en) * | 2019-06-28 | 2019-09-27 | 中国电建集团成都勘测设计研究院有限公司 | Arch dam pour construction control method |
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