CN107153747B - Two-parameter curve tunnel section and hydraulic design method - Google Patents

Two-parameter curve tunnel section and hydraulic design method Download PDF

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CN107153747B
CN107153747B CN201710413716.8A CN201710413716A CN107153747B CN 107153747 B CN107153747 B CN 107153747B CN 201710413716 A CN201710413716 A CN 201710413716A CN 107153747 B CN107153747 B CN 107153747B
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武周虎
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Abstract

The invention belongs to the technical field of hydraulic tunnel engineering design, and relates to a two-parameter curve tunnel section and hydraulic design method, also called WU type two-parameter curve tunnel section and hydraulic design method, the process steps comprise five steps of establishing a WU type two-parameter curve equation, establishing an area formula of the WU type two-parameter curve tunnel section, determining the clearance area and the water depth in the tunnel of the WU type two-parameter curve tunnel, determining the width-height ratio of the WU type two-parameter curve tunnel section and determining the width and the height of the WU type two-parameter curve tunnel section, the section shape and the corresponding water passing capacity of the tunnel are designed, wherein the section shape is represented by an independent two-parameter curve equation, the continuity, the conductibility, the stress condition and the smoothness of the curve (inner contour line) and the derivative thereof are good, and the method is particularly suitable for section design and engineering construction of a non-pressure tunnel, and the method is also suitable for section design and engineering construction of pressure tunnels with good geological conditions and low water pressure.

Description

Two-parameter curve tunnel section and hydraulic design method
The technical field is as follows:
the invention belongs to the technical field of hydraulic tunnel engineering design, and relates to a two-parameter curve tunnel section and hydraulic design method, also called a WU type two-parameter curve tunnel section and hydraulic design method, which is used for designing the section shape and the corresponding water passing capacity of a tunnel, wherein the section shape is represented by an independent two-parameter curve equation, and the continuity, the conductibility, the stress condition and the smoothness of the curve (inner contour line) and the derivative thereof are good, so that the two-parameter curve tunnel section design method is particularly suitable for the section design and the engineering construction of a non-pressure tunnel, and is also suitable for the section design and the engineering construction of a pressure tunnel with better geological conditions and lower water pressure.
Background art:
the hydraulic tunnel is a water passing tunnel which is excavated in a mountain or underground and is used for irrigation, power generation, water supply, water drainage, water delivery, construction diversion and navigation, and the hydraulic tunnel is divided into a non-pressure tunnel and a pressure tunnel: the tunnel with water flow in the tunnel and free water surface is called a pressureless tunnel; the tunnel which is filled with water flow and makes the tunnel wall bear certain water pressure is called pressure tunnel. The common tunnel section shapes comprise four types, namely a round shape, a square round shape (an urban portal shape), a horseshoe shape, an egg shape (a high arch shape) and the like, and the urban portal shape, the horseshoe shape and the egg shape are combined by a plurality of sections, such as circular arcs, elliptic arcs, straight lines and the like, in an intersecting or tangent mode except for the round section. The shape of the urban gate opening is a straight-wall flat-bottom circular arch or an inclined side-wall flat-bottom circular arch; the horseshoe shape comprises standard horseshoe shape, horseshoe shape (I type, II type, III type, special type), and flat bottom horseshoe shape (I type, II type, special type); the egg shape (high arch shape) comprises a semi-ellipse and semi-circle combined up and down type, a four-arc egg shape and a six-arc egg shape (I type and II type); in addition, the shape of a large-section hydraulic tunnel with two circular arc inverted arch curved walls is also provided; the pressure tunnel mostly adopts a circular cross section, if the diameter of the tunnel and the internal and external water pressure are not large, other cross section shapes which are convenient for construction can be adopted, the pressure tunnel mostly adopts a circular arch straight wall-shaped cross section, the shape of the circular arch straight wall-shaped cross section can be suitable for bearing the vertical pressure of the mountains, is convenient for excavation and lining construction, and bears larger water flow velocity, so that the circular arch straight wall-shaped cross section shape is suitable for the conditions of better geological conditions and smaller pressure of the mountains, when the pressure of the mountains is larger, a thicker lining is needed, and tunnels with other cross section shapes need to be used based on the consideration of economy; when surrounding rock conditions are poor, not only can the pressure of the mountain rock vertically downwards be achieved, but also the pressure of the mountain rock laterally upwards and upwards at the bottom can be achieved, the U-shaped cross section is adopted, the U-shaped cross section is formed by combining a plurality of circular arcs, the capacity of bearing external pressure is higher than that of a circular arch straight wall, and construction is complex; the section curve of the egg shape (high arch shape) is closer to the pressure curve, the stress condition is good, and the method is suitable for the conditions of poor geological condition or large pressure of the mountain rock.
The curve (inner contour) function at the intersection of the tunnel sections is continuous, but not conductive, nor smooth; the curve function at the tangent point of the tunnel section is continuous, although the curve function is conductive and smooth, the first derivative is not smooth, and the second derivative is discontinuous; the curvature of the curve at the intersection (tangent) point of the tunnel section has sudden change, the stress condition is poor, the combination mode of the current hydraulic tunnel section shape is various, the curve shape of the tunnel section is complex, the division and the calculation formula of hydraulic design are complicated and different, and the unified standard of design and construction is lacked.
In the existing tunnel section design, except that most of pressure tunnels adopt circular sections, the pressure-free tunnel part adopts an urban portal section (suitable for the conditions of better geological conditions, vertical rock pressure bearing and smaller side pressure), under other conditions, the adopted tunnel section shape has the confusion of 'selection', particularly, the section of the horseshoe-shaped tunnel and the egg-shaped tunnel has up to 10 shapes, the section shapes of the horseshoe-shaped tunnel and the egg-shaped tunnel are formed by connecting and combining a plurality of sections of circular arcs, elliptical arcs, straight lines and the like, when the circular arcs, the elliptical arcs, the straight lines and the like are specifically selected, the radius is taken, the circle center is taken, the center angle is large, and the position of an intersecting (tangent) point is taken, the pressure-free tunnel is carefully analyzed and determined by careful calculation. The hydraulic design of the tunnel section needs to adopt different mathematical formulas to calculate and confirm hydraulic elements in different zones according to the positions of the connection points, if the surrounding rock stability and the pressure condition of the mountain rock are different, the width-height ratio (width and height) of the tunnel section needs to be adjusted, and then the section shape design, the hydraulic design, the structural design, the lining construction design and the like of the tunnel need to be carried out again, so that the complexity, the complexity and the workload are high. Therefore, the WU type two-parameter curve tunnel section defined by the inventor and the water conservancy design method are researched and designed to design the structural shape of the tunnel section, which is simple in operation, scientific in principle, good in acceptance condition and strong in practicability, improve the design efficiency, reduce the labor intensity, have scientific and application value and have good social and application prospects.
The invention content is as follows:
the invention aims to overcome the defects of the existing tunnel section shape design, and seeks to design a tunnel section shape represented by an independent two-parameter equation and a hydraulic design method, and designs a curve (inner contour) and a derivative thereof with good continuity, conductibility, stress conditions and smoothness so as to replace the section shapes of horseshoe-shaped tunnels, egg-shaped tunnels and large-section tunnels.
In order to achieve the purpose, the process steps of the two-parameter curve tunnel section and the water conservancy design method comprise five steps of establishing a WU type two-parameter curve equation, establishing an area formula of the WU type two-parameter curve tunnel section, determining the clearance area and the water depth in the tunnel of the WU type two-parameter curve tunnel, determining the width-height ratio of the WU type two-parameter curve tunnel section and determining the width and the height of the WU type two-parameter curve tunnel section:
(1) calculating a pollutant diffusion model: firstly, establishing a WU type two-parameter curve equation, deducing the similarity relation between stress flow and pollutant diffusion according to the similarity principle of momentum and mass transfer, deducing an equal concentration standard curve equation of pollutant diffusion to be used as an equal stress standard curve equation, wherein the curve is a tunnel section curve shape which eliminates the stress concentration phenomenon and has good stress condition, and accordingly establishing a WU type two-parameter curve equation 1:
Figure BDA0001313069250000031
wherein z is a vertical coordinate from the midpoint of the bottom of the tunnel section to the upper part, and the value range of z is more than or equal to 0 and less than or equal to H; h is the height of the section of the tunnel; y is a transverse coordinate perpendicular to the z axis, and the value range is that-W/2 is not less than y is not more than W/2; w is the width of the section of the tunnel, and the vertical coordinate corresponding to the maximum width is zwH/e ≈ 0.367879H; the mathematical constant e is 2.718282, and then a pollutant diffusion model is calculated by the established curve equation;
(2) determining the section area of the tunnel: firstly, establishing a WU type two-parameter curve tunnel section area formula, wherein the clearance area of the tunnel section is one of important parameters for designing the tunnel section, and calculating the integral of equation 1 on z between 0 and H to establish the WU type two-parameter curve tunnel section area formula:
Figure BDA0001313069250000032
obtaining by integral operation:
① headroom calculation equation 2:
Figure BDA0001313069250000033
wherein the content of the first and second substances,is the maximum area coefficient;
② formula 3 for calculating the water passing area of the WU type two-parameter curve tunnel at any water depth h:
Figure BDA0001313069250000042
wherein H' is H/H is relative water depth; area coefficient
Figure BDA0001313069250000043
Mu is directly obtained by calculation according to an MATLAB numerical integration program; for example, when h' is 0.8, calculating to obtain μ 0.700197 according to a MATLAB numerical integration program, and then obtaining 88.04% of the water passing area occupying the clearance area according to formula 2 and formula 3 and the ratio of formula 3 to formula 2, thereby completing the determination of the tunnel section area;
(3) determining the tunnel clearance area and the water depth in the tunnel of a WU type two-parameter curve: according to the design flow of tunnel, the safety and the super capacity of leaking increase flow of comprehensive consideration, adopt open channel hydraulics formula to confirm tunnel area of crossing A according to the mode of intaking of non-pressure tunnel, for stable free flow state in guaranteeing the hole, need reserve certain headroom above the surface of water, confirm the headroom of non-pressure tunnel according to the principle that area of crossing accounts for tunnel section headroom 80%, formula 4 promptly: a. themAccording to the condition, the water depth H in the tunnel corresponding to the tunnel water passing area A is obtained by trial calculation according to the formula 2 and the formula 3, the water depth H is 0.715383H, the requirement that the fullness H/H is 0.715383 and is not more than 0.75 is met, and the clearance height delta H above the water surface is H-H is 0.284617H;
(4) determining the width-to-height ratio of the cross section of the WU type two-parameter curve tunnel: the aspect ratio of the tunnel section is adapted to the ground stress condition, if the horizontal ground stress is larger than the vertical ground stress, the section with smaller height and larger width is adopted, if the vertical ground stress is larger than the horizontal ground stress, the section with larger height and smaller width is adopted, according to the classification level of the stability of the surrounding rocks of the tunnel and the pressure conditions of the vertical and lateral mountains, determining that the width-to-height ratio a of the cross section of the tunnel is W/H, the I-level surrounding rocks and the II-level surrounding rocks have better stability and smaller lateral pressure, the width-to-height ratio a of the cross section of the tunnel ranges from 0.67 to 1.0, the III-level surrounding rocks and the IV-level surrounding rocks have poorer stability and larger lateral pressure, the width-to-height ratio a of the cross section of the tunnel ranges from 1.0 to 1.5, the conditions of poor geological conditions and large pressure of the mountains and the soil tunnel, the width-to-height ratio a of the cross section of the tunnel ranges from 0.9 to 1.1, and the tunnel is used for major engineering, carrying out optimization design on the aspect ratio of the tunnel section through finite element analysis of the mechanical properties of the tunnel surrounding rock;
(5) determining the width and the height of the section of the tunnel with the WU type two-parameter curve: the clearance area A calculated according to the step (2)mSubstituting the width-height ratio a determined in the step (4) into a formula 2 to obtain the height and the width of the WU type two-parameter curve tunnel section, wherein the height and the width are respectively a formula 5:
Figure BDA0001313069250000051
w is aH, the construction requirements that the height of the cross section of the WU type two-parameter curve tunnel is not less than 1.8m and the width of the cross section of the tunnel is not less than 1.5m are met, after the width and the height of the cross section of the tunnel are determined, the WU type two-parameter curve equation 1 meeting the design water passing capacity is uniquely determined, and the structural shape of the cross section of the tunnel is uniquely determined.
Compared with the prior art, the invention converts the concentration distribution analytic solution of a river two-dimensional convection diffusion simplified equation based on the equal-intensity central point source discharge condition mentioned in Chinese patent equal-concentration line rapid observation method (patent number 201710281857.9) of a river transverse diffusion coefficient, solves a standard curve equation of river pollutant equal concentration, and deduces the similarity relation between stress flow (diffusion) and pollutant diffusion by applying the similarity principle of momentum and mass transfer on the basis of repeated drawing and actual observation and document retrieval and comparative analysis, namely: the WU-type curve tunnel section is matched with the existing horseshoe-shaped, egg-shaped and large-section tunnel shape by adjusting the width and height parameters of the tunnel section, and on the premise of keeping the advantages of the horseshoe-shaped, egg-shaped and large-section tunnels, the defects of complexity, complexity and large workload of the traditional tunnel section design are overcome, the section shape design of the hydraulic tunnel is more flexible and convenient, the stress performance of the tunnel is more reasonable, the integrity is better, and the tunnel can replace the horseshoe-shaped tunnel, The cross section shapes of the egg-shaped tunnel and the large-cross-section tunnel are better adapted to the development requirements of the construction technology of the special-shaped shield tunneling machine; the principle is scientific and reliable, the design steps are simple, the workload is low, the economic cost is low, and the continuity, the conductibility, the stress condition and the smoothness of the designed curve (inner contour line) and the derivative thereof are good.
Description of the drawings:
FIG. 1 is a schematic block diagram of a process step flow of a two-parameter curve tunnel section and water conservancy design method related by the invention.
Fig. 2 is a schematic cross-sectional structural diagram according to step (1) in example 1 of the present invention.
Fig. 3 is a schematic cross-sectional structural diagram of the aspect ratio of 0.67 according to step (4) in example 1 of the present invention.
Fig. 4 is a schematic cross-sectional structural diagram having an aspect ratio of 1.0 according to step (4) in example 1 of the present invention.
Fig. 5 is a schematic cross-sectional structural diagram having an aspect ratio of 1.5 according to step (4) in example 1 of the present invention.
Fig. 6 is a schematic diagram of a cross-sectional structure of the document numbers [1,2] in table 1 in embodiment 2 of the present invention.
Fig. 7 is a schematic diagram of a cross-sectional structure according to document number [3] in table 1 in embodiment 2 of the present invention.
FIG. 8 is a sectional view of U-shaped form (type II) of document No. [3] in Table 1 in accordance with example 2 of the present invention.
Fig. 9 is a schematic diagram of a cross-sectional structure according to document number [4] in table 1 in embodiment 2 of the present invention.
Fig. 10 is a schematic diagram of a cross-sectional structure according to document number [5] in table 1 in embodiment 2 of the present invention.
Fig. 11 is a schematic diagram of a cross-sectional structure according to document number [6] in table 1 in embodiment 2 of the present invention.
Fig. 12 is a schematic diagram of a cross-sectional structure according to document number [7] in table 1 in embodiment 2 of the present invention.
Fig. 13 is a schematic diagram of a cross-sectional structure according to document number [8] in table 1 in embodiment 2 of the present invention.
Fig. 14 is a schematic diagram of a cross-sectional structure according to document number [9] in table 1 in embodiment 2 of the present invention.
Fig. 15 is a schematic cross-sectional structural diagram according to document number [10] in table 1 in embodiment 2 of the present invention.
Fig. 16 is a schematic cross-sectional structural diagram according to document number [11] in table 1 in embodiment 2 of the present invention.
Fig. 17 is a schematic cross-sectional structural view according to embodiment 3 of the present invention.
The specific implementation mode is as follows:
the invention is further illustrated by the following examples in conjunction with the accompanying drawings.
Example 1:
the specific process steps of the two-parameter curve tunnel section and the water conservancy design method related by the embodiment comprise five steps of establishing a WU type two-parameter curve equation, establishing an area formula of the WU type two-parameter curve tunnel section, determining a clearance area and water depth in the tunnel of the WU type two-parameter curve tunnel, determining the width-height ratio of the WU type two-parameter curve tunnel section and determining the width and height of the WU type two-parameter curve tunnel section:
(1) establishing a WU type two-parameter curve equation: according to the similarity principle of momentum and mass transfer, deducing the similarity relation between stress flow (diffusion) and pollutant diffusion, deducing an isoconcentration standard curve equation of pollutant diffusion, using the equation as an isostress standard curve equation, wherein the curve is a tunnel section curve shape which eliminates the stress concentration phenomenon and has good stress condition, and establishing a WU type two-parameter curve equation 1 according to the equation:
Figure BDA0001313069250000071
wherein z is a vertical coordinate from the midpoint of the bottom of the tunnel section to the upper part, and the value range of z is more than or equal to 0 and less than or equal to H; h is the height (maximum height) of the section of the tunnel; y is a transverse coordinate perpendicular to the z axis, and the value range is that-W/2 is not less than y is not more than W/2; w is the width (maximum width) of the section of the tunnel, and the vertical coordinate (position height) corresponding to the maximum width is zwH/e ≈ 0.367879H; the mathematical constant e is 2.718282; WU type two parameter curve tunnel section drawn by equation 1And its characteristic dimensions are shown in fig. 2;
(2) establishing a WU type area formula of the section of the tunnel with the two-parameter curve: the clearance area of the tunnel section is one of important parameters of the design of the tunnel section, and the integral of equation 1 on z is 0-H, and a WU type two-parameter curve tunnel section area formula is established:obtaining by integral operation:
①, formula 2 for calculating clearance area:
Figure BDA0001313069250000082
wherein the content of the first and second substances,is the maximum area coefficient;
②, and a water passing area calculation formula 3 of the WU type two-parameter curve tunnel at any water depth h:
Figure BDA0001313069250000084
wherein H' (═ H/H) is the relative water depth; area coefficient
Figure BDA0001313069250000085
Mu is directly calculated according to MATLAB (mathematic laboratory) numerical integration program; for example, when h' is 0.8, the calculated value of μ is 0.700197 according to the MATLAB numerical integration program, and 88.04% of the water passing area occupying the clearance area is obtained according to the formula 2 and the formula 3 and the ratio of the formula 3 to the formula 2;
(3) determining the clearance area of the WU type two-parameter curve tunnel and the water depth in the tunnel: according to the design flow of tunnel, the safety and the super capacity of leaking increase flow of comprehensive consideration, adopt open channel hydraulics formula to confirm tunnel area A of crossing according to the intaking (mouthful) mode of non-pressure tunnel, for stable free flow state in guaranteeing the hole, need reserve certain headroom above the surface of water, confirm the headroom of non-pressure tunnel according to the principle that area of crossing accounts for tunnel section headroom 80%, formula 4 promptly: a. themUnder the condition of A/0.8, the formula 2 and the formula 3 are used for processingTrial calculation is carried out to obtain the tunnel water depth H corresponding to the tunnel water passing area A, which is 0.715383H, and simultaneously meets the requirement that the fullness H/H is 0.715383 and is not more than 0.75, and the clearance height delta H above the water surface is H-H is 0.284617H;
(4) determining the width-to-height ratio of the cross section of the WU type two-parameter curve tunnel: the aspect ratio of the tunnel section is adapted to the ground stress condition, if the horizontal ground stress is larger than the vertical ground stress, the section with smaller height and larger width is adopted, if the vertical ground stress is larger than the horizontal ground stress, the section with larger height and smaller width is adopted, determining the width-to-height ratio (a is W/H) of the section of the tunnel according to the classification level of the stability of the surrounding rocks of the tunnel and the pressure conditions of the vertical and lateral mountains, wherein the first-level surrounding rocks and the second-level surrounding rocks have better stability and smaller lateral pressure, the width-to-height ratio a of the section of the tunnel ranges from 0.67 to 1.0, the third-level surrounding rocks and the fourth-level surrounding rocks have poorer stability and larger lateral pressure, the width-to-height ratio a of the section of the tunnel ranges from 1.0 to 1.5, the conditions of poor geological conditions and large pressure of the mountains and the soil cave have the width-to-height ratio a of the section of the tunnel ranges from 0.9 to 1.1, and the tunnel is used for major engineering and in areas with, carrying out optimization design on the aspect ratio of the tunnel section through finite element analysis of the mechanical properties of the tunnel surrounding rock; the WU type two-parameter curve tunnel cross-sectional shapes with aspect ratios of 0.67, 1.0 and 1.5, plotted by equation 1, are shown in fig. 3,4 and 5, respectively;
(5) determining the width and the height of the section of the tunnel with the WU type two-parameter curve: the clearance area A calculated according to the step (2)mSubstituting the width-height ratio a determined in the step (4) into a formula 2 to obtain the height and the width of the WU type two-parameter curve tunnel section, wherein the height and the width are respectively a formula 5:w is aH, the construction requirements that the height of the cross section of the WU type two-parameter curve tunnel is not less than 1.8m and the width of the cross section of the tunnel is not less than 1.5m are met, after the width and the height of the cross section of the tunnel are determined, the WU type two-parameter curve equation 1 meeting the design water passing capacity is uniquely determined, and the structural shape of the cross section of the tunnel is uniquely determined.
Example 2:
this embodiment relates to and establishes two parameter curve tunnel sections and water conservancyVerifying the method, according to two parameters of width W and height H of 11 type tunnel sections such as horseshoe shape, egg shape and the like in a reference document given in a table 1, drawing corresponding WU type two-parameter curve tunnel sections by adopting an equation 1 respectively, as shown in figures 6 to 16, wherein a dotted line in the figure represents the WU type two-parameter curve tunnel section, and a thin dot and dash line represents a maximum width line of the WU type two-parameter curve tunnel section; as can be seen from fig. 6 to 16, the WU type two-parameter curve tunnel section is very close to the 11 type tunnel section curves in the references, such as horseshoe shape, egg shape, etc., and most of the curves are well matched, and particularly, the WU type two-parameter curve tunnel section is more highly matched with the horseshoe shape (special shape) section of the wenzhou mei tunnel in fig. 10, the hexagonal egg shape (type i) section in fig. 14, and the large two-arc inverted arch wall section of the wuzhuang tunnel in the north-water central line engineering in fig. 16. The relative vertical coordinate z corresponding to the maximum width of the tunnel section in the corresponding type of the references in fig. 10, 14 and 16wthe/H is 0.384615, 0.292129 and 0.358491 respectively, and the relative vertical coordinate z corresponds to the maximum width of the cross section of the tunnel with the WU type two-parameter curvewAnd the/H is approximately equal to 1/e and approximately equal to 0.367879, which shows that the stress conditions of the corresponding tunnel sections are close. As shown in Table 1, the average value of the relative vertical coordinates corresponding to the maximum width of the section of the 11-type tunnel in the reference, such as the horseshoe-shaped tunnel and the egg-shaped tunnel, is zw0.377463, the difference of relative vertical coordinates 0.367879 corresponding to the maximum width of the WU-type two-parameter curve tunnel section is only 2.61%, which shows that the WU-type two-parameter curve tunnel section is consistent with the average characteristics of 11-type tunnel sections such as horseshoe shape, egg shape and the like in the reference, the WU-type two-parameter curve tunnel section pressure curve is close to the 11-type tunnel section pressure curve such as horseshoe shape, egg shape and the like in the reference, the stress condition of the WU-type two-parameter curve tunnel section and the 11-type tunnel section such as horseshoe shape, egg shape and the like in the reference is good, and the essence of the hydraulic tunnel section curve is seized.
TABLE 1 characteristic parameter table of tunnel section in reference
Figure BDA0001313069250000101
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[7] Hydraulic calculation of Wenhui, Lifengling, Flat-bottomed horseshoe section [ J ] agricultural engineering bulletin, 2013,29(10):130-
[8] LIFENGLINING, Wenhui, TUNING YU, an approximate algorithm for normal water depth of egg-shaped section pipeline [ J ]. Changjiang river of people, 2008,39(18):77-78.
[9] Li RuoBing, Zhang Shichang, calculation of six-arc egg-shaped section critical water depth and water depth of contracted section of open channel [ J ] Wuhan university journal (engineering edition), 2012,45(4):463 and 467.
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[11] Sunxiang, Li hong Jian, Zhu Yong, Large-section hydraulic tunnel scheme optimization design [ J ] Shijiazhuang railway college academic, 2005(3).
Example 3:
the embodiment relates to an example of performing tunnel section shape and hydraulic design by using a two-parameter curve tunnel section and a hydraulic design method. The design flow of a water delivery project is 50m3And/s, the increased flow is counted by 20 percent, a non-pressure tunnel needs to be constructed for the reason of topography, the non-pressure tunnel needs to pass through mountains with larger side pressures of class III and class IV surrounding rocks, and the drainage capacity, the roughness and the specific pressure drop condition of the tunnel inlet are determined according to the conditions of the drainage capacity, the tunnel interior roughness and the specific pressure drop of the tunnel inletThe average flow velocity in the tunnel is designed according to the condition of 1.80 m/s. Hydraulic design is carried out according to equation 1 of the WU type two-parameter curve tunnel section and hydraulic design method and a corresponding calculation formula, and according to a water flow continuous equation: water delivery flow is equal to water passing area multiplied by average flow speed, water passing area A in reverse thrust tunnel is equal to 1.2 multiplied by 50/1.8 is equal to 33.33m2Calculating the clearance area A of the pressureless tunnel according to the formula 4m＝A/0.8＝41.67m2According to the characteristics of classification III and IV of stability of surrounding rock crossing of the tunnel and larger lateral pressure, the width-to-height ratio a of the tunnel section is 1.25, the height H of the WU type two-parameter curve tunnel section is 6.50m, the width W of the tunnel section is 8.10m, and the vertical coordinate z corresponding to the maximum width is calculated by a formula 5wThe water depth H of the tunnel corresponding to the water passing area a of the tunnel is 0.715383H 4.65m, the clearance height Δ H above the water surface is 0.284617H 1.85m, and the WU type two-parameter curve tunnel section drawn according to the above design parameters is shown in fig. 17.

Claims (1)

1. A water conservancy design method based on a two-parameter curve tunnel section is characterized by comprising the following concrete process steps of establishing a WU type two-parameter curve equation, establishing an area formula of the WU type two-parameter curve tunnel section, determining the clearance area and the water depth in the tunnel of the WU type two-parameter curve tunnel, determining the width-height ratio of the WU type two-parameter curve tunnel section and determining the width and the height of the WU type two-parameter curve tunnel section:
(1) calculating a pollutant diffusion model: firstly, establishing a WU type two-parameter curve equation, deducing the similarity relation between stress flow and pollutant diffusion according to the similarity principle of momentum and mass transfer, deducing an equal concentration standard curve equation of pollutant diffusion to be used as an equal stress standard curve equation, wherein the curve is a tunnel section curve shape which eliminates the stress concentration phenomenon and has good stress condition, and accordingly establishing a WU type two-parameter curve equation 1:
Figure FDA0002302235070000011
wherein z is a vertical coordinate from the midpoint of the bottom of the tunnel section to the upper part, and the value range of z is more than or equal to 0 and less than or equal to H; h is the height of the section of the tunnel; y is perpendicular toThe value range of the transverse coordinate of the z axis is-W/2 to y to W/2; w is the width of the section of the tunnel, and the vertical coordinate corresponding to the maximum width is zwH/e ≈ 0.367879H; the mathematical constant e is 2.718282, and then a pollutant diffusion model is calculated by the established curve equation;
(2) determining the section area of the tunnel: firstly, establishing a WU type two-parameter curve tunnel section area formula, wherein the clearance area of the tunnel section is one of important parameters for designing the tunnel section, and calculating the integral of equation 1 on z between 0 and H to establish the WU type two-parameter curve tunnel section area formula:obtaining by integral operation:
① headroom calculation equation 2:
Figure FDA0002302235070000013
wherein the content of the first and second substances,
Figure FDA0002302235070000014
is the maximum area coefficient;
② formula 3 for calculating the water passing area of the WU type two-parameter curve tunnel at any water depth h:
Figure FDA0002302235070000015
wherein H' is H/H is relative water depth; area coefficient
Figure FDA0002302235070000021
Mu is directly obtained by calculation according to an MATLAB numerical integration program; when h' is 0.8, calculating according to an MATLAB numerical integration program to obtain mu-0.700197, and then obtaining 88.04% of the water passing area occupying the clearance area according to a formula 2, a formula 3 and a ratio of the formula 3 to the formula 2 to complete the determination of the section area of the tunnel;
(3) determining the tunnel clearance area and the water depth in the tunnel of a WU type two-parameter curve: according to the design flow of the tunnel, the flow is increased by comprehensively considering the safety and the over-discharge capacity, and the flow is determined by adopting an open channel hydraulics formula according to the water inlet mode of the pressureless tunnelTunnel water passing area A, for stable free flow state in guaranteeing the hole, need reserve certain headroom above the surface of water, confirm the headroom of non-pressure tunnel according to the principle that water passing area accounts for tunnel section headroom 80%, equation 4 promptly: a. themAccording to the condition, the water depth H in the tunnel corresponding to the tunnel water passing area A is obtained by trial calculation according to the formula 2 and the formula 3, the water depth H is 0.715383H, the requirement that the fullness H/H is 0.715383 and is not more than 0.75 is met, and the clearance height delta H above the water surface is H-H is 0.284617H;
(4) determining the width-to-height ratio of the cross section of the WU type two-parameter curve tunnel: the aspect ratio of the tunnel section is adapted to the ground stress condition, if the horizontal ground stress is larger than the vertical ground stress, the section with smaller height and larger width is adopted, if the vertical ground stress is larger than the horizontal ground stress, the section with larger height and smaller width is adopted, according to the classification level of the stability of the surrounding rocks of the tunnel and the pressure conditions of the vertical and lateral mountains, determining that the width-to-height ratio a of the cross section of the tunnel is W/H, the I-level surrounding rocks and the II-level surrounding rocks have better stability and smaller lateral pressure, the width-to-height ratio a of the cross section of the tunnel ranges from 0.67 to 1.0, the III-level surrounding rocks and the IV-level surrounding rocks have poorer stability and larger lateral pressure, the width-to-height ratio a of the cross section of the tunnel ranges from 1.0 to 1.5, the conditions of poor geological conditions and large pressure of the mountains and the soil tunnel, the width-to-height ratio a of the cross section of the tunnel ranges from 0.9 to 1.1, and the tunnel is used for major engineering, carrying out optimization design on the aspect ratio of the tunnel section through finite element analysis of the mechanical properties of the tunnel surrounding rock;
(5) determining the width and the height of the section of the tunnel with the WU type two-parameter curve: the clearance area A calculated according to the step (2)mSubstituting the width-height ratio a determined in the step (4) into a formula 2 to obtain the height and the width of the WU type two-parameter curve tunnel section, wherein the height and the width are respectively a formula 5:
Figure FDA0002302235070000022
w is aH, the construction requirements of the height of the cross section of the WU type two-parameter curve tunnel of not less than 1.8m and the width of not less than 1.5m are met, after the width and the height of the cross section of the tunnel are determined, the WU type two-parameter curve equation 1 meeting the design water passing capacity is uniquely determined, and the structural shape of the cross section of the tunnel is uniqueIs determined.
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