CN107153747A - Two-parameter curve tunnel section and hydraulic design method - Google Patents
Two-parameter curve tunnel section and hydraulic design method Download PDFInfo
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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
Technical field：
The invention belongs to hydraulic tunnel engineering design field, it is related to a kind of two parameter curves tunnel section and water conservancy is set
Meter method, also known as the parameter curve tunnel section of WU types two and Hydraulic Design Method, section configuration and phase for designing tunnel
The discharge capacity answered, section configuration therein is characterized by a two independent parameter curve equations, the curve (Internal periphery
Line) and its continuity, the property led, stress condition and the slickness of derivative it is good, the Section Design for the non-pressure tunnel that is particularly suitable for use in and
Engineering construction, is equally applicable to geological conditions preferable and the relatively low pressurized tunnel of water pressure Section Design and engineering construction.
Background technology：
Hydraulic tunnel, which refers in massif, or underground is dug is used to irrigating, generate electricity, supply water, sluice, water delivery, construction diversion
With the water hole excessively of navigation, hydraulic tunnel is divided into non-pressure tunnel and pressurized tunnel：Current tunnel with table in hole claims
For non-pressure tunnel；Current are full of whole tunnel section and hole wall is born the tunnel referred to as pressurized tunnel of certain water pressure.It is common
Tunnel cross-section form include four classes such as circle, square circular (gateway opening shape), the shape of a hoof and egg type (high arch form), except circular cross section
Outside, gateway opening shape, the shape of a hoof and egg type section are all using intersecting or tangent shape by multi-section-lines such as circular arc, elliptic arc and straight lines
Formula is combined.Gateway opening shape uses the flat dome-shaped of stalk or the flat dome-shaped of oblique side wall；The shape of a hoof include the standard shape of a hoof,
The shape of a hoof (I type, II type, III type, special type), the flat shape of a hoof (I type, II type, special type)；Egg type (high arch form) include semiellipse with
Combined, four circular arc egg types and the six circular arc egg types (I type, II type) up and down of semicircle；In addition, also two circular arc inverted arch song wall is big
The shapes such as section hydraulic tunnel；Circular cross section is used pressurized tunnel more, also can be using just if hole footpath and inside and outside water pressure are less
In other section configurations of construction, circular arch stalk shape section being used non-pressure tunnel, the shape of circular arch stalk shape section can be fitted more
In bearing vertical rock pressure, and it is easy to excavate and lining construction, bears larger water volume flow rate, so, circular arch stalk shape is broken
Face shape is adapted to geological conditions preferably and the less situation of rock pressure, when rock pressure is larger, it is necessary to thicker lining cutting,
Considering, it is necessary to use the tunnel of other section configurations based on economy；When wall rock condition is poor, do not only have mountain vertically downward
Rock pressure power, and when also having the rock pressure of lateral and bottom up, using u-shaped cross-section shape, u-shaped cross-section is by several
Partial arc is combined, and the ability for bearing external pressure is high compared with circular arch stalk shape, but it is complex to construct；Egg type (high arch form)
Sectional curve and pressure curve relatively, stress condition is good, is adapted to features as poor geologic condition or the big situation of rock pressure.
Curve (inner outline) continuous at tunnel section joining, but can not lead, it is also rough；In tunnel
Curvilinear function at section points of tangency is continuous, although can lead and smooth, but first derivative is rough, and second dervative does not connect
It is continuous；Intersect bent curvature of a curve at (cutting) point in tunnel section to be mutated, stress condition is poor, current hydraulic tunnel section configuration
Combination it is various, tunnel section curve shape is complicated, and the subregion and calculation formula of the Hydraulic Design are numerous and diverse and different,
Lack design and the unified standard built.
In the design of existing tunnel section, except most of pressurized tunnel uses circular cross section, non-pressure tunnel part uses city
Beyond door opening shape section (be adapted to geological conditions preferably and bear the less situation of vertical rock pressure, lateral pressure), at remaining
In the case of, which type of tunnel cross-section form there is the puzzlement of " selection " using, the particularly shape of a hoof and egg type tunnel section is more
Up to 10 kinds of shapes, the shape of a hoof is connecting and group by multi-section-lines such as circular arc, elliptic arc and straight lines with egg type tunnel cross-section form
Close, in several sections of lines such as specifically chosen circular arc, elliptic arc and straight line, radius take the how many, center of circle take where, central angle is much, phase
When friendship (cutting) point position is taken wherein, it will carefully analyze, conscientiously calculate determination.The Hydraulic Design of tunnel section also needs to basis
Tie point position, the calculating and confirmation of hydraulic elements is carried out using different mathematical formulae subregions, if surrounding rock stability and mountain
, it is necessary to adjust the ratio of width to height (width and height) of tunnel section when rock pressure condition is different, and then need to re-start tunnel
Crosssection shape design, the Hydraulic Design, structure design and lining construction design etc., its complexity, triviality and workload are not greatly
Say and explain.Therefore, a kind of parameter curve tunnel section of WU types two defined with inventor of R ＆ D design and hydraulic engineering design method
The tunnel section planform that design operation is simple, scientific in principle, Requirements for Acceptance are good and practical, improves design efficiency, subtracts
Light work intensity, has science and applies valency, it may have good society and application prospect very much.
The content of the invention：
It is an object of the invention to overcome the shortcoming that existing tunnel cross-section form design is present, seek design one kind by independence
Two parametric equations characterize tunnel cross-section form and Hydraulic Design Method, design continuity, the property led and stress condition
Good curve (inner outline) and its derivative with slickness, to substitute the shape of a hoof, egg type and the section configuration of tunnel of large section.
To achieve these goals, the technique step of two parameter curves tunnel section of the present invention and hydraulic engineering design method
It is rapid to include setting up the parameter curve equation of WU types two, setting up the area formula of the parameter curve tunnel section of WU types two, determine WU types two
The depth of water in parameter curve tunnel headroom area and hole, determine the parameter curve tunnel section the ratio of width to height of WU types two and determine the ginseng of WU types two
Number curve tunnel section width and height totally five steps：
(1) pollutant diffusion model is calculated：The parameter curve equation of WU types two is first set up, according to momentum and the phase of mass transfer
Like property principle, there are similarity relationships between inference stress flow and pollutant diffusion, derive the isoconcentration mark of pollutant diffusion
Directrix curve equation, as iso-stress calibration curve equation, the curve breaks to eliminate the good tunnel of stress concentration phenomenon, stress condition
Surface curve shape, sets up the parameter curve equation 1 of WU types two accordingly：Wherein, z is from tunnel
The upward vertical coordinate in section bottom midpoint, span is 0≤z≤H；H is the height of tunnel section；Y is perpendicular to z-axis
Lateral coordinates, span is-W/2≤y≤W/2；W is the width of tunnel section, and the corresponding vertical coordinate of Breadth Maximum is zw
=H/e ≈ 0.367879H；Math constant e is 2.718282, then calculates pollutant diffusion model by the curvilinear equation set up；
(2) tunnel section area is determined：The area formula of the parameter curve tunnel section of WU types two is first set up, tunnel section
Headroom area is one of important parameter of tunnel section design, and definite integral is sought on z=0~H to equation 1, WU types two are set up
The area formula of parameter curve tunnel section：Integrated computing is obtained：
1. headroom areal calculation formula 2：Wherein,
For maximum area coefficient；
2. during any depth of water h parameter curve tunnel of WU types two discharge area calculation formula 3：
Wherein, h '=h/H is relative water depth；Area coefficientμ is directly according to MATLAB numerical integration procedures
Calculating is obtained；For example, as h '=0.8, being calculated according to MATLAB numerical integration procedures and obtaining μ=0.700197, further according to public affairs
The ratio of formula 2 and formula 3 and formula 3 and formula 2 is worth to discharge area accounts for headroom area 88.04%, completes tunnel section
The determination of area；
(3) the parameter curve tunnel headroom area of WU types two and the depth of water in hole are determined：According to the design discharge of tunnel, synthesis is examined
Consider safety and let out ability enlargement discharge with super, determine that tunnel crosses water using hydraulics of open channels formula according to the water intake mode of non-pressure tunnel
Area A, in order to ensure to be more than stable free flow state, the water surface to need reserved certain headroom in hole, tunnel is accounted for according to discharge area
The principle of hole section headroom area 80% determines the headroom area of non-pressure tunnel, i.e. formula 4：Am=A/0.8, by this condition,
Depth of water h=0.715383H in the corresponding holes of A of tunnel discharge area is obtained by tentative calculation by formula 2 and formula 3, is filled while meeting
The head room Δ the h=H-h=0.284617H more than requirement of full scale h/H=0.715383≤0.75, water surface；
(4) the parameter curve tunnel section the ratio of width to height of WU types two is determined：The ratio of width to height of tunnel section should be with crustal stress condition phase
Adapt to, if horizontal crustal stress is more than vertical crustal stress, the larger section of width using highly smaller, if vertical crustal stress is big
When horizontal crustal stress, the less section of width using highly larger, according to Wall Rock of Tunnel Stability Classification rank with it is vertical
With lateral rock pressure situation, determine the ratio of width to height a=W/H of tunnel section, I, the stability of II grade of country rock preferably, lateral pressure compared with
Small, the ratio of width to height a spans of tunnel section are 0.67~1.0, III, less stable, the lateral pressure of IV grade of country rock it is larger, tunnel
The ratio of width to height a spans of hole section are 1.0~1.5, and the big situation of features as poor geologic condition, rock pressure and soil cave, tunnel break
The ratio of width to height a spans in face are 0.9~1.1, and Important Project and in geological conditions complex area passes through Wall Rock of Tunnel power
The finite element analysis for learning characteristic carries out the optimization design of tunnel section the ratio of width to height；
(5) the parameter curve tunnel section width of WU types two and height are determined：The headroom area A that will be calculated according to step (2)m
The height and width that the ratio of width to height a substitution formula 2 determined with step (4) obtain the parameter curve tunnel section of WU types two are respectively public affairs
Formula 5：W=aH, and the height of the parameter curve tunnel section of WU types two should be met not less than 1.8m and width not
After construction requirement less than 1.5m, the width and height of determining tunnel section, the parameter of WU types two of design discharge capacity is met
Fitting equation 1 is just uniquely determined, and the planform of tunnel section is just uniquely determined.
The present invention compared with prior art, is quickly seen based on a kind of isoconcentrate of river transverse diffusion coeficient of Chinese patent
The equal strength central point source emission condition that survey method (Patent No. 201710281857.9) is mentioned, spreads to river two-dimensional convection
The concentration distribution analytic solutions of reduced equation are converted, and solve Mixing Coefficient in Rectangular Channels isoconcentration calibration curve equation, are being painted repeatedly
On the basis of figure and actual observation, literature search and comparative analysis, with momentum and the similarity principle of mass transfer, inference should
There are similarity relationships between power stream (diffusion) and pollutant diffusion, i.e.,：Isoconcentration standard curve also should be iso-stress standard
Curve, defines implication and threshold value about symbol in isoconcentration calibration curve equation accordingly, obtains the WU types two that inventor defines
Parameter curve tunnel section and Hydraulic Design Method, section configuration and corresponding discharge capacity for designing tunnel, specific stream
Journey is to use the tunnel cross-section form characterized by two independent parameter curve equations, by the width and height that adjust tunnel section
Parameter, reaches WU type curved tunnel sections and is coincide with the existing shape of a hoof, egg type and tunnel of large section shape, is keeping horseshoe
On the premise of shape, egg type and tunnel of large section advantage, complicated, the cumbersome and workload of conventional tunnel section design lacking greatly is overcome
Point, makes the crosssection shape design of hydraulic tunnel more flexibly, conveniently, the stress performance of tunnel more rationally, globality more preferably, energy
The section configuration of the shape of a hoof, egg type and tunnel of large section is enough substituted, preferably to adapt to special-shaped shield excavation machine construction technology
Demand for development；Its scientific in principle is reliable, and design procedure is simple, and workload is small, and financial cost is low, the curve (inner outline) of design
And its continuity, the property led, stress condition and the slickness of derivative are good.
Brief description of the drawings：
Fig. 1 is the processing step flow schematic block of two parameter curves tunnel section of the present invention and hydraulic engineering design method
Figure.
Fig. 2 is the section structure principle schematic that the step of the embodiment of the present invention 1 (1) is related to.
Fig. 3 is the section structure principle schematic that the ratio of width to height that the step of the embodiment of the present invention 1 (4) is related to is 0.67.
Fig. 4 is the section structure principle schematic that the ratio of width to height that the step of the embodiment of the present invention 1 (4) is related to is 1.0.
Fig. 5 is the section structure principle schematic that the ratio of width to height that the step of the embodiment of the present invention 1 (4) is related to is 1.5.
Fig. 6 is that the Literature of 2 table of the embodiment of the present invention 1 numbers the section structure principle schematic that [1,2] are related to.
Fig. 7 is that the Literature of 2 table of the embodiment of the present invention 1 numbers the section structure principle schematic that [3] are related to.
Fig. 8 is that the Literature of 2 table of the embodiment of the present invention 1 numbers the sectional drawing that [3] shape of a hoof (II type) is related to.
Fig. 9 is that the Literature of 2 table of the embodiment of the present invention 1 numbers the section structure principle schematic that [4] are related to.
Figure 10 is that the Literature of 2 table of the embodiment of the present invention 1 numbers the section structure principle schematic that [5] are related to.
Figure 11 is that the Literature of 2 table of the embodiment of the present invention 1 numbers the section structure principle schematic that [6] are related to.
Figure 12 is that the Literature of 2 table of the embodiment of the present invention 1 numbers the section structure principle schematic that [7] are related to.
Figure 13 is that the Literature of 2 table of the embodiment of the present invention 1 numbers the section structure principle schematic that [8] are related to.
Figure 14 is that the Literature of 2 table of the embodiment of the present invention 1 numbers the section structure principle schematic that [9] are related to.
Figure 15 is that the Literature of 2 table of the embodiment of the present invention 1 numbers the section structure principle schematic that [10] are related to.
Figure 16 is that the Literature of 2 table of the embodiment of the present invention 1 numbers the section structure principle schematic that [11] are related to.
Figure 17 is the section structure principle schematic that the embodiment of the present invention 3 is related to.
Embodiment：
Below by embodiment, and with reference to accompanying drawing, the invention will be further described.
Embodiment 1：
The two parameter curve tunnel sections and the concrete technology step of hydraulic engineering design method that the present embodiment is related to include setting up
The parameter curve equation of WU types two, set up the area formula of the parameter curve tunnel section of WU types two, determine the parameter curve tunnel of WU types two
The depth of water in hole headroom area and hole, determine the parameter curve tunnel section the ratio of width to height of WU types two and determine the parameter curve tunnel of WU types two
Section width and height totally five steps：
(1) the parameter curve equation of WU types two, is set up：According to momentum and the similarity principle of mass transfer, inference stress flow
There are similarity relationships between the diffusion of (diffusion) and pollutant, derive the isoconcentration calibration curve equation of pollutant diffusion, make
For iso-stress calibration curve equation, the curve is the good tunnel section curve shape of elimination stress concentration phenomenon, stress condition, according to
This sets up the parameter curve equation 1 of WU types two：Wherein, z be from tunnel section bottom midpoint to
On vertical coordinate, span be 0≤z≤H；H is the height (maximum height) of tunnel section；Y is the transverse direction perpendicular to z-axis
Coordinate, span is-W/2≤y≤W/2；W is the width (Breadth Maximum) of tunnel section, the corresponding vertical seat of Breadth Maximum
It is z to mark (position height)w=H/e ≈ 0.367879H；Math constant e is 2.718282；The ginseng of WU types two drawn by equation 1
Number curve tunnel section and its characteristic size are as shown in Figure 2；
(2) area formula of the parameter curve tunnel section of WU types two, is set up：The headroom area of tunnel section is tunnel section
One of important parameter of design, definite integral is sought to equation 1 on z=0~H, sets up the parameter curve tunnel section of WU types two
Area formula：Integrated computing is obtained：
1., headroom areal calculation formula 2：Wherein,
For maximum area coefficient；
2., during any depth of water h parameter curve tunnel of WU types two discharge area calculation formula 3：
Wherein, h ' (=h/H) is relative water depth；Area coefficientμ is directly according to MATLAB (Mathematical Experiments
Room) numerical integration procedure calculate obtain；For example, as h '=0.8, calculated according to MATLAB numerical integration procedures obtain μ=
0.700197, it is worth to discharge area further according to the ratio of formula 2 and formula 3 and formula 3 and formula 2 and accounts for headroom area
88.04%；
(3) depth of water in the parameter curve tunnel headroom area of WU types two and hole, is determined：It is comprehensive according to the design discharge of tunnel
Consider that safety lets out ability enlargement discharge with super, tunnel is determined using hydraulics of open channels formula according to water inlet (mouth) mode of non-pressure tunnel
Hole discharge area A, in order to ensure to be more than stable free flow state, the water surface to need reserved certain headroom in hole, according to flow surface
Product accounts for the principle of tunnel section headroom area 80% to determine the headroom area of non-pressure tunnel, i.e. formula 4：Am=A/0.8, by this
Condition, depth of water h=0.715383H in the corresponding holes of A of tunnel discharge area is obtained by formula 2 and formula 3 by tentative calculation, simultaneously full
The head room Δ the h=H-h=0.284617H more than requirement of sufficient degree of filling h/H=0.715383≤0.75, water surface；
(4) the parameter curve tunnel section the ratio of width to height of WU types two, is determined：The ratio of width to height of tunnel section should be with crustal stress condition phase
Adapt to, if horizontal crustal stress is more than vertical crustal stress, the larger section of width using highly smaller, if vertical crustal stress is big
When horizontal crustal stress, the less section of width using highly larger, according to Wall Rock of Tunnel Stability Classification rank with it is vertical
With lateral rock pressure situation, determine the ratio of width to height (a=W/H) of tunnel section, I, the stability of II grade of country rock preferably, lateral pressure
Smaller, the ratio of width to height a spans of tunnel section are 0.67~1.0, III, less stable, the lateral pressure of IV grade of country rock it is larger,
The ratio of width to height a spans of tunnel section are 1.0~1.5, the big situation of features as poor geologic condition, rock pressure and soil cave, tunnel
The ratio of width to height a spans of section are 0.9~1.1, and Important Project and in geological conditions complex area passes through Wall Rock of Tunnel
The finite element analysis of mechanical characteristic carries out the optimization design of tunnel section the ratio of width to height；The ratio of width to height drawn by equation 1 is 0.67,
The 1.0 and 1.5 parameter curve tunnel cross-section form of WU types two is respectively as shown in Fig. 3,4 and 5；
(5) the parameter curve tunnel section width of WU types two and height, are determined：The headroom area that will be calculated according to step (2)
AmThe ratio of width to height a determined with step (4), which substitutes into formula 2 and obtains the height and width of the parameter curve tunnel section of WU types two, is respectively
Formula 5：W=aH, and the height of the parameter curve tunnel section of WU types two should be met not less than 1.8m and width
After construction requirement not less than 1.5m, the width and height of determining tunnel section, the WU types two for meeting design discharge capacity are joined
Number curve equation 1 is just uniquely determined, and the planform of tunnel section is just uniquely determined.
Embodiment 2：
The present embodiment is related to the checking to two parameter curve tunnel sections and hydraulic engineering design method, the ginseng provided according to table 1
Width W and height H bis- parameter of 11 kinds of pattern tunnel sections such as the shape of a hoof and egg type in document are examined, is distinguished using equation 1
The corresponding parameter curve tunnel section of WU types two is drawn, as shown in Fig. 6~Figure 16, dotted line represents the parameter curve tunnel of WU types two in figure
Section, thin dashed line represents the line of maximum breadth of the parameter curve tunnel section of WU types two；By Fig. 6~Figure 16, it can be seen that WU types
11 kinds of pattern tunnel section curves such as the shape of a hoof and egg type in two parameter curve tunnel sections and bibliography closely, greatly
Stapled section is good, particularly the parameter curve tunnel section of WU types two and Figure 10 Wenzhou the Mei Yu tunnels shape of a hoof (special type) section,
The bent wall big cross section of the circular arc egg types of Figure 14 six (I type) section and the circular arc inverted arch of Figure 16 Route Wu Zhuan tunnels two
Degree of agreement is higher.Figure 10, Figure 14 pattern tunnel section Breadth Maximum corresponding with Figure 16 bibliography are corresponding relatively vertical
Coordinate zw/ H is respectively 0.384615,0.292129 and 0.358491, with the parameter curve tunnel section Breadth Maximum of WU types two
Corresponding relatively vertical coordinate zw/ H=1/e ≈ 0.367879 are approached, and illustrate that the stress condition of corresponding tunnel section is approached.By table
1 finds out, the corresponding relatively vertical coordinate of 11 kinds of pattern tunnel section Breadth Maximums such as the shape of a hoof and egg type is averaged in bibliography
It is worth for zw/ H=0.377463, relatively vertical coordinate 0.367879 corresponding with the parameter curve tunnel section Breadth Maximum of WU types two
2.61% is differed only by, illustrates the parameter curve tunnel section of WU types two and 11 kinds of pattern tunnels such as the shape of a hoof and egg type in bibliography
The average characteristics of section are consistent, the parameter curve tunnel section pressure curve of WU types two and the shape of a hoof and egg type etc. 11 in bibliography
Plant pattern tunnel section pressure curve to approach, illustrate the parameter curve tunnel section of WU types two and the shape of a hoof and egg type in bibliography
Stress condition Deng 11 kinds of pattern tunnel sections is good, has caught the essence of hydraulic tunnel sectional curve.
The characterisitic parameter table of tunnel section in the bibliography of table 1
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Embodiment 3：
The present embodiment is related to one and carries out tunnel cross-section form using two parameter curve tunnel sections and Hydraulic Design Method
With the example of the Hydraulic Design.The design discharge of certain water delivery engineering is 50m3/ s, enlargement discharge is included in by 20%, because of landform reason,
Need to build a non-pressure tunnel, non-pressure tunnel will pass through III, IV grade of larger massif of country rock lateral pressure, according to tunnel import
Roughness and than drop condition in discharging capacity, hole, mean flow rate presses 1.80m/s condition design in hole.It is bent according to the parameter of WU types two
Line tunnel section and the equation of Hydraulic Design Method 1 and corresponding calculation formula carry out the Hydraulic Design, continuously square according to current
Journey：Water delivery flow=discharge area × mean flow rate, it is counter to push away discharge area A=1.2 × 50/1.8=33.33m in hole2, by public affairs
Formula 4 calculates the headroom area A for obtaining non-pressure tunnelm=A/0.8=41.67m2, according to tunnel pass through surrounding rock mass stability classification III,
IV grade and the characteristics of larger lateral pressure, the ratio of width to height a for taking tunnel section is 1.25, calculates that to obtain the parameter of WU types two bent by formula 5
The height H of line tunnel section is that 6.50m, width W are 8.10m, the corresponding vertical coordinate z of Breadth MaximumwFor 2.39m, tunnel mistake
The head room Δ h=0.284617H=more than depth of water h=0.715383H=4.65m in the corresponding holes of water area A, water surface
1.85m, it is as shown in figure 17 according to the parameter curve tunnel section of WU types two that above design parameter is drawn.
Claims (1)
1. a kind of two parameter curves tunnel section and hydraulic engineering design method, it is characterised in that concrete technology step includes setting up WU types
Two parameter curve equations, the area formula for setting up the parameter curve tunnel section of WU types two, determine that the parameter curve tunnel of WU types two is net
The depth of water in empty area and hole, determine the parameter curve tunnel section the ratio of width to height of WU types two and determine the parameter curve tunnel section of WU types two
Width and height totally five steps：
(1) pollutant diffusion model is calculated：The parameter curve equation of WU types two is first set up, according to momentum and the similitude of mass transfer
, there are similarity relationships in principle, derive that the isoconcentration standard of pollutant diffusion is bent between inference stress flow and pollutant diffusion
Line equation, as iso-stress calibration curve equation, the curve is bent to eliminate the good tunnel section of stress concentration phenomenon, stress condition
Wire shaped, sets up the parameter curve equation 1 of WU types two accordingly：Wherein, z is from tunnel section
The upward vertical coordinate in bottom midpoint, span is 0≤z≤H；H is the height of tunnel section；Y is the transverse direction perpendicular to z-axis
Coordinate, span is-W/2≤y≤W/2；W is the width of tunnel section, and the corresponding vertical coordinate of Breadth Maximum is zw=H/e
≈0.367879H；Math constant e is 2.718282, then calculates pollutant diffusion model by the curvilinear equation set up；
(2) tunnel section area is determined：First set up the area formula of the parameter curve tunnel section of WU types two, the headroom of tunnel section
Area is one of important parameter of tunnel section design, and definite integral is sought on z=0~H to equation 1, the parameter of WU types two is set up
The area formula of curved tunnel section：Integrated computing is obtained：
1. headroom areal calculation formula 2：Wherein,For
Maximum area coefficient；
2. during any depth of water h parameter curve tunnel of WU types two discharge area calculation formula 3：
Wherein, h '=h/H is relative water depth；Area coefficientμ is directly according to MATLAB numerical integration procedures
Calculating is obtained；For example, as h '=0.8, being calculated according to MATLAB numerical integration procedures and obtaining μ=0.700197, further according to public affairs
The ratio of formula 2 and formula 3 and formula 3 and formula 2 is worth to discharge area accounts for headroom area 88.04%, completes tunnel section
The determination of area；
(3) the parameter curve tunnel headroom area of WU types two and the depth of water in hole are determined：According to the design discharge of tunnel, peace is considered
Quan Yuchao lets out ability enlargement discharge, and tunnel discharge area is determined using hydraulics of open channels formula according to the water intake mode of non-pressure tunnel
A, in order to ensure to be more than stable free flow state, the water surface to need reserved certain headroom in hole, accounting for tunnel according to discharge area breaks
The principle of face headroom area 80% determines the headroom area of non-pressure tunnel, i.e. formula 4：Am=A/0.8, by this condition, by public affairs
Formula 2 and formula 3 obtain depth of water h=0.715383H in the corresponding holes of A of tunnel discharge area by tentative calculation, while meeting degree of filling
The head room Δ the h=H-h=0.284617H more than requirement of h/H=0.715383≤0.75, water surface；
(4) the parameter curve tunnel section the ratio of width to height of WU types two is determined：The ratio of width to height of tunnel section should be adapted with crustal stress condition,
If horizontal crustal stress is more than vertical crustal stress, the larger section of width using highly smaller, if vertical crustal stress is more than water
During the stress of level land, the less section of width using highly larger, according to Wall Rock of Tunnel Stability Classification rank and vertical and side
To rock pressure situation, determine the ratio of width to height a=W/H of tunnel section, I, the stability of II grade of country rock preferably, lateral pressure it is smaller,
The ratio of width to height a spans of tunnel section are 0.67~1.0, III, less stable, the lateral pressure of IV grade of country rock it is larger, tunnel
The ratio of width to height a spans of section are 1.0~1.5, the big situation of features as poor geologic condition, rock pressure and soil cave, tunnel section
The ratio of width to height a spans be 0.9~1.1, Important Project and in geological conditions complex area passes through Wall Rock of Tunnel mechanics
The finite element analysis of characteristic carries out the optimization design of tunnel section the ratio of width to height；
(5) the parameter curve tunnel section width of WU types two and height are determined：The headroom area A that will be calculated according to step (2)mAnd step
Suddenly the height and width that the ratio of width to height a substitution formula 2 that (4) are determined obtain the parameter curve tunnel section of WU types two are respectively formula 5：W=aH, and the height of the parameter curve tunnel section of WU types two should be met be not less than not less than 1.8m with width
After 1.5m construction requirement, the width and height of determining tunnel section, the parameter curve of WU types two of design discharge capacity is met
Equation 1 is just uniquely determined, and the planform of tunnel section is just uniquely determined.
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