CN117892403A - General program calculation method and terminal for tunnel orthogonal intersection lining engineering quantity - Google Patents
General program calculation method and terminal for tunnel orthogonal intersection lining engineering quantity Download PDFInfo
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Abstract
The invention discloses a general program calculation method and a terminal for tunnel intersection lining engineering quantity, which relate to the field of tunnel intersection engineering quantity calculation and comprise the following steps: establishing a three-dimensional model according to the contour parameters and the support parameters of the tunnel and the transverse channel, and establishing a three-dimensional coordinate system in the three-dimensional model; calculating to obtain the total volume V 1 formed by the outer contour of the transverse channel and the outer contour of the tunnel from the gradual change section by utilizing a fixed integral deduction volume formula and a Simpson integral method; and calculating to obtain the total volume V 2 formed by the inner contour of the transverse channel and the outer contour of the tunnel from the gradual change section; and obtaining the secondary lining volume of the intersection transition section according to the difference value. The method is used for calculating the three-dimensional volume enclosed by any circular arc on the transverse channel at the gradual change section of the intersection and the corresponding circular arc on the tunnel, further combining based on a unified calculation formula, and can be used for calculating the engineering quantity of the intersection of the tunnel, and the method can realize universality, accuracy, high efficiency and autonomous controllability after programming.
Description
Technical Field
The invention relates to the field of tunnel intersection engineering quantity calculation, in particular to a general program calculation method and a general program calculation terminal for tunnel orthogonal intersection lining engineering quantity.
Background
In order to meet the requirements of ventilation rescue and the like, a crosswalk passage and a crosswalk passage are usually arranged between main holes or between the main holes and the flat guide. For the engineering quantity of the intersection of the transverse channel and the tunnel, particularly the engineering quantity of the transition section, the three-dimensional intersection is a complex three-dimensional figure in terms of three-dimensional space, the traditional method estimates the engineering quantity of the three-dimensional model by using the two-dimensional section engineering quantity of specific places, and the calculation result is necessarily rough. If an accurate calculation result is required to be obtained, a complex geometric model is required to be built in three-dimensional software, corresponding engineering quantities (such as primary support, secondary lining and the like) are obtained through Boolean operation, three-dimensional models are required to be built at intersections formed by different inner contours, transverse channels with different support parameters and tunnels, and the models have no universality.
Therefore, in order to promote the highway digitization process, an autonomous and controllable calculation method which can meet the accuracy of intersection engineering quantity calculation and ensure the universality is necessary in the tunnel digitization process.
Disclosure of Invention
The invention aims to solve the defects of the prior art, and provides a general program calculation method and a terminal for tunnel orthogonal intersection lining engineering quantity, which are used for calculating the three-dimensional volume enclosed by any circular arc on a transverse channel at an intersection gradual change section and a corresponding circular arc on a tunnel, further combining based on a unified calculation formula, and realizing universality, accuracy, high efficiency and autonomous controllability after the method is programmed.
The invention is realized by the following technical scheme:
A general program calculation method for tunnel orthogonal intersection lining engineering quantity comprises a tunnel and a transverse channel which are orthogonal to each other, and further comprises the following steps:
S1: establishing a three-dimensional model according to contour parameters and supporting parameters of a tunnel and a transverse channel, and establishing a three-dimensional coordinate system in the three-dimensional model, wherein the cross section of the transverse channel is used as an X-Y coordinate system, and the cross section of the tunnel is used as a Z-Y coordinate system;
S2: calculating the volume of a three-dimensional graph formed by an ith arc H i on the cross section of the outer contour of the transverse channel to a jth arc S j on the cross section of the outer contour of the tunnel by utilizing a constant-integration deduction volume formula and a Simpson integration method from the gradual change section of the intersection of the transverse channel and the tunnel, and obtaining the total volume V 1 formed by the outer contour of the transverse channel and the outer contour of the tunnel from the gradual change section through the sum of the volumes of the three-dimensional graphs calculated by each arc;
Calculating the volume of a three-dimensional graph formed from an ith arc H i on the cross section of the inner contour of the transverse channel to a jth arc S j on the cross section of the outer contour of the tunnel, and obtaining the total volume V 2 formed by the inner contour of the transverse channel and the outer contour of the tunnel from the gradual change section through the sum of the volumes of the three-dimensional graphs calculated by each arc;
The arc H i and the arc S j have the same intersection of Y value ranges in a coordinate system;
S3: and obtaining the secondary lining volume of the intersection transition section according to the difference between V 1 and V 2.
Compared with the prior art, the method is a complex three-dimensional figure in terms of three-dimensional space, the traditional method estimates the engineering quantity of a three-dimensional model by using two-dimensional section engineering quantities at specific positions, the calculation result is necessarily rough, the three-dimensional model is independently established at intersections consisting of transverse channels and tunnels with different inner contours and different support parameters, and the model has no universality. The invention can calculate the tunnel section engineering quantities of intersection lining which are orthogonal to the tunnel by 90 degrees and of transverse channels in different section forms such as single-core circle, three-core circle and five-core circle, and particularly can calculate the tunnel section engineering quantities such as tunnel intersection graded section lining section body excavation quantity, reserved deformation quantity, primary support injection concrete quantity, secondary lining concrete quantity and the like.
In a still further aspect, the step S2, before deriving the formula according to the fixed integral, further includes the following steps:
In the three-dimensional coordinate system, a certain section of arc H i equation in the inner contour of the transverse channel is set as (X-a) 2+(y-b)2＝r2, and the central line of the transverse channel is set as x=x 0; let a certain arc S j equation in the tunnel outline orthogonal to the transverse tunnel be (Z-c) 2+(y-d)2＝R2, and the initial position of the lining transition section of the transverse tunnel on any side of the tunnel be z=z 0.
In a further aspect, in the step S2, a volume formula derived by using the fixed integral is represented by formula one:
Wherein y epsilon [ y 1,y2 ] refers to the intersection of the y value ranges of the transverse channel arc segment and the tunnel arc segment.
In a still further aspect, in the step S2, the deriving the volume formula using the fixed integral further includes the following deriving steps:
according to a certain section of arc H i equation in the inner profile of the transverse channel and X 0 is more than or equal to X, the formula II can be obtained:
according to a certain section of arc S j equation and Z is larger than or equal to Z 0 in the tunnel outer contour of the cross channel, the formula III can be obtained:
Let the constant C 1＝X0-a,C2＝c-Z0, and substituting the two and three formulas into the one formula:
let then:
in a further scheme, in the step S2, according to the simpson integration method, a general formula of a volume of a stereoscopic graph formed by the ith section of transverse channel arc H i and the jth section of tunnel arc S j may be obtained:
in the method, in the process of the invention,
Y ij and y ij2 are the upper and lower limits of intersection of the y-value ranges of the transverse channel arc segment and the tunnel arc segment.
Still further, when the y-value ranges of the two arcs have no intersection, V Hi-Sj =0.
In a further scheme, in the step S2, according to the general formula, a total volume formula enclosed by the transverse channel profile and the outer profile of the second liner of the tunnel from the transition section is obtained by deducting:
further, according to a total volume formula formed by the transverse channel profile and the secondary lining profile of the tunnel by encircling from the transition section, the total volume V 1 and the total volume V 2 are calculated respectively, and the secondary lining volume of the transition section of the intersection is calculated by a difference formula, wherein the difference formula is as follows:
V Two-lining ＝V1-V2；
compared with the prior art, the invention has the following advantages and beneficial effects:
The invention provides a general program calculation method and a terminal for tunnel orthogonal intersection lining engineering quantity, which are used for calculating a three-dimensional volume formed by surrounding any circular arc on a transverse channel at an intersection gradual change section and a corresponding circular arc on a tunnel, further combining based on a unified calculation formula, and realizing universality, accuracy, high efficiency and autonomous controllability after the method is programmed. The invention can calculate the tunnel section engineering quantities of intersection lining which are orthogonal to the tunnel by 90 degrees and of transverse channels in different section forms such as single-core circle, three-core circle and five-core circle, and particularly can calculate the tunnel section engineering quantities such as tunnel intersection graded section lining section body excavation quantity, reserved deformation quantity, primary support injection concrete quantity, secondary lining concrete quantity and the like.
Drawings
In order to more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the drawings that are needed in the examples will be briefly described below, it being understood that the following drawings only illustrate some examples of the present invention and therefore should not be considered as limiting the scope, and that other related drawings may be obtained from these drawings without inventive effort for a person skilled in the art. In the drawings:
fig. 1 is a schematic structural diagram of a junction transition section according to an embodiment of the present invention;
FIG. 2 is a diagram of the positional relationship between a lateral tunnel and a tunnel according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of parameters in a coordinate system of an arc of H i in a cross-section of a cross-channel according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of parameters in a coordinate system of a segment S j of an arc in a tunnel cross-section according to an embodiment of the present invention;
Fig. 5 is a schematic diagram of calculation steps according to an embodiment of the present invention.
Detailed Description
For the purpose of making apparent the objects, technical solutions and advantages of the present invention, the present invention will be further described in detail with reference to the following examples and the accompanying drawings, wherein the exemplary embodiments of the present invention and the descriptions thereof are for illustrating the present invention only and are not to be construed as limiting the present invention.
Example 1:
The embodiment 1 provides a general program calculation method for tunnel orthogonal intersection lining engineering quantity, which is shown in fig. 1-5 and comprises the following specific steps:
1. First, a general formula is determined according to a coordinate system: as shown in fig. 1, in the three-dimensional coordinate system, a certain arc H 1 equation in the left half side of the inner contour of the transverse channel is set as (X-a) 2+(y-b)2＝r2, and the center line of the transverse channel is set as x=x 0; let a certain section of arc S1 equation in the outer contour of the tunnel two lining orthogonal to the transverse channel be (Z-c) 2+(y-d)2＝R2, and the leftmost side of the tunnel (the starting position of the lining transition section of the transverse channel) be z=z 0. Since the intersection lining which is orthogonal at 90 degrees is symmetrical about the central line of the transverse channel, only the left half part of the transverse channel needs to be studied when the lining engineering quantity is calculated.
As shown in fig. 2 and 3, by using the constant integral, the volume of the solid figure enclosed from the intersection transition to the complete intersection with the tunnel arc S1 by the arc H1 on the lateral channel is deduced to be:
Wherein y epsilon [ y 1,y2 ] refers to the intersection of the y value ranges of the transverse channel arc segment and the tunnel arc segment. Considering that X 0 is larger than or equal to X for the left half side of the transverse channel and Z is larger than or equal to Z 0 for the tunnel arc section. Thus, from (X-a) 2+(y-b)2＝r2 and X 0 ≡x:
From (Z-c) 2+(y-d)2＝R2 and z.gtoreq.Z 0:
Let the constant C 1＝X0-a,C2＝c-Z0, and let (2) and (3) be substituted into (1) as follows:
Let then (4) be written as:
2. the formula integrates. (5) The formula is a constant integral about the variable y, wherein the variables except the variable y are constants, and the constants are substituted to obtain an integral result so as to obtain the volume of the stereoscopic graph. However, the original function of f (y) is difficult to find, and cannot be calculated by a conventional analytical method. Therefore, the fixed integral of the formula (5) can be calculated by adopting a numerical integral-simpson integral method. The simpson integration method is a numerical integration method that estimates the constant integral of a function over a given interval. The method approximates the integrated function by using a quadratic function, thereby obtaining more accurate integral estimation. Specifically, the simpson integration method divides the integration interval [ y 1,y2 ] into n intervals, each of which has a length h= (y 2-y1)/n. Compared with other numerical integration methods, the simpson integration method has higher precision.
And (3) by writing a program code of a simpson integration method of the (5) type fixed integration, an integration result can be obtained, and a corresponding volume can be obtained. Further, a general formula of the volume of the three-dimensional graph formed by the ith section of transverse channel arc Hi and the jth section of tunnel arc Sj can be obtained:
in the method, in the process of the invention,
Y ij1 and y ij2 are upper and lower limits of intersection of the y value ranges of the cross-channel arc segment and the tunnel arc segment, and V Hi-Sj =0 when the y value ranges of the two arcs are not intersected.
Further, the total volume enclosed by the inner contour of the transverse channel and the outer contour of the second lining of the tunnel from the transition section is as follows:
3. And finally, calculating the engineering quantity. As shown in fig. 4, taking the intersection secondary lining concrete graded section engineering quantity as an example, the engineering quantity can be obtained by performing simple subtraction calculation on two volumes which can be directly calculated by the formula (7):
V Two-lining ＝V1-V2....................(8)
Wherein V 1 is the total volume enclosed by the outer contour of the second lining of the transverse channel and the outer contour of the second lining of the tunnel from the gradual change section, V 2 is the total volume enclosed by the inner contour of the transverse channel and the outer contour of the second lining of the tunnel from the gradual change section, and V 1、V2 can be calculated by (7).
Similarly, other engineering quantities can be subjected to basic calculation through the formula (7), and the result is obtained through simple linear combination.
In the scheme, the three-dimensional volume formed by the surrounding of any circular arc on the transverse channel at the transition section of the intersection and the corresponding circular arc on the tunnel is calculated, and is further combined based on a unified calculation formula, so that the method can be used for calculating the engineering quantity of the intersection of the tunnel, and can realize universality, accuracy, high efficiency and autonomous controllability after the method is programmed. The invention can calculate the tunnel section engineering quantities of intersection lining which are orthogonal to the tunnel by 90 degrees and of transverse channels in different section forms such as single-core circle, three-core circle and five-core circle, and particularly can calculate the tunnel section engineering quantities such as tunnel intersection graded section lining section body excavation quantity, reserved deformation quantity, primary support injection concrete quantity, secondary lining concrete quantity and the like.
Example 2
In some exemplary embodiments, the present embodiment further provides a general program computing terminal device for tunnel orthogonal intersection lining engineering quantity, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor, where the processor implements, when executing the computer program, a three-dimensional volume enclosed by any arc on a transverse channel at a gradual transition section of an intersection and a corresponding arc on a tunnel as in embodiment 1, and further combines based on a unified computing formula, so that the method can be used for computing tunnel intersection engineering quantity, and after programming the method, the minimum technical scheme of the general program computing method for tunnel orthogonal intersection lining engineering quantity can be implemented.
It will be appreciated by those skilled in the art that embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Those of ordinary skill in the art will appreciate that implementing all or part of the above facts and methods may be accomplished by a program to instruct related hardware, the program involved or the program may be stored in a computer readable storage medium, the program when executed comprising the steps of: the corresponding method steps are introduced at this time, and the storage medium may be a ROM/RAM, a magnetic disk, an optical disk, or the like.
The foregoing description of the embodiments has been provided for the purpose of illustrating the general principles of the invention, and is not meant to limit the scope of the invention, but to limit the invention to the particular embodiments, and any modifications, equivalents, improvements, etc. that fall within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (10)
1. The general program calculation method for the tunnel orthogonal intersection lining engineering quantity comprises a tunnel and a transverse channel which are orthogonal to each other, and is characterized by further comprising the following steps:
S1: establishing a three-dimensional model according to contour parameters and supporting parameters of a tunnel and a transverse channel, and establishing a three-dimensional coordinate system in the three-dimensional model, wherein the cross section of the transverse channel is used as an X-Y coordinate system, and the cross section of the tunnel is used as a Z-Y coordinate system;
S2: calculating the volume of a three-dimensional graph formed by an ith arc H i on the cross section of the outer contour of the transverse channel to a jth arc S j on the cross section of the outer contour of the tunnel by utilizing a constant-integration deduction volume formula and a Simpson integration method from the gradual change section of the intersection of the transverse channel and the tunnel, and obtaining the total volume V 1 formed by the outer contour of the transverse channel and the outer contour of the tunnel from the gradual change section through the sum of the volumes of the three-dimensional graphs calculated by each arc;
Calculating the volume of a three-dimensional graph formed from an ith arc H i on the cross section of the inner contour of the transverse channel to a jth arc S j on the cross section of the outer contour of the tunnel, and obtaining the total volume V 2 formed by the inner contour of the transverse channel and the outer contour of the tunnel from the gradual change section through the sum of the volumes of the three-dimensional graphs calculated by each arc;
The arc H i and the arc S j have the same intersection of Y value ranges in a coordinate system;
S3: and obtaining the secondary lining volume of the intersection transition section according to the difference between V 1 and V 2.
2. The method for calculating the tunnel orthogonal intersection lining engineering quantity according to claim 1, wherein in the step S2, before deriving the formula according to the definite integral, the method further comprises the steps of:
In the three-dimensional coordinate system, a certain section of arc H i equation in the inner contour of the transverse channel is set as (X-a) 2+(y-b)2＝r2, and the central line of the transverse channel is set as x=x 0; let a certain arc S j equation in the tunnel outline orthogonal to the transverse tunnel be (Z-c) 2+(y-d)2＝R2, and the initial position of the lining transition section of the transverse tunnel on any side of the tunnel be z=z 0.
3. The general program calculation method for tunnel orthogonal intersection lining engineering quantities according to claim 2, wherein in the step S2, a volume formula derived by using a definite integral is represented by formula one:
Wherein y epsilon [ y 1,y2 ] refers to the intersection of the y value ranges of the transverse channel arc segment and the tunnel arc segment.
4. A method for general program calculation of tunnel orthogonal intersection lining construction quantity according to claim 3, wherein in the step S2, the derivation of the volume formula by using the fixed integral further comprises the following derivation steps:
according to a certain section of arc H i equation in the inner profile of the transverse channel and X 0 is more than or equal to X, the formula II can be obtained:
according to a certain section of arc S j equation and Z is larger than or equal to Z 0 in the tunnel outer contour of the cross channel, the formula III can be obtained:
Let the constant C 1＝X0-a,C2＝c-Z0, and substituting the two and three formulas into the one formula:
Let then:
5. The general program calculation method for tunnel orthogonal intersection lining engineering quantity according to claim 4, wherein in the step S2, a general formula of a volume of a three-dimensional figure formed by the ith section of transverse channel arc H i and the jth section of tunnel arc S j is obtained according to the simpson integration method:
In the method, in the process of the invention,
Y ij1 and y ij2 are the upper and lower limits of intersection of the y-value ranges of the transverse channel arc segment and the tunnel arc segment.
6. The general program calculation method for tunnel orthogonal intersection lining engineering quantities according to claim 5, wherein V Hi-Sj = 0 when the y value ranges of the two arcs have no intersection.
7. The general procedure calculation method for tunnel orthogonal intersection lining engineering quantities according to claim 5, wherein in the step S2, according to the general formula, a total volume formula formed by the transverse channel profile and the tunnel secondary lining profile from the transition section is derived as follows:
8. The general program calculation method for tunnel orthogonal intersection lining engineering quantity according to claim 7, wherein the total volume V 1 and the total volume V 2 are calculated according to a total volume formula formed by enclosing a transverse channel profile and a secondary lining profile of a tunnel from a transition section, and the secondary lining volume of the transition section of the intersection is calculated by a difference formula, and the difference formula is as follows:
V Two-lining ＝V1-V2。
9. A terminal comprising at least one processor and a memory communicatively coupled to the at least one processor; wherein the memory stores instructions executable by the at least one processor to enable the at least one processor to perform a tunnel orthogonal intersection lining engineering quantity general program calculation method according to any one of claims 1 to 8.
10. A storage medium storing a computer program, wherein the computer program when executed by a processor implements a general program calculation method for tunnel orthogonal intersection lining engineering quantity according to any one of claims 1 to 8.
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