CN106055795B - tunnel ventilation wall roughness assessment method - Google Patents

tunnel ventilation wall roughness assessment method Download PDF

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CN106055795B
CN106055795B CN201610380329.4A CN201610380329A CN106055795B CN 106055795 B CN106055795 B CN 106055795B CN 201610380329 A CN201610380329 A CN 201610380329A CN 106055795 B CN106055795 B CN 106055795B
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tunnel
excavation contour
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张恒
吴瑾
涂鹏
林放
王路
孙建春
张超
刘效成
陈寿根
周泽林
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Southwest Jiaotong University
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Abstract

The invention discloses an tunnel ventilation wall roughness evaluation method which comprises the steps of measuring an axial direction actual excavation contour line and a cross section actual excavation contour line of a tunnel, calculating a tunnel ventilation wall average roughness, calculating a roughness constant value of the axial direction actual excavation contour line, and calculating tunnel ventilation wall roughness according to the tunnel ventilation wall average roughness and axial direction roughness constant information.

Description

tunnel ventilation wall roughness assessment method
Technical Field
The invention relates to an tunnel ventilation wall roughness assessment method.
Background
At present, the construction of a long tunnel is mainly based on a drilling and blasting method and combined with trackless transportation, the ventilation problem during construction becomes problems which are faced first, how to smoothly discharge dirty wind becomes a key point of rapid tunnel construction, but in the ventilation design and construction process of tunnels in China, the influence of tunnel wall roughness on the actual ventilation effect is hardly considered, the average wall roughness in tunnels and the equivalent diameter of tunnel sections are mainly taken as the main factors of ventilation design in the ventilation design specification of highway tunnels (JTJ026.1-1999), and the on-way resistance coefficient in channels is calculated according to the factors, the tunnel wall roughness is an important parameter reflecting the ventilation condition of the tunnels, so that the design of the long tunnel ventilation system is directly influenced, therefore, the evaluation of the tunnel wall roughness is the important factor in the design of the long tunnel, but at present, a simple, convenient and effective method for evaluating the tunnel wall roughness is not available, and great difficulty is brought to the ventilation design of the tunnel system, so that the ventilation economy and the safety of the tunnel are difficult to guarantee.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides methods for evaluating the roughness of the ventilation wall surface of the tunnel, so as to solve the problems that the existing method for evaluating the roughness of the wall surface of the tunnel is complex and has low accuracy.
In order to achieve the purpose of the invention, the invention adopts the technical scheme that:
tunnel ventilation wall roughness assessment method is provided, which comprises the following steps:
taking n meters of tunnels along the axial direction of the tunnels as evaluation sections, and respectively measuring at least 5 axial direction actual excavation contour lines and at least 3 cross section actual excavation contour lines at different positions of the tunnels in the evaluation sections; wherein n is more than or equal to 10;
calculating to obtain the average rough height of the ventilation wall surface of the tunnel according to the information of the actual excavation contour line in the axial direction, the actual excavation contour line of the cross section and the designed excavation contour line;
dividing the actual excavation contour line in the axial direction into m sections, respectively adopting a sinusoidal unit rough model, a square unit rough model and a triangular unit rough model to simplify the model of each section, and selecting an optimal simplified model of each section;
calculating to obtain a rough constant corresponding to each sections of the actual excavation contour line in the axial direction according to the optimal simplified model type of each section, and calculating to obtain a rough constant value of the actual excavation contour line in the axial direction according to the rough constant information of each section;
summing and averaging rough constant values of the actual excavation contour lines in the axial direction at different positions of the tunnel to obtain rough constants in the axial direction of the tunnel;
and evaluating to obtain the roughness of the ventilation wall surface of the tunnel according to the average rough height of the ventilation wall surface of the tunnel and the rough constant information in the axial direction.
The method comprises the following steps of taking n meters of tunnels along the axial direction of the tunnels as evaluation sections, and respectively measuring and obtaining the axial direction actual excavation contour lines and the cross section actual excavation contour lines at different positions of the tunnels in the evaluation sections, wherein the steps comprise the following steps:
taking a 10-meter tunnel as an evaluation section along the axial direction of the tunnel, taking 5 axial direction datum lines respectively positioned at the arch crown, the left arch shoulder, the right arch shoulder, the left arch waist and the right arch waist of the tunnel in the evaluation section, and measuring along the axial direction datum lines to obtain 5 axial direction actual excavation contour lines;
and in the evaluation section, tunnel cross sections are taken to be measured at intervals of 5 meters along the direction of the cross section of the tunnel, and 3 actual excavation contour lines of the cross sections are obtained.
The step of calculating the average rough height of the tunnel ventilation wall surface according to the information of the actual excavation contour line in the axial direction, the actual excavation contour line of the cross section and the designed excavation contour line specifically comprises the following steps:
calculating the average rough height of the tunnel in the axial direction and the average rough height of the cross section at different positions by adopting the following formulas according to the actual excavation contour line in the axial direction, the area enveloped by the designed excavation contour line and the length of the designed excavation contour line;
Figure GDA0002261694700000031
wherein Rh is the average roughness height, and S is the area enveloped by the actual excavation contour line and the design excavation contour line; l is the length of the designed excavation contour line;
summing and averaging the average rough height in the axial direction and the average rough height in the cross section at different positions of the tunnel to obtain the average rough height in the axial direction and the average rough height in the cross section of the tunnel;
and summing and averaging the average rough height of the tunnel in the axial direction and the average rough height of the cross section to obtain the average rough height of the ventilation wall surface of the tunnel.
The method comprises the following steps of dividing the actual excavation contour line in the axial direction into m sections, simplifying each section by respectively adopting a sinusoidal unit rough model, a square unit rough model and a triangular unit rough model, and selecting the optimal simplified model of each section:
dividing the actual excavation contour line in the axial direction into m sections by taking the intersection point of the actual excavation contour line and the design excavation contour line as a node, wherein the length of each section is Xi，(i＝1,...m)；
Model simplification is carried out on each sections by respectively adopting a sine curve unit rough model, a square unit rough model and a triangular unit rough model to obtain 3 simplified models, and the optimal simplified model of each sections is obtained by calculating and screening by adopting the following formula;
Figure GDA0002261694700000032
wherein S isOriginal sourceFor actual and design excavation contours, STriangle shapeFor simplifying the rough model of the triangular unit obtained and designing the envelope area of the excavation contour line, SSquare shapeFor simplifying the rough model of the square unit obtained and designing the envelope area of the excavation contour line, SSinusoidal shapeThe obtained sine curve unit rough model and the envelope area of the designed excavation contour line are simplified.
The step of calculating the rough constant corresponding to each sections of the actual excavation contour line in the axial direction according to the optimal simplified model type of each sections, and calculating the rough constant value of the actual excavation contour line in the axial direction according to the rough constant information of each sections specifically comprises the following steps:
respectively calculating the rough constants Rc of the sine curve unit rough model, the triangle unit rough model and the square unit rough model by adopting the following formulas;
Rc1＝0.264+0.328e-(2L)/1.183
Rc2＝0.327+0.341e-(2L)/2.753
Rc3＝0.439+0.401e-(2L)/2.376
wherein Rc1 is the roughness constant of the sine-curve unit roughness model, Rc2 is the roughness constant of the square unit roughness model, and Rc3 is the roughness constant of the triangle unit roughness model; 2L is the coarse pitch, the coarse pitch 2L is numerically equal to 2Xi；
Calculating to obtain a rough constant corresponding to each sections of actual excavation contour lines in the axial direction by adopting the formula according to the optimal simplified model type of each sections;
according to the rough constant information of each sections, calculating by adopting the following formula to obtain the rough constant value of the actual excavation contour line in the axial direction;
Figure GDA0002261694700000041
wherein n is the length of the assessment segment.
The invention has the beneficial effects that:
the method obtains two most important parameters of the average roughness height Rh and the roughness constant Rc for evaluating the roughness of the ventilation wall surface of the tunnel, the two parameters can reflect the roughness of the wall surface of the tunnel most truly and accurately, the evaluation method is simple and convenient, the problems that the evaluation of the roughness of the wall surface of the tunnel is complex and difficult to determine at present are effectively solved, and the method has a huge application prospect.
According to the tunnel ventilation wall surface average roughness height Rh and the tunnel roughness constant Rc, the wall surface roughness in tunnel ventilation can be determined, the wind speed, the wind quantity and the pollutant concentration distribution rule of wind flow in the tunnel can be obtained more accurately, a guiding effect is provided for the construction ventilation design of the tunnel and underground engineering, and the tunnel ventilation wall surface average roughness height Rh and the tunnel roughness constant Rc have important theoretical significance and practical value.
The method of the invention not only makes up the defects of the current tunnel wall roughness evaluation method, but also provides important scientific basis for tunnel ventilation design, ensures the economy and safety of tunnel ventilation, and has important engineering significance.
Drawings
Fig. 1 is a diagram of an actual excavation contour line of a tunnel at a vault position according to an embodiment of the present invention;
fig. 2 is a diagram of an actual excavation contour line of a tunnel at a left arch shoulder position according to an embodiment of the present invention;
fig. 3 is a diagram of an actual excavation contour line of a tunnel at a right spandrel position according to an embodiment of the present invention;
fig. 4 is a diagram of an actual excavation contour line of a tunnel at a left arch position according to an embodiment of the present invention;
fig. 5 is a diagram of an actual excavation contour line of a tunnel at a right arch position according to an embodiment of the present invention;
fig. 6 is a diagram of an actual excavation profile of a tunnel cross section with a distance of 2+000 at the diversion tunnel number 1 according to the embodiment of the present invention;
FIG. 7 is a practical excavation contour line diagram of the cross section of a tunnel at mileage 2+010 of a diversion tunnel No. 1 in the embodiment of the invention;
fig. 8 is a diagram of an actual excavation profile of a tunnel cross section at mileage 2+015 of the diversion tunnel number 1 in the embodiment of the invention;
FIG. 9 is a schematic diagram of a sinusoidal element roughness model;
FIG. 10 is a schematic diagram of a square cell roughness model;
FIG. 11 is a schematic diagram of a triangular unit coarse model;
FIG. 12 is a simplified schematic diagram of a tunnel model;
FIG. 13 is a simplified model diagram of an actual excavation contour line of a tunnel at a vault position according to an embodiment of the present invention;
fig. 14 is a schematic diagram of a model after simplifying an actual excavation contour line of a tunnel at a left arch shoulder position according to an embodiment of the present invention;
fig. 15 is a schematic diagram of a model after simplifying an actual excavation contour line of a tunnel at a right spandrel position according to an embodiment of the present invention;
fig. 16 is a schematic diagram of a model after simplifying an actual excavation contour line of a tunnel at a left arch position according to an embodiment of the present invention;
fig. 17 is a schematic diagram of a simplified model of an actual excavation contour line of a tunnel at a right arch position according to an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate the understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and it will be apparent to those of ordinary skill in the art that various changes may be made without departing from the spirit and scope of the present invention as defined and defined in the appended claims, and is intended to protect the inventive concepts conceived of by the present invention.
According to embodiments of the invention, the tunnel ventilation wall roughness assessment method comprises the following specific steps:
(1) measurement data: taking a 10-meter tunnel as an evaluation section along the axial direction of the tunnel in a tunnel section with the same surrounding rock conditions, taking 5 datum lines along the axial direction in the evaluation section, wherein the 5 datum lines are respectively positioned at a vault, a left arch shoulder, a right arch shoulder, a left arch waist and a right arch waist, and measuring 5 actual excavation contour lines of the tunnel along the axial datum line direction by using a total station, namely the actual excavation contour lines along the axial direction; measuring actual excavation contour lines of the cross section of the tunnel every 5 meters from the end face in the evaluation section to obtain 3 actual excavation contour lines of the cross section;
(2) calculating average rough height of ventilation wall surface of tunnel
According to the area S enveloped by the actual excavation contour line and the designed excavation contour line of the tunnel and the length l of the designed excavation contour line, the average rough height of 5 actual excavation contour lines in the axial direction of the tunnel and the average rough height of 3 actual excavation contour lines in the cross section are respectively calculated by a formula (1);
summing and averaging the average rough heights of the actual excavation contour lines of the 3 cross sections of the tunnel to obtain the average rough height of the cross section of the tunnel of the evaluation section; summing and averaging the average rough heights of the 5 actual excavation contour lines in the axial direction to obtain the average rough height of the tunnel in the axial direction of the evaluation section;
and summing and averaging the average rough height of the cross section of the tunnel and the average rough height in the axial direction of the tunnel to obtain the average rough height of the ventilation wall surface of the tunnel of the evaluation section.
Figure GDA0002261694700000061
(3) Tunnel wall simplification
Dividing the actual excavation contour line in the axial direction into m sections by taking the intersection point of the actual excavation contour line in the axial direction of the tunnel and the designed excavation contour line as a node, wherein the length of each section is Xi，(i＝1,...m)；XiThe half wavelength L of the rough model is used, and the value of the maximum rough height h of the rough model is less than or equal to the maximum rough height of the actual excavation contour line
Figure GDA0002261694700000072
(i＝1,...,m)；
Model simplification is carried out on each sections by respectively adopting a sine curve unit rough model, a square unit rough model and a triangular unit rough model, 3 simplified models are obtained for each section, calculation is carried out by utilizing a formula (2), and an optimal simplified model of each section is obtained by screening from the 3 simplified models;
wherein S isOriginal sourceFor actual and design excavation contours, STriangle shapeFor simplifying the rough model of the triangular unit obtained and designing the envelope area of the excavation contour line, SSquare shapeFor simplifying the rough model of the square unit obtained and designing the envelope area of the excavation contour line, SSinusoidal shapeThe obtained sine curve unit rough model and the envelope area of the designed excavation contour line are simplified.
(4) Calculating the roughness constant Rc
A calculation formula (3) among a sine curve unit rough model, a rough spacing 2L and a rough constant value Rc1, a calculation formula (4) among a square unit rough model, a rough spacing 2L and a rough constant value Rc2, and a calculation formula (5) among a triangular unit rough model, a rough spacing 2L and a rough constant value Rc3 are obtained by a method of combining computational fluid dynamics software Fluent and order exponential decay fitting.
Rc1＝0.264+0.328e-(2L)/1.183(3)
Rc2＝0.327+0.341e-(2L)/2.753(4)
Rc3＝0.439+0.401e-(2L)/2.376(5)
Wherein the coarse pitch 2L is numerically equal to 2Xi。
According to the optimal simplified model type of each segments, calculating by using (3), (4) or (5) to obtain a rough constant Rc corresponding to each segments of axial direction actual excavation contour linesi(i＝1,...,m)；
According to the rough constant information of each sections, respectively calculating by using a formula (6) to obtain rough constant values of 5 actual excavation contour lines in the axial direction;
Figure GDA0002261694700000081
then, summing and averaging the rough constant values of the 5 actual excavation contour lines in the axial direction to obtain the rough constant in the axial direction of the evaluation section; since tunnel ventilation is only related to the axial roughness constant, only the axial roughness constant is calculated here.
(5) Evaluating tunnel ventilation wall roughness
According to the average rough height of the ventilation wall surface of the tunnel and the rough constant Rc of the tunnel, tunnel construction ventilation calculation is carried out by adopting fluid dynamics software, and the wall roughness in tunnel ventilation simulation can be determined by inputting the two parameters, so that the wind speed, the wind quantity and the pollutant concentration distribution rule of wind current in the tunnel can be obtained more accurately, a guidance effect is provided for the construction ventilation design of the tunnel and underground engineering, and the method has important theoretical significance and practical value.
Examples of the experiments
The method for evaluating the roughness of the ventilation wall surface of the tunnel by using the mileage of the diversion tunnel No. 1 of the brocade screen diversion tunnel 2+ 005-2 +015 as an evaluation section comprises the following steps:
1) and (3) data measurement: the tunnel evaluation section measures the actual excavation contour line of the tunnel by using a mid-latitude ZTS600 type total station with the angle measurement precision of 2'; measuring actual excavation contour lines of 5 of the mileage ranges 2+ 005-2 +015 of the No. 1 diversion tunnel along axial direction reference lines of a tunnel vault, a left arch shoulder, a right arch shoulder, a left arch waist and a right arch waist respectively to obtain 5 groups of measurement results as shown in the figures 1-5; then, the actual excavation contour lines of the cross sections are respectively tested from the end faces of 000, 010 and 015 of the tunnel, and 3 groups of measurement results are obtained and are shown in fig. 6 to 8.
2) Calculating the average roughness height of the ventilation wall surface of the tunnel: calculating the area S enveloped by the actual excavation contour line and the designed excavation contour line of the tunnel and the length l of the designed excavation contour line in a Computer Aided Design (CAD), and respectively calculating the average rough height of 5 axial direction actual excavation contour lines and the average rough height of 3 cross section actual excavation contour lines of the tunnel by using a formula (1);
and finally, summing and averaging the average rough height of the cross section of the tunnel and the average rough height of the axial direction of the tunnel to obtain the average rough height of the ventilation wall surface of the tunnel of the evaluation section, wherein the average rough height of the cross section of the tunnel is 0.222m, the average rough height of 5 actual excavation contour lines in the axial direction is summed and averaged to obtain the average rough height of the axial direction of the tunnel of the evaluation section, and the average rough height of the cross section of the tunnel and the average rough height of the axial direction of the tunnel is summed and averaged to obtain the average rough height of the ventilation wall surface of the tunnel.
Figure GDA0002261694700000091
3) The wall surface of the tunnel is simplified: by using actual excavationDividing the actual excavation contour line in the axial direction into m sections, selecting a sine unit rough model, a square unit rough model and a triangular unit rough model, simplifying each sections respectively, and taking the length X of each sectioni(i ═ 1.. said., m) is used as half-wavelength L of rough model, and the value of maximum rough height h of rough model is less than or equal to maximum rough height of said section of actual excavation contour line
Figure GDA0002261694700000093
(i ═ 1.. said., m), 3 simplified models are obtained for each segment, and the optimal simplified model for the segment is selected from the 3 simplified models by using the formula (2).
Figure GDA0002261694700000092
Wherein S isOriginal sourceFor actual and design excavation contours, STriangle shapeFor simplifying the rough model of the triangular unit obtained and designing the envelope area of the excavation contour line, SSquare shapeFor simplifying the rough model of the square unit obtained and designing the envelope area of the excavation contour line, SSinusoidal shapeThe obtained sine curve unit rough model and the envelope area of the designed excavation contour line are simplified.
FIGS. 9-11 are schematic diagrams of a sine-shaped unit coarse model, a square-shaped unit coarse model and a triangular unit coarse model, respectively; FIG. 12 is a simplified schematic diagram of an overall model of a tunnel; fig. 13 to 17 are models of a vault, a left arch shoulder, a right arch shoulder, a left arch waist and a right arch waist, which are simplified by measuring actual excavation contour lines along axial direction datum lines, respectively;
4) calculating the rough constants, namely obtaining a calculation formula (3) among a sinusoidal unit rough model, a rough spacing 2L and a rough constant value Rc1, a calculation formula (4) among a square unit rough model, a rough spacing 2L and a rough constant value Rc2 and a calculation formula (5) among a triangular unit rough model, a rough spacing 2L and a rough constant value Rc3 by utilizing a method of combining computational fluid dynamics software Fluent and order exponential decay fitting.
Rc1＝0.264+0.328e-(2L)/1.183(3)
Rc2＝0.327+0.341e-(2L)/2.753(4)
Rc3＝0.439+0.401e-(2L)/2.376(5)
Wherein the coarse pitch 2L is numerically equal to 2Xi。
According to the optimal simplified model type of each segments, calculating the rough constant Rc corresponding to each segments by using the formula (3), (4) or (5)i(i ═ 1.. multidot.m), and then the rough constant values of 5 actual excavation contour lines in the axial direction are calculated by using the formula (6); and finally, summing and averaging the rough constant values of the 5 axial direction actual excavation contour lines to obtain the axial direction rough constant 0.214 of the evaluation section.
Figure GDA0002261694700000101
5) Evaluating tunnel ventilation wall roughness
According to the average rough height of the ventilation wall surface of the tunnel and the rough constant Rc of the tunnel, tunnel construction ventilation calculation is carried out by adopting fluid dynamics software, and the wall roughness in tunnel ventilation simulation can be determined by inputting the two parameters, so that the wind speed, the wind quantity and the pollutant concentration distribution rule of wind current in the tunnel can be obtained more accurately, a guidance effect is provided for the construction ventilation design of the tunnel and underground engineering, and the method has important theoretical significance and practical value.

Claims (1)

1, tunnel ventilation wall roughness assessment method, the concrete steps are as follows:
(1) measurement data: taking a 10-meter tunnel as an evaluation section along the axial direction of the tunnel in a tunnel section with the same surrounding rock conditions, taking 5 datum lines along the axial direction in the evaluation section, wherein the 5 datum lines are respectively positioned at a vault, a left arch shoulder, a right arch shoulder, a left arch waist and a right arch waist, and measuring 5 actual excavation contour lines of the tunnel along the axial datum line direction by using a total station, namely the actual excavation contour lines along the axial direction; measuring actual excavation contour lines of the cross section of the tunnel every 5 meters from the end face in the evaluation section to obtain 3 actual excavation contour lines of the cross section;
(2) calculating average rough height of ventilation wall surface of tunnel
According to the area S enveloped by the actual excavation contour line and the designed excavation contour line of the tunnel and the length l of the designed excavation contour line, the average rough height of 5 actual excavation contour lines in the axial direction of the tunnel and the average rough height of 3 actual excavation contour lines in the cross section are respectively calculated by a formula (1);
summing and averaging the average rough heights of the actual excavation contour lines of the 3 cross sections of the tunnel to obtain the average rough height of the cross section of the tunnel of the evaluation section; summing and averaging the average rough heights of the 5 actual excavation contour lines in the axial direction to obtain the average rough height of the tunnel in the axial direction of the evaluation section;
summing and averaging the average rough height of the cross section of the tunnel and the average rough height in the axial direction of the tunnel to obtain the average rough height of the ventilation wall surface of the tunnel of the evaluation section;
Figure FDA0002261694690000011
(3) tunnel wall simplification
Dividing the actual excavation contour line in the axial direction into m sections by taking the intersection point of the actual excavation contour line in the axial direction of the tunnel and the designed excavation contour line as a node, wherein the length of each section is Xi，(i＝1,...m)；XiThe half wavelength L of the rough model is used, and the value of the maximum rough height h of the rough model is less than or equal to the maximum rough height of the actual excavation contour line
Figure FDA0002261694690000012
Model simplification is carried out on each sections by respectively adopting a sine curve unit rough model, a square unit rough model and a triangular unit rough model, 3 simplified models are obtained for each section, calculation is carried out by utilizing a formula (2), and an optimal simplified model of each section is obtained by screening from the 3 simplified models;
wherein S isOriginal sourceFor actual and design excavation contours, STriangle shapeFor simplifying the rough model of the triangular unit obtained and designing the envelope area of the excavation contour line, SSquare shapeFor simplifying the rough model of the square unit obtained and designing the envelope area of the excavation contour line, SSinusoidal shapeIn order to simplify the obtained sine curve unit rough model and design the envelope area of the excavation contour line;
(4) calculating the roughness constant Rc
Obtaining a calculation formula (3) among a sinusoidal unit rough model, a rough spacing 2L and a rough constant value Rc1, a calculation formula (4) among a square unit rough model, a rough spacing 2L and a rough constant value Rc2, and a calculation formula (5) among a triangular unit rough model, a rough spacing 2L and a rough constant value Rc3 by utilizing a method of combining computational fluid dynamics software Fluent and order exponential decay fitting;
Rc1＝0.264+0.328e-(2L)/1.183(3)
Rc2＝0.327+0.341e-(2L)/2.753(4)
Rc3＝0.439+0.401e-(2L)/2.376(5)
wherein the coarse pitch 2L is numerically equal to 2Xi；
According to the optimal simplified model type of each segments, calculating by using (3), (4) or (5) to obtain a rough constant Rc corresponding to each segments of axial direction actual excavation contour linesi(i＝1,...,m)；
According to the rough constant information of each sections, respectively calculating by using a formula (6) to obtain rough constant values of 5 actual excavation contour lines in the axial direction;
then, summing and averaging the rough constant values of the 5 actual excavation contour lines in the axial direction to obtain the rough constant in the axial direction of the evaluation section; since tunnel ventilation is only related to the axial roughness constant, only the axial roughness constant is calculated here;
5) evaluating tunnel ventilation wall roughness
According to the average rough height of the ventilation wall surface of the tunnel and the rough constant Rc of the tunnel, tunnel construction ventilation calculation is carried out by adopting fluid dynamics software, and the wall surface roughness in the tunnel ventilation simulation can be further determined by inputting the two parameters.
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