I know how to calculate the slope

1.

The percentage slope is the percentage of the elevation difference between two points and its distance. Its calculation formula is as follows: slope = (elevation difference / distance) X100%

when expressed as a percentage, I = H / L × 100%, for example, 3% slope means that every 100 meters of the distance, the vertical direction rises (falls) 3 meters; 1% refers to the distance every 100 meters, vertical direction up (down) 1 meter. And so on

In fact, the slope is simply the tan value of a right angle neighbor (the angle of the ground)

according to the slope classification of the geomorphological survey and geomorphological mapping Committee of the International Geographical Union, the grade of slope is determined as follows: 0 °～ zero point five ° For plain, & gt; zero point five °～ two ° It is a micro slope, & gt; two °～ five ° For gentle slope, & gt; five °～ fifteen ° Is the slope, & gt; fifteen °～ thirty-five ° It is a steep slope, & gt; thirty-five °～ fifty-five ° It is a steep slope; fifty-five °～ ninety ° It is a vertical wall

< H2 > extended data:

cross slope is the slope in the transverse direction of subgrade (pavement), which is generally 2% to facilitate drainage, especially when the longitudinal slope is small; In order to counteract the centrifugal force, it is necessary to set the superelevation on the bend, that is, the inner bend is low and the outer bend is high

the longitudinal gradient is the longitudinal gradient of the subgrade (pavement), which is also the gradient of the route as we usually say. The gradient should not be too small (not concive to drainage), not too steep (not concive to driving and safety), and there are certain restrictions on the slope length. When calculating, divide the height difference by the horizontal distance to get the slope value, which is expressed in percentage

the gradient of expressway will not exceed 3% ～ 5%

the gradient of first-class highway will not exceed 4% ～ 6%

the gradient of second-class highway will not exceed 5% ～ 7%

the gradient of third-class highway will not exceed 6% ～ 8%

the gradient of fourth-class highway will not exceed 6% ～ 9%

2. Simple analysis:
uphill reces vehicle load by 200 kg
(300-100)
that is to say, uphill consumes 2 / 3 of the power.
this simplified ratio can be regarded as the cosine of the slope

If:
when the vehicle weight is 100 kg,
((300 + 100) - (100 + 100)) / (300 + 100) = 1 / 2
this is the cosine value of the slope.

3. The ratio of vertical height (H) to horizontal width (L) of slope is called slope (or slope ratio)

set the slope angle as α， When the slope is I, the

slope is generally written as 1 ∶ M

the larger the slope is, the larger the slope angle is, and the steeper the slope is

"slope" and "slope angle"
[edit this paragraph]
when learning the trigonometric function of acute angle, the term slope appeared

when building dykes, dams, canals and rivers, we often need to indicate the slope inclination. The sign of slope is often seen on the sign beside the uphill road. In the figure, the ratio of the vertical height h to the horizontal width l of the slope is called the slope of the slope. If I is used to represent slope, then I = H / L

from the meaning of slope, we can see that "slope" is a ratio, it does not represent an angle

we call the angle between the slope and the horizontal plane slope angle α The relationship between slope and slope angle is I = H / L = TG α

e to °＜α＜ ninety ° Internal, TG α Is an increasing function, that is, when the slope angle α When the slope increases, the slope also increases. It can be seen that the larger the slope angle is, the greater the slope is, that is to say, the steeper the slope is

it can be seen that the slope angle represents an angle, and the slope represents the tangent function of the angle. The difference between the two is obvious

in our daily life, we often understand the angle of a slope as a slope. For example, when it is difficult for a car to go uphill, we say, "the slope is too steep." In fact, this sentence means "the slope angle of this hillside is too big", but it is not said in life. Therefore, it is easy to bring this misunderstanding into mathematics learning and confuse the two different concepts of slope and slope angle

the following example can help us understand the concepts of slope and slope angle

for example, in the figure, the cross section of a railway subgrade is an isosceles trapezoid ABCD, and its slope and angle (accurate to 0.1) are calculated according to the data in the figure

the solution is AE ⊥ BC, e is perpendicular foot< According to the properties of isosceles trapezoid, be = (BC-AD) / 2 = 9.28, I = AE / be = TG α= 0.625

α= thirty-two °

4. Generally, the ratio of the vertical height h to the horizontal width l of the slope is called the tangent value of the slope angle

5. Slope is the degree of steepness and slowness of surface unit. The ratio of vertical height h to horizontal width l of slope is usually called slope (or slope ratio), which is expressed by letter I
there are four ways to express slope: percentage method, degree method, density method and fraction method, among which percentage method and degree method are more commonly used
(1) percentage method
is the most commonly used method for slope, that is, the percentage of elevation difference between two points and their horizontal distance. The calculation formula is as follows: slope = (elevation difference / horizontal distance) X100%
when percentage is used,
that is, I = H / L × 100%
for example, slope 3% means that every 100 meters of horizontal distance, the vertical direction rises (falls) 3 meters; 1% means that every 100 meters of horizontal distance, the vertical direction rises (falls) by 1 meter. And so on
(2) degree method
the slope is expressed by degree and calculated by inverse trigonometric function. The formula is as follows:
tan α( Slope) = elevation difference / horizontal distance
so α( Slope) = tan-1 (elevation difference / horizontal distance)
tangent and sine of different angles
angle tangent sine
0 ° 0% 0%
5 ° 9% 9%
10 ° 18% 17%
30 ° 58% 50%
45 ° 100% 71%
60 ° 173% 87%
90 ° The slope of a slope is I = 1:2. If a person walks up the slope for 100 meters, how many meters will his height rise.
solution: because slope the ratio of vertical height h to horizontal width l of the slope is usually called slope (or slope ratio), which is expressed by the letter I. It is usually expressed as a percentage
then, there is: the height rises to: X & sup2+ 2X)²= 100²< br />5X²= 100²
x √ 5 = 100
x = 100 / √ 5 because √ 5 = √ 5 / √ 5 * √ 5
x = 20 √ 5
it is simplified as: 100 * √ 5 / 5 = 20 √ 5m.
in fact, the slope is simply the tan value of a right angle neighbor (the angle of the ground).
the professional committee of geomorphological survey and field mapping of international geographic society divides the slope into seven levels: 0-2 ° Plain to slightly inclined slope, 2-5 ° Gentle slope, 5-15 ° Slope, 15-25 ° Steep slope, 25-35 ° Steep slope, 35-55 ° Steep slope, & gt; fifty-five ° Vertical slope
Chinese mainland stipulates > twenty-five ° It can't be cultivated
in the Loess Plateau of Northwest China ° And 25 ° They are the lower limit and upper limit critical slope angle of surface water erosion.

6.

The slope gradient shall be determined according to the actual situation of excavation depth, soil quality and groundwater. Generally speaking, when there is no underground water, the excavation depth of the vertical wall of the foundation pit (groove) without support and slope in the earth excavation with natural humidity shall not be greater than 1 m in sand, 1.25 m in sandy soil, 1.5 m in clay, and 2 m in particularly solid soil

extended data

I. slope steepness is expressed by the ratio of vertical distance and horizontal distance between two points on the slope

for example, when the slope is 1:1.5, the horizontal distance is 1.5 when the vertical distance is 1. The value is related to the height of the slope and the properties of the subgrade. When the height of the slope is high, the slope should be changed by sections or special design should be made. Because of the need of safety and beauty of expressway, the cross section of subgrade should be designed as flow line. That is to say, flat slope and circular corner are adopted

In order to simplify the calculation, the slope stability analysis with mechanical method is treated as plane problem

The internal friction angle of loose sandy soil and gravel is larger, the cohesion is smaller, and the fracture surface is similar to the linear fracture surface method

The results show that the cohesive force of cohesive soil is larger, the internal friction angle is smaller, and the sliding surface is cylindrical and bowl shaped, which is similar to circular surface

source of reference: Network - slope gradient

source of reference: Network - subgrade slope

7. Check the hydraulic calculation table according to D, Q, V and fullness

in the specific calculation, given the design flow Q and pipeline roughness coefficient n, it is necessary to calculate the pipe diameter D, hydraulic radius r, fullness, pipeline slope and velocity
there are five unknowns in the two equations, so it is necessary to assume three first and find the other two. The calculation is complex. In order to simplify the calculation, the hydraulic calculation chart is often used, that is, the hydraulic calculation chart drawn by the relationship between the hydraulic factors such as flow rate, pipe diameter, slope, velocity, fullness and roughness coefficient
for each chart, the pipe diameter and roughness coefficient are known, and the curve on the chart shows the relationship between flow rate, velocity, slope and fullness. Among these four factors, knowing two of them can find out the other two. How to use hydraulic calculation chart should be mastered
example: the known roughness coefficient is 0.014, the flow rate is 32L / s, the pipe diameter is 300 mm, and the fullness is 0.55, so the velocity and slope can be calculated
solution: first, find the diagram with a pipe diameter of 300 mm. There are four groups of lines on the diagram. The vertical line represents the flow rate, the horizontal line represents the hydraulic gradient, the oblique line from left to right represents the flow rate, and the oblique line from right to left represents the fullness. The number on each line represents the corresponding value
find out the vertical line with the flow rate of 32L / s and the inclined line with the fullness of 0.55 from the figure. If the intersection point of the two lines falls on the horizontal line with the slope of 0.0038, the slope is 0.0038, and it falls between the flow rate of 0.8m/s and 0.85m/s, which is estimated to be 0.81m/s

example: the known roughness coefficient is 0.014, the pipe diameter is 400mm, the flow rate is 41l / s, the flow rate is 0.9m/s, and the slope and fullness are calculated
solution: the vertical line with a flow rate of 41l / s and the inclined line with a flow rate of 0.9m/s are found by using the diagram with a pipe diameter of 400mm. If the intersection of the two lines falls on the horizontal line with a slope of 0.0043, the slope is 0.0043 and falls between the two inclined lines with a fullness of 0.35 and 0.4, and the estimated fullness is 0.39.

8.

The calculation formula of cross slope is as follows:
cross slope = 2 (center pile elevation side pile elevation) / measured width of pavement * 100%

where: Center pile elevation refers to the elevation of center pile used as location survey in line construction survey
elevation of side pile = elevation of middle pile ± Transverse slope × Half width of road

cross slope

the maximum longitudinal slope value of all levels of highway:

plain micro Hill (%) mountain heavy Hill (%)

Highway 3, 5

grade I 4, 6

grade II 5, 7

grade III 6, 8

grade IV 6, 9

in order to drain, the pavement and shoulder should have certain slope, I1 and I? express. It varies with the smoothness of the pavement, if the concrete pavement I1 is 1% - 1.5%; The I1 of asphalt pavement is 1.5% - 2.5%; i? Generally 1% - 2% larger than I1. Slope = height difference / horizontal distance

development data

the cross slope is the slope in the transverse direction of subgrade (pavement), generally 2%, which is for the convenience of drainage, especially when the longitudinal slope is small; In order to counteract the centrifugal force, it is necessary to set the superelevation on the bend, that is, the inner bend is low and the outer bend is high. The longitudinal gradient is the longitudinal gradient of subgrade (pavement), that is, the gradient of the route as we usually say. The gradient should not be too small (not concive to drainage) or too steep (not concive to driving and safety). At the same time, there are certain restrictions on the slope length. When calculating, divide the height difference by the horizontal distance to get the slope value, which is expressed in percentage

9.

1. The cross slope ratio of road is the cross slope. Calculation formula: (center point elevation sideline point elevation) / (distance from center point to sideline point)

2. Cross slope:

refers to the cross slope of road width and roadside belt. It refers to the lateral inclination of pavement, divider, sidewalk, green belt, etc. Expressed as a percentage

generally, the slope ratio of the slope is in the form of 1: m, where m is the slope coefficient, which is equal to the cotangent of the slope toe. It can be seen that the slope ratio and the slope coefficient are reciprocal to each other. As shown in the figure, for a slope with a height of 200 and a horizontal projection of 100, the slope ratio is expressed as 1:0.5, and the slope coefficient is 0.5

10. No matter what well it is, the hydraulic slope calculation is the same
along the direction of groundwater flow, set up an observation log at each end of the two points where you want to measure the hydraulic gradient (it is generally good to find it nearby) to measure the water head. The head difference / distance between two points = hydraulic gradient