Slope Ratio

The two most common slopes used in road construction are the foreslope and backslope. The foreslope extends from the outside of the shoulder to the bottom of the ditch. The backslope extends from the top of the cut at the existing grade to the bottom of the ditch. The amount of slope in a foreslope or backslope is the ratio of horizontal distance to vertical distance (fig. 15-15). That means that for every one

(1) foot of vertical (up or down), the horizontal distance changes proportionally. The following are equations to compute slope ratio:

1. If the base and the height are known factors, but not the slope, use the following:

Base Height = Slope (B+H=S

2. If the slope ratio and the height are known factors, but not the base, use the following:

Slope x Height = Base

(S x H = B)

3. If the base and the slope ratio are known factors, but not the height, use the following:

Base Slope = Height (B S = H)

Figure 15-15.-Slope ratio.

Cross Sections

A cross-sectional view (fig. 15-16) that is given for a road project is a cutaway end view of a proposed station between the left slope and the right slope. Typical cross sections are plotted at any intermediate place where there is a distance change in slope along the center line where the natural ground profile and grade line correspond. The cross section displays the slope limits, the slope ratio, and the horizontal distance between centerline stakes and shoulder stakes. It also shows the vertical distance of the proposed cut or fill at the shoulder and centerline stakes.

To compute the area of a cross section, you must first break it down into geometric figures (squares, triangles, etc.). (See fig. 15-17.) Compute each area separately, then total the results to obtain the total square feet.

Figure 15-16.-Cross section.

Figure 15-17.-geometric sections of a cross section. 15-13

To compute the square feet area of a SQUARE or RECTANGLE (fig. 15-18), use the following equation:

Area = Base x Height or (A = B x H).

Since a RIGHT TRIANGLE is a square or rectangle cut in half diagonally, the same equation can be used to compute the area and the result divided by 2 (fig. 15-19). For example,

Another geometric figure you may encounter in a cross section is a TRAPEZOID (fig. 15-20). The equation to compute the area of a trapezoid is as follows:

The next step is to compute the total area in the cross section (fig. 15-21). This is accomplished by adding the results of each geometric figure in the cross

Figure 15-18.-Area of a square and rectangle.

Figure 15-19.-Area of a triangle. 15-14

section. This value is the total end area of the crosssectional view.

To compute the amount of cubic yards between two cross sections, use the following equation:

To compute the equation, take the area of one end section (cross section) plus the area of the other end and multiply the sum of the two areas by a constant factor of 1.85. This value should now be multiplied by the distance between the two end areas to determine the number of cubic yards. (See fig. 15-21.)