Wes Marshall, P.E. University of ConnecticutFebruary 2007

CE 276Site Design

Chapter 3 –Slope Formula Application

What did we talk about last week?

Plotting Contours Interpolation

Mathematical Equations Graphical Method Cross-Section Method

Slopes & Calculating Slopes Slope Analysis Plan

Calculating Slope

S = DE/L = Rise / Run S = Slope (or gradient) DE = Difference in elevation between the end

points of a line L = Horizontal distance

Ris

e

Run

Other Ways to Express Slope

Slope is often described as a ratio such as 2:1

This equates to 2 units of horizontal distance for every 1 units of vertical elevation

Slope can also be shown in degrees, minutes, and seconds

Chapter 3Slope Formula Application

Slope Analysis

A slope analysis is used to depict the steepness of the terrain It should be used in conjunction with other

information (i.e. wetlands, vegetation, soils, etc.) to establish site constraints

Helps determine the best areas for locating buildings, roads, parking lots, and other uses on a particular site

Slope Analysis

Requires the following information:

Horizontal ScaleContour IntervalPercent Slope Categories

Slope Analysis

Being able to quickly & legibly create a slope analysis plan by hand is an important skill that can be used during design charrettes & client/public participation meetings when using a computer is not practical

Slope Analysis

Grading

Grading

Objectives of grading:

To change the form of the natural landscape to serve a particular use

To slope the surface in order to ensure proper drainage of storm water

Computers in Grading

Useful tool in topography analysis We already discussed the Slope Analysis

Plan, but there are other applications such as:Elevation PlansAspect (slope orientation) Plans3-D ViewsCross-SectionsCut & Fill Volumes

Computers in Grading

Contour Plan of Mount St. Helens 20 m contour lines

and 100 m index lines.

Computers in Grading

Slope Analysis Plan

Computers in Grading

DEM classified into 200 m classes

Digital elevation data can be used to derive many different types of analyses including:

Contours Slope Aspect surface hydrology watershed boundaries

Computers in Grading

Aspect Plan Indicates the

direction a slope faces (derived from the DEM)

Computers in Grading

3-D Model of Slope Analysis

Grading Around Buildings

Storm water should be directed away from buildings in order to: Avoid leakage into interior spaces Avoid saturating the soils (which reduces

the bearing capacity of the soil) Avoid moisture on the buildings

Drainage away from a building is often called positive drainage

Grading Around Buildings

Given: Spot Elevations

on building corners

Slope away from building (i.e. 3%)

Find: Contours

Building

Path/Road Layout & Grading

The design of a road often may not exceed a maximum gradient This may be due to:

ADA accessibility constraintsZoning codesRoad guidelines, or Commonsense

Example

Design a path from Point A to the Dock with a maximum slope of 4%

Example

S = DE L

0.04 = 1 L

L = 25 feet d

Example

Draw an arc of radius = 25’ at the proper scale from Point A

Mark intersections with next contour

Anything within shaded area is longer than 25’ & thus steeper than 4%

Example

Continue strategy on a contour-by-contour basis until reaching dock

Path should depend upon overall design intent, views, soils, etc.

Cross Slope Grading

Cross slopes Prevents ponding of surface water Required on paths, driveways,

roads and other flat areas Also done on roads & paths

Sheds water to gutters or into the grass in order to keep the higher central surface from becoming inundated with water

Typically 1% to 2%

Cross Slope Grading

Step 1 Find the difference in elevation from

one side of the path to the other For this example, use a slope of 2%

Cross Slope Grading

Slope(S) = Difference in Elevation(DE) Horizontal Distance(L)

Cross Slope Grading

Plug in known information:0.02 = DE 5.0'

DE = 0.1'

Cross Slope Grading

S = 4%

B C

Step 2 Find the distance along the path necessary

to reach the point at the same elevation ofthe original contour

Cross Slope Grading

Distance from

pt. B to pt. C.

S = 4%

B C

the distance along the path necessary to reach the point at the same elevation as the original 92.0 contour

=

Cross Slope Grading

S = 4%

B CL = 2.5’

Plug in known information:0.04 = 0.1 L

L = 2.5

Cross Slope Grading

Combine steps to simplify the equation Can calculate a number of perpendicular

offsets quickly and efficiently

S = 4%

B CL = 2.5’

Cross Slope Grading

Perpendicular offset = location of the initial elevation on the other side of the path (or parking lot, road, terrace, etc.) Used whenever there are two slopes involved

rather than just one

S = 4%

B CL = 2.5’

Cross Slope Grading

S = 4%

B CL = 2.5’

DE = L S

DE = (Path Width)(Cross Slope)S = Longitudinal SlopeL = Perpendicular Offset

Cross Slope Grading

Step 3 Connect the points with the same elevation

This is the beginning of your proposed contour

Cross Slope Grading

Step 4 Connect either end of the diagonal line with the

existing contour line Make a smooth transition and place heavy tabs or

dots at the point at which they connect Continue this process for the rest of the contours

Terrace Grading

Another common grading problem Required on most hillside environments 3 Types

On Fill

In Cut

Partially on fill & partially in cut

Terrace Grading

Terrace measuring

25’ by 40’ South edge at

elevation 220.0’ Slope downward at

3% toward the north for drainage

Terrace Grading

Side slopes will be graded at a ratio of 3:1

This equates to 1 foot drop for every 3 feet of horizontal distance

Terrace Grading

One reason for a relatively steep is to return to the existing grade in the shortest distance possible

Why? This reduces the

area of disturbance caused by grading

Can reduce cost

Terrace Grading

Make a checklist of the criteria looking at the problem description:

South edge @ 220.0’

Terrace sloped @ 3% to North

Side slopes graded @ 3:1

Terrace Grading

First step: Determine the

elevation along the north, or lower, edge of the terrace

DE = S x L The north edge is

0.03 x 25 ft = 0.75 ft lower than the south edge

Terrace Grading

220.0 - 0.75 = 219.25’

Thus, the spot elevations along north side of terrace are 219.25’

Terrace Grading

Next Step: Determine the

distance from the north edge of the terrace to the 219-ft contour line

Terrace Grading

Since the side slopes are to be graded at 3:1

the horizontal distance from the terrace edge to the 219-ft contour line is 0.75 ft as calculated by the following proportion:

x = horizontal distance from 219.25 to 219.0

0.25 = elev. difference from 219.25 to 219.0

31

=

x = (0.25 x 3)/1 = 0.75 ft

x0.25

Terrace Grading

This distance is marked off along lines drawn perpendicular to the terrace at the northeast and northwest corners

Terrace Grading

From the point of the 219 spot elevation:

The whole number spot elevations (i.e. 218, 217, 216, etc.) can be located by progressing along the line in 3-ft increments

For every 3 ft of horizontal distance, there is a 1-ft vertical drop

These points are used for the construction of the proposed contour lines.

Terrace Grading

Same procedure is followed at the south edge of the terrace

Terrace Grading

Lines are drawn perpendicular to the terrace at the southeast and southwest corners

Terrace Grading

Since the elevation of the south edge is already at the whole number, 220…

The remaining whole number spot elevations can be located by progressing out from the edge in 3-ft increments

Terrace Grading

Begin with the 219’ contour line

Draw straight lines through the 219-ft spot elevations until the lines of adjacent sides intersect

The proposed 219-ft contour line is a closed contour since it never intersects with the 219-ft contour line already existing on the site

Terrace Grading

Terrace Grading

Proceed with the proposed 218’ contour line following the same technique:

The new 218’ contour line intersects the existing 218’ contour line at two points

Terrace Grading

Terrace Grading

Continue successively lower contour lines (217, 216, 215, etc.) until the point is reached where existing contours are no longer disturbed

Terrace Grading

Terrace Grading

Delineate the area as a limit of construction line

The point of no fill (or cut) occurs where the two grade lines intersect

When there is no intersection of existing and proposed contour lines to delineate the no fill (or cut) line easily…

A section showing the proposed and existing grade lines may be constructed

Terrace Grading

Shaping the side slopes

What is shown is difficult to construct and maintain

It usually does not blend well with the surrounding landscape

Thus, the contours are given a smoother and more rounded appearance

Terrace Grading

Road Grading

TerminologyCrown = Difference in elevation

between the edge and the centerline of a roadway

Purpose: Allows water to drain from centerVisually separate opposing lanes of traffic

Crowns

Crowns are typically achieved by having the center of the road or path higher than the two edges

Crowns

Parabolic

Tangential

Reverse(infrequently used)

Section Plan

Crowns

Crowns can be characterized by:

Height

Ratio

Percentage

Road Grading

Terminology Curb = Vertical separation at the

edge of a roadway

Purpose: To direct & restrict storm runoff To provide vertical separation and safety for

pedestrians, bicyclists, etc.

Barrier Curb

Curbs

Beveled

Rounded

MountableNon-mountable

Road Grading

Terminology Swale = Constructed or natural drainage

channel with a vegetated surface

Gutter = Paved swale

Purpose: To intercept, direct, and control

storm water runoff

Swales

Swales are often found along roads for drainage

Swales are most often characterized by their depth

Swales

Vegetated Parabolic Swale

Paved Gutter

Combinationcurb & gutter

Swales

All 3 swales shown below have 3% grade & 15’ width

6” Deep

12” Deep

18” Deep

Swales

Swales are designed to convey water as part of an OPEN storm water system They are not meant to be continuously wet

Typically have parabolic cross-section

Typically lined with grass

Tricks to Drawing Contour Lines

Turn the plan so that you are looking in the downhill direction If drawn correctly, the contour lines should

look like a cross section with an exaggerated vertical scaleA swale should look like a valleyA crown should look like a ridgeThe shoulder should slope away from the road

Road Grading

Road grading with swales & curbs can be a little tricky

This figure depicts the plan & section for all 3 components (road, swale, curb) together

Road Grading

Given: 3% Slope Along Street 25.42 Spot Elevation 6” Parabolic Crown

Height 4” Swale Height 6” Curb Height 2% Slope Across Sidewalk

Downward Toward StreetFind: 25’ Contour Line

Road Grading