1. Wes Marshall, P.E. University of Connecticut February 2007 CE 276 Site Design Chapter 3 –Slope Formula Application

2. What did we talk about last week?  Plotting Contours  Interpolation Mathematical Equations Graphical Method Cross-Section Method  Slopes & Calculating Slopes Slope Analysis Plan

3. 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 Rise Run

4. 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

5. Chapter 3 Slope Formula Application

6. 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

7. Slope Analysis  Requires the following information: Horizontal Scale Contour Interval Percent Slope Categories

11. 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

12. Slope Analysis

13. Grading

14.  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

15. Computers in Grading  Useful tool in topography analysis We already discussed the Slope Analysis Plan, but there are other applications such as: Elevation Plans Aspect (slope orientation) Plans 3-D Views Cross-Sections Cut & Fill Volumes

16. Computers in Grading  Contour Plan of Mount St. Helens 20 m contour lines and 100 m index lines.

17. Computers in Grading  Slope Analysis Plan

18. 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

19. Computers in Grading  Aspect Plan Indicates the direction a slope faces (derived from the DEM)

20. Computers in Grading  3-D Model of Slope Analysis

21. 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

22. Grading Around Buildings  Given: Spot Elevations on building corners Slope away from building (i.e. 3%)  Find: Contours Building

23. Path/Road Layout & Grading  The design of a road often may not exceed a maximum gradient This may be due to: ADA accessibility constraints Zoning codes Road guidelines, or Commonsense

24. Example  Design a path from Point A to the Dock with a maximum slope of 4%

25. Example S = DE L 0.04 = 1 L L = 25 feet dd

26. 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%

27. Example  Continue strategy on a contour-by- contour basis until reaching dock  Path should depend upon overall design intent, views, soils, etc.

28. 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%

29. 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%

30. Cross Slope Grading Slope(S) = Difference in Elevation(DE) Horizontal Distance(L)

31. Cross Slope Grading Plug in known information: 0.02 = DE 5.0' DE = 0.1'

32. Cross Slope Grading Distance from pt. B to pt. C. = the distance along the path necessary to reach the point at the same elevation as the original 92.0 contour S = 4% BC Plug in known information: 0.04 = 0.1 L L = 2.5  Step 2 Find the distance along the path necessary to reach the point at the same elevation of the original contour

33. Cross Slope Grading Distance from pt. B to pt. C. S = 4% BC the distance along the path necessary to reach the point at the same elevation as the original 92.0 contour =

34. Cross Slope Grading S = 4% BC L = 2.5’ Plug in known information: 0.04 = 0.1 L L = 2.5

35. Cross Slope Grading  Combine steps to simplify the equation Can calculate a number of perpendicular offsets quickly and efficiently S = 4% BC L = 2.5’

36. 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% BC L = 2.5’

37. Cross Slope Grading S = 4% BC L = 2.5’ DE = L S DE = (Path Width)(Cross Slope) S = Longitudinal Slope L = Perpendicular Offset

38. Cross Slope Grading  Step 3 Connect the points with the same elevation This is the beginning of your proposed contour

39. 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

40. Terrace Grading Another common grading problem  Required on most hillside environments  3 Types On Fill In Cut Partially on fill & partially in cut

41. Terrace Grading  Terrace measuring 25’ by 40’ South edge at elevation 220.0’ Slope downward at 3% toward the north for drainage

42. 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

43. 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

44. 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

45. 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

46. Terrace Grading  220.0 - 0.75 = 219.25’  Thus, the spot elevations along north side of terrace are 219.25’

47. Terrace Grading  Next Step: Determine the distance from the north edge of the terrace to the 219-ft contour line

48. 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 3131 = x = (0.25 x 3)/1 = 0.75 ft x 0.25

49. Terrace Grading  This distance is marked off along lines drawn perpendicular to the terrace at the northeast and northwest corners

50. 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.

51. Terrace Grading Same procedure is followed at the south edge of the terrace

52. Terrace Grading  Lines are drawn perpendicular to the terrace at the southeast and southwest corners

53. 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

54. 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

55. Terrace Grading

56.  Proceed with the proposed 218’ contour line f ollowing the same technique: The new 218’ contour line intersects the existing 218’ contour line at two points

57. Terrace Grading

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

59. Terrace Grading

60.  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

61. 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

62. Terrace Grading

63. Road Grading  Terminology Crown = Difference in elevation between the edge and the centerline of a roadway Purpose: Allows water to drain from center Visually separate opposing lanes of traffic

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

65. Crowns Parabolic Tangential Reverse (infrequently used) SectionPlan

66. Crowns  Crowns can be characterized by: Height Ratio Percentage

67. 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.

68. Barrier Curb Curbs Beveled Rounded Mountable Non-mountable

69. 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

70. Swales  Swales are often found along roads for drainage  Swales are most often characterized by their depth

71. Swales Vegetated Parabolic Swale Paved Gutter Combination curb & gutter

72. Swales All 3 swales shown below have 3% grade & 15’ width 6” Deep 12” Deep 18” Deep

73. 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

76. 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 scale A swale should look like a valley A crown should look like a ridge The shoulder should slope away from the road

77. 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

78. 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 Street Find: 25’ Contour Line

79. Road Grading