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Dr.Dirt Papers by Dan Atcheson
GENERAL TOPICS
CONVERSION FACTORS THE SECRET TO TECHNICAL SUCCESS
HOW TO DETERMINE THE AVERAGE DEPTH OF CUT OR FILL WITHIN A GIVEN AREA
BALANCING TWO SEPARATE JOB FILES
HERE'S A SIMPLE, INEXPENSIVE METHOD TO HELP YOU LEARN EARTHWORK
DETERMINING PLAN SCALE WHEN GIVEN AN AREA ONLY
DETERMINING THE ACTUAL SCALE OF AN ENLARGED OR REDUCED DRAWING
USING A DIGITIZER TO TAKE OFF ROADWORK QUANTITIES
BALANCING TOPSOIL STRIPPED AND TOPSOIL REPLACED
ENTERING EXISTING ELEVATION IN RELATIVELY FLAT TERRAIN
HOW TO RELOCATE A DRAWING ON A DIGITIZER BOARD
TAKING OFF A PROJECT THAT HAS REMOVAL EXCAVATION

CONVERSION FACTORS THE SECRET TO TECHNICAL SUCCESS
Learning to work with conversion factors has helped me simplify and solve problems in a mechanical, almost fool-proof manner. Before we proceed, consider and understand the following principles:
1. A conversion factor is used to convert from one unit to another (e.g., feet to inches)
2. A conversion factor is always equal to one (e.g., 12 inches per foot, 3 feet per yard, etc.)
3. A conversion factor is always expressed as a fraction (e.g. 12 in./LF, 3 LF/Yd, etc.).
4. Conversion from one unit to another is always done by multiplying conversion factors.
From the discussion thus far, you probably realize that you use conversion factors every day of your life, but here is what you might not be aware of: Like numerator and denominator units of multiplied fractions cancel out one another. Knowing this, we can set up a conversion problem mechanically so that every unwanted unit is canceled and the desired (target) unit remains unscathed

EXAMPLE: Convert 100 yards (Yd.) to centimeters (cm.).
Solution: 100 Yd x 3 ft/Yd x 12 in./ft. x 2.54 cm./in. = 9144 cm.

In the problem above, we multiplied the numbers in the numerators to make the conversion. However, there are situations when the denominator contains a number, requiring division.

EXAMPLE: Assuming it requires 1.4 loose cubic yards (LCY) to yield a compacted cubic yard (CCY), determine how many CCY a 14-LCY truckload of dirt will yield? 
Solution: 14 LCY x CCY/1.4LCY = 10 CCY


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HOW TO DETERMINE THE AVERAGE DEPTH OF CUT OR FILL WITHIN A GIVEN AREA
Use the following equations to determine the average depth of cut or fill within a given area:
Average Depth of Cut = Volume of Cut (CY) x 27 / Area of Cut (s.f.)
Average Depth of Fill = Volume of Fill (CY) x 27 / Area of Fill (s.f.)

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BALANCING TWO SEPARATE JOB FILES
You can balance two job files by using the Dr. Dirt Balance Equation:
Change in Depth = Net Import (or Export) x 27/Total Site Areas
For example, let's assume that Job File 1 requires an import of 10,000 LCY (Loose CY) and Job File 2 requires an export of 4000 LCY. Also assume Job File 1 has a site perimeter area of 20,000 SF and Job File 2 has an area of 16,000 SF. The Net Import is 10,000 LCY - 4000 LCY = 6000 LCY. The total site area is 20,000 SF + 16,000 SF = 36,000 SF. Therefore, the proposed elevations throughout both sites must be changed by:
Change in Depth = 6000 LCY x 27/36,000 SF = 4.5 Feet
Since both projects require a net import, the fill is less than the cut; therefore, to balance the sites, the sites must be lowered by 4.5 feet.

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HERE'S A SIMPLE, INEXPENSIVE METHOD TO HELP YOU LEARN EARTHWORK
One of the best ways to learn the science of estimating earthwork quantities is to study cross sections through a site. The easiest way to create cross sections is to purchase a set of color-dyed pipe cleaners, and cull out two red and two blue sticks. We will use red to indicate the existing surface and blue to indicate the proposed surface. Lay a red stick and a blue stick diagonally so that they form an elongated X. You have created a cross section showing cut on one side of the intersection of sticks and fill on the other side. Now lay a second red stick below and parallel to the first red stick. We will consider this second red stick as the existing surface after topsoil stripping.
You can immediately see how the cut and fill quantities are affected; e.g., cut is reduced and fill is increased. You can lay a second blue stick below and parallel to the first blue stick to represent the proposed surface prior to replacing topsoil. You should now be able to see that the fill is decreased and the cut is increased.
You can further your education by fashioning additional sticks to represent the subgrade surface of a parking lot or slab by bending a stick into a "Panama hat" shape.

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DETERMINING PLAN SCALE WHEN GIVEN AN AREA, ONLY
Situation: You have a grading plan with a plan scale of 1" = 40'. The engineer has also given you a well-defined (measurable) work area of 5.76 acres. However, no dimensions are given anywhere on the plan, not even a scale bar. Using the given scale, your site perimeter area results in 18.3 acres. Obviously, the plan has been reduced so that the given scale is incorrect.
Question: What scale must be used to produce the correct results?
Solution: You can use the following equation to solve the problem:
Correct Scale =
In the given problem, the correct scale is:
Correct Scale = = 22.44 ft./in.

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DETERMINING THE ACTUAL SCALE OF AN ENLARGED OR REDUCED DRAWING
When a blueprint has been reduced or enlarged, you can still use the given scale to measure plan dimensions accurately. The factor by which the plan scale has been reduced or enlarged can be determined by:
Scale Factor = Printed Plan Dimension
Scaled Dimension (Using Original Scale)
EXAMPLE: Assuming an original scale of 1" = 20', find the scale factor if a given plan dimension of 250 feet measures 55 feet at the original scale of 1" = 20'.
Solution: The Scale Factor is: Scale Factor = 250'/55' = 4.545
Therefore, any dimension scaled at 1" = 20' must be multiplied by 4.545 in order to obtain the correct length. Note: Never apply the factor to a printed dimension entered directly into your calculator. Apply the factor only to dimensions measured with your scale.
The Quest Estimating Systems have a Compensate Scale feature that automatically determines the correct scale to use on any enlarged or reduced drawing; however, you can check your accuracy in setting the Compensate Scale feature by using the following formula:
Actual Scale = Printed Dimension x Original Scale
Measured Dimension (Using Original Scale)
EXAMPLE: Determine the actual scale of the drawing discussed in the example above.
Solution: The actual scale is:
Actual Scale = 250' x 20'/55' = 90.91 feet per inch

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USING A DIGITIZER TO TAKE OFF ROADWORK QUANTITIES
WHEN GIVEN LEFT, RIGHT AND CENTERLINE PROFILES
1. Set both the horizontal and vertical scales.
2. Digitize all cut areas along the right shoulder. Note: Do not clear the working total, but allow it to run a cumulative total as you proceed.
3. Digitize the cut areas along the centerline twice.
4. Multiply the cumulative total by the width of the road, shoulder to shoulder, then divide the result by 27. The result will be the CY volume of cut between the shoulders.
5. Clear the working total, then repeat Steps 1 through 4 to account for the fill areas.

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BALANCING TOPSOIL STRIPPED AND TOPSOIL REPLACED
Although you can use the Balance Feature in Quest for Earthwork to balance the volume of topsoil stripped with the volume of topsoil replaced, the easiest way to perform this task is through simple mathematics. Since volume is expressed as:
Volume = Area x Depth
We can determine the depth of topsoil replaced in order to get a topsoil balance by:
Depth of Topsoil Replaced = Volume of Topsoil Stripped (cf) /Respread Area
For example, let's say you have stripped 1000 CY of topsoil and would like to respread it over a a 15,000 square-foot area. The depth of topsoil replaced will be:

Depth = 1000 CY x 27/15000
= 1.8 feet

Sometimes, the depth of topsoil respread required to achieve a topsoil balance exceeds the depth allowed by the designer. You can determine the maximum allowable volume of topsoil replaced by:
Volume of Allowable Topsoil Replaced = Maximum Depth Allowed x Respread Area
For example, if the maximum allowable depth of topsoil replaced in the previous example is 1 foot, the maximum volume of topsoil replaced is:

Volume of Topsoil Replaced = 1 Ft x 15,000 SF
= 15,000 cf/27
= 556 CY


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ENTERING EXISTING ELEVATIONS IN RELATIVELY FLAT TERRAIN
In many areas where the existing terrain shows little vertical relief, existing elevations are often given as single points. The most accurate way to deal with this is to connect them, using the Point Contour feature in the Quest for Earthwork system. Here's how I do it:
1. Mark each existing point with a colored pencil.
2. Starting at the bottom of the drawing, take a yardstick and lay it across the drawing, horizontally and use a colored pen to mark those that lie close to the horizontal line.
Note: Mark the points, only; don't draw a line using the yardstick.
3. Move the yardstick up and mark the next series of points, using a different pen color. Using the alternate colors will help keep you from entering conflicting elevations by crossing other point contours, or entering elevations, more than once. You need only two colors to do this.
4. Continue in this fashion until all pertinent existing elevations have been entered.
5. Take off each series of points, using the Point Contour feature of the system.
Note 1: The Point Contour option is discussed in the Earthwork user manual.
Note 2: Also, keep in mind that since elevation data is extrapolated from one point to the next along a point contour, the takeoff will be much more accurate than if single points are entered. The difference in accuracy is paramount to someone's being blindfolded and asked to describe the contents of the top of a desk while being allowed to sweep your hand across the desk in many locations, versus being allowed to touch the desk at several locations.
Note 3: Be watchful of radical elevation changes. Those would indicate a mound, or a swale through the site. Such points should be connected, individually, as well. This could mean a circular-shaped point contour within other horizontal point contours. But be careful not to cross point contours, since extrapolated data down each line could create a conflict.

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HOW TO RELOCATE A DRAWING ON A DIGITIZER BOARD
I'm often required to relocate a drawing after removing it from the board. The easiest way to relocate the drawing is to place the point of the stylus pen over a strategic point on the drawing, such as a building corner. Pretend that the stylus is attached to the drawing, stylus point-to-corner, and gently move the drawing across the board until the stylus pen position shown on the monitor is directly over the building corner on the monitor. Then check another point, such one kitty-cornered to the first. After verifying enough points, hold your breath and carefully tape the drawing to the board.

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TAKING OFF A PROJECT THAT HAS REMOVAL EXCAVATION
In some areas, such as the mountainous regions of the Southwest, valleys in the mountains are filled with alluvial material which is not good to build on, primarily due to the silt content, so the earthwork contractor is required to excavate the undesirable material, as well as cut and fill to proposed grades. In such cases, there are usually three pay quantities: mass excavation, removal excavation and fill. Here's how you take off such a project:
1. Take off the project, as drawn.
2. Take off the project from proposed grades to the removal grades.
Note: Read my paper entitled "The Copy/Paste and Cut/Paste Routine in Quest for Earthwork-A Very Handy Tool."
Basic Definitions:
Cut is the volume of cutting required to get from existing grades to proposed grades, as drawn on the plans. Cut is also defined as Mass Excavation. This quantity is obtained in Step 1, above.
Fill is the volume of filling required to get from existing grades to proposed grades, as drawn on the plans. This quantity is also obtained in Step 1.
Note: Cut and Fill for such a project are shown schematically in the cross section in Figure 1 as the orange shaded regions (Cut 1) and the blue shaded regions (Fill 1), respectively.
Removal Excavation is the volume of cutting required above and beyond the cut required to get to finished grade in order to remove undesirable soil. This volume will be defined as Cut 2 in an equation that follows. This quantity is obtained by taking off the project from proposed grades to the removal grades (Step 2, above).
Note: Removal Excavation is shown schematically in Figure 1 as the area beneath the Cut 1 and Fill 1 regions; that is, the region encompassed by the green line.
Removal Grades are elevations that were shot in the field at the bottom of the Removal Excavation. These have to be determined after the work starts, since the engineer must determine the extent of removal grades in the field, to ensure that all undesirable material has been removed.
Referring to Figure 1, Cut 2 is shown schematically as the region encompassed by the red line. Since Cut 2 is the cutting required to excavate from proposed grades to removal grades, Cut 2 includes cutting through Fill in the original takeoff. Referring to Figure 1, I used the following equation to determine the Removal Excavation Quantity:
Removal Excavation = Cut 2 - Fill 1
Figure 1

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