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newSchoolWorks.com › VoTechWorks › Building & Construction › Heavy Equipment Operation › Grade Reading for Heavy Equipment Operators › Lesson 2
BLD-HEAV08-07 · Lesson 2 · 12 clock hours · lab

Benchmark Elevation and Cut/Fill Math

Objective. Using a builder's level, rod, and field notes, students will calculate instrument height, rod readings, and cut or fill values at five designated points on a flat or gently sloping surface, with each result within 0.05 ft of the instructor's verified answer.

⚠ Pending professional review

This lesson, its worked examples and its practice questions has not yet been verified by a licensed professional engineer or master tradesperson or by a certification or approval body. It is a study draft and may contain errors. Do not use it as instructions for work on a job site or on live equipment. Always follow your instructor, your supervising professional, and current official references and regulations.

VoTechWorks program approval and accreditation are still in progress. Credentials are issued only by the certifying bodies named in each program, after their own exams.

Why Grade Reading Matters on the Job

Every cut you make with a dozer or grader and every fill you place with a scraper must match the engineer's plan grade. If your machine runs too high, concrete or asphalt crews have to make up the difference. If you go too low, you waste fill material and compact time. The builder's level and Philadelphia rod are the field tools that tell you, in feet and hundredths, exactly where the ground stands relative to where it needs to be.

The Builder's Level and How It Works

An automatic (self-leveling) builder's level contains a compensator that keeps the line of sight perfectly horizontal once the instrument is roughly leveled with its leveling screws. Set the tripod on firm ground, attach the level, center the circular bubble, and the instrument does the fine leveling automatically. Never leave a level on an active job pad where equipment is running — a vibration or strike can damage the compensator. Set up at a safe distance from machine travel lanes, and always use the lens cap when not reading.

Key Concepts: Benchmark, HI, Backsight, and Foresight

Benchmark (BM): A point of known elevation, often marked with a brass disk or a survey nail in concrete. All your calculations start here.

Backsight (BS): The first rod reading you take — always on the benchmark or a turning point of known elevation. Adding the backsight to the benchmark elevation gives you the Height of Instrument (HI).

> HI = Benchmark Elevation + Backsight Reading

Height of Instrument (HI): The elevation of the line of sight through the level. This number stays constant for every reading taken from that instrument setup.

Foresight (FS): A rod reading taken at any point whose elevation you want to find. Subtracting the foresight from the HI gives you the ground elevation at that point.

> Ground Elevation = HI − Foresight Reading

Cut and Fill

Once you know the existing ground elevation at a stake, compare it to the plan grade elevation shown on the data sheet.

> Cut = Existing Elevation − Plan Grade Elevation

> Fill = Plan Grade Elevation − Existing Elevation

Note that plan grade is often the top of subbase or subgrade, not the finished surface. If the data sheet specifies a subgrade depth (for example, 0.50 ft below plan grade for gravel base), subtract that depth from the plan grade before calculating cut or fill.

Shrink and Swell Factors

Soil changes volume when it is disturbed. Shrinkage means compacted fill occupies less volume than the loose material you hauled. Swell means excavated material expands when loosened. Your instructor will supply the specific factors for today's exercise. The general rule is:

Always use the factors given on the problem sheet — never guess soil behavior on a real job.

Setting Up Field Notes

A standard differential-leveling field-notes form has columns for: Station, Backsight (BS), HI, Foresight (FS), Elevation, Plan Grade, and Cut/Fill. Fill every column before moving to the next station. Incomplete notes are useless notes — and on a real project, they can lead to costly grade errors.

Label the benchmark at the top of the page with its known elevation. After your last foresight, check your arithmetic: the last elevation should close back to within an acceptable tolerance of the starting benchmark if you run a loop.

Safety Points for This Lab

1. PPE: Hard hat, safety glasses, and steel-toed boots are required on the pad at all times.

2. Striking stakes: Wear gloves when swinging the sledgehammer. Check that no one is within the swing arc before striking.

3. Equipment traffic: The outdoor pad may be used by other classes. Stay in your designated work zone and maintain awareness of any moving machinery. If a machine approaches, stop work and step back until it clears.

4. Carrying the rod: Carry the Philadelphia rod horizontally, below shoulder height, to avoid striking overhead utilities or other people. Call out "rod coming through" when moving in a group.

5. Tripod stability: Firmly press tripod legs into the ground. A tipping level can be damaged beyond repair and can injure bystanders.

Closing the Loop and Checking Your Work

After you read all five stakes, return your rod to the benchmark and take a final backsight. If your computed elevation of the benchmark from this check reading differs from the known elevation by more than the acceptable closure tolerance for the exercise, re-run your notes to find the error. A systematic error (same direction every time) usually means a rod-reading mistake or a math error in HI. A random error often means the rod was not held plumb — use a rod level or gently rock the rod and take the lowest reading, which corresponds to the plumb position.

Key terms10

Benchmark (BM)A fixed point of known elevation from which all leveling measurements in a survey loop begin and end.
Backsight (BS)The rod reading taken on a point of known elevation; added to that elevation to establish the Height of Instrument.
Height of Instrument (HI)The elevation of the level's line of sight, calculated as benchmark elevation plus backsight reading.
Foresight (FS)A rod reading taken at an unknown point; subtracted from HI to find the ground elevation at that point.
CutA condition where existing ground elevation is higher than plan grade, requiring removal of material.
FillA condition where existing ground elevation is lower than plan grade, requiring addition of material.
Shrink FactorA decimal value expressing how much fill material compresses during compaction, used to calculate the extra bank volume needed.
Plan GradeThe target elevation specified on construction drawings for the finished or subgrade surface at a given station.
Philadelphia RodA graduated surveying rod read through the level's telescope to measure the vertical distance from the ground to the instrument's line of sight.
Closure ToleranceThe maximum allowable difference between the known benchmark elevation and the elevation calculated after completing a leveling loop.

Worked examples4

1. The benchmark elevation is 100.00 ft. You set up the builder's level and read a backsight of 4.82 ft on the benchmark rod. Then you read a foresight of 3.16 ft at Station 1. What is the HI and the elevation at Station 1?
  1. Step 1 — Calculate HI: HI = BM elevation + BS = 100.00 + 4.82 = 104.82 ft
  2. Step 2 — Calculate Station 1 elevation: Elevation = HI − FS = 104.82 − 3.16 = 101.66 ft
Answer: HI = 104.82 ft; Station 1 elevation = 101.66 ft
2. Using the setup from Example 1 (HI = 104.82 ft), the plan grade at Station 1 is 102.40 ft, and the subgrade depth is 0.50 ft below plan grade. The foresight at Station 1 was 3.16 ft (existing elevation 101.66 ft). Is this a cut or fill, and by how much?
  1. Step 1 — Find the subgrade target elevation: Subgrade elevation = Plan grade − subgrade depth = 102.40 − 0.50 = 101.90 ft
  2. Step 2 — Compare existing ground to subgrade target: Existing elevation (101.66 ft) is lower than subgrade target (101.90 ft), so this is a FILL condition.
  3. Step 3 — Calculate fill amount: Fill = Subgrade target − Existing elevation = 101.90 − 101.66 = 0.24 ft
Answer: Fill of 0.24 ft is needed at Station 1.
3. At Station 3, the existing elevation is 103.55 ft and the plan grade is 102.80 ft (no subgrade depth adjustment). A shrink factor of 0.15 applies if fill is needed. Determine cut or fill, the gross amount, and — if fill — the bank volume required per square foot of area.
  1. Step 1 — Compare elevations: Existing (103.55 ft) is higher than plan grade (102.80 ft), so this is a CUT condition.
  2. Step 2 — Calculate cut: Cut = Existing − Plan grade = 103.55 − 102.80 = 0.75 ft
  3. Step 3 — No shrink factor applies to a cut (shrink applies to fill placement). The answer is a cut of 0.75 ft. The shrink factor is not used here.
Answer: Cut of 0.75 ft at Station 3; shrink factor does not apply to a cut.
4. A fill section requires 0.60 ft of compacted fill over a 1 sq ft area (bank volume = 0.60 cubic feet of compacted material needed). The shrink factor is 0.20, meaning compacted fill shrinks 20% from its loose/bank state. How many cubic feet of bank material must be hauled to achieve 0.60 cu ft of compacted fill?
  1. Step 1 — Understand the shrink factor: If material shrinks 20%, then 1.00 cu ft of bank material yields only 0.80 cu ft of compacted fill (1.00 − 0.20 = 0.80).
  2. Step 2 — Set up the equation: Bank volume × (1 − shrink factor) = Compacted volume needed, so Bank volume = Compacted volume ÷ (1 − shrink factor).
  3. Step 3 — Solve: Bank volume = 0.60 ÷ (1 − 0.20) = 0.60 ÷ 0.80 = 0.75 cu ft
Answer: 0.75 cubic feet of bank material must be hauled to produce 0.60 cu ft of compacted fill.

The math in this lesson2

Learners compute HI as benchmark plus backsight and station elevation as HI minus foresight.
7.NS.17.RP.3
Brush up in the math halls at newSchoolWorks.com:
In class: Instructor demonstrates the differential-leveling loop on the classroom's outdoor pad: setting up the level, reading the backsight on a known benchmark, recording instrument height (HI), reading foresights, and entering data in a standard level-notes form; students repeat the setup in pairs and record their own readings. · Students complete a series of ten paper-based cut/fill calculation problems drawn from plan profiles—given existing ground elevation, finished grade elevation, and subgrade depth, they calculate net cut or fill and apply a shrink or swell factor using instructor-supplied values—then check answers against a key. · Field exercise: instructor drives five stakes in the ground at known elevations; students use the level and rod to determine each stake's elevation and then calculate whether the stake represents a cut or fill relative to a plan grade provided on a data sheet, recording findings on a standard field-notes form.
Materials: Automatic builder's level with tripod, Philadelphia rod (or equivalent), field-note book, calculator, printed benchmark and plan-grade data sheets, five survey stakes, sledgehammer, tape measure, NCCER Heavy Equipment Level 2 module on Grade Setting
Check: All five field points within 0.05 ft of instructor's verified elevations; paper calculation worksheet scored 80% or higher; field-notes form complete with backsight, HI, foresight, and cut/fill columns filled correctly.

Practice check8

Answer each question, then check it. Nothing is recorded; this is your own practice.

NCCER Heavy Equipment — Grade Setting / Leveling Math
1. The benchmark elevation is 98.50 ft. The backsight rod reading on the benchmark is 5.10 ft. What is the Height of Instrument (HI)?
NCCER Heavy Equipment — Grade Setting / Leveling Math
2. With an HI of 103.60 ft, you read a foresight of 4.75 ft at Station 2. What is the ground elevation at Station 2?
NCCER Heavy Equipment — Grade Setting / Cut-Fill Calculation
3. The existing ground elevation at a stake is 101.20 ft. The plan grade is 102.00 ft. Which statement is correct?
NCCER Heavy Equipment — Earthwork Volume and Material Factors
4. A section requires 1.00 cu ft of compacted fill. The shrink factor is 0.25. How many cubic feet of bank material are needed?
NCCER Heavy Equipment — Instrument Operation and Error Control
5. Why is the rod held as plumb (vertical) as possible when taking a reading?
OSHA 10 — Personal Protective Equipment / Construction Safety
6. Which PPE combination is required during the stake-driving portion of this lab?
NCCER Heavy Equipment — Grade Setting / Quality Control
7. A leveling loop returns to the benchmark and the computed closing elevation is 100.08 ft. The known benchmark elevation is 100.00 ft. The acceptable closure tolerance for this exercise is 0.05 ft. What should the student do?
NCCER Heavy Equipment — Grade Setting / Cut-Fill Calculation
8. The plan grade at a station is 101.50 ft and the subgrade depth is 0.42 ft below plan grade. The existing ground elevation is 101.75 ft. What is the cut or fill required to reach subgrade?
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