Cut & Fill Earthwork
Safety & Types of Excavation
Before calculating a single cubic yard, understand the safety context and what kind of earthwork you’re dealing with.
Hazard Elimination
Identify and eliminate or control all hazards before work begins. Use pre-task planning, job hazard analyses, and daily safety briefings.
Work Methods
Use safe work methods — no shortcuts. Establish exclusion zones around machines, enforce spotter requirements, and use signal persons for backing operations.
Site Conditions
Maintain stable haul roads, adequate lighting, clear sight lines, dust control, and signage. Manage weather impacts on slope stability and footing.
Machine Hazard Zones
Keep workers clear of swing arcs, dump zones, and haul roads. Large trucks, cranes, and compactors create lethal hazard zones that must be enforced.
- Large volume of soil removed over a wide area
- Primary challenge: moving material efficiently
- Examples: highway cuts, dam foundations, site grading
- Equipment: off-highway trucks, scrapers, dozers
- Volume calculation: cross-section method → mass diagram
- Confined area — digging down for foundations
- Primary challenge: workspace constraints, wall stability
- Examples: building basements, bridge piers, utility vaults
- Walls often need shoring, soldier piles, or tiebacks
- Volume: grid method (not cross-section)
Reading Project Plans
Three view types appear on every set of construction contract documents. You must be able to read all three before estimating earthwork quantities.
Plan View (Fig. 3.2)
- Bird’s-eye overhead view
- Horizontal alignment: roads, curves, drainage
- Stationing along the centerline
- Road width, ditches, cut/fill slopes
- Curve geometry: Δ (delta angle), R (radius), T (tangent length), L (arc length)
Profile View (Fig. 3.3)
- Vertical cut along the centerline
- X-axis = stations, Y-axis = elevation
- Dashed line = existing ground surface
- Solid line = proposed final grade line
- BVC = Begin Vertical Curve
- EVC = End Vertical Curve
- PVI = Point of Vertical Intersection (grade change)
- Grade % shown for each tangent segment
Cross-Section View (Figs. 3.4–3.6)
- Vertical cut ⊥ (perpendicular) to centerline
- Shows shape of earthwork at one station
- Fill section: grade above existing ground
- Cut section: grade below existing ground
- Sidehill: one side cut, other side fill
- Taken every 100 ft (uniform terrain)
- Every 25 ft (tight curves, rapid elevation change)
| Type | What It Looks Like | Earthwork Condition | Common Location |
|---|---|---|---|
| Full Fill | Grade line entirely above existing ground; wide flat top, sloped sides rising from ground | All fill — bring material in and compact | Low ground, valley approaches, flat areas |
| Full Cut | Grade line entirely below existing ground; inverted trapezoid carved into hillside | All cut — remove and haul material away | Hills, ridges, elevated terrain |
| Sidehill | Grade line intersects existing ground at centerline; cut on high side, fill on low side | Both cut AND fill in same section | Hillsides where road cuts into slope on one side |
Core Concepts
The foundational ideas you must understand before any calculation. Get these wrong and everything downstream is wrong.
Natural, undisturbed “in situ” state. The reference unit for all mass diagram calculations. Measured in the cut. Volume is smallest of the three states.
After placement and compaction in a fill. Denser than bank — takes LESS volume. Fill cross-sections are measured in CCY, then converted to BCY for the mass diagram.
Excavated and loaded into a truck. Swells due to voids. Takes MORE volume than bank. Used for truck payload and fleet calculations only — NOT used in the mass diagram.
| Material | Swell Factor (LCY/BCY) | Shrinkage Factor (BCY/CCY) | Compaction Factor (CCY/BCY) | Notes |
|---|---|---|---|---|
| Common Earth | 1.25 | 1.11 (÷0.90) | 0.90 | Most roadway work; standard assumption |
| Sand & Gravel | 1.10–1.15 | 1.05–1.15 | 0.87–0.95 | Varies by gradation and moisture |
| Clay | 1.30–1.40 | 1.15–1.35 | 0.74–0.87 | High swell; difficult to compact uniformly |
| Rock (blasted) | 1.40–1.60 | 0.77–0.91 | 1.10–1.30 | Rock compacts to LESS than bank; shrinkage <1.0 |
Organic topsoil — unsuitable for structural fill
Upper layer of organic material from decomposed vegetation. Cannot be used as structural fill because it is too compressible. Must be removed first.
Fill height determines requirement
Embankment <5 ft high: ALL organic material under the fill footprint must be stripped. Embankment >5 ft: may be acceptable to leave if only a few inches thick.
Subtract from usable cut
Stripping volume is SUBTRACTED from gross cut BCY (Col 8 = Col 4 − Col 6). This reduces the usable material — stripping is wasted or stockpiled, not used as fill.
Add to fill requirement
Stripping volume is ADDED to fill CCY (Col 9 = Col 5 + Col 7). The stripped layer must be replaced with structural fill material, so more fill is needed.
Running algebraic sum at each station
The Y-value on the mass diagram. Positive = net surplus cut. Negative = net fill deficit. Computed cumulatively from station 0+00 to project end.
Horizontal line on the mass diagram
Where it intersects the mass curve twice, cut between those points exactly supplies the fill needed. The line length = maximum haul distance. The Q value = quantity hauled.
Excess cut — haul off-site
When cut exceeds fill in a zone, surplus material is wasted (disposed off-site). The contractor must price disposal distance, tipping fees, and truck cycle time.
Fill deficit — import from pit
When fill needed exceeds available cut, material must be borrowed from an off-site pit. Price includes excavation, loading, hauling, and compaction from the borrow source.
Unit of haul work (sta.-yd)
Moving 1 CY through 1 station (100 ft) = 1 station-yard. Area enclosed by balance line and mass curve = station-yards. Used to calculate overhaul cost.
Extra pay for long hauls
When haul distance exceeds the free haul limit (typically 500–1,000 ft), the contractor is paid for the excess. Cost = overhaul volume × excess distance × unit price per sta.-yd.
All Formulas
Every formula from the textbook chapter, with variable definitions and worked mini-examples. Memorize [3.4] first — it drives everything else.
[3.1] Area of a Triangle
Use when a cross-section or portion of a cross-section is triangular in shape.
[3.2] Area of a Trapezoid
Example: A trapezoidal cut section 3 ft deep at left edge, 5 ft deep at right edge, 24 ft wide:
A = ((3+5)/2) × 24 = 4 × 24 = 96 sf
[3.3] General Trapezoidal Area (Multiple Strips)
Used when a cross-section is divided into multiple equal-width strips. Precision: ±0.5%
Also used to compute area under the mass diagram curve (for average haul calculation).
[3.4] Average-End-Area Volume — THE PRIMARY FORMULA
A₁, A₂ = End-area cross-sections at each station (square feet)
L = Distance between the two stations (feet) — typically 50 ft or 100 ft
÷ 27 = Converts cubic feet to cubic yards (1 yd³ = 27 ft³)
Precision: ±1.0% | Slightly overestimates actual volume (conservative for estimating)
Worked Example: Two cut sections 100 ft apart: A₁ = 250 sf, A₂ = 410 sf
V = ((250+410)/2) × (100/27) = 330 × 3.704 = 1,222 BCY
Fill: CCY → BCY (Adjusted Fill)
= Fill (CCY) × Shrinkage Factor (1.11)
Example: 500 CCY ÷ 0.90 = 556 BCY | Or: 500 × 1.11 = 556 BCY (same result)
Average Haul Distance (from Mass Diagram)
Result in stations — multiply by 100 to convert to feet.
Q = the vertical height of the balance line (the quantity of material hauled) in BCY.
[3.5] Average Grade Percent
Negative grade = downhill loaded haul → favorable (gravity assists)
Positive grade = uphill loaded haul → unfavorable (reduces equipment production)
This grade feeds directly into equipment production calculations (grade resistance adjustments).
Mass Ordinate (Running Sum)
Positive → surplus cut to that point | Negative → fill deficit to that point
Earthwork Volume Sheet
The volume sheet is the engine of earthwork estimating. Every column feeds the next. Master the column logic and you can build this in any spreadsheet.
| Col | Name | Unit | How It’s Calculated | Notes |
|---|---|---|---|---|
| (1) | Station | — | Survey stations from field measurements | Typically 50 or 100 ft intervals; 25 ft on tight curves |
| (2) | End-Area Cut | sf | Cross-section area of cut at this station (from plans or field survey) | 0 if no cut. Use [3.1]–[3.3] for manual calc |
| (3) | End-Area Fill | sf | Cross-section area of fill at this station | Both 2 & 3 can be non-zero on sidehill sections |
| (4) | Volume of Cut | BCY | Formula [3.4]: ((Col2_prev + Col2_curr)/2) × L/27 | Between this station and the previous one |
| (5) | Volume of Fill | CCY | Formula [3.4] applied to fill areas (Col 3) | Fill is in CCY — must convert before mass diagram |
| (6) | Stripping Cut | BCY | Formula [3.4] applied to strip areas in cut sections | Topsoil volume removed from cut; cannot be used as fill |
| (7) | Stripping Fill | CCY | Formula [3.4] applied to strip areas in fill sections | Organic material under fill footprint that must be replaced |
| (8) | Total Cut | BCY | Col 4 − Col 6 | Usable cut after subtracting stripping |
| (9) | Total Fill | CCY | Col 5 + Col 7 | Total fill needed including stripped area replacement |
| (10) | Adjusted Fill | BCY | Col 9 ÷ 0.90 (or × 1.11 for common earth) | Converts CCY fill to BCY — required for mass diagram |
| (11) | Algebraic Sum | BCY | Col 8 − Col 10 | Positive = net cut surplus. Negative = fill deficit. |
| (12) | Mass Ordinate | BCY | Running cumulative total of Col 11 from station 0+00 | This column is plotted to create the mass diagram |
| Sta (1) | EA Cut sf (2) | EA Fill sf (3) | Vol Cut bcy (4) | Vol Fill ccy (5) | Strip Cut bcy (6) | Strip Fill ccy (7) | Tot Cut bcy (8) | Tot Fill ccy (9) | Adj Fill bcy (10) | Alg Sum bcy (11) | Mass Ord bcy (12) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 0+00 | 0 | 0 | — | — | — | — | — | — | — | — | 0 |
| 0+50 | 0 | 115 | 0 | 106 | 0 | 18 | 0 | 124 | 138 | −138 | −138 |
| 1+00 | 0 | 112 | 0 | 210 | 0 | 30 | 0 | 240 | 267 | −267 | −405 |
| 2+00 | 0 | 54 | 0 | 307 | 0 | 44 | 0 | 351 | 390 | −390 | −796 |
| 2+50 | 64 | 30 | 59 | 78 | 0 | 22 | 59 | 100 | 111 | −52 | −847 |
| 3+00 | 120 | 0 | 170 | 28 | 26 | 0 | 144 | 28 | 31 | +114 | −734 |
| 4+00 | 160 | 0 | 519 | 0 | 76 | 0 | 443 | 0 | 0 | +443 | −291 |
| 5+00 | 317 | 0 | 883 | 0 | 74 | 0 | 809 | 0 | 0 | +809 | +518 |
| 6+00 | 51 | 0 | 681 | 0 | 60 | 0 | 621 | 0 | 0 | +621 | +1,140 |
| 6+50 | 46 | 6 | 90 | 6 | 21 | 0 | 69 | 6 | 6 | +63 | +1,202 ← TP |
| 7+00 | 0 | 125 | 43 | 121 | 25 | 0 | 18 | 146 | 163 | −120 | +1,082 |
| 8+00 | 0 | 186 | 0 | 576 | 0 | 81 | 0 | 657 | 730 | −730 | +352 |
| 8+50 | 0 | 332 | 0 | 480 | 0 | 69 | 0 | 549 | 610 | −610 | −257 |
Mass Diagram
The most powerful tool in earthwork planning. Plot Column 12 vs stations, draw balance lines, and instantly see quantities, directions, and haul distances.
Mass Diagram — Table 3.1 Example Data
Rising curve = cutting
When the mass ordinate increases station-to-station, the project is generating surplus cut material. Steeper rise = larger cut volume per station interval.
Falling curve = filling
When the mass ordinate decreases, fill is consuming material. Steeper fall = larger fill volume being placed per station interval.
Turning point = cut/fill transition
The peak or valley where the curve reverses corresponds exactly to the station where existing ground crosses the grade line on the profile view.
Balance line = one complete haul
A horizontal line intersecting the curve at two points defines a zone where cut equals fill. The line’s horizontal length = maximum haul distance for that zone.
Direction of haul
Curve ABOVE balance line → haul left to right (up-station). Curve BELOW balance line → haul right to left (down-station). This determines which way trucks travel loaded.
Area = station-yards (haul work)
Area enclosed between mass curve and balance line = volume × distance = station-yards of work. This is used to compute overhaul cost.
| Mass Curve Behavior | What It Means | Required Action |
|---|---|---|
| Curve ends above start level | Net surplus cut — more cut than fill | Waste excess material off-site. Price disposal. |
| Curve ends below start level | Net fill deficit — more fill than cut | Import borrow from pit. Price delivery and compaction. |
| Curve returns exactly to start level | Perfectly balanced — rare | No waste or borrow. Haul only. |
| Short horizontal balance line (≤300 ft) | Short haul zone | Use dozers. Most economical for this distance. |
| Medium balance line (300–5,000 ft) | Scraper range haul | Push-loaded scrapers. Plan pusher dozer. |
| Long balance line (≥5,000 ft) | Long haul zone | Excavator + truck fleet. Higher cost per CY but necessary. |
| Haul Distance | Equipment Type | How to Use the Mass Diagram |
|---|---|---|
| 0 – 300 ft | Bulldozer (pushing) | Draw dozer balance line at ~300 ft length. Volume between line and curve = dozer yardage. |
| 300 – 5,000 ft | Scraper (push-loaded) | Draw scraper balance line within this range. Scraper yardage = Q at that balance line. |
| 5,000 ft + | Excavator + Trucks | Longer balance line or off-site haul. Cycle time and truck fleet drive production. |
| Off-site | Highway trucks (waste/borrow) | Material that falls outside the project’s haul balance — must be wasted or borrowed. |
Structural Excavation
Confined pit excavation for foundations, basements, and below-grade structures. Different rules, different quantities method, different safety concerns.
Soldier Piles & Lagging (Fig. 3.16–3.17)
Vertical steel H-piles driven into ground at regular intervals. As excavation proceeds, horizontal timber lagging boards are placed between the piles to retain the soil face. Common in urban environments.
Sheet Piling
Interlocking steel sheets driven in a continuous wall before excavation begins. Provides a watertight barrier. The entire perimeter wall is driven first, then excavation proceeds inside.
Soil Nailing (Fig. 3.18)
Steel bars drilled and grouted horizontally into the existing soil at regular vertical intervals. Reinforces the face of the cut wall in place. No driven elements — drilled through the existing face.
Rakers / Struts (Fig. 3.19)
Diagonal braces installed from the wall face to the excavation floor. Resist lateral earth pressure pushing the wall inward. Major disadvantage: they obstruct the excavation floor, complicating work.
Tieback Systems
Horizontal anchors drilled through the wall into the soil or rock behind it, then grouted. Far superior to rakers — they keep the floor clear. Tiebacks and the wall often remain permanently in place.
Slurry Walls
For high water tables. Trench excavated under bentonite slurry (fluid pressure keeps trench open), then filled with reinforced concrete. Excavation proceeds inside the finished wall. Very expensive but watertight.
Works from perimeter
If the site perimeter has access, a long-reach excavator can dig and swing material up and over the pit walls to trucks waiting at grade. Best for relatively shallow excavations.
Trucks drive into pit
A temporary earthen ramp is left in one corner of the excavation. Excavators load trucks at the bottom; trucks drive up the ramp to dump at grade. The ramp is the last thing removed.
Pass material up a chain
Multiple excavators positioned on benches pass bucket loads up from the bottom. Used to remove the final ramp and in very deep pits. Labor intensive but sometimes the only option.
Control the groundwater
Sumps (gravel-lined collection pits) collect groundwater that seeps into the excavation. Pumps continuously remove water to keep the floor dry and workable. Investigate water table depth before design.
Pricing & Equipment Spreads
How earthwork quantities become a bid price. The mass diagram tells you what to move; production calculations tell you how many machines, how long it takes, and what it costs.
| Quantity Source | Native Unit | Convert To | Conversion |
|---|---|---|---|
| Mass diagram / volume sheet | BCY | BCY | Reference unit — no conversion needed |
| Truck payload (rated) | LCY | BCY | Payload (LCY) × Load Factor = BCY per load |
| Compactor production (spec) | CCY | BCY | CCY ÷ 0.90 = BCY produced |
| Borrow pit material | BCY | BCY | Same unit — direct addition |
| Bid item in contract | As specified | Match | Owner’s preferred units define the bid |
Use the mass diagram
Draw balance lines for each equipment type. Each zone between intersection points = one haul scenario with its own quantity (Q) and average haul distance.
Load + haul + dump + return
Cycle time = fixed time (load + spot + dump) + variable time (haul distance ÷ speed × 2). Variable time changes with average haul distance from the mass diagram.
Match loader production rate
Fleet size = Loader production (BCY/hr) ÷ Truck production per truck (BCY/hr). Round up to whole trucks. Then check: does the fleet exceed spec density requirements?
Time per zone
Duration = Zone volume (BCY) ÷ Spread production rate (BCY/day). Sum all zones for total project duration. This feeds the schedule.
Equipment hours × rates
Cost = (Equipment cost/hr × hours) + Fuel + Operator wages. Divide by BCY moved to get unit cost. Compare to historical data for sanity check.
Cost + markup
Total cost = unit cost × quantity. Add overhead and profit markup. This becomes your bid line item. Include waste disposal and borrow costs as separate line items.
Calculator
Compute end-area volumes, apply stripping and shrinkage, and get net BCY contribution to the mass ordinate — all in one step.
End-Area Volume
Stripping (Optional)
Conversion Factors
Results
Glossary of Key Terms
Every important term from the chapter, defined clearly. If you’re new, read this first.
Self-Check Questions
Ten questions covering every major concept. Try to answer each one before revealing the answer. This mirrors the type of problems found on exams and in the field.
Flashcards
Click any card to flip. 24 cards covering every concept, formula, and common exam question from both the textbook and study guide.
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