Quantity Surveys (Kavanagh)

Lump-Sum vs. Unit-Price Contracts

Lump-Sum: One price for all work (e.g., demolition) Unit-Price: Each item category bid separately (cut, fill, concrete, fence, etc.). Total = sum of (unit price × quantity). Most construction projects use unit-price. — Kavanagh Ch. 17, p. 552

Progress Payments

Payments based on quantities supplied by surveyor and inspector. Processed: • At end of time period (e.g., monthly), or • At completion of agreed project stages Owner usually holds back % until guarantee period expires. — Kavanagh Ch. 17, p. 552

Trapezoidal Rule Formula

Area = X × [(h₁ + hₙ)/2 + h₂ + h₃ + ... + hₙ₋₁] Where: • X = common interval • h = offset measurements Assumes straight lines between offset endpoints. — Kavanagh Ch. 17, p. 556

Simpson's One-Third Rule Formula

A = (1/3) × interval × (h₁ + hₙ + 2Σhₒdd + 4Σhₑᵥₑₙ) Requirements: • Odd number of offsets • Equal intervals Assumes parabolic curves—more precise than trapezoidal. — Kavanagh Ch. 17, Eq. 17.2, p. 557

Simpson's Rule: Handling Even Number of Offsets

If you have an even number of offsets: 1. Use Simpson's rule for the odd number portion 2. Use trapezoidal technique for the remaining area 3. Add the two results — Kavanagh Ch. 17, p. 558

Trapezoidal vs. Simpson's One-Third Rule

Trapezoidal: • Assumes straight lines between offsets • Works with any number of offsets • Less precise Simpson's: • Assumes parabolic curves • Requires odd number of offsets • More precise for irregular boundaries — Kavanagh Ch. 17, p. 557

Planimeter

Device for measuring areas on plans/maps. Components: • Graduated measuring drum • Tracing arm • Pole arm with anchor needle Trace boundary → drum measures proportional to area. Useful for end areas, watershed areas, construction quantities. — Kavanagh Ch. 17, p. 560

Shrinkage (Earthwork)

Occurs when excavated material is placed and compacted. 1 cu. yd excavated → less than 1 cu. yd after compaction. Typical range: 10-15% (up to 40% with organic material) Greatest for silts, clays, loams. — Kavanagh Ch. 17, p. 566

Swell (Earthwork)

Occurs when solid rock is blasted and placed. 1 cu. yd solid rock → more than 1 cu. yd shattered. Typical range: 15-20% Must account for in cut/fill balancing. — Kavanagh Ch. 17, p. 566

Cross Sections for Quantity Surveys

Ground elevations taken at RIGHT ANGLES to proposed route. Types: • Cut section: proposed below existing ground • Fill section: proposed above existing ground • Transition section: both cut and fill Used to compute end areas at each station. — Kavanagh Ch. 17, p. 568

End Area Computation Method

1. Choose datum elevation below lowest point 2. Compute area between ground and datum 3. Compute area between subgrade and datum 4. Subtract: End Area = Area 1 - Area 2 (For cut: ground area - subgrade area) (For fill: subgrade area - ground area) — Kavanagh Ch. 17, p. 570

Average End-Area Formula

V = [(A₁ + A₂)/2] × L Where: • A₁, A₂ = end areas at adjacent stations • L = distance between stations Divide by 27 for cubic yards. Metric: answer in cubic meters. — Kavanagh Ch. 17, Eq. 17.4, p. 568

Prismoidal Formula

V = L/6 × (A₁ + 4Aₘ + A₂) Where: • A₁, A₂ = end areas • Aₘ = middle area (from averaged DIMENSIONS, not averaged areas) • L = length More precise—use for expensive materials (concrete). — Kavanagh Ch. 17, Eq. 17.5, p. 573

CRITICAL: Aₘ in Prismoidal Formula

Aₘ is NOT the average of A₁ and A₂! Aₘ is calculated from dimensions that are averages of corresponding dimensions in A₁ and A₂. Common mistake: (A₁ + A₂)/2 ≠ Aₘ — Kavanagh Ch. 17, p. 573

Mass Diagram

Graphical representation of cumulative earthwork. Cuts = positive (+) Fills = negative (-) Plotted at each station below profile. Useful for: • Determining waste or borrow volumes • Haul (transportation) planning • Cut/fill balance analysis — Kavanagh Ch. 17, p. 566-567

Volume from Contour Areas

V = I × (C₁ + C₂) / 2 Where: • V = volume (cu. ft or m³) • C₁, C₂ = areas enclosed by adjacent contours • I = contour interval Useful for water storage and irregular stockpiles. — Kavanagh Ch. 17, Eq. 17.3, p. 567

Borrow Pit Volume Computation

Grid method: 1. Layout grid (e.g., 50-ft squares) 2. Determine depth at each grid corner 3. Volume per square = [(a+b+c+d)/4] × base area 4. Sum all grid volumes Partial grids computed as wedges or quarter-cones. — Kavanagh Ch. 17, p. 567

Final (As-Built) Surveys

Purpose: • Record what was actually built • Verify construction matches design • Document unexpected features found Timing: After construction completed As-built drawings archived on CD/DVD after guarantee period. — Kavanagh Ch. 17, p. 574

Common Quantity Survey Units

Linear: ft, m (curb, pipe, fence) Area: sq. ft, m², acres, ha (sod, clearing) Volume: cu. ft, m³, cu. yd (cut, fill, concrete) Weight: tons, tonnes (granular, asphalt, steel) 1 ton = 2,000 lb = 0.907 metric tonnes — Kavanagh Ch. 17, Table 17.1, p. 553

Unit Conversions

Cubic feet to cubic yards: ÷ 27 1 acre = 43,560 sq. ft 10 square chains = 1 acre 1 m³ = 35.31 cu. ft 1 cu. yd = 0.765 m³ — Kavanagh Ch. 17, p. 568