Formula Sheet: Construction Methods

Earthwork and Grading

Volume Calculations

Average End Area Method: \[V = \frac{A_1 + A_2}{2} \times L\]

• V = volume (ft³ or m³)
• A₁ = area of first cross-section (ft² or m²)
• A₂ = area of second cross-section (ft² or m²)
• L = distance between sections (ft or m)
• Note: Most accurate when end areas are similar in size and shape

Prismoidal Formula: \[V = \frac{L}{6}(A_1 + 4A_m + A_2)\]

• V = volume (ft³ or m³)
• L = distance between end sections (ft or m)
• A₁ = area of first end section (ft² or m²)
• A_m = area of middle section (ft² or m²)
• A₂ = area of second end section (ft² or m²)
• Note: More accurate than average end area method, especially for transitional sections

Prismoidal Correction: \[C_p = \frac{L}{12}(C_1 - C_2)(D_1 - D_2)\]

• C_p = prismoidal correction (ft³ or m³)
• L = distance between sections (ft or m)
• C₁, C₂ = center heights at sections 1 and 2 (ft or m)
• D₁, D₂ = widths at sections 1 and 2 (ft or m)
• Subtract from average end area volume to get prismoidal volume

Cut and Fill Volumes

Borrow Pit Method (Grid Method): \[V = \frac{A}{4}(h_1 + h_2 + h_3 + h_4)\]

• V = volume for one grid cell (ft³ or m³)
• A = area of grid cell (ft² or m²)
• h₁, h₂, h₃, h₄ = depth at four corners (ft or m)
• Total volume = sum of all grid cells, accounting for shared corners

Corner Usage in Grid Method:

• Corner used by 1 square: multiply height by 1
• Corner used by 2 squares: multiply height by 2
• Corner used by 3 squares: multiply height by 3
• Corner used by 4 squares: multiply height by 4

\[V_{total} = \frac{A}{4}(\Sigma h_1 + 2\Sigma h_2 + 3\Sigma h_3 + 4\Sigma h_4)\]

Volume Conversions and Adjustments

Bank, Loose, and Compacted Volumes: \[V_L = V_B \times L\] \[V_C = V_B \times C\]

• V_B = bank (in-place) volume
• V_L = loose volume
• V_C = compacted volume
• L = load factor (swell factor) > 1
• C = compaction factor <>

Shrinkage: \[S = \frac{V_B - V_C}{V_B} \times 100\%\]

• S = shrinkage percentage
• V_B = bank volume
• V_C = compacted volume

Swell: \[Swell = \frac{V_L - V_B}{V_B} \times 100\%\]

• V_L = loose volume
• V_B = bank volume

Load Factor (Swell Factor): \[L = \frac{100 + \% \text{ Swell}}{100}\] Shrinkage Factor: \[S_f = \frac{100 - \% \text{ Shrinkage}}{100}\]

Mass Diagram

Properties of Mass Diagram:

• Ordinate = cumulative volume (algebraic sum of cuts and fills)
• Ascending line = cut section
• Descending line = fill section
• Peak = end of cut; beginning of fill
• Valley = end of fill; beginning of cut
• Horizontal line intersecting curve = balanced cut and fill (haul)
• Vertical distance between balance line and curve = volume being hauled

Concrete Operations

Concrete Mix Proportions

Yield: \[Y = \frac{W_c + W_w + W_{fa} + W_{ca}}{W_c/S_{Gc} + W_w + W_{fa}/S_{Gfa} + W_{ca}/S_{Gca}}\]

• Y = yield (ft³ or m³)
• W = weight of each component (lb or kg)
• S_G = specific gravity of each component
• Subscripts: c = cement, w = water, fa = fine aggregate, ca = coarse aggregate

Absolute Volume Method: \[V_{total} = V_c + V_w + V_{fa} + V_{ca} + V_a\]

• V_total = 1 unit volume (typically 1 yd³ or 1 m³)
• V_a = volume of entrained air
• Each component volume = Weight / (Specific Gravity × Unit Weight of Water)

Water-Cement Ratio: \[w/c = \frac{W_w}{W_c}\]

• w/c = water-cement ratio by weight
• W_w = weight of water (lb or kg)
• W_c = weight of cement (lb or kg)

Concrete Placement

Concrete Volume for Forms: \[V = A \times h\]

• V = volume (ft³ or yd³)
• A = plan area (ft²)
• h = thickness or height (ft)
• Convert ft³ to yd³: divide by 27

Concrete Placement Rate: \[R = \frac{V}{t}\]

• R = placement rate (yd³/hr or m³/hr)
• V = volume placed (yd³ or m³)
• t = time (hours)

Number of Truck Loads: \[N = \frac{V_{total}}{V_{truck}}\]

• N = number of loads (round up)
• V_total = total volume required (yd³ or m³)
• V_truck = capacity per truck (yd³ or m³)

Formwork Pressure

Lateral Pressure on Formwork (ACI 347): For walls with rate of placement R ≤ 7 ft/hr: \[P = 150 + 9000R/T\] For walls with rate of placement R > 7 ft/hr: \[P = 150 + 43,400/T + 2800R/T\] Maximum Pressure: \[P_{max} = 150h \text{ or } 2000 \text{ psf (whichever is less)}\]

• P = lateral pressure (lb/ft² or psf)
• R = rate of placement (ft/hr)
• T = temperature of concrete (°F)
• h = height of concrete (ft)
• Note: For columns and walls; limited to maximum values

Simplified Pressure for Columns: \[P = C_w C_c \gamma_c h\]

• P = lateral pressure (psf)
• C_w = coefficient for unit weight of concrete
• C_c = coefficient for column dimension
• γ_c = unit weight of concrete (pcf)
• h = height of fresh concrete (ft)
• Maximum = 150 pcf × height or 3000 psf, whichever is less

Equipment Productivity and Operations

Basic Productivity

Theoretical Productivity: \[Q = \frac{q \times N}{C_T}\]

• Q = production rate (units/hr)
• q = capacity per cycle (units)
• N = number of cycles per hour
• C_T = cycle time (min)

Actual Productivity: \[P_{actual} = P_{theoretical} \times E \times J\]

• P_actual = actual production
• E = efficiency factor (typically 0.75-0.90)
• J = job condition factor (0.80-1.00)

Cycle Time: \[C_T = T_L + T_H + T_D + T_R + T_M\]

• C_T = total cycle time (min)
• T_L = load time (min)
• T_H = haul time (min)
• T_D = dump/unload time (min)
• T_R = return time (min)
• T_M = maneuvering time (min)

Excavation Equipment

Bucket/Scraper Production: \[P = \frac{q \times 60 \times E}{C_T}\]

• P = production (yd³/hr bank measure or BCY/hr)
• q = heaped bucket capacity (yd³)
• E = efficiency factor (decimal)
• C_T = cycle time (min)
• 60 = minutes per hour conversion

Bucket Fill Factor: \[V_{actual} = V_{rated} \times F\]

• V_actual = actual bucket volume
• V_rated = rated heaped capacity
• F = bucket fill factor (0.60-1.00)
• Varies with material: sand = 0.95-1.00; hard clay = 0.80-0.90; rock = 0.60-0.75

Dozer Production (Slot Dozing): \[P = \frac{q \times 60 \times E \times L}{C_T \times S}\]

• P = production (BCY/hr)
• q = blade capacity (LCY)
• E = efficiency factor
• L = load factor (conversion from loose to bank)
• C_T = cycle time (min)
• S = shrinkage factor if needed

Hauling Equipment

Truck/Hauler Production: \[P = \frac{C \times 60 \times E}{C_T} \times \frac{1}{L}\]

• P = production (BCY/hr)
• C = truck capacity (LCY)
• E = efficiency factor
• C_T = total cycle time (min)
• L = load factor (loose to bank conversion)

Haul Time: \[T_H = \frac{D \times 60}{V}\]

• T_H = haul time (min)
• D = haul distance (miles or km)
• V = average haul speed (mph or km/hr)
• 60 = conversion factor (minutes per hour)

Number of Trucks Required: \[N = \frac{C_{T,truck}}{C_{T,loader}}\]

• N = number of trucks (round up for integer)
• C_T,truck = truck cycle time (min)
• C_T,loader = loader cycle time (min)
• Ensures continuous loading operation

Fleet Matching: \[P_{hauler} = P_{loader}\] \[N \times \frac{C_{hauler}}{C_{T,hauler}} = \frac{C_{loader}}{C_{T,loader}}\]

• Balance production rates between loading and hauling equipment

Grading and Compaction

Compaction Production: \[P = \frac{W \times S \times L \times E \times N}{12}\]

• P = production (yd²/hr per inch of compacted thickness)
• W = compacted width per pass (ft)
• S = compactor speed (ft/min)
• L = lift thickness (in)
• E = efficiency factor
• N = number of passes required
• 12 = conversion factor

Roller Passes Required: \[N = \frac{\text{Specified Density}}{\text{Density per Pass}}\]

• N = number of passes
• Typically 4-6 passes for adequate compaction

Compaction Volume Production: \[V = \frac{W \times S \times L \times E}{27 \times N}\]

• V = volume production rate (yd³/hr)
• W = width (ft)
• S = speed (ft/min)
• L = lift thickness (ft)
• E = efficiency
• N = number of passes
• 27 = ft³/yd³ conversion

Dewatering and Drainage

Flow to Trenches and Excavations

Steady-State Flow to Trench (Dupuit): \[q = \frac{k(H^2 - h^2)}{L}\]

• q = flow per unit length (ft³/day/ft or m³/day/m)
• k = hydraulic conductivity (ft/day or m/day)
• H = original water table height above impermeable layer (ft or m)
• h = water table height in trench (ft or m)
• L = distance from trench to boundary (ft or m)
• Assumes unconfined aquifer, horizontal flow

Total Flow to Trench: \[Q = q \times l\]

• Q = total flow rate (ft³/day or m³/day)
• q = flow per unit length (ft³/day/ft)
• l = length of trench (ft or m)

Well Point Systems

Drawdown for Single Well Point: \[s = \frac{Q}{2\pi kH}\ln\left(\frac{R}{r}\right)\]

• s = drawdown (ft or m)
• Q = pumping rate (ft³/day or m³/day)
• k = hydraulic conductivity (ft/day or m/day)
• H = initial saturated thickness (ft or m)
• R = radius of influence (ft or m)
• r = well radius (ft or m)
• For confined aquifer

Radius of Influence: \[R = C\sqrt{kH}\]

• R = radius of influence (ft or m)
• C = empirical constant (typically 3000 in ft units when time in days)
• k = hydraulic conductivity (ft/day or m/day)
• H = saturated thickness (ft or m)

Well Point Spacing: \[S = 2\sqrt{R^2 - d^2}\]

• S = spacing between well points (ft or m)
• R = radius of influence (ft or m)
• d = required drawdown distance from well point line (ft or m)

Pump Capacity

Required Pump Capacity: \[Q_p = Q \times SF\]

• Q_p = pump capacity required (gpm, ft³/min, or L/s)
• Q = calculated flow rate
• SF = safety factor (typically 1.5 to 2.0)

Pump Head: \[H_p = H_s + H_d + H_f + H_v\]

• H_p = total pump head (ft or m)
• H_s = suction lift (ft or m)
• H_d = discharge head (ft or m)
• H_f = friction losses (ft or m)
• H_v = velocity head (ft or m)

Cranes and Rigging

Crane Capacity and Load

Net Crane Capacity: \[C_{net} = C_{rated} - W_{hook} - W_{block}\]

• C_net = net lifting capacity (tons or kN)
• C_rated = rated crane capacity at given radius and boom length (tons or kN)
• W_hook = weight of hook (tons or kN)
• W_block = weight of block and tackle (tons or kN)

Maximum Allowable Load: \[L_{max} = \frac{C_{net}}{SF}\]

• L_max = maximum load that can be lifted (tons or kN)
• SF = safety factor (typically 1.25 for personnel lifts, varies by application)

Total Suspended Load: \[W_{total} = W_{load} + W_{rigging}\]

• W_total = total suspended weight (lb, tons, kg, or kN)
• W_load = weight of object being lifted
• W_rigging = weight of slings, spreader bars, etc.

Sling Tension and Angles

Tension in Vertical Sling (Single Leg): \[T = W\]

• T = tension in sling (lb or kN)
• W = total weight being lifted (lb or kN)

Tension in Angled Sling (Two Legs, Symmetrical): \[T = \frac{W}{2\cos\theta}\]

• T = tension in each leg (lb or kN)
• W = total weight (lb or kN)
• θ = angle from vertical
• Valid for two equal-length legs at same angle

Horizontal Force Component: \[F_H = T\sin\theta = \frac{W\tan\theta}{2}\]

• F_H = horizontal force component (lb or kN)
• T = sling tension
• θ = angle from vertical

Sling Tension with Multiple Legs: \[T = \frac{W}{n \times \cos\theta}\]

• T = tension per leg (lb or kN)
• W = total weight (lb or kN)
• n = number of supporting legs
• θ = angle from vertical
• Assumes equal load distribution

Sling Angle Factor:

• 0° (vertical): factor = 1.000
• 30° from vertical: factor = 1.155
• 45° from vertical: factor = 1.414
• 60° from vertical: factor = 2.000
• Multiply weight by factor to get tension per leg
• Maximum recommended angle from vertical: 60°

Basket Hitch and Choker Hitch

Basket Hitch (Vertical Load): \[T = \frac{W}{2}\]

• T = tension in each leg (lb or kN)
• W = total weight (lb or kN)
• Both legs support the load equally

Choker Hitch Efficiency: \[T_{effective} = T_{rated} \times E_c\]

• T_effective = effective choker capacity (lb or kN)
• T_rated = rated sling capacity for vertical hitch (lb or kN)
• E_c = choker efficiency factor (typically 0.75)

Soil Compaction

Compaction Relationships

Dry Density: \[\gamma_d = \frac{\gamma_{wet}}{1 + w}\]

• γ_d = dry unit weight (pcf or kN/m³)
• γ_wet = wet (total) unit weight (pcf or kN/m³)
• w = water content (decimal, not percentage)

Percent Compaction: \[PC = \frac{\gamma_{d,field}}{\gamma_{d,max}} \times 100\%\]

• PC = percent compaction (%)
• γ_d,field = field dry density (pcf or kN/m³)
• γ_d,max = maximum dry density from lab test (pcf or kN/m³)

Relative Compaction: \[RC = \frac{\gamma_{d,field}}{\gamma_{d,lab}} \times 100\%\]

• RC = relative compaction (%)
• Typically specified as 90%, 95%, or 100% of maximum dry density

Zero Air Voids (ZAV) Line: \[\gamma_{d,ZAV} = \frac{\gamma_w \times G_s}{1 + w \times G_s}\]

• γ_d,ZAV = zero air voids dry density (pcf or kN/m³)
• γ_w = unit weight of water (62.4 pcf or 9.81 kN/m³)
• G_s = specific gravity of soil solids
• w = water content (decimal)
• Represents theoretical maximum density with no air voids

Field Compaction Control

In-Place Density (Sand Cone Method): \[\gamma_{wet} = \frac{W_{wet}}{V}\]

• γ_wet = wet unit weight (pcf or kN/m³)
• W_wet = wet weight of soil from hole (lb or kg)
• V = volume of hole (ft³ or m³)

Volume of Hole (Sand Cone): \[V = \frac{W_{sand}}{\gamma_{sand}}\]

• V = volume of test hole (ft³ or m³)
• W_sand = weight of sand filling hole (lb or kg)
• γ_sand = calibrated density of sand (pcf or kN/m³)

Moisture Content: \[w = \frac{W_{water}}{W_{dry}} \times 100\%\]

• w = moisture content (%)
• W_water = weight of water (lb or g)
• W_dry = dry weight of soil (lb or g)

Temporary Structures and Shoring

Scaffold Loading

Uniformly Distributed Load: \[w = \frac{W_{total}}{A}\]

• w = uniform load (psf or kPa)
• W_total = total weight on platform (lb or kN)
• A = platform area (ft² or m²)

Scaffold Capacity Check: \[w_{actual} \le w_{rated}\]

• w_actual = actual load including dead load, workers, materials, and equipment (psf)
• w_rated = rated scaffold capacity (psf)
• Typical ratings: light duty = 25 psf, medium duty = 50 psf, heavy duty = 75 psf

Falsework and Shoring Loads

Construction Live Load: \[LL = 50 + 75\left(\frac{A - 200}{1000}\right) \text{ psf}\]

• LL = construction live load (psf), minimum 50 psf
• A = area (ft²)
• For areas > 200 ft²; maximum need not exceed 100 psf

Total Falsework Load: \[P = DL + LL + W_c + W_f\]

• P = total load (psf or kPa)
• DL = dead load of concrete and reinforcement (psf)
• LL = construction live load (psf)
• W_c = weight of formwork (psf)
• W_f = weight of falsework (psf)

Trench Shoring

Lateral Earth Pressure (Active): \[p = K_a \gamma h\]

• p = lateral earth pressure (psf or kPa)
• K_a = active earth pressure coefficient
• γ = unit weight of soil (pcf or kN/m³)
• h = depth below surface (ft or m)

Active Earth Pressure Coefficient: \[K_a = \frac{1 - \sin\phi}{1 + \sin\phi} = \tan^2\left(45° - \frac{\phi}{2}\right)\]

• K_a = active earth pressure coefficient (dimensionless)
• φ = angle of internal friction (degrees)

Resultant Force on Shoring: \[F = \frac{1}{2}K_a \gamma h^2\]

• F = resultant lateral force per unit length (lb/ft or kN/m)
• K_a = active earth pressure coefficient
• γ = unit weight of soil (pcf or kN/m³)
• h = depth of excavation (ft or m)
• Acts at h/3 from bottom of excavation

Site Layout and Control

Haul Distance and Economics

Free Haul: \[FH = V \times D_f\]

• FH = free haul volume-distance (yd³-stations or m³-m)
• V = volume (yd³ or m³)
• D_f = free haul distance (stations or m)
• Free haul distance typically included in earthwork bid price

Overhaul: \[OH = V \times (D_{total} - D_f)\]

• OH = overhaul volume-distance (yd³-stations or m³-m)
• V = volume (yd³ or m³)
• D_total = total haul distance (stations or m)
• D_f = free haul distance (stations or m)
• Paid separately beyond free haul distance

Economic Haul Distance: \[D_e = D_f + \frac{C_{borrow} + C_{disposal}}{C_{overhaul}}\]

• D_e = economic haul distance (stations or m)
• D_f = free haul distance (stations or m)
• C_borrow = cost to borrow ($/yd³)
• C_disposal = cost to dispose of waste ($/yd³)
• C_overhaul = cost per unit overhaul ($/yd³-station)
• Beyond this distance, borrow/waste is more economical than hauling

Grade Stakes and Slope Stakes

Cut/Fill at Station: \[h = E_{existing} - E_{design}\]

• h = cut (positive) or fill (negative) height (ft or m)
• E_existing = existing ground elevation (ft or m)
• E_design = design grade elevation (ft or m)

Horizontal Distance to Slope Stake: \[d = \frac{h}{s} + \frac{w}{2}\]

• d = horizontal distance from centerline to slope stake (ft or m)
• h = cut or fill depth (ft or m)
• s = side slope (decimal, e.g., 2:1 = 0.5)
• w = roadway width (ft or m)

Slope Ratio: \[s = \frac{\text{Vertical}}{\text{Horizontal}} = \frac{1}{n}\]

• s = slope (decimal or ratio)
• n = horizontal distance per unit vertical (e.g., 2 in "2:1")
• Example: 2:1 slope means 2 ft horizontal for 1 ft vertical, s = 0.5

Asphalt Paving Operations

Asphalt Quantity Calculations

Asphalt Volume: \[V = L \times W \times T\]

• V = volume (ft³)
• L = length (ft)
• W = width (ft)
• T = thickness (ft)
• Convert to tons: multiply by asphalt density (typically 145-150 pcf) ÷ 2000

Tonnage Required: \[W = \frac{L \times W \times T \times \gamma}{2000}\]

• W = weight in tons
• L = length (ft)
• W = width (ft)
• T = compacted thickness (ft)
• γ = unit weight of compacted asphalt (pcf, typically 145-150)
• 2000 = lb/ton conversion

Area from Tonnage: \[A = \frac{W \times 2000}{\gamma \times T}\]

• A = area covered (ft²)
• W = weight of asphalt (tons)
• γ = compacted unit weight (pcf)
• T = compacted thickness (ft)

Paving Production

Paver Production Rate: \[P = W \times S \times T \times E \times \gamma\]

• P = production rate (tons/hr)
• W = paving width (ft)
• S = paving speed (ft/hr or ft/min × 60)
• T = mat thickness (ft)
• E = efficiency factor
• γ = compacted density (tons/ft³)

Paving Speed: \[S = \frac{P}{W \times T \times \gamma \times E}\]

• S = paving speed (ft/min or ft/hr)
• P = paver capacity (tons/hr)
• Other variables as above

Concrete Paving Operations

Concrete Pavement Quantities

Concrete Pavement Volume: \[V = \frac{L \times W \times T}{27}\]

• V = volume (yd³)
• L = length (ft)
• W = width (ft)
• T = thickness (ft)
• 27 = ft³/yd³ conversion

Slab-on-Grade Volume: \[V = \frac{A \times T}{27}\]

• V = volume (yd³)
• A = slab area (ft²)
• T = thickness (ft)

Joint Spacing

Contraction Joint Spacing: \[S \le 24T \text{ to } 36T\]

• S = joint spacing (ft)
• T = slab thickness (in)
• Maximum joint spacing typically 15-20 ft for plain concrete pavement
• L/W ratio should be 1.0 to 1.3 for slab panels

Blasting Operations

Explosive Calculations

Powder Factor: \[PF = \frac{W_e}{V}\]

• PF = powder factor (lb/yd³ or kg/m³)
• W_e = weight of explosive (lb or kg)
• V = volume of rock blasted (yd³ or m³)
• Typical range: 0.75-1.5 lb/yd³ for rock excavation

Burden Distance: \[B = k_b \times d_h\]

• B = burden distance (ft or m)
• k_b = burden coefficient (typically 25-40 for diameter in inches)
• d_h = blast hole diameter (in or mm)
• Burden = shortest distance to free face

Spacing: \[S = (1.0 \text{ to } 1.5) \times B\]

• S = spacing between holes (ft or m)
• B = burden distance (ft or m)
• Spacing typically 1.2 to 1.5 times burden

Stemming Height: \[L_s = 0.7B \text{ to } 1.0B\]

• L_s = stemming height (ft or m)
• B = burden distance (ft or m)
• Stemming = unfilled portion at top of hole

Subdrill: \[L_{sd} = 0.2B \text{ to } 0.5B\]

• L_sd = subdrill depth (ft or m)
• B = burden distance (ft or m)
• Subdrill = depth drilled below final excavation grade

Safety and Ergonomics

OSHA Excavation Requirements

Trench Depth Classifications:

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• Depth 5-20 ft: protective system required (sloping, shoring, or shielding)
• Depth > 20 ft: protective system must be designed by registered professional engineer

Maximum Allowable Slope (H:V):

• Stable Rock: vertical (90°)
• Type A soil: 3/4:1 (53°)
• Type B soil: 1:1 (45°)
• Type C soil: 1.5:1 (34°)

Soil Type Definitions:

• Type A: Cohesive soil with unconfined compressive strength ≥ 1.5 tsf (144 kPa); clay, silty clay, sandy clay
• Type B: Cohesive soil with unconfined compressive strength 0.5 to 1.5 tsf (48-144 kPa); angular gravel, silt, silt loam
• Type C: Cohesive soil with unconfined compressive strength ≤ 0.5 tsf (48 kPa); granular soils, submerged soil, soil from which water is freely seeping

Fall Protection

Fall Protection Requirements:

• Fall protection required when working at heights ≥ 6 ft (general construction)
• Steel erection: ≥ 15 ft (but 6 ft at leading edges)
• Scaffolds: ≥ 10 ft
• Guardrails required when workers exposed to fall of ≥ 6 ft

Guardrail Specifications:

• Top rail height: 42 in ± 3 in (39-45 in)
• Midrail height: approximately 21 in (halfway between top rail and platform)
• Top rail must withstand 200 lb force in any direction
• Toeboards: minimum 3.5 in high when tools/materials present

Cost Estimating and Scheduling

Equipment Ownership and Operating Costs

Average Annual Investment: \[AAI = \frac{P(n+1) + S(n-1)}{2n}\]

• AAI = average annual investment ($)
• P = purchase price ($)
• S = salvage value ($)
• n = useful life (years)

Straight-Line Depreciation: \[D = \frac{P - S}{n}\]

• D = annual depreciation ($)
• P = purchase price ($)
• S = salvage value ($)
• n = useful life (years)

Hourly Ownership Cost: \[C_o = \frac{D + I + T + Ins + Storage}{H}\]

• C_o = hourly ownership cost ($/hr)
• D = annual depreciation ($)
• I = annual interest cost ($)
• T = annual taxes ($)
• Ins = annual insurance ($)
• Storage = annual storage cost ($)
• H = annual working hours (hr/yr)

Hourly Operating Cost: \[C_{op} = F + L + M + R + O\]

• C_op = hourly operating cost ($/hr)
• F = fuel cost ($/hr)
• L = lubrication cost ($/hr)
• M = maintenance and repair cost ($/hr)
• R = replacement cost for wear items ($/hr)
• O = operator cost ($/hr)

Total Hourly Equipment Cost: \[C_T = C_o + C_{op}\]

• C_T = total hourly cost ($/hr)

Production Cost

Unit Cost: \[UC = \frac{C_T}{P}\]

• UC = unit production cost ($/unit)
• C_T = total hourly cost ($/hr)
• P = production rate (units/hr)

Project Duration: \[T = \frac{Q}{P \times E \times H}\]

• T = time to complete (days)
• Q = total quantity (units)
• P = production rate (units/hr)
• E = efficiency factor
• H = working hours per day

Material Properties and Conversions

Common Unit Weights

Concrete:

• Normal weight concrete: 145-150 pcf (23-24 kN/m³)
• Lightweight concrete: 90-115 pcf (14-18 kN/m³)
• Reinforced concrete (for estimating): 150 pcf (23.6 kN/m³)

Asphalt:

• Compacted asphalt concrete: 145-150 pcf (23-24 kN/m³)
• Loose asphalt: 90-100 pcf (14-16 kN/m³)

Soils (Bank Measure):

• Sand and gravel: 100-120 pcf (16-19 kN/m³)
• Clay (wet): 110-130 pcf (17-20 kN/m³)
• Clay (dry): 90-110 pcf (14-17 kN/m³)
• Rock (blasted): 150-170 pcf (24-27 kN/m³)

Typical Load and Swell Factors

Load Factors (Swell):

• Clay: 1.25-1.40 (25-40% swell)
• Sand/gravel: 1.10-1.15 (10-15% swell)
• Rock (blasted): 1.50-1.80 (50-80% swell)
• Common excavation: 1.25 (25% swell)

Shrinkage Factors:

• Clay: 0.90-0.95 (5-10% shrinkage)
• Sand/gravel: 0.88-0.93 (7-12% shrinkage)
• Rock: 0.65-0.75 (25-35% shrinkage)

Volume Conversions

Common Conversions:

• 1 yd³ = 27 ft³
• 1 acre-foot = 43,560 ft³ = 1613.3 yd³
• 1 station = 100 ft
• 1 m³ = 35.315 ft³ = 1.308 yd³

Temporary Facilities

Site Access and Haul Roads

Minimum Haul Road Width: \[W = 3 \times W_v + C\]

• W = total road width (ft or m)
• W_v = width of widest vehicle (ft or m)
• C = clearance allowance (ft or m)
• For two-way traffic; single lane = 1.5 × vehicle width

Ramp/Road Grade:

• Maximum sustained grade for loaded haul trucks: 8-10%
• Maximum short-term grade: 12-15%
• Construction access roads: typically ≤ 10%

Erosion and Sediment Control

Sediment Basin Volume: \[V = 3600 \times Q \times T\]

• V = basin volume (ft³)
• Q = peak runoff rate (ft³/s or cfs)
• T = detention time (typically 2-3 hours for sediment settling)
• 3600 = seconds per hour conversion

Rational Method for Runoff: \[Q = CiA\]

• Q = peak runoff rate (cfs)
• C = runoff coefficient (dimensionless, 0-1)
• i = rainfall intensity (in/hr)
• A = drainage area (acres)

Quality Control Testing

Concrete Testing

Slump Test Acceptance:

• Specified slump ≤ 4 in: tolerance = ± 1 in
• Specified slump > 4 in: tolerance = ± 1.5 in

Compressive Strength Acceptance (ACI 318):

• Every test (average of 2 cylinders) ≥ f'_c - 500 psi
• Average of any 3 consecutive tests ≥ f'_c
• f'_c = specified compressive strength

Number of Concrete Test Specimens:

• Minimum one test (set of cylinders) per 150 yd³
• Minimum one test per 5,000 ft² of surface area
• Minimum one test per day for each class of concrete

Asphalt Testing

Asphalt Density Requirements: \[D_{min} = 0.92 \times D_{max}\]

• D_min = minimum acceptable density
• D_max = maximum laboratory density (Marshall or Superpave)
• Typically 92% of maximum theoretical density for in-place asphalt

Percent Air Voids: \[V_a = \left(1 - \frac{D_{field}}{D_{max}}\right) \times 100\%\]

• V_a = percent air voids (%)
• D_field = field density (pcf)
• D_max = maximum theoretical density (pcf)
• Typical specification: 3-5% air voids