Formula Sheet: Pavement Design

Flexible Pavement Design - AASHTO Method

AASHTO Structural Number (SN) Equation

The fundamental equation for flexible pavement design:

\[\log_{10}(W_{18}) = Z_R \cdot S_0 + 9.36 \cdot \log_{10}(SN + 1) - 0.20 + \frac{\log_{10}\left[\frac{\Delta PSI}{4.2 - 1.5}\right]}{0.40 + \frac{1094}{(SN + 1)^{5.19}}} + 2.32 \cdot \log_{10}(M_R) - 8.07\]

Where:

• W₁₈ = Predicted number of 18-kip (80 kN) equivalent single axle loads (ESALs)
• Z_R = Standard normal deviate for desired reliability level (dimensionless)
• S₀ = Combined standard error of traffic prediction and performance prediction (dimensionless)
• SN = Structural number (dimensionless), indicating required pavement thickness
• ΔPSI = Difference between initial serviceability index and terminal serviceability index (dimensionless)
• M_R = Resilient modulus of subgrade soil (psi)

Structural Number (SN) Components

The structural number is calculated from layer thicknesses and coefficients:

\[SN = a_1 \cdot D_1 + a_2 \cdot D_2 \cdot m_2 + a_3 \cdot D_3 \cdot m_3\]

Where:

• a₁ = Layer coefficient for asphalt concrete surface course (per inch)
• D₁ = Thickness of asphalt concrete surface course (inches)
• a₂ = Layer coefficient for base course (per inch)
• D₂ = Thickness of base course (inches)
• m₂ = Drainage coefficient for base course (dimensionless)
• a₃ = Layer coefficient for subbase course (per inch)
• D₃ = Thickness of subbase course (inches)
• m₃ = Drainage coefficient for subbase course (dimensionless)

Reliability Factor (Z_R)

Standard normal deviate values for common reliability levels:

• 50% reliability: Z_R = 0.000
• 60% reliability: Z_R = -0.253
• 70% reliability: Z_R = -0.524
• 75% reliability: Z_R = -0.674
• 80% reliability: Z_R = -0.841
• 85% reliability: Z_R = -1.037
• 90% reliability: Z_R = -1.282
• 95% reliability: Z_R = -1.645
• 99% reliability: Z_R = -2.327

Standard Error (S₀)

Typical values for combined standard error:

• Flexible pavements: S₀ = 0.40 to 0.50
• Rigid pavements: S₀ = 0.30 to 0.40

Present Serviceability Index (PSI)

Initial and terminal serviceability values:

• p₀ = Initial PSI, typically 4.2 for new flexible pavements
• p_t = Terminal PSI (design serviceability level)
• Major highways: p_t = 2.5 or higher
• Minor roads: p_t = 2.0
• ΔPSI = p₀ - p_t

Resilient Modulus (M_R)

Correlation between CBR and resilient modulus:

\[M_R = 1500 \times \text{CBR} \text{ (psi)}\]

Where:

• M_R = Resilient modulus (psi)
• CBR = California Bearing Ratio (%), typically between 3% and 80%

Alternative correlation for fine-grained soils (A-4 through A-7):

\[M_R = 2555 \times \text{CBR}^{0.64} \text{ (psi)}\]

Drainage Coefficients (m_i)

Drainage coefficients account for drainage quality and moisture exposure:

Quality of Drainage	Percent of Time Pavement Structure is Exposed to Moisture Levels Approaching Saturation
	<1% | 1-5% | 5-25% | >25%
Excellent	1.40-1.35 | 1.35-1.30 | 1.30-1.20 | 1.20
Good	1.35-1.25 | 1.25-1.15 | 1.15-1.00 | 1.00
Fair	1.25-1.15 | 1.15-1.05 | 1.00-0.80 | 0.80
Poor	1.15-1.05 | 1.05-0.80 | 0.80-0.60 | 0.60
Very Poor	1.05-0.95 | 0.95-0.75 | 0.75-0.40 | 0.40

Equivalent Single Axle Load (ESAL)

Load Equivalency Factors (LEF)

Convert mixed traffic to equivalent 18-kip single axle loads:

\[W_{18} = \sum_{i=1}^{n} (N_i \times LEF_i)\]

Where:

• W₁₈ = Total 18-kip ESALs
• N_i = Number of axle load applications of type i
• LEF_i = Load equivalency factor for axle type i

ESAL Calculation for Design Period

\[ESAL = ADT \times \% \text{ Trucks} \times N \times 365 \times G \times D \times L\]

Where:

• ESAL = Design ESALs for analysis period
• ADT = Average daily traffic (vehicles per day)
• % Trucks = Percentage of trucks in traffic stream (decimal)
• N = Number of years in design period
• G = Growth factor (dimensionless)
• D = Directional distribution factor (typically 0.5)
• L = Lane distribution factor

Traffic Growth Factor

For compound growth rate:

\[G = \frac{(1 + r)^n - 1}{r}\]

Where:

• G = Growth factor (dimensionless)
• r = Annual growth rate (decimal)
• n = Design period (years)

For zero growth (r = 0):

\[G = n\]

Lane Distribution Factor (L)

Percentage of truck traffic in design lane:

• 1 lane each direction: L = 1.00
• 2 lanes each direction: L = 0.80 to 0.90
• 3 lanes each direction: L = 0.60 to 0.70
• 4+ lanes each direction: L = 0.50 to 0.60

Rigid Pavement Design - AASHTO Method

AASHTO Rigid Pavement Design Equation

\[\log_{10}(W_{18}) = Z_R \cdot S_0 + 7.35 \cdot \log_{10}(D + 1) - 0.06 + \frac{\log_{10}\left[\frac{\Delta PSI}{4.5 - 1.5}\right]}{1 + \frac{1.624 \times 10^7}{(D + 1)^{8.46}}} + (4.22 - 0.32 \cdot p_t) \cdot \log_{10}\left[\frac{S_c' \cdot C_d \cdot (D^{0.75} - 1.132)}{215.63 \cdot J \cdot \left[D^{0.75} - \frac{18.42}{(E_c/k)^{0.25}}\right]}\right]\]

Where:

• W₁₈ = Predicted 18-kip ESALs
• Z_R = Standard normal deviate
• S₀ = Combined standard error (typically 0.30-0.40 for rigid pavements)
• D = Slab thickness (inches)
• ΔPSI = p₀ - p_t (typically 4.5 - 2.5 = 2.0 for rigid pavements)
• p_t = Terminal serviceability index
• S_c' = Modulus of rupture of concrete (psi)
• C_d = Drainage coefficient
• J = Load transfer coefficient
• E_c = Elastic modulus of concrete (psi)
• k = Modulus of subgrade reaction (pci)

Modulus of Rupture of Concrete (S_c')

Estimated from compressive strength:

\[S_c' = 9 \times \sqrt{f_c'} \text{ (psi)}\]

Or alternatively:

\[S_c' = 2.3 \times \sqrt{f_c'} \text{ (MPa)}\]

Where:

• S_c' = Modulus of rupture (28-day flexural strength)
• f_c' = Compressive strength of concrete at 28 days

Elastic Modulus of Concrete (E_c)

For normal weight concrete:

\[E_c = 57000 \times \sqrt{f_c'} \text{ (psi)}\]

In SI units:

\[E_c = 4700 \times \sqrt{f_c'} \text{ (MPa)}\]

Where:

• E_c = Elastic modulus of concrete
• f_c' = Compressive strength of concrete (same units as E_c)

Modulus of Subgrade Reaction (k)

For subgrade directly under slab:

\[k = M_R / 19.4 \text{ (pci)}\]

Where:

• k = Modulus of subgrade reaction (pci = pounds per cubic inch)
• M_R = Resilient modulus of subgrade (psi)

Effective Modulus of Subgrade Reaction (Composite k-value)

When base/subbase layers are present, use composite k-value chart or:

\[k_{eff} = k \times \left(1 + \frac{E_{sb}}{E_{sg}} \cdot \frac{D_{sb}}{D}\right)^{0.33}\]

Where:

• k_eff = Effective modulus of subgrade reaction (pci)
• k = Modulus of subgrade reaction on top of subgrade (pci)
• E_sb = Elastic modulus of subbase (psi)
• E_sg = Elastic modulus of subgrade (psi)
• D_sb = Thickness of subbase (inches)
• D = Thickness of concrete slab (inches)

Load Transfer Coefficient (J)

Values based on load transfer capability:

• Doweled joints or CRCP: J = 2.5 to 3.2
• Aggregate interlock (nondoweled): J = 3.2 to 3.8
• Asphalt shoulder: J = 3.6 to 4.2
• Typical value for doweled joints: J = 3.2

Drainage Coefficient for Rigid Pavements (C_d)

Quality of Drainage	Percent of Time Pavement Structure is Exposed to Moisture Levels Approaching Saturation
	<1% | 1-5% | 5-25% | >25%
Excellent	1.25-1.20 | 1.20-1.15 | 1.15-1.10 | 1.10
Good	1.20-1.15 | 1.15-1.10 | 1.10-1.00 | 1.00
Fair	1.15-1.10 | 1.10-1.00 | 1.00-0.90 | 0.90
Poor	1.10-1.00 | 1.00-0.90 | 0.90-0.80 | 0.80
Very Poor	1.00-0.90 | 0.90-0.80 | 0.80-0.70 | 0.70

Relative Damage (u_r)

For erosion analysis and fatigue analysis in rigid pavements:

\[u_r = \frac{C_1 \times P}{S_c' \times b \times h^2}\]

Where:

• u_r = Relative damage (dimensionless)
• C₁ = Coefficient related to edge stress
• P = Wheel load (lbs)
• S_c' = Modulus of rupture (psi)
• b = Radius of relative stiffness (inches)
• h = Slab thickness (inches)

Mechanistic-Empirical Pavement Design

Radius of Relative Stiffness

For rigid pavements:

\[\ell = \left[\frac{E_c \times h^3}{12 \times (1 - \mu^2) \times k}\right]^{0.25}\]

Where:

• ℓ = Radius of relative stiffness (inches)
• E_c = Elastic modulus of concrete (psi)
• h = Slab thickness (inches)
• μ = Poisson's ratio of concrete (typically 0.15)
• k = Modulus of subgrade reaction (pci)

Critical Pavement Responses

Tensile Strain at Bottom of Asphalt Layer (ε_t):

• Controls fatigue cracking in flexible pavements
• Computed using layered elastic theory or finite element analysis

Compressive Strain at Top of Subgrade (ε_c):

• Controls rutting and permanent deformation
• Computed using layered elastic theory

Asphalt Institute Thickness Design

Minimum asphalt concrete thickness over base:

Traffic (ESALs)	Minimum AC Thickness (inches)
< 50,000	1.0 (or surface treatment)
50,000 - 150,000	2.0
150,000 - 500,000	2.5
500,000 - 2,000,000	3.0
2,000,000 - 7,000,000	3.5
> 7,000,000	4.0

Subgrade and Material Properties

California Bearing Ratio (CBR)

Definition:

\[CBR = \frac{\text{Unit stress required to penetrate test material}}{\text{Unit stress required to penetrate standard crushed stone}} \times 100\%\]

Standard penetration stresses:

• 0.1 inch penetration: 1000 psi
• 0.2 inch penetration: 1500 psi

Typical CBR values:

• Clay (soft): CBR = 2-4%
• Clay (medium): CBR = 4-8%
• Silty clay: CBR = 5-10%
• Sand (poorly graded): CBR = 10-25%
• Sand (well graded): CBR = 25-40%
• Gravel: CBR = 30-60%
• Crushed stone: CBR = 80-100%

R-Value (Resistance Value)

Relationship between R-value and CBR:

\[R = \frac{100}{10 + 0.3 \times CBR}\]

Where:

• R = Resistance value (dimensionless, 0-100)
• CBR = California Bearing Ratio (%)

Soil Support Value (SSV)

Used in some pavement design methods:

\[SSV = 0.2 + 0.008 \times CBR\]

Where:

• SSV = Soil support value (dimensionless)
• CBR = California Bearing Ratio (%)

Layer Coefficients

Typical Layer Coefficient Values (a_i)

Asphalt Concrete Surface Course:

• a₁ = 0.35 to 0.44 per inch (typical: 0.42)
• Higher values for higher quality asphalt concrete

Base Course:

• Crushed stone (a₂): 0.14 per inch
• Dense-graded crushed stone (a₂): 0.14 per inch
• Cement-treated base (a₂): 0.14 to 0.23 per inch
• Bituminous treated base (a₂): 0.30 to 0.40 per inch
• Lime-stabilized (a₂): 0.15 to 0.30 per inch

Subbase Course:

• Granular subbase (a₃): 0.10 to 0.14 per inch
• Sand-gravel (a₃): 0.11 per inch
• Cement-treated subbase (a₃): 0.15 to 0.20 per inch

Layer Coefficient from Elastic Modulus

For granular base materials:

\[a_2 = 0.249 \times \log_{10}(E_2) - 0.977\]

For granular subbase materials:

\[a_3 = 0.227 \times \log_{10}(E_3) - 0.839\]

Where:

• a₂, a₃ = Layer coefficients (per inch)
• E₂, E₃ = Elastic modulus of base or subbase (psi)

Thermal and Environmental Effects

Temperature Adjustment for Asphalt Modulus

Asphalt stiffness varies with temperature. Mean annual air temperature (MAAT) is used to estimate pavement temperature.

Mean Pavement Temperature:

\[T_{pav} = T_{air} + \frac{18°F \times h}{h + 4}\]

Where:

• T_pav = Mean pavement temperature (°F)
• T_air = Mean annual air temperature (°F)
• h = Depth below pavement surface (inches)

Frost Penetration Depth

Stefan equation for frost depth:

\[X = \sqrt{\frac{48 \times k \times F}{L}}\]

Where:

• X = Frost penetration depth (inches)
• k = Thermal conductivity (BTU/(hr·ft·°F))
• F = Freezing index (degree-days)
• L = Latent heat of fusion (144 BTU/lb for water)

Pavement Performance and Distress

International Roughness Index (IRI)

IRI measures pavement roughness:

• Units: inches/mile or meters/kilometer
• New pavements: IRI < 60 in/mi (< 0.95 m/km)
• Good pavements: IRI = 60-94 in/mi (0.95-1.5 m/km)
• Acceptable pavements: IRI = 95-120 in/mi (1.5-1.9 m/km)
• Poor pavements: IRI > 170 in/mi (> 2.7 m/km)

Fatigue Cracking Model (Asphalt Institute)

\[N_f = 0.00432 \times C \times \left(\frac{1}{\varepsilon_t}\right)^{3.291} \times \left(\frac{1}{E}\right)^{0.854}\]

Where:

• N_f = Allowable number of load repetitions to fatigue cracking
• ε_t = Tensile strain at bottom of asphalt layer (in/in)
• E = Asphalt elastic modulus (psi)
• C = Correction factor (typically 1.0 for 50% reliability)

Permanent Deformation (Rutting) Model

\[N_d = 1.365 \times 10^{-9} \times \left(\frac{1}{\varepsilon_c}\right)^{4.477}\]

Where:

• N_d = Allowable number of load repetitions to limit rutting
• ε_c = Compressive strain at top of subgrade (in/in)

Joint and Crack Design for Rigid Pavements

Joint Spacing

Maximum joint spacing for plain jointed concrete pavement:

\[L_{max} = 24 \times h\]

Where:

• L_max = Maximum joint spacing (feet)
• h = Slab thickness (inches)
• Typical range: 12 to 15 feet for plain concrete pavements

Dowel Bar Design

Required dowel diameter:

\[d = \left(\frac{4 \times P}{\pi \times f_b}\right)^{0.5}\]

Where:

• d = Dowel diameter (inches)
• P = Design wheel load (lbs)
• f_b = Allowable bearing stress (typically 2000-4000 psi)

Typical dowel bar dimensions:

• Slab thickness 6-8 inches: 1 inch diameter, 18 inches long
• Slab thickness 9-11 inches: 1.25 inches diameter, 18 inches long
• Slab thickness 12-14 inches: 1.5 inches diameter, 18 inches long

Tie Bar Design

Required cross-sectional area of tie bars:

\[A_s = \frac{b \times h \times w \times f}{\rho \times f_s}\]

Where:

• A_s = Total cross-sectional area of tie bars per joint (in²)
• b = Slab width (feet)
• h = Slab thickness (inches)
• w = Unit weight of concrete (typically 150 pcf)
• f = Coefficient of friction (typically 1.5)
• ρ = Percentage of subgrade drag to be resisted (typically 0.75)
• f_s = Allowable stress in steel (typically 2/3 of yield strength)

Thermal Stress in PCC Slabs

Thermal stress due to temperature differential:

\[\sigma_T = \frac{C_T \times E_c \times \alpha \times \Delta T}{2 \times (1 - \mu)}\]

Where:

• σ_T = Thermal stress (psi)
• C_T = Coefficient depending on slab dimensions (dimensionless)
• E_c = Elastic modulus of concrete (psi)
• α = Coefficient of thermal expansion of concrete (typically 5 × 10^-6 per °F)
• ΔT = Temperature differential through slab thickness (°F)
• μ = Poisson's ratio (typically 0.15 for concrete)

Overlay Design

Effective Structural Number for Existing Pavement

\[SN_{eff} = a_1 \times D_1 + a_2 \times D_2 \times m_2 + a_3 \times D_3 \times m_3\]

Adjusted for condition:

\[SN_{eff} = CF \times SN_{existing}\]

Where:

• SN_eff = Effective structural number of existing pavement
• CF = Condition factor (0 to 1.0, based on distress surveys)
• SN_existing = Original structural number

Required Overlay Thickness

\[SN_{overlay} = SN_{future} - SN_{eff}\]

Where:

• SN_overlay = Required structural number for overlay
• SN_future = Required structural number for future traffic
• SN_eff = Effective structural number of existing pavement

Convert to thickness:

\[D_{overlay} = \frac{SN_{overlay}}{a_{overlay}}\]

Where:

• D_overlay = Thickness of overlay (inches)
• a_overlay = Layer coefficient of overlay material (per inch)

Condition Factor (CF)

Based on pavement condition assessment:

• Excellent condition (minimal distress): CF = 0.9 to 1.0
• Good condition (slight distress): CF = 0.7 to 0.9
• Fair condition (moderate distress): CF = 0.5 to 0.7
• Poor condition (severe distress): CF = 0.2 to 0.5
• Failed condition: CF < 0.2

Drainage Design for Pavements

Time to Drain

\[t = \frac{H \times n_e \times L^2}{k \times H \times S + 2 \times k \times H_r}\]

Simplified for common conditions:

\[t = \frac{n_e \times L^2}{k \times S \times H}\]

Where:

• t = Time to drain to 50% saturation (hours or days)
• n_e = Effective porosity (dimensionless)
• L = Drainage path length (feet)
• k = Permeability coefficient (ft/hr or ft/day)
• S = Slope of drainage layer (ft/ft)
• H = Thickness of drainage layer (feet)
• H_r = Height of water in drainage layer (feet)

Drainage Quality Based on Time to Drain

• Excellent: Water removed in 2 hours
• Good: Water removed in 1 day
• Fair: Water removed in 1 week
• Poor: Water removed in 1 month
• Very Poor: Water not drained in 1 month

Stabilized Bases and Subbases

Cement Stabilization

Cement content for stabilization:

\[\text{Cement Content (\%)} = \frac{\text{Weight of cement}}{\text{Dry weight of soil}} \times 100\%\]

Typical cement contents:

• Sand: 6-10% by weight
• Silt: 8-12% by weight
• Clay: 10-14% by weight
• Granular materials: 3-6% by weight

Lime Stabilization

Lime requirement for clay soils:

\[\text{Lime Content (\%)} = 2\% \text{ to } 8\% \text{ by dry weight}\]

Initial consumption of lime (ICL):

• Determined by Eades and Grim pH test
• Minimum pH of 12.4 required for effective stabilization

Asphalt Stabilization

Asphalt emulsion content:

\[\text{Emulsion Content (\%)} = 4\% \text{ to } 10\% \text{ by dry weight of aggregate}\]

Typical applications:

• Sandy materials: 4-7% emulsion
• Silty materials: 6-10% emulsion

Geosynthetics in Pavement Design

Base Course Reduction Factor (BCR)

Thickness reduction with geotextile reinforcement:

\[h_{with} = \frac{h_{without}}{BCR}\]

Where:

• h_with = Required base thickness with geotextile (inches)
• h_without = Required base thickness without geotextile (inches)
• BCR = Base course reduction factor (typically 1.2 to 2.0)

Traffic Benefit Ratio (TBR)

Increase in traffic capacity with geosynthetic reinforcement:

\[TBR = \frac{N_{with}}{N_{without}}\]

Where:

• TBR = Traffic benefit ratio (dimensionless)
• N_with = Number of load cycles to failure with geosynthetic
• N_without = Number of load cycles to failure without geosynthetic
• Typical values: TBR = 2 to 10 depending on application

Pavement Deflection Analysis

Falling Weight Deflectometer (FWD)

Deflection basin parameters are used to back-calculate layer moduli.

Surface Curvature Index (SCI):

\[SCI = D_0 - D_{12}\]

Base Damage Index (BDI):

\[BDI = D_{12} - D_{24}\]

Where:

• D₀ = Deflection at center of load plate (mils)
• D₁₂ = Deflection at 12 inches from load center (mils)
• D₂₄ = Deflection at 24 inches from load center (mils)

Benkelman Beam Deflection

Pavement strength assessment based on rebound deflection.

Allowable deflection: Function of traffic volume and pavement type, typically:

• Heavy traffic (> 1000 trucks/day): < 0.25 inches
• Medium traffic (200-1000 trucks/day): 0.25-0.40 inches
• Light traffic (< 200 trucks/day): 0.40-0.60 inches

Economic Analysis

Present Worth of Costs

\[PW = C_0 + \sum_{i=1}^{n} \frac{C_i}{(1 + r)^{t_i}}\]

Where:

• PW = Present worth of all costs ($)
• C₀ = Initial construction cost ($)
• C_i = Cost of maintenance or rehabilitation at time t_i ($)
• r = Discount rate (decimal)
• t_i = Time when cost C_i occurs (years)
• n = Number of future costs

Equivalent Uniform Annual Cost (EUAC)

\[EUAC = PW \times \frac{r \times (1 + r)^n}{(1 + r)^n - 1}\]

Where:

• EUAC = Equivalent uniform annual cost ($/year)
• PW = Present worth ($)
• r = Discount rate (decimal)
• n = Analysis period (years)

Asphalt Mix Design

Marshall Mix Design Parameters

Marshall Stability:

• Minimum values depend on traffic level
• Light traffic: 750 lbs minimum
• Medium traffic: 1200 lbs minimum
• Heavy traffic: 1800 lbs minimum

Flow:

• Acceptable range: 8 to 16 (0.01 inch units)

Percent Air Voids (V_a)

\[V_a = \left(1 - \frac{G_{mb}}{G_{mm}}\right) \times 100\%\]

Where:

• V_a = Percent air voids in compacted mix (%)
• G_mb = Bulk specific gravity of compacted mix
• G_mm = Maximum theoretical specific gravity of mix
• Typical design range: 3% to 5%

Voids in Mineral Aggregate (VMA)

\[VMA = 100 - \frac{G_{mb} \times P_s}{G_{sb}}\]

Where:

• VMA = Voids in mineral aggregate (%)
• G_mb = Bulk specific gravity of compacted mix
• P_s = Percent aggregate by total weight of mix (%)
• G_sb = Bulk specific gravity of aggregate

Voids Filled with Asphalt (VFA)

\[VFA = \frac{VMA - V_a}{VMA} \times 100\%\]

Where:

• VFA = Voids filled with asphalt (%)
• VMA = Voids in mineral aggregate (%)
• V_a = Air voids (%)
• Typical design range: 65% to 78%

Effective Asphalt Content (P_be)

\[P_{be} = P_b - P_{ba}\] \[P_{ba} = \frac{G_{sb} \times (G_{se} - G_{sb})}{G_{se} \times G_{sb}} \times 100\]

Where:

• P_be = Effective asphalt content (% by total weight of mix)
• P_b = Total asphalt content (% by total weight of mix)
• P_ba = Absorbed asphalt content (%)
• G_sb = Bulk specific gravity of aggregate
• G_se = Effective specific gravity of aggregate

Superpave Mix Design

Design Aggregate Structure

N_design (Number of gyrations):

• < 0.3 million ESALs: N_design = 50
• 0.3 to 3 million ESALs: N_design = 75
• 3 to 10 million ESALs: N_design = 100
• 10 to 30 million ESALs: N_design = 100
• > 30 million ESALs: N_design = 125

Performance Grade (PG) Asphalt Binder Selection

PG XX-YY where:

• XX = Average 7-day maximum pavement temperature (°C)
• YY = Minimum pavement temperature (°C)

Pavement temperature estimation:

\[T_{pav,high} = T_{air,high} + 20°C\] \[T_{pav,low} = T_{air,low} - 2°C\]

Where:

• T_pav,high = Maximum pavement design temperature (°C)
• T_air,high = Average 7-day maximum air temperature (°C)
• T_pav,low = Minimum pavement design temperature (°C)
• T_air,low = Minimum air temperature (°C)

Portland Cement Concrete Mix Design

Water-Cement Ratio (w/c)

Compressive strength relationship:

\[f_c' = \frac{K_1}{K_2^{(w/c)}}\]

Where:

• f_c' = 28-day compressive strength (psi)
• w/c = Water-cement ratio by weight
• K₁, K₂ = Constants dependent on materials and curing

Maximum w/c ratios for durability:

• Severe exposure: w/c ≤ 0.45
• Moderate exposure: w/c ≤ 0.50
• Mild exposure: w/c ≤ 0.55

ACI Absolute Volume Method

Volume balance equation:

\[V_c + V_w + V_a + V_{air} + V_{agg} = 1.0 \text{ yd}^3\]

Where:

• V_c = Absolute volume of cement (yd³)
• V_w = Absolute volume of water (yd³)
• V_a = Absolute volume of admixtures (yd³)
• V_air = Volume of air (yd³)
• V_agg = Absolute volume of aggregate (yd³)

Recommended Air Content

For frost resistance:

• 3/4 inch maximum aggregate: 6% ± 1.5%
• 1 inch maximum aggregate: 5.5% ± 1.5%
• 1.5 inch maximum aggregate: 5% ± 1.5%
• 2 inch maximum aggregate: 4.5% ± 1.5%
• 3 inch maximum aggregate: 4% ± 1.0%