Pavement Design (Flexible and Rigid) - Cheat Sheet
Your last-minute revision companion for flexible and rigid pavement design. Master subgrade strength measures, tire contact mechanics, traffic loading conversions (ESAL), and design paradigms in 30 minutes.
Flexible Pavement Fundamentals
Formulas
Structural Number (SN) = a₁D₁ + a₂m₂D₂ + a₃m₃D₃
Meaning
a₁, a₂, a₃ = layer coefficients; D₁, D₂, D₃ = layer thicknesses (cm or inches); m₂, m₃ = drainage factors; SN = overall structural capacity
Watch out
Mix inch and cm units carefully — be explicit. Layer coefficients vary by material (AC ≈ 0.40, base ≈ 0.14, subbase ≈ 0.07).
When to use
AASHTO flexible pavement design; when designing asphalt layer composition
CBR Design Thickness: t = (P √W) / (K × CBR) or equivalent layer tables
Meaning
t = total pavement thickness (cm); P = wheel load (kN); W = number of repetitions; K = design factor; CBR = subgrade bearing ratio (%)
Watch out
CBR is a ratio (%), not an absolute value. Use correct K factor from design standards (DPWH, AASHTO).
When to use
CBR method for flexible pavement (simple design for low-traffic roads, common in PH highways)
Common values
Value
0.35–0.45
Symbol
a₁
Quantity
Asphalt Concrete layer coefficient
Value
0.10–0.15
Symbol
a₂
Quantity
Granular base layer coefficient
Value
0.05–0.10
Symbol
a₃
Quantity
Subbase layer coefficient
Value
1.0
Symbol
m (good)
Quantity
Good drainage factor
Value
0.4–0.6
Symbol
m (poor)
Quantity
Poor drainage factor
Important facts
- Flexible pavements deflect visibly under load (look 'soft'); rutting and fatigue cracking are primary failure modes.
- Load is distributed through layers at a shallow angle (45° to 60°) — thin surface must be stiff to prevent excessive strain.
- Drainage coefficient m reflects moisture and drainage quality: m = 1.0 (good) to m = 0.4 (poor); poor drainage reduces layer stiffness.
- In the Philippines (tropical climate, monsoon seasons), base drainage is critical — design m₂, m₃ conservatively (m ≤ 0.8).
- Overlay design uses remaining life concept: existing SN + overlay SN ≥ new design SN for extended period.
Key definitions
Flexible Pavement
Example
AC surface + aggregate base + subbase over compacted subgrade (typical 75–150 mm AC on Philippine roads).
Layered asphalt system that deflects with subgrade; load distributed through granular layers; failure by rutting and fatigue cracking.
California Bearing Ratio (CBR)
Example
CBR = 5% → poor subgrade (needs thick pavement); CBR = 20% → good subgrade (thinner pavement sufficient).
Penetration test (2.5 mm piston) expressing soil bearing capacity as % of standard crushed stone; higher CBR = stronger subgrade, thinner pavement.
Layer Coefficient (a)
Example
Asphalt concrete: a₁ ≈ 0.40; granular base: a₂ ≈ 0.14; subbase: a₃ ≈ 0.07.
Structural contribution of 1 cm (or 1 inch) thickness of a pavement material; directly proportional to material stiffness.
Diagrams to know
- Flexible pavement layer system (AC → base → subbase → subgrade with typical thicknesses).
- Load distribution angle and pressure bulb beneath flexible pavement.
- Rutting and fatigue cracking failure modes (visible surface profile vs subsurface crack propagation).
Rigid Pavement Fundamentals
Formulas
k = p / δ
Meaning
k = modulus of subgrade reaction (MN/m³ or kN/m³); p = applied pressure (kPa); δ = deflection (m)
Watch out
k is NOT CBR. k is a modulus (stiffness), not a ratio. Units: kPa/m = MN/m³. Common values: 30–100 MN/m³.
When to use
From plate load test (typically 75 cm or 30 in. diameter plate); used for rigid (PCC slab) pavement design.
Westergaard Stress (critical interior or edge): σ = (0.75P) / h² or σ = (0.529P) / h² (edge load)
Meaning
σ = flexural stress (kPa); P = wheel load (N); h = slab thickness (mm)
Watch out
Interior loads are less severe than edge loads; edge stress ≈ 1.3 × interior stress. Must include safety factor and load equivalency.
When to use
Calculate maximum bending stress in PCC slab under single wheel load; compare to concrete modulus of rupture (f'c or MR).
PCC Slab Thickness (from load and stress): h = √(kP / (σ × k_coefficient))
Meaning
h = required slab thickness; P = wheel load; σ = allowable stress (from f'c); k = subgrade reaction
Watch out
Stress depends on both load AND slab stiffness (h). Joint spacing and load transfer efficiency affect design.
When to use
AASHTO or DPWH rigid design; size slab to limit stress below modulus of rupture.
Common values
Value
150–200 mm
Symbol
h
Quantity
Typical PCC slab thickness (flexible sub-base)
Value
200–250 mm
Symbol
h
Quantity
Typical PCC slab thickness (rigid base)
Value
3.5–4.5 MPa
Symbol
f'c or MR
Quantity
Modulus of rupture (road PCC)
Value
30–50 MN/m³
Symbol
k
Quantity
Subgrade reaction (sandy soil)
Value
50–100 MN/m³
Symbol
k
Quantity
Subgrade reaction (clay soil)
Value
150–250 MN/m³
Symbol
k
Quantity
Subgrade reaction (stabilized base)
Important facts
- Rigid slabs distribute load through bending stiffness — the slab acts like a beam on elastic foundation.
- Joint spacing must balance thermal/shrinkage cracking risk vs cost; typical 4–6 m for arterial roads.
- Dowel bars (12–16 mm dia, 300–600 mm spacing) transfer load across joints; transverse tie bars hold longitudinal joint together.
- Faulting (differential settlement at joints) is a major distress in poorly maintained rigid pavements; load transfer failure is common.
- PCC slabs on weak subgrade (low k) require thicker slab or improved base to limit edge stress and pumping risk.
Key definitions
Rigid Pavement
Example
150–200 mm PCC slab on 100–150 mm base; joints at 4–6 m intervals (doweled or tied).
Stiff PCC slab on subbase; load spread by slab bending over large area; controlled cracking via joints.
Modulus of Subgrade Reaction (k)
Example
Sandy soil: k ≈ 30–50 MN/m³; clay soil: k ≈ 50–100 MN/m³; stabilized base increases k to 150+ MN/m³.
Stiffness of the foundation under a rigid slab: pressure per unit deflection (kPa/m or MN/m³).
Modulus of Rupture (f'c or MR)
Example
Typical: MR ≈ 3.5–4.5 MPa for road-grade PCC; test per ASTM C78 or AS 1012.10.
Flexural strength of PCC — the maximum bending stress concrete can sustain before cracking.
Load Transfer Efficiency (LTE)
Example
A 100 kN load on one slab side with LTE = 80% transfers 80 kN to adjacent slab via dowels.
Fraction of load transferred across a joint; doweled joints: LTE ≈ 75–95%; tied joints: LTE ≈ 50–70%.
Diagrams to know
- PCC slab on elastic foundation with load bulb and stress distribution.
- Dowel bar and tie-bar configuration at joints (transverse and longitudinal).
- Westergaard stress distribution diagram (critical interior, edge, and corner load positions).
- Faulting and erosion at joints — loss of base support, joint deterioration.
Subgrade and Foundation Strength
Formulas
CBR (%) = (Load @ 2.5 mm pen. / Std. Load) × 100
Meaning
CBR = bearing ratio; load at 2.5 mm penetration on test soil; std. load for crushed stone ≈ 1370 kN
Watch out
CBR only applies to flexible design. Must use correct standard load value (1370 kN). Soaked vs unsoaked CBR differ significantly.
When to use
Interpret CBR test results; classify soil for flexible pavement design (standard penetration test per ASTM D1883).
k = p / δ (MN/m³ = kPa / m)
Meaning
k = modulus of subgrade reaction from plate load test; convert units carefully: kPa ÷ m = MN/m³
Watch out
k varies with plate diameter and test conditions; larger plates give lower k. Standard plate diameter is 75 cm (30 in.).
When to use
Rigid pavement design; plate load test (75 cm plate) gives direct k measurement.
Common values
Value
< 3%
Symbol
CBR
Quantity
Very poor subgrade (CBR)
Value
3–6%
Symbol
CBR
Quantity
Poor subgrade (CBR)
Value
6–12%
Symbol
CBR
Quantity
Fair subgrade (CBR)
Value
12%
Symbol
CBR
Quantity
Good subgrade (CBR)
Important facts
- Philippine tropical soils (laterite, volcanic ash) typically CBR = 4–12%; good quality improved base: CBR = 20–40%.
- Subgrade must be compacted to specification (95–98% Standard Proctor); poor compaction results in differential settlement and pavement failure.
- Plate load test is destructive; typically done on new projects or investigation sites; less common for routine QC.
- k increases with better drainage and stabilization; cement-stabilized base: k ≈ 150–250 MN/m³ vs natural base: k ≈ 30–50 MN/m³.
- Soaked CBR (after 4-day soak) is ~30–40% lower than unsoaked; Philippine standards typically require soaked CBR for design.
Key definitions
Subgrade
Example
Natural soil compacted to 95% Standard Proctor density; CBR tested at 0.1" penetration per ASTM D1883.
In-situ or compacted soil foundation beneath pavement; its bearing capacity (CBR or k) determines required pavement thickness.
Plate Load Test
Example
At 70 kPa, deflection = 1.25 mm → k = 70 kPa ÷ 0.00125 m = 56 MN/m³.
In-situ test measuring foundation stiffness; 75 cm rigid plate jacked down; pressure vs deflection plotted to find k.
Subgrade Reaction
Example
Sandy soil k = 40 MN/m³ vs clay soil k = 80 MN/m³; clay is stiffer, allows thinner slab.
Upward resistance of foundation soil per unit deflection; stiffer soil = higher k; controls slab thickness in rigid design.
Diagrams to know
- CBR penetration curve (load vs depth) and 2.5 mm penetration point.
- Plate load test setup: reaction beam, dial gauge, pressure vs deflection graph.
- Relationship between CBR and required pavement thickness (nomogram or design table).
Tire Contact and Wheel Load Mechanics
Formulas
A_contact = P / p
Meaning
A_contact = tire contact area (mm² or cm²); P = wheel load (N or kN); p = tire inflation pressure (MPa or kPa)
Watch out
Units must match: if P is in N and p is in N/mm² (MPa), result is mm². Convert carefully: 0.7 MPa = 0.7 N/mm².
When to use
Estimate contact stress and area; important for fatigue analysis and pressure bulb depth in flexible pavements.
Contact Stress (mean): q = P / A_contact = p (tire pressure)
Meaning
q = contact stress ≈ tire inflation pressure (for circular contact); uniform pressure distribution assumption
Watch out
Contact stress ≠ tire pressure exactly; stress distribution is non-uniform (higher at center). Use tire pressure as conservative upper bound.
When to use
Quick estimate of stress on pavement surface; typical truck tire: 0.6–0.9 MPa.
Depth of pressure bulb: z_max ≈ 1.5 × a (a = contact radius)
Meaning
z_max = approximate depth where 90% of load effect is concentrated; a = √(A_contact / π)
Watch out
Pressure bulb widens with depth. If subgrade is at ~1.5 m, wheel load effect is significant; drainage at depth is critical.
When to use
Estimate stress at depth (subgrade); if pressure bulb reaches weak layer, pavement may fail prematurely.
Common values
Value
0.7–0.9 MPa
Symbol
p
Quantity
Standard truck tire inflation pressure
Value
~57,000 mm² (~570 cm²)
Symbol
A
Quantity
Contact area for 40 kN wheel at 0.7 MPa
Value
~62,500 mm² (~625 cm²)
Symbol
A
Quantity
Contact area for 50 kN wheel at 0.8 MPa
Important facts
- Tire inflation pressure in Philippines: 0.7–0.9 MPa (7–9 bar) for trucks; higher pressure → smaller contact area → higher surface stress.
- Contact area assumption (P/p) is simplified; actual distribution depends on tire construction and deflection.
- Dual wheels on rear axles reduce contact stress by ~30% vs single wheel (larger total contact area); critical for thick asphalt design.
- Pressure bulb depth controls which pavement layers carry most load stress; shallow bulb concentrates stress in surface layer.
- Underinflated tires increase contact area, reduce surface stress but increase deflection and rutting risk.
Key definitions
Tire Contact Area
Example
40 kN wheel at 0.7 MPa → A ≈ 57,000 mm² ≈ 570 cm² (roughly 24 × 24 cm square).
Footprint of tire on pavement; related to wheel load and inflation pressure; higher pressure = smaller contact area.
Pressure Bulb
Example
Small contact area (high inflation pressure) → narrow, deep pressure bulb; large contact area (low pressure) → wide, shallow bulb.
Zone below pavement surface where stress from wheel load is concentrated; depth ≈ 1–2 × contact radius.
Equivalent Single Wheel Load
Example
Two 50 kN wheels (100 kN tandem) ≈ ~90–95 kN equivalent single wheel due to load spreading.
Standard wheel load used for design (typically 40 kN or 50 kN in Philippines); dual wheels treated as single equivalent load.
Diagrams to know
- Tire contact area footprint and pressure distribution (Boussinesq stress distribution).
- Pressure bulb shape and depth for different contact areas and loads.
- Comparison: narrow deep bulb (high tire pressure) vs wide shallow bulb (low tire pressure).
Traffic Loading and ESAL Conversion
Formulas
LEF = (W / W_std)⁴
Meaning
LEF = load equivalency factor (damage equivalence ratio); W = actual axle load (kN); W_std = standard axle (80 kN in most standards)
Watch out
Fourth-power relationship is approximate (AASHTO refines by axle type, pavement structure, and CBR). Small load increase = large damage increase: 100 kN → LEF ≈ 2.4.
When to use
Convert mixed traffic (cars, trucks, buses) to equivalent 80 kN single-axle loads for design traffic prediction.
Design ESAL = Σ(LEF_i × N_i) over design life
Meaning
Design ESAL = total cumulative 80 kN equivalent load passes; N_i = number of passes of axle type i; sum over all years of design period
Watch out
Must account for traffic growth rate (typically 3–5% annually); Design ESAL can be 10–50× initial year traffic for 20–year design life.
When to use
Estimate total traffic demand for pavement design; compare to pavement's allowable ESAL (from SN or thickness equations).
Annual ESAL (Year 1) = AADT × 365 × λ (λ = heavy vehicle fraction × directional factor × LEF)
Meaning
AADT = average daily traffic; λ = lane factor (depends on truck %), growth factor for design life applies after
Watch out
λ varies widely: 2-lane road might be 0.04–0.10 (4–10% trucks), while industrial road 0.20–0.40. Lane assignment matters (right lane carries more trucks).
When to use
Start pavement design: convert daily traffic count to annual ESAL; multiply by growth factor for design life ESAL.
Common values
Value
80 kN
Symbol
W_std
Quantity
Standard axle load
Value
0.06
Symbol
LEF
Quantity
LEF for 40 kN axle
Value
0.30
Symbol
LEF
Quantity
LEF for 60 kN axle
Value
2.44
Symbol
LEF
Quantity
LEF for 100 kN axle
Value
3.16
Symbol
LEF
Quantity
LEF for 120 kN axle
Value
0.002–0.01
Symbol
LEF
Quantity
LEF for typical car (passenger vehicle)
Value
2.0–2.5 ESAL
Symbol
Total LEF
Quantity
Typical truck (2-axle, 100 kN rear)
Important facts
- Fourth-power law (LEF = (W/80)⁴) is the backbone of traffic design — small increases in load cause disproportionately large damage.
- Design ESAL ≈ Year-1 ESAL × Growth Factor; 20-year design life with 3% growth ≈ 1.8–2.0× traffic multiplication.
- Philippines: trucks typically classified as 2-axle (40–60 kN rear) or 3-axle (80–120 kN rear dual); buses are medium trucks.
- Right lane (slow lane) carries 70–90% of truck traffic on 2-lane roads; directional factor ≈ 0.5; lane distribution ≈ 0.7–0.9.
- High-volume routes (arterial roads): ESAL = millions to tens of millions over 20 years. Rural roads: ESAL = hundreds of thousands.
Key definitions
Equivalent Single Axle Load (ESAL)
Example
A 100 kN single axle = 2.44 ESAL; a 50 kN axle = 0.24 ESAL; one truck (two axles 60 + 80 kN) ≈ 1.5–2.5 ESAL total.
Standardized unit of traffic damage: one 80 kN single axle load. All axles converted to ESAL for consistent design comparison.
Load Equivalency Factor (LEF)
Example
120 kN axle: LEF = (120/80)⁴ = 3.16 → 3.16× more damaging than standard axle.
Ratio of damage caused by one actual axle to damage by one standard 80 kN axle; fourth-power relationship.
Average Daily Traffic (AADT)
Example
On a National Highway: AADT = 3,000–5,000 veh/day. On a barangay road: AADT = 100–300 veh/day.
Total vehicle count in both directions divided by 365 days; baseline for traffic prediction.
Traffic Growth Factor
Example
3% growth, 20-year design life → growth factor ≈ 1.81 (final-year traffic ~1.8× year-1 traffic).
Multiplier accounting for increasing traffic over design life; depends on annual growth rate and design period.
Diagrams to know
- LEF vs axle load curve (fourth-power relationship; exponential increase above 80 kN).
- Traffic composition and LEF contribution by vehicle type (cars ≈ 0.002 ESAL each, trucks ≈ 1–3 ESAL each).
- Growth curve: ESAL accumulation over design life (linear on semi-log: exponential in reality).
Design Methods & Standards (Philippines Context)
Formulas
CBR Method Thickness: t = (P √W) / (K × CBR) (cm)
Meaning
t = total pavement thickness; P = wheel load (kN); W = number of repetitions; K = design constant (varies 0.008–0.012); CBR = subgrade bearing ratio (%)
Watch out
K factor is empirical and varies by standard; different K values yield significantly different thicknesses. Use DPWH K or equivalent.
When to use
DPWH Road Design Manual; simpler alternative to AASHTO SN for low-traffic roads and rural highways in Philippines.
AASHTO Flexible Design: log(W₁₈) = Z_R S_o + 9.36 log(SN+1) − 0.20 + log(Δ PSI / (4.2 − 1.5)) / (0.4 + 1094/(SN+1)⁵·19)
Meaning
W₁₈ = cumulative 80 kN ESALs; SN = structural number; Z_R = reliability factor; S_o = standard deviation; Δ PSI = serviceability loss
Watch out
Complex empirical equation; requires tables/nomograph. Z_R and S_o depend on reliability level (70–95%); Δ PSI typically 2.0–2.5.
When to use
AASHTO 1993 design; if using AASHTO in Filipino exams (less common, but appears in advanced design questions).
AASHTO Rigid Design: log(W₁₈) = Z_R S_o + 7.35 log(D+1) − 0.06 + (log(Δ PSI/(4.5−1.5))) / (1.624 − 0.0844/(D+1)⁸·⁴⁶)
Meaning
D = PCC slab thickness (inches); other terms same as flexible; used for rigid pavement thickness selection.
Watch out
D is in inches (convert if given in mm). Equation is even more complex than flexible; use design software or nomographs.
When to use
AASHTO rigid design; less common in Philippines but important for major concrete highways.
Common values
Value
85–90%
Symbol
R
Quantity
Reliability (national highways)
Value
80–85%
Symbol
R
Quantity
Reliability (provincial roads)
Value
70–80%
Symbol
R
Quantity
Reliability (barangay roads)
Value
0.40
Symbol
S_o
Quantity
Standard deviation (typical)
Value
4.0–4.2
Symbol
PSI_0
Quantity
Initial PSI (new pavement)
Value
1.5–2.0
Symbol
PSI_f
Quantity
Terminal PSI (acceptable end-of-life)
Important facts
- Philippine standard design life: 20 years for national roads; 15 years for provincial roads; 10 years for barangay roads.
- DPWH uses CBR method as primary design approach; AASHTO used mainly for advanced design and international standards alignment.
- Reliability level selection: 70–80% for low-traffic roads; 85–90% for major highways; > 95% for critical routes.
- Standard deviation S_o: typically 0.35–0.45 (accounts for material variability, construction, traffic prediction uncertainty).
- Design load ESAL must include growth factor over entire design life — often 1.5–2.5× year-1 traffic.
Key definitions
DPWH (Department of Public Works and Highways)
Example
DPWH Road Design Manual specifies CBR method, layer thicknesses, and construction specifications for national roads.
Philippine national road authority; sets design and construction standards; Road Design Manual is reference standard in Philippines.
Structural Number (SN)
Example
SN = 3.5 (low-traffic rural road); SN = 5.0 (medium-traffic). Required SN determined from AASHTO design equation.
Dimensionless pavement capacity index; SN = a₁D₁ + a₂m₂D₂ + a₃m₃D₃; larger SN = stronger pavement, handles more ESAL.
Serviceability
Example
New pavement PSI ≈ 4.2; failing pavement PSI ≈ 1.5; typical design ΔPSI = 2.0–2.7.
Pavement's ability to serve traffic; measured by Present Serviceability Index (PSI, 0–5 scale). ΔPSI = initial PSI − final PSI.
Reliability (R)
Example
R = 90% means 90% chance pavement won't fail within design life; Z_R (standard normal deviate) ≈ −1.282 for R = 90%.
Statistical confidence that designed pavement will meet traffic demand without distress; typically 80–90% for major roads.
Diagrams to know
- DPWH pavement design nomogram (CBR vs thickness).
- AASHTO design equation solution paths (nomograph or computer).
- Sensitivity analysis: how SN changes with reliability, serviceability, traffic.
Must remember
- Flexible pavements distribute load through layers (rutting & fatigue cracking); Rigid pavements carry load by slab bending (joints control cracking). Design approach, failure modes, and rehabilitation differ fundamentally.
- CBR is for flexible design (penetration test, % ratio); k = p/δ is for rigid design (modulus from plate test, MN/m³). Use the correct parameter for the pavement type.
- Tire contact area A = P/p (wheel load ÷ tire pressure). Higher pressure → smaller footprint → higher surface stress. Units: MPa & N → mm².
- LEF = (W/80)⁴ — fourth-power relationship. A 100 kN axle = 2.44 ESAL (nearly 2.5× damage). Small load increases cause disproportionate damage increases.
- Design ESAL = Year-1 ESAL × Growth Factor. Traffic grows over design life; 20-year design at 3% growth ≈ 1.8–2.0× multiplication. Must account for growth in pavement selection.
- Layer Structural Number (SN) = a₁D₁ + a₂m₂D₂ + a₃m₃D₃. Asphalt ≈ 0.40, Base ≈ 0.14, Subbase ≈ 0.07. Drainage factor m = 0.4–1.0; poor drainage = low m.
- Westergaard stress (rigid pavement): σ = 0.75P/h² (interior) or ≈1.3× interior (edge load). Must stay below modulus of rupture (MR ≈ 3.5–4.5 MPa). Joint load transfer (dowels) affects stress distribution.
- Philippine standard: DPWH CBR method for flexible; design life 20 yr (national), 15 yr (provincial), 10 yr (barangay). Tropical climate → moisture control critical; good base drainage is essential.
- Pressure bulb depth ≈ 1–2 × contact radius. If subgrade is weak, pressure bulb may reach it. Larger contact area (low tire pressure, dual wheels) → wider, shallower bulb; concentrates less stress at depth.
- Modulus of subgrade reaction k increases with stabilization: natural base k ≈ 30–50 MN/m³; cement-stabilized base k ≈ 150–200 MN/m³. Better base → thinner slab required.
Last minute tips
- On exam, identify the pavement TYPE first (flexible = asphalt, rigid = concrete). This determines which design approach (CBR & SN vs Westergaard & k) and which failure modes (rutting/fatigue vs flexural cracking/faulting) are relevant. Wrong type = wrong entire solution.
- Watch units with tire contact area: P in kN (multiply by 1000 to get N), p in MPa (= N/mm²). Then A = P(N) / p(N/mm²) = mm². Convert final answer to cm² if needed. Mixing inch/metric is a common trap.
- Fourth-power law: LEF = (W/80)⁴. Memorize key values: 50 kN = 0.14, 60 kN = 0.30, 80 kN = 1.0, 100 kN = 2.44. If load increases 25% (80 → 100), damage increases ~144% (1.0 → 2.44). Intuitive check: larger exponent = steeper increase.
- ESAL accumulation: Always apply growth factor to Year-1 ESAL. For 20-year design at 3% annual growth, growth factor ≈ 1.81. If Year-1 ESAL = 50,000, then Design ESAL ≈ 90,000+. Skip growth factor = underdesign.
- CBR vs k: If problem gives subgrade test result and asks for flexible design → use CBR method. If asks for rigid pavement → use k and Westergaard. Confusing them is an instant mark loss. Note: k can be estimated from CBR (rough: k ≈ 2000 × CBR in MN/m³), but better to use measured value if given.
Comparison tables
Flexible vs Rigid Pavement Design & Behavior
| Aspect | Flexible (Asphalt) | Rigid (PCC Concrete) |
|---|---|---|
| Load Distribution Mechanism | Through layered material stiffness; load spreads at 45–60° angle | Slab bending (beam on elastic foundation); load spreads ~3× contact width |
| Design Parameter (Strength) | CBR (California Bearing Ratio, %); used for flexible design thickness | k (modulus of subgrade reaction, MN/m³); used for slab thickness |
| Critical Design Input (Traffic) | Design ESAL (equivalent 80 kN axle loads) | Design ESAL (equivalent 80 kN axle loads); plus joint spacing & load transfer |
| Primary Failure Mode | Rutting (permanent deformation) & fatigue cracking (bottom-up propagation from tension in base/AC) | Flexural cracking (top-down from bending stress); joint faulting; pumping at joints |
| Layer Composition | AC surface (40 mm–50 mm) + base + subbase + subgrade | PCC slab (150–250 mm) + subbase (100–150 mm) + subgrade |
| Joint Requirement | None required; thermal stress accommodated by deflection | Transverse joints every 4–6 m; doweled or tied; critical for load transfer & crack control |
| Maintenance & Rehabilitation | Overlay (place new AC on existing); can rehabilitate without full removal; relatively quick repairs | Concrete patching, full slab replacement, or diamond grinding; more costly; longer construction time |
| Cost (initial) / Durability | Lower initial; 15–20 year design life; requires periodic seal coat, overlay maintenance | Higher initial; 25–40 year design life (well-maintained); lower maintenance if joints work properly |
| Climate Sensitivity (Philippines: tropical, monsoon) | High: moisture infiltration → base weakening, rutting; good drainage critical; reflective cracking if overlaid | Moderate: joints allow expansion/contraction; surface sealing prevents water ingress; less affected by base weakness |
| Design Standard (Philippines) | DPWH CBR method; AASHTO SN method (less common) | AASHTO rigid design; DPWH guidelines; Westergaard stress formula |
CBR Classification & Pavement Thickness Implications
| CBR Range (%) | Soil Classification | Typical Soil Type | Minimum Pavement Thickness (mm, 10,000 ESAL) |
|---|---|---|---|
| < 3 | Very Poor | Clay, silt; soft laterite | 400–600 mm (stabilization required) |
| 3–6 | Poor | Clayey sand, poorly graded soil | 300–400 mm |
| 6–12 | Fair | Sandy soil, laterite | 200–300 mm |
| 12–20 | Good | Laterite, sandy gravel | 150–200 mm |
| > 20 | Excellent | Crushed stone, stable aggregate | 100–150 mm (or less) |
Common LEF Values (Quick Reference for 80 kN Standard Axle)
| Axle Load (kN) | LEF (Load Equivalency Factor) | Interpretation |
|---|---|---|
| 40 | 0.06 | 1 axle = 0.06 ESAL; ~16 axles = 1 ESAL |
| 50 | 0.14 | 1 axle = 0.14 ESAL; ~7 axles = 1 ESAL |
| 60 | 0.30 | 1 axle = 0.30 ESAL; ~3 axles = 1 ESAL |
| 80 | 1.00 | 1 axle = 1 ESAL; standard reference |
| 100 | 2.44 | 1 axle = 2.44 ESAL; 2.4× more damaging |
| 120 | 3.16 | 1 axle = 3.16 ESAL; heavily overloaded |
Modulus of Subgrade Reaction (k) — Typical Values by Foundation Type
| Foundation Type | k Range (MN/m³) | Characteristics | Suitable for Rigid Design |
|---|---|---|---|
| Poor clay (soft, wet) | 10–30 | Low stiffness; high settlement risk | Poor; may require stabilization |
| Sandy soil (natural) | 30–50 | Moderate stiffness; drainage good | Acceptable; standard design |
| Laterite (compacted) | 50–80 | Good stiffness; common in Philippines | Good; typical for PH roads |
| Clay (well-drained, compacted) | 60–100 | Good stiffness; CBR 12–20% | Good; standard |
| Cement-stabilized base | 100–180 | Stiff, durable; increased bearing | Excellent; allows thinner slab |
| Bituminous-stabilized base | 80–120 | Good stiffness; good drainage | Excellent; intermediate option |
Diagrams
Pavement Design Decision Tree: Flexible vs Rigid
Decision flowchart for selecting flexible vs rigid pavement based on traffic, climate, and maintenance priorities. Shows typical Philippine conditions and key design steps for each type.
Critical Pavement Design Formulas & Variables Map
Comprehensive mind map organizing all key formulas, layer coefficients, typical values, and relationships. Quick visual reference for formula selection and variable meanings during exam.