Factors affecting Pavement Design
Traffic and loading
Traffic is the most important factor in the pavement design. The key factors include contact pressure, wheel load, axle configuration, moving loads, load, and load repetitions.
- Contact pressure: The tire pressure is an important factor, as it determines the contact area and the contact pressure between the wheel and the pavement surface. Even though the shape of the contact area is elliptical, for sake of simplicity in the analysis, a circular area is often considered.
- Wheel load: The next important factor is the wheel load which determines the depth of the pavement required to ensure that the subgrade soil is not failed. Wheel configuration affect the stress distribution and detection within pavement. Many commercial vehicles have dual rear wheels which ensure that the contact pressure is within the limits. The normal practice is to convert dual wheel into an equivalent single wheel load so that the analysis is made simpler.
- Axle configuration: The load carrying capacity of the commercial vehicle is further enhanced by the introduction of multiple axles.
- Moving loads: The damage to the pavement is much higher if the vehicle is moving at creep speed. Many studies show that when the speed is increased from 2 km/hr to 24 km/hr, the stresses and detection reduced by 40 percent.
- Repetition of Loads: The influence of traffic on pavement not only depend on the magnitude of the wheel load, but also on the frequency of the load applications. Each load application causes some deformation and the total deformation is the summation of all these. Although the pavement deformation due to single axle load is very small, the cumulative effect of number of load repetition is significant. Therefore, modern design is based on the total number of standard axle load (usually 80 kN single axle).
The following material properties are important for both Flexible and rigid pavements.
- When pavements are considered as linear elastic, the elastic moduli and poisson ratio of subgrade and each component layer must be specified.
- If the elastic modulus of a material varies with the time of loading, then the resilient modulus, which is elastic modulus under repeated loads, must be selected in accordance with a load duration corresponding to the vehicle speed.
- When a material is considered non-linear elastic, the constitutive equation relating the resilient modulus to the state of the stress must be provided.
However, many of these material properties are used in visco-elastic models which are very complex and in the development stage. This book covers the layered elastic model which requires the modulus of elasticity and Poisson's ratio only.
Environmental factors affect the performance of pavement materials and cause various damages. Environmental
factors that affect pavement are of two types, temperature and precipitation and they are discussed
- Temperature: The effect of temperature on asphalt pavements is different from that of concrete pavements. Temperature affects the resilient modulus of asphalt layers, while it induces curling of concrete slab. In rigid pavements, due to difference in temperatures of top and bottom of slab, temperature stresses or frictional stresses are developed.
While in Flexible pavement, dynamic modulus of asphaltic concrete varies with temperature. Frost heave causes differential settlements and pavement roughness. Most detrimental effect of frost penetration occurs during the spring break up period when the ice melts and subgrade is a saturated condition.
- Precipitation: The precipitation from rain and snow affects the quantity of surface water in filtrating into the subgrade and the depth of ground water table. Poor drainage may bring lack of shear strength, pumping, loss of support, etc
Flexible pavements are those, which on the whole have low or negligible flexural strength and are rather flexible in their structural action under the loads.
A typical flexible pavement consists of four components: 1. soil subgrade 2. sub-base course 3. base course 4. surface course.
(i) Stress Under Road Surface as per Boussineq’s Equation,
σz = vertical stress at depth z.
q = surface pressure.
z = depth at which σz is computed.
a = radius loaded area.
(ii) As per IRC
Maximum legal axle load = 8170 kg
Equivalent single wheel load = 4085 kg.
(v) Equivalent Single Wheel Load (ESWL)
Methods of Flexible Pavement Design
(i) Group Index Method
G.I = 0.2a + 0.005ac + 0.01bd
(ii) C.B.R Method
(b) The thickness of Pavement, (T)
where, P = Wheel load in kg.
CBR = California bearing ratio in percent
p = Tyre pressure in kg/cm2
A = Area of contact in cm2.
a = Radius of contact area.
(c) Number of a heavy vehicle per day for design (A),
where, A = No. of vehicles at the end of design period.
P = Number of heavy vehicles per day at least count.
r = Annual rate of increase of heavy vehicles
n = Number of years between the last count & the year of completion of construction.
(d) CBR Method of pavement design by cumulative standard axle load,
Ns = Cumulative number of standard axle load
A’ = Number of the commercial vehicle per day when construction is completed considering the number of lanes.
n = Design life of the pavement, taken as 10 to 15 years.
F = Vehicle damage factor.
D = Lane distribution factor
(iii) California Resistance Value Method
where, T = Total thickness of pavement, (cm)
k = Numerical constant = 0.166
T.I = Traffic Index
T.I = 1.35(EWL)0.11
R = Stabilometer resistance value
C = Choesiometer value.
where, T1 & T2 are the thickness values of any two pavement layers & C1 & C2 are their corresponding Cohesiometer values.
(iv) Triaxial Method
(a) Thickness of pavement required for single layer, (TS)
where, TS = Thickness in cm
P = Wind load in kg
X = Traffic coefficient
Y = Rainfall coefficient
ES = Modulus of elasticity of subgrade soil (kg/cm2)
a = Radius of contact area (cm)
Δ = Design deflection (0.25 cm)
(b) Thickness of Pavement Consist of Two layer system,
where, EP = Modulus of elasticity of pavement material
(v) MC Load Method
where, T = Required thickness of gravel base (cm)
P = Gross wheel load, (kg)
k = Base course constant.
(vi) Burmister Method (Layered System)
Displacement equations given by Burmister are,
where, are Poisons ratio for soil subgrade & pavement.
For single layer, F2 = 1
P = Yielded pressure
ES = Subgrade modulus
a = Radius of loaded area
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Rigid pavements are those which posses note worthy flexural strength or flexural rigidity. The stresses are not transferred from grain to grain to the lower layers as in the ease of flexible pavement layers. The rigid pavements are made of Portland cement concrete-either plain, reinforced or prestressed concrete. The plain cement concrete slabs are expected to take-up about 40 kg/cm2 flexural stress.
(i) Modulus of subgrade reaction (k),
where, k = Modulus of subgrade reaction (kg/cm2/cm)
p = Pressure required for ‘Δ’ deflection (kg/cm2)
Δ = Deflection(cm)
For 75 cm dia plate, Δ = 1.25 mm
(ii) Radius of Relative Stiffness (l)
where, l = Radius of relative stiffness, cm
E = Modulus of elasticity of cement concrete (kg/cm2)
μ = Poisson’s ratio for concrete = 0.15
h = Slap thickness (cm)
k = Subgrade modulus or modulus of subgrade reaction (kg/cm3)
(iii) Equivalent Radius of Resisting Section (b)
when a < 1.724 h
(b) b=a when a > 1.724h
where, a = Radius of contact area (cm)
h = Slab thickness (cm)
(iv) Glodbeck’s Formula for Stress due to Corner Load
where, SC = Stress due to corner load (kg/cm2)
P = Corner load assumed as a concentrated point load, (kg)
h = Thickness of slab (cm).
(v) Westergards Stress Equation
(a) Stress at Interior Loading (Si)
(b) Stress at Edge Loading (Se)
(c) Stress at Corner Loading (Sc)
where, h = Slab thickness (cm)
P = Wheel load (kg)
a = Radius of contact area (cm)
l = Radius of relative stiffness (cm)
b = Radius at resisting section (cm).
(vi) Warping Stresses
(a) Stress at Interior Region
where, Warping stress at interior region (kg/cm2)
E = Modulus of elasticity of concrete, (kg/cm2)
α = Coefficient of thermal expansion (/°c)
CX = Coefficient based on in desired direction.
Cy = Coefficient based on in right angle to the above direction.
μ = Poissons’s ratio ∼ 0.15
LX & Ly are the dimensions of the slab considering along X & y directions along the length & width of slab.
(b) Stress at Edge Region
(c) Stress Corner Region
where, a = Radius of contact area
l = Radius of relative stiffness
(vii) Frictional Stress (Sf)
where, SF = Frictional stress (kg/cm2)
W = Unit weight of concrete, (kg/cm3)
f = Friction constant or coefficient of subgrade restraint
L = Slab length (m)
B = Slab width (m)
(viii) Combination of Stresses
- Critical Combination During Summer
(a) Stress for edge/interior regions at Bottom = (+ load stress) + (warping stress of day time) – Frictional stress
(b) Stress for corner region at top = (+ load stress + warping stress at night)
2. Critical Combination During Winter
(a) Stress for edge/interior at bottom = (+ load stress + warping stress at day time + Frictional stress)
(b) Stress for corner at top = (load stress + warping stress at night)
Design of Joints in Cement Concrete Pavements
(i) The spacing of expansion joints, (Le)
Where, δ’ = Maximum expansion in slab (cm)
Le = Spacing of expansion joint (m)
α = Coefficient of thermal expansion of concrete (/°c)
(ii) The spacing of the contraction joint, (Lc)
(a) When reinforcement is not provided
where, Lc = Spacing of contraction joint (m)
SC = Allowable stress in tension in cement concrete.
f = Coefficient friction ∼ 1.5
w = Unit weight of cement concrete (kg/m3).
(b) When reinforcement is provided
where, SS = Allowable tensile stress in steel (kg/cm2)
AS = Total area of steel in cm2.
(iii) Longitudinal Joints
where, AS = Area of steel required per meter length of joint (cm2)
b = Distance between the joint & nearest free edge (m)
h = Thickness of the pavement (cm)
f = Coeff. of friction ∼ 1.5
w = Unit wt. of concrete (kg/cm3)
Ss = Allowable working stress in tension for steel (kg/cm2)
where, Lt = Length of tie bar
SS = Alloable stress in tension (kg/cm2) ∼ 1400
Sb = Allowable bond stress in concrete (kg/cm2)
= 24.6 kg/cm2 for deformed bars
= 17.5 kg/cm2 for plain tie bars
d = diameter of tie bar (cm).
IRC recommendations for design of cement concrete pavements
Ad = P’[1+r](n+20)
where, Ad = Number of commercial vehicles per day (laden weight > 3 tonnes)
P’ = Number of commercial vehicles per day at last count.
r = Annual rate of increase in traffic intensity.
n = Number of years between the last traffic count & the commissioning of new cement concrete pavement.