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Pavement Analysis and Design
Pavement Types- overview
Pavement Types
• Road pavement – a structure of superimposed layers of selected and processed material that is placed on a foundation/ subgrade.
• Traditionally pavements are divided into two categories - flexible and rigid
• This categorization is on the basis of how the pavement responds to load and climatic conditions
Pavement Types
•Flexible pavements : bituminous surfacing over base, subbase and subgrade
•Rigid pavement : Portland cement concrete slab with or without base and placed over subgrade
Flexible Pavement
•Flexible pavements- surfaced with bituminous (or asphalt) materials. These types of pavements are called "flexible" since the total pavement structure "bends" or "deflects" due to traffic loads.
•A flexible pavement structure - composed of several layers of materials which can accommodate this "flexing
Flexible pavements
Conventional flexible pavements- layered systems with better materials at top where intensity of stress is high and interior at the bottom where stress is low.
Examples of flexible pavements
Surface layer of flexible pavement
Cross section of WBM
Load Distribution –
Flexible Pavement
Basic Structural Elements of Flexible Pavement
Material layers are usually arranged within a pavement structure in order of descending load bearing capacity with the highest load bearing capacity material (and most expensive) on the top and the lowest load bearing capacity material (and leastexpensive) on the bottom.
•Surface Course- contact with traffic loads
•provides characteristics such as friction, smoothness, noise control, rut resistance and drainage.
•prevents entrance of surface water into the underlying base, subbase and subgrade
•This top structural layer of material is sometimes subdivided into two layers: the wearing course (top) and binder course(bottom).
•Surface courses are most often constructed out of HMA.
•Base Course- immediately beneath the surface course.
•provides additional load distribution and contributes to drainage
•Base courses are usually constructed out of crushed aggregateor HMA.
•Subbase Course- between the base course and subgrade.
•primarily as structural support but it can also minimize the intrusion of fines from the subgrade into the pavement structure and improve drainage.
•Generally consists of lower quality materials than the base course but better than the subgrade soils.
•A subbase course is not always needed or used.
•Subbase courses are generally constructed out of crushed aggregate or engineered fill.
Bituminous pavement
http://www.heroncay.com/WEB-MD/HCLVBB/DIRECTIONS/IMG_9306-Expressway%20Ends%20Sign.jpg
WBM
WBM
Rigid Pavement
-high flexural strength
-Load- through slab action
-Structural failure
-- joints
--stresses- load, temperature
Concrete Pavement
Design Approaches
empirical
analytical/theoretical/rational
Pavement Design
Determination of combination of thickness of various layers in most economical way to sustain the load for given input parameters such that no part of the structure is excessively stressed.
Pavement Analysis
- stress/strain/ deflection at any point in the pavement system for applied wheel load conditions
Design Approaches
Empirical Design
Relationships between design inputs (e.g., loads, materials, layer configurations and environment) and pavement failure were determined using experience, experimentation or a combination of both.
Although the scientific basis for these relationships is not firmly established, they can be used with confidence as long as the limitations with such an approach are recognized.
Specifically, it is not prudent to use an empirically derived relationship to describe phenomena that occur outside the range of the original data used to develop the relationship.
Empirical Approach- Design
CBR Method of Pavement Design
Input:
CBR Value ( strength of subgrade) and Traffic details ( No. of commericialvehilces, standard axle load (msa), damage factor (VDF), annual rate of growth of traffic…etc)
)1(]1)1[(365
FXr
rAXN
x
S
−+=
Traffic, msa
Thickness of pavement
CBR of soil
IRC: 37 –1984 Empirical Method
�Analytical/ Mechanistic / Rational�Takes into Account the Mechanistic Behaviour of Pavement Components
�Structural Responses of Pavement to applied load are analyzed
�Critical Responses having strong bearing on the performance are identified and Controlled during design
Analytical Design Approach
IRC-37-2001 ( mechanistic approach)
365 X A [ (1+r)n - 1 ]Nc = ----------------------------- x F x D
rwhere,
Nc = Cumulative Standard Axles to be catered for in the design
A = Initial traffic, in the year of construction, in terms of the
number of commercial vehicles per day
r = annual growth rate of commercial traffic.
n = Design life in years
F = VDF (number of standard axles per Commercial axle)
D = Lane Distribution Factor
IRC-37-2001 ( mechanistic approach)
· Wheel Load: Standard load (8.2T)- To convert all wheel loads- std. wheel load- AASHTO load equivalency factors(ESLF). Measured using-portable weigh pad
ni= no. of passes of the ith axle load group
Generally damage due to wheel load – fourth power formula
GroupiforEALFFgroupsloadaxleofnomwherenFEASL thi
m
iii === ∑
=;.
1
VDF calculation
Axle Load Survey
SlNo
Load on Tyre Axle Load Frequency of Axle load (T)
Front Rear Front Rear 0-2
2-4 4-6
6-8
8-10
10-12 12-14 14-16 16-18 18-20
1
2
3
4
5
6
Axle Load Group, T
Mid PointT
Frequency AASHTOEquivalency factor
EquivalentStd. axles
0-2 01
2-4 03
4-6 05
6-8 07
VDF
Sum=
VDF= sum of equivalent std. axles/ No. of commercial vehicles observed
AASHTO Equivalency factor: Forth power law
n1
n2
n3 (5/8.2)4
(3/8.2)4
(1/8.2)4 n1*(1/8.2)4
n2*(3/8.2)4
n3*(5/8.2)4
Mechanistic-Empirical Design
Unlike an empirical approach, a mechanistic approach seeks to explain phenomena only by reference to physical causes.
Design phenomena : stresses, strains and deflectionswithin a pavement structure, and the physical causes are the loads and material properties of the pavement structure.
The relationship between these phenomena and their physical causes is typically described using a mathematical model. Various mathematical models can be used.
Mechanistic Method of flexible pavement Design
Basic advantages of a mechanistic-empirical pavement design method over a purely empirical one are:
•It can be used for both existing pavement rehabilitation and new pavement construction.
•Accommodates changing load types.
•Better characterize materials.
•Uses material properties that relate better to actual pavement performance.
•Provides more reliable performance predictions.
•Better defines the role of construction.
•Accommodates environmental and aging effects on materials.
Contact pressure, pP
E, µ
Circular contact area, radius “a”
r
z
σσσσz
ττττzr
σσσσrσσσσt
ττττrz
Analysis of linear elastic multilayer system
three normal stresses (vertical, radial, tangential) and one
shear stress (ττττzr = ττττzr ) on any cylindrical element in a homogenous, isotropic material
2a
p
Layer 1
Layer 2
Layer 3
Layer n
E1, µµµµ1
E2, µµµµ2
E3, µµµµ3
En, µµµµn
h1
h2
h3
αααα
Elastic multilayered system - Assumptions
• The material in each layer is homogeneous
• The material in each layer is isotropic
• The materials are linearly elastic with an elastic modulus of E and a Poisson’s ratio of µ
• The layers are infinite in areal extent
• Each layer is of finite thickness except the nth layer.
• The material is weightless
Elastic multilayered system - Assumptions
• Uniform pressure applied at surface over circular contact area
• Continuity conditions
• For full friction between layers (same vertical stress, shear stress, vertical displacement and radial displacement)
• For frictionless (smooth) interface, Zero shear stress at each side of the interface
• No shearing forces at the surface – some models consider them
Elastic multilayered system - Assumptions
K1 = E1/E2, k2 = E2/E3, A = a/h2, H = h1/h2
Peattie charts and Jones’ tables for obtaining different stress parameters for a given combination of K1, K2, A and H
sz1 = (ZZ1)p; sz2 = (ZZ2)p(sz1 – sr1) = (ZZ1 – RR1)p(sz2 – sr2) = (ZZ2 – RR2)p(sz2 – sr3) = (ZZ2 – RR3)p
Five coefficients ZZ1, ZZ2, (ZZ1-RR1), ZZ2-RR2) and (ZZ2-RR3) to be obtained from charts and tables
3 - layer systems
Computation of two critical strains
Tensile strain at the bottom of first layer and vertical compressive strain on subgrade
er1 = (sr1/E1 – m1*st1/E1 – m1*sz1/E1)For m1 = 0.5 and since st1= sr1 due to symmetry)er1 = (1/2E1)*(sr1- sz1)
ez3 = (sz2/E3 – m3*st3/E3 – m3*sr3/E3)= (1/2E3)*(sz2 – sr3) (for Poisson ratio of 0.5)
3 - layer systems
Commercial software
No. of software are available for analysis of layered systems with different capabilities
No. of layers that can be handled
Loading – normal and shear stresses at surface
Rough and smooth interfaces
FEM analysis for non-linear analysis of pavements layers (especially the granular layers)
Analysis of layered systems
� Fatigue Cracking of Bituminous bound Layer
– Caused by Repeated Application of Wheel Loads of Commercial Vehicles
� Rutting along Wheel paths
– Due to Permanent Deformation in pavement layers (mainly in subgrade)
Main Structural Failures
h1
h2
E1, µ1
E2, µ2
E3, µ3
εz
εt
Critical Pavement Responses
Tensile Strain at the Bottom of Bituminous layer
Vertical Strain on Top on Subgrade
Inputs to Mechanistic Pavement Design
Strength of all layers
Poisson ratio values
Standard Load , tyre pressure
Traffic Loads- standard axle ( msa)
Temperature
Failure criteria ( Rutting and fatigue failures)
Rut Depth
Bituminous Layer
Granular Layer
Subgrade
Crocodile Cracking
Rigid Pavement
Rigid pavements
•These are portland cement concrete pavements, which may or may not incorporate underlying layers of stabilized or unstabilized granular materials.
• Since PCC is quite stiff, rigid pavements do not flex appreciably to accommodate traffic loads
•Rigid pavement, because of PCC's high stiffness, tends to distribute the load over a relatively wide area of subgrade
•The concrete slab itself supplies most of a rigid pavement's structural capacity.
•Flexible pavement uses more flexible surface course and distributes loads over a smaller area and relies on a combination of layers for transmitting load to the subgrade
Rigid Pavement
Concrete Pavements
• Deflections are very small and hence the name “rigid pavement”
• The high flexural strength of the slab is predominant and the subgrade strength does not have as much importance as it has in the case of flexible pavements
• Usually finite slabs with joints (jointed concrete pavements)
• Continuous slabs also can be constructed (without joints). Usually with reinforcement
Concrete Pavements
Concrete Slab
Granular Base
Subgrade
Concrete Pavements
Subgrade
Concrete Slab
Subbase or base
Longitudinal joint
Transverse joints
Dowel barsTie bars
Concrete Pavement
Concrete Pavement - Components
• Concrete Slab
• Granular or stabilised base
• Granular or stabilised subbase
• Subgrade
• Joints are the other main features of concrete pavement significantly affecting its performance
Concrete Pavements
Stresses in slabs are caused by
• Wheel loads – flexural (repeated applications)
• Temperature differential within the thickness of the slab causing curling
• Uniform temperature variation causing shrinkage or expansion
• Change in moisture and the corresponding volumetric change in subgrade, base or slab
• A combination of all these factors
Concrete Pavements – Mechanical Model
The two commonly used models for concrete pavements differ in their assumption about foundation
Dense liquid / spring / Winkler foundation
Elastic foundation
Foundation Types
Slab on Spring Foundation
Most commonly used
No shear strength
Suitable for soft cohesive soils
Slab on Elastic layers
Complex analysis
Suitable for stiff base layers
Spring Foundation
Slab on Spring Foundation
Foundation is represented by its spring constant known as modulus of subgrade reaction (k)
K determined by conducting plate load test
Radius of relative stiffness of slab and subgrade
p = k ∆∆∆∆
Reactive pressure on foundation, p a D
Radius of relative stiffness of slab and subgrade
Stiffness term for a slab = (Eh3/(12(1-m2))
Equating this to kl4, where k is the modulus of subgrade reaction and “l” is the radius of relative stiffness of slab and subgrade
l = ((Eh3/(12 k (1- m2)))(1/4)
Modulus of Subgrade Reaction
Plate Load Test
Reaction frame
Stiff loading plate
Hydraulic Jack
Load is gradually increased and the deflection of the foundation observed
Modulus of Subgrade Reaction
Plate Load Test
750mm plate
Correction for moisture
Determined for 1.25mm
Settlement, ∆
Be
ari
ng
Pre
ssu
re,
p
K = p / ∆∆∆∆
Westergaard’s Analysis
Slab on Winkler Foundation
Considered three wheel load positions for analysis
Corner, edge, interior
Wheel Load Stresses
Westergaard (1926) developed equations for solution of load stresses at three critical regions of the slab – interior, corner and edge
Interior – Load in the interior and away from all the edges
Edge – Load applied on the edge away from the corners
Corner – Load located on the bisector of the corner angle
Wheel Load Stresses
Interior
Edge Corner
Wheel Load Stresses
Westergaard solutions for a Poisson ratio of 0.15 for concrete
Interior loading (tensile stress at the slab bottom)
σσσσi (psi) = (0.3162P/h2) 4 log10 (l / b) + 1.069)
Edge loading (tensile stress at the slab bottom)
σσσσe (psi) = (0.572P/h2) 4 log10 (l / b) + 0.359)
Corner loading (tensile stress at slab top)
σσσσc (psi) = (3P/h2) 1 – ((a (2)(1/2)) / l)0.6
Wheel Load Stresses
Where,
P = wheel load, lbs
h = slab thickness, inches
a = radius of wheel contact area (circular contact)
b = radius of resisting section, inches
= (1.6a2 + h2)(1/2) – 0.675 (h) for a < 1.724 h
= a when a >= 1.724 h
l = radius of relative stiffness, inches
Curling Stresses in a Finite Slab
x
y
Lx
Ly
sx = (CxEaDt)/(2(1- m2)
+ (CymEaDt)/(2(1- m2)
= ((EaDt)/(2(1- m2))(Cx + mCy)
sy = ((EaDt)/(2(1- m2))(Cy + mCx)
a = Coefficient of thermal expansion of concrete
Interior
Bradbury Coefficients
1.2
1.0
0.8
0.6
0.4
0.2
0.00.0 5 10 15
Warp
ing
Str
ess C
oeff
icie
nt,
C
Ratio B/l
B = Free length or width of slab
Curling Stresses
Edge Stresses
σ = (CEaDt)/2
Corner Stress - Negligible
Stresses due to Friction• Volumetric change in concrete induces tensile stresses in concrete and
• Causes opening of joints leading to reduction in load transfer efficiency
Stresses due to Temperature Difference within the slab
• Due to temperature differential within the slab thickness
• Day Time – The slab curls up (top convex)
• Night time – slab curls down (top concave)
• Due to weight of slab and resistance offered by the foundation, stresses are induced
Stresses due to Temperature Difference within the slab
T1 > T2
T2
T1 > T2
T2
Day time
Night time
C
T
T
C
Critical Combination of Stresses
Night Time
Thermal stresses (tension at top) compensate stresses due to loads (compression at top)
Afternoon
Thermal stresses will be additive to load stresses
Concrete Pavements without expansion joints –End restraint stresses (compression) in summer
Flexible Pavements
Load distribution from grain to grain
Possess less flexural strength
Design is based on Foundation layer strength and wheel load associated parameters
Temperature stresses not considered, however modulus value of bituminous layer is selected based on temperature
sub base, base course, surface course are the layer over foundation [subgrade]
Examples of Flexible Pavements
Water Bound Macadam (WBM), Wet Mix Macadam (WMM), Earthen Roads, All types of bituminous pavement [ BC, BM, SDBM, PM…etc]
Design Methods: IRC:37-2001 [In India] for BC
IRC: SP:20-2002 for Rural roads
AASHTO- 2002; AUSTROADS, SHELL Method
Design input parameters
• Strength of foundation layer and other layers
• Traffic, wheel load associated parameters such as standard axle load [ 8.2 t], tyre pressure, Vehicle damage factor,
•Performance criteria [ relating rutting and fatigue with critical parameters and controlling these to avoid failure in these modes]
Relating strains with life of the pavement
[N with strain]
Rigid Pavement
Load distribution- slab action { wider area]
Posses high flexural strength
Design is based on wheel load, temperature
Depends less on foundation layer parameters
Placed directly over subgrade[ foundation] or on base course.
Rigid Pavement Design
IRC: 58-2002 [ In India]
AASHTO Rigid Pavement Design
PCA Method
Rigid Pavement Design
Load stresses- three places [ interior, edge and corner]
stresses using Westergaard Analysis
Rigid Pavement- Stress equations
Interior loading (tensile stress at the slab bottom)
σσσσi (psi) = (0.3162P/h2) 4 log10 (l / b) + 1.069)
Edge loading (tensile stress at the slab bottom)
σσσσe (psi) = (0.572P/h2) 4 log10 (l / b) + 0.359)
Corner loading (tensile stress at slab top)
σσσσc (psi) = (3P/h2) 1 – ((a (2)(1/2)) / l)0.6
Rigid Pavement Design
Similarly
Temperature stresses at three locations
Combination of stress [ load and temperature stress]- to be compared with flexural strength of the concrete to calculate the thickness of concrete slab.
No. of joints are present- these are to be designed [ expansion, contraction, long. Joint…etc]