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]