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Dr. P. NANJUNDASWAMY Department of Civil Engineering S J College of Engineering Mysore – 570 006 [email protected]

Dr. P. NANJUNDASWAMY Department of Civil Engineering S J … · 2018-01-11 · Dr. P. NANJUNDASWAMY Department of Civil Engineering S J College of Engineering Mysore –570 006 [email protected]

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Dr. P. NANJUNDASWAMYDepartment of Civil Engineering

S J College of EngineeringMysore – 570 006

[email protected]

Outline

Introduction

Background on Stress and Strain in Flexible pavements

Approaches for Stress Analysis

Multi-Layer Computer Programs

Introduction

Typical Flexible Pavement Section can be idealized as a multi-layered system

Soil Subgrade

Sub-base course

Base course

Surface course

having different material properties

Introduction

Methods of designing flexible pavements

Empirical with or without a soil test

Limiting shear failure

Mechanistic empirical

Currently, the design is largely empirical

Mechanistic design is becoming more prevalent

Introduction

Mechanistic approach requires the accurate evaluation of

StressesStrainsDeflections

in pavements due to wheel loads

Basics

Stress

Deflection/Deformation

Strain

Stiffness

Poisson’s Ratio

Hooke’s Theory of Elasticity

Principle of Superposition

Approaches

To compute Stresses, Strains & Deflections

Layered elastic methods

Two-dimensional (2D) FE modeling

Three-dimensional (3D) FE modeling

Layered Elastic Approach

Is the most popular and easily understood procedure.

In this method, the system is divided into an arbitrary number of horizontal layers

The thickness of each individual layer and material properties may vary from one layer to the next.

But in any one layer the material is assumed to be homogeneous and linearly elastic.

Layered Elastic Approach

Although the layered elastic method is more easily implemented than finite element methods, it still has severe limitations:

materials must be homogenous andlinearly elastic within each layer

the wheel loads applied on the surface must be axi-symmetric

2D Finite Element Analysis

Plane strain or axis-symmetric conditions

are generally assumed.

It can rigorously handle material anisotropy,

material nonlinearity, and a variety of

boundary conditions – more applicable to

practical situations

Unfortunately, 2D models can not

accurately capture non-uniform tire contact

pressure and multiple wheel loads.

3D Finite Element Analysis

To overcome the limitations inherent in

2D modeling approaches, 3D finite

element models are becoming more

widespread.

With 3D FE analysis, we can study the

response of flexible pavements under

spatially varying tire pavement contact

pressures.

Single Layer Elastic Solutions

P

MaterialE and µ

Vertical Stress

HorizontalRadial Stress

Horizontal Tangential Stress

Shear Stress

Shear Stress

Point LoadHomogeneous Half-Space

Single Layer Elastic Solutions

Cylindrical Coordinates

Boussinesq Theory – Point Load

Stresses

Boussinesq Theory – Point Load

Strains

Boussinesq Theory – Point Load

Deflections

Circular Load – Uniform Vertical Stress

Vertical Stress

MaterialE and µ

Shear Stress

Shear Stress

Homogeneous Half-Space

CircularLoad

Horizontal Tangential Stress

HorizontalRadial Stress

Circular Load – Axis of symmetry

Stresses

At r = 0

Circular Load – Axis of symmetry

Strains

At r = 0

Circular Load – Axis of symmetry

Vertical Deflection

When Poisson’s ratio is 0.5

On the Surface (z = 0)

Circular Load – Uniform Vertical Stress

Foster and Ahlvin Charts (1954)

In the charts

Circular Load – Vertical Stress

After Foster and Ahlvin (1954)

Circular Load – Radial Stress

After Foster and Ahlvin (1954)

Circular Load – Tangential Stress

After Foster and Ahlvin (1954)

Circular Load – Shear Stress

After Foster and Ahlvin (1954)

Circular Load – Vertical Deflection

After Foster and Ahlvin (1954)

Stresses in Layered Systems

Comparison of calculated and measured stressesSource : Herner, HRB, 1955

Two Layer Elastic Solutions

Two Layer Elastic system

p

h E1, µ1

2 a

∞E2, µ2

Two Layer Elastic Solutions

Burmister’s Theory

Vertical stress Distribution (h/a = 1 and μ = 0.5)Source : Burmister, HRB 177, 1958

Two Layer Elastic Solutions

Vertical interface stresses (Source : Huang, 1969)

Surface Deflections - Burmister

Flexible plate

Rigid plate

Surface Deflections - Burmister

E2 / E1

h/a

Vertical surface Deflections (Source : Burmister, 1943)

Vertical Interface Deflections

Vertical Interface Deflections (Source : Huang, 1969)

Vertical Interface Deflections

Vertical Interface Deflections (Source : Huang, 1969)

Vertical Interface Deflections

Vertical Interface Deflections (Source : Huang, 1969)

Vertical Interface Deflections

Vertical Interface Deflections (Source : Huang, 1969)

Equivalent Single Layer Concept

Odemark approximate method

Equivalent Thickness

Utilising Single layer solutions

Equivalent Single Layer Concept

Odemark approximate method

Equivalent Thickness for two layer system

when μ1 = μ2

Utilising Single layer solutions

Three Layer Systems

Three Layer Elastic system

σz2

σ'r2

σr2

σz1

σ'r1

σr1

p

h1E1, µ1

2 a

E2, µ2

E3, µ3

h2

Interface 1

Interface 2

Jones’ Tables

Jones’ Tables

Jones’ Tables

(Source : Jones, 1962)

Jones’ Tables

Stress factors : ZZ1, ZZ2, ZZ1-RR1, ZZ2-RR2

Jones’ Tables

Peattie’s Charts

(Source : Peattie, 1962)

Peattie’s Charts

(Source : Peattie, 1962)

Peattie’s Charts

(Source : Peattie, 1962)

Computer Programs

To calculate stresses, strains and deflections of a layered elastic system

Gradually became more sophisticated in capability to handle

• Linear elastic materials

• Nonlinear elastic granular materials

• Vertical and horizontal loads

• Elastic multilayer systems under multiple wheel loads

• Stress dependent materials

• Finite element linear and nonlinear analysis

Computer Programs

Examples Include :

• BISTRO and BISAR (from Shell)

• ELSYM5 (from Chevron)

• ALIZEIII (LCPC) and CIRCLY (from MINCAD)

• DAMA (from Asphalt Institute)

• SAPIV and ELSYM5 (from University of California)

• ILLI-PAVE (Raad and Figueroa, 1980)

• PDMAP (Finn et al., 1986)

• MICH-PAVE (Harichandran et al., 1989)

• KENLAYER (Huang, 1993)

• Everstress (Washington State DOT, 1995)

Thank you