3 Stress and Strain

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STRESS AND STRAIN

1 INTRODUCTION

1.1 IN-SITU STRESS (GEOSTATIC STRESS)



1.2 LINEAR ELASTICITY

Assumption

Principle of Superposition



Generalized Hooke’s Law

1.3 TRAFFIC LOADING ON PAVEMENT SYSTEMS



2 HOMOGENEOUS MASS (ELASTIC HALF-SPACE)

2.1 EQUATIONS

Stress Caused by a Point Load (Boussinesq, 1883)



Stress Caused by a Circular Load

Strains Caused by a Circular Load

Deflection Caused by a Circular Load



Rigid vs. Flexible Loading

Here, q is an average pressure (total load/area)

Multiple Wheel Loads





2.2 SOLUTIONS BY CHARTS (FASTER AND AHLVIN, 1954)

Loaded shape: circular area with a radius “a”

Assumes the half-space is incompressible ( = 0.5)

Ahlvin and Ulery (1962) presented a series of equations and tables for ≠ 0.5. Poulos and Davis (1974) summarized various solutions

(http://www.ce.ncsu.edu/usucger/PandD/PandD.htm).

Vertical stressz



Radial stressr

Tangential stress t



Shear stress rz

Vertical deflection w







3 LAYERED SYSTEMS

3.1 OVERVIEW

Basic Assumptions

Each layer is homogeneous, isotropic, and linearly elastic.

Material is weightless and infinite in areal extent.

Each layer has a finite thickness h, but lowest layer is infinite in thickness.

Uniform pressure q → a circular area of radius a → applied on the surface

No friction on the interface

Continuity conditions are satisfied at the interface.

Development

1943: Burmister developed the solutions for a two-layer system..

1945: Burmister developed the solutions for a three-layer system.

1967: Huang applied to a multi-layer system.



3.2 TWO-LAYER SYSTEM (BURMISTER, 1943)

3.2.1 VERTICAL STRESS

Function of pavement (AC)→reduce the vertical stress on the subgrade → criteria for the

detrimental pavement deformation

Vertical stress distribution in two-layered system under the center of a circular loaded area

All the charts are for = 0.5.

Using the Shell deformation criterion and the AASHTO equation, Huang et al. (1984) developed:



3.1.1 VERTICAL SURFACE DEFLECTION



3.1.2 VERTICAL INTERFACE DEFLECTION





3.1.3 CRITICAL TENSILE STRAIN

Fatigue cracking = f(tensile strain)

Critical tensile strain:

e

Most cases, the critical tensile strain occurs under the center of the loaded area where shear

stress is zero.

But, if h1 /a and E1 /E2 are small → the critical tensile strain occurs at some distance from the

center.







4 TRAFFIC LOADING AND VOLUME

Traffic is the most important factor in pavement designs

Loading magnitude and configuration and Load of repetition

4.1 ESWL (EQUIVALENT SINGLE-WHEEL LOAD)

Initiating during the World War Ⅱ

Criteria for dual-wheel loads based on single-wheel loads

Based on vertical stress

Boyd and Foster (1950) method







4.2 EALF (EQUIVALENT AXLE LOAD FACTOR)

Thickness of pavement is governed by the # of repetitions

standard axle load (18-kip (80 kN=8ton) single-axle load)

Multi-axle load or other single-axle load (≠18 kip) ⇒ EALF (design load) EALF = f(type of pavement, thickness or structural capacity, terminal condition)

4.2.1 FLEXIBLE PAVEMENT (AASHTO METHOD: AASHO ROAD TEST)



- EALF using Eq 6.20(a) considers pt and SN ⇒ not consistent with theory

pt or SN ↓ ------ EALF ↑

- Disadvantage of this eqation

EALF = f(SN) but, SN=f(layer thickness , EALF)

- Asphalt Institute

AASHTO equivalent factor with pt=2.5 and SN=5 ⇒ Table 6.4 (next page)





4.2.2 RIGID PAVEMENT (AASHTO METHOD)



5 KENLAYER COMPUTER PROGRAM

See Handout

REFERENCES

도로공학, 천병식, 고용일, 새론, 1998

도로포장공학, 남영국, 구미서관, 2004

최신도로공학총론, 남영국, 최한중, 청문각, 1996

An Introduction to Geotechnical Engineering, Holtz and Kovacs, Prentice Hall, 1981.

Highway Pavement Design, Lecture by Prof. Kim, North Carolina State University

Pavement Analysis and Design, Huang, Prentice Hall, 2004

Pavement Engineering, Lecture by Prof. Choi, Korea University

Principles of Geotechnical Engineering, Das, Thomson, 2006.

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3 Stress and Strain