stress and strain - pnu-LID

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 stressz

Radial stressr

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.