stress-and-strain

1. STRESS AND STRAIN
1 INTRODUCTION
1.1 IN-SITU STRESS (GEOSTATIC STRESS)

2. 1.2 LINEAR ELASTICITY
 Assumption
 Principle of Superposition

3.  Generalized Hooke’s Law
1.3 TRAFFIC LOADING ON PAVEMENT SYSTEMS

4. 2 HOMOGENEOUS MASS (ELASTIC HALF-SPACE)
2.1 EQUATIONS
 Stress Caused by a Point Load (Boussinesq, 1883)

5.  Stress Caused by a Circular Load
 Strains Caused by a Circular Load
 Deflection Caused by a Circular Load

6.  Rigid vs. Flexible Loading
Here, q is an average pressure (total load/area)
 Multiple Wheel Loads

8. 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

9.  Radial stressr
 Tangential stress t

10.  Shear stress rz
 Vertical deflection w

13. 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.

14. 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:

15. 3.1.1 VERTICAL SURFACE DEFLECTION

16. 3.1.2 VERTICAL INTERFACE DEFLECTION

18. 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.

21. 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

24. 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)

25. - 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)

27. 4.2.2 RIGID PAVEMENT (AASHTO METHOD)

28. 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.