Pavement Design

Pavement Stress Analysis Software

University of Florida

Topic 2b – Pavement Stress Analysis Software

1. Multilayer Elastic Theory

E1, ν1

E2, ν2

E3, ν3

∞

h1

h2

a = radius

q = pressure

Point A Point B

Assumptions (p. 60): • Each Layer

– Continuous – Homogeneous – Isotropic – Linearly Elastic – Material is weightless & infinite in areal extent – Finite thickness (except last layer)

Properties @ A = Properties @ B

Same properties in all directions

Hooke’s Law

�� = 1

� �� − ν �� + ��

1. Multilayer Elastic Theory (cont.)

Assumptions (cont.): • Load

– Circular – Vertical – Uniformly distributed

• Full friction between layers – Same z, rz, w, ur @ interface

• Each layer continuously supported

Point A Point B

E1, ν1

E2, ν2

E3, ν3

∞

h1

h2

a = radius

q = pressure

Why do we want full friction between layers?

Topic 2b – Pavement Stress Analysis Software

2. Computer Program KENPAVE

Program should be on a CD at the back of your textbook

Topic 2b – Pavement Stress Analysis Software

2.1 System

• Multilayer elastic analysis system • Elastic theory assumptions apply

Topic 2b – Pavement Stress Analysis Software

2.2 Loads

Circular, uniform pressure

PARAMETER ACTUAL LOAD

LOAD=0 Single wheel

LOAD=1 Dual wheel

X

Y X – Longitudinal (direction of traffic) Y – Transverse

LOAD=2 Dual tandem

X

Y

YW

YW

XW

Topic 2b – Pavement Stress Analysis Software

2.3 Material Properties

• Material types – 1 = Linear elastic – 2 = Nonlinear elastic – 3 = Linear viscoelastic – 4 = Combination of 2 & 3

t

ε

ε

σ 1

2

3

Topic 2b – Pavement Stress Analysis Software

2.4 Procedure

• Create input file – Use LAYERINP to define type of analysis, material, thickness, load, points of interest

• Perform the analysis – Use KENLAYER to run the analysis

• Retrieve the output – Output is stored in a .TXT file – Spreadsheets are useful for post-processing and plotting

Sign convention: – Positive (+) = Compression – Negative (-) = Tension

Is there a way to find out?

Topic 2b – Pavement Stress Analysis Software

2.5 KENLAYER Example 1

a = 5”

q = 100 psi

E3=10,000 psi ; ν3=0.45

E1=500,000 psi ; ν1=0.35

E2=50,000 psi ; ν2=0.40

∞

h1= 6”

h2= 12”

Given: • Three-layer system • Uniform circular load • Linear elastic materials

Calculate: • Maximum deflection • Critical tensile strain • Critical compressive strain

Where would the critical/maximum values occur?

– Maximum deflection δmax @ z=0 – Critical tensile strain εt @ bottom of AC layer – Critical compressive strain εc @ top of subgrade

Topic 2b – Pavement Stress Analysis Software

2.5 KENLAYER Example 1 (cont.)

Topic 2b – Pavement Stress Analysis Software

2.5 KENLAYER Example 1 (cont.)

Topic 2b – Pavement Stress Analysis Software

2.5 KENLAYER Example 1 (cont.)

Topic 2b – Pavement Stress Analysis Software

2.5 KENLAYER Example 1 (cont.)

Topic 2b – Pavement Stress Analysis Software

2.5 KENLAYER Example 1 (cont.)

Topic 2b – Pavement Stress Analysis Software

2.5 KENLAYER Example 1 (cont.)

Topic 2b – Pavement Stress Analysis Software

2.5 KENLAYER Example 1 (cont.)

• Single wheel load is analyzed in axisymmetric space

Topic 2b – Pavement Stress Analysis Software

2.5 KENLAYER Example 1 (cont.)

Output format:

Topic 2b – Pavement Stress Analysis Software

Given: • Three-layer system • Dual wheel load • Elastic material

∞

8”

4”

14” 4” q=100 psi a=4 in

E1=200,000 psi ν1 =0.35

E2=15,000 psi ν2 =0.45

E3=5,000 psi ν3 =0.45

Plane of Symmetry

x

xx

x

x

xx

x

x x x

x

Check output

2.6 KENLAYER Example 2

Calculate: 1. δmax 2. εt 3. εc

Where would the critical/maximum values occur?

Topic 2b – Pavement Stress Analysis Software

2.6 KENLAYER Example 2 (cont.)

• Dual wheel load is analyzed in spatial coordinates

Topic 2b – Pavement Stress Analysis Software

2.6 KENLAYER Example 2 (cont.)

Output format:

Topic 2b – Pavement Stress Analysis Software

2.6 KENLAYER Example 2 (cont.)

Which strain is considered critical for: - Cracking? - Rutting? - At which location?

Output format:

• Results for each point (x,y) at each requested depth (z)

Topic 2b – Pavement Stress Analysis Software

(x,y) z δ σz σ1 σ3 σ2 εh εz ε1 ε3 ε2

Point No.

Vertical Coord.

Vertical Displ.

Vertical Stress

Major Principal Stress

Minor Principal Stress

Interm. Principal Stress

Horizontal ‘Principal’ Strain

Vertical Strain

Major Principal Strain

Minor Principal Strain

Interm. Principal Strain

2.6 KENLAYER Example 2 (cont.)

Output format:

• Results for each point (x,y) at each requested depth (z)

τ

σσ1σ3 σ2

Principal stresses act on planes where τ = 0

τmax

(x,y) z δ σz σ1 σ3 σ2 εh εz ε1 ε3 ε2

Point No.

Vertical Coord.

Vertical Displ.

Vertical Stress

Major Principal Stress

Minor Principal Stress

Interm. Principal Stress

Horizontal ‘Principal’ Strain

Vertical Strain

Major Principal Strain

Minor Principal Strain

Interm. Principal Strain

Topic 2b – Pavement Stress Analysis Software

���� = �� − �� 2

Homework Assignment

a = 5”

q = 100 psi

E3=10,000 psi ; ν3=0.45

E1=1,000,000 psi ; ν1=0.35

E2=20,000 psi ; ν2=0.40

∞

h1= 6”

h2= 12”

Given: • Three-layer system • Uniform circular load • Linear elastic materials

Calculate: • Plot deflection basin • Critical tensile strain • Critical compressive strain • Estimate the number of cycles to failure (Nf & Nd) • Identify the dominant failure mode • Compare results to Example 1

Topic 2b – Pavement Stress Analysis Software