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