Page 89 - SAPEM-Chapter-10-2nd-edition-2014

South African Pavement Engineering Manual
Chapter 10: Pavement Design

Table 30. Transfer Function and Constants for Shear Failure (Granular Materials)

N = 10 (α +β)
(20)
= Number of equivalent standard axles to safeguard against shear failure
Where N
α, β = Constants, values shown below
= Stress Ratio, defined in Equation (21)
F

2 φ φ
σ �K �tan �45 + � − 1�� + 2 K C tan �45 + �
3
2
2
F =
(σ −σ )
1
3
(21)
σ φ + C
F = 3 term term
(σ −σ )
3
1

Where σ 1 , σ 3 = Major and minor principle stresses acting in the middle of the granular
1
layer (compressive stress positive)
C = Cohesion
φ = Angle of Internal Friction
= Values given below for material codes
C term
= Values given below for material codes
φ term
K = Constant for moisture
• 0.65 for saturated (wet)
• 0.8 for moderate
• 0.95 for normal
Constants for Equation (20)
Reliability Level α β
95% (Category A) 2.605122 3.480098
90% (Category B) 2.605122 3707667
80% (Category C) 2.605122 3.983324
50% (Category D) 2.605122 4.510819
C and Ø-Terms for Equation (21)
Moisture Condition
Material Dry Moderate Wet
Code
Ø-term C-term Ø-term C-term Ø-term C-term
G1 8.61 392 7.03 282 5.44 171
G2 7.06 303 5.76 221 4.46 139
G3 6.22 261 5.08 188 3.93 115
G4 5.50 223 4.40 160 3.47 109
G5 3.60 143 3.30 115 3.17 83
G6 2.88 103 2.32 84 1.76 64
2
EG4 4.02 140 3.50 120 3.12 100
3
EG5 3.37 120 2.80 100 2.06 80
4
EG6 1.63 100 1.50 80 1.40 60
Notes
1. If a tensile stress, i.e., a negative σ 3 is calculated, σ 3 is reset to zero and σ 1 is increased by the value of σ 3. The net result is
that (σ 1 – σ 3) remains the same, and σ 3 = 0.
2. EG4: broken down cemented material, G5/G6 parent material
3. EG5: broken down cemented material, G7/G8 parent material
4. EG6: broken down cemented material, G9/G10 parent material

This 1996 SAMDM granular materials transfer function is are the most commonly used when implementing the
SAMDM.

(ii) Wolff Model (1993)
An alternative damage model for permanent deformation in crushed and natural granular layers (G1 to G6) for use in
the SAMDM was developed by Wolff (1993, 1994). The model relates the stress state in a granular layer of a specific
strength to the permanent deformation caused by repetitions of that stress state. The model was developed from
Heavy Vehicle Simulator (HVS) testing over a period of approximately ten years. The HVS tests indicated that

Section 7: Structural Capacity Estimation: Flexible Pavements
Page 78