**Lecture notes in Transportation Systems Engineering**

**3 August 2009**

**Fixed traffic:** Thickness of pavement is governed by single load and
number of load repetitions is not considered.
The heaviest wheel load anticipated is used for design purpose.
This is an old method and is rarely used today for pavement design.

**Fixed vehicle:** In the fixed vehicle procedure, the thickness is governed
by the number of repetitions of a standard axle load.
If the axle load is not a standard one, then it must be converted to an
equivalent axle load by number of repetitions of given axle load and its
equivalent axle load factor.

**Variable traffic and vehicle:** In this approach, both traffic and vehicle
are considered individually, so there is no need to assign an equivalent factor
for each axle load.
The loads can be divided into a number of groups and the stresses, strains,
and deflections under each load group can be determined separately; and used
for design purposes.
The traffic and loading factors to be considered include axle loads, load
repetitions, and tyre contact area.

- equalancy concept is based on equal stress;
- contact area is circular;
- influence angle is 45; and
- soil medium is elastic, homogeneous, and isotropic half space.

(1) |

where is the wheel load, is the center to center distance between the two wheels, is the clear distance between two wheels, and is the desired depth.

**Repetition of axle loads:**
The deformation of pavement due to a single application of axle load may be
small but due to repeated application of load there would be accumulation of
unrecovered or permanent deformation which results in failure of pavement.
If the pavement structure fails with number of repetition of load
and for the same failure criteria if it requires number of repetition of
load , then and are considered equivalent.
Note that, and equivalency depends on the failure criterion
employed.

*Equivalent axle load factor:* An equivalent axle load factor (EALF)
defines the damage per pass to a pavement by the type of axle relative
to the damage per pass of a standard axle load.
While finding the EALF, the failure criterion is important.
Two types of failure criterias are commonly adopted: fatigue cracking and
ruttings.
The fatigue cracking model has the following form:

(2) |

(3) |

(4) |

(5) |

(6) |

Axle | No.of Load | EALF | ||

Load | Repetition | |||

i | (KN) | () | () | |

1 | 40 | 10000 | = 0.0625 | 625 |

2 | 80 | 1000 | = 1 | 1000 |

3 | 160 | 100 | = 16 | 1600 |

Axle | No.of Load | EALF | ||

Load | Repetition | |||

i | (KN) | () | () | |

1 | 120 | 1000 | = 6.200 | 6200 |

2 | 160 | 100 | = 22.63 | 2263 |

3 | 40 | 10000 | = 0.04419 | 441.9 |

Axle | No.of Load | EALF | ||

Load | Repetition | |||

i | (KN) | () | () | |

1 | 40 | 10000 | = 0.2065 | 2065 |

2 | 60 | 1000 | = 1 | 1000 |

3 | 120 | 200 | = 14.825 | 2965.081 |

The Figure shows straining of a specimen under a repeated load test. At the initial stage of load applications, there is considerable permanent deformation as indicated by the plastic strain in the Figure . As the number of repetition increases, the plastic strain due to each load repetition decreases. After 100 to 200 repetitions, the strain is practically all-recoverable, as indicated by in the figure.

In pavements the load applied are mostly transient and the type and duration of loading used in the repeated load test should simulate that actually occurring in the field. When a load is at a considerable distance from a given point, the stress at that point is maximum. It is therefore reasonable to assume the stress pulse to be a haversine or triangular loading, and the duration of loading depends on the vehicle speed and the depth of the point below the pavement surface. Resilient modulus test can be conducted on all types of pavement materials ranging from cohesive to stabilized materials. The test is conducted in a triaxial device equipped for repetitive load conditions.

- It can be used for both existing pavement rehabilitation and new pavement construction
- It can accommodate changing load types
- It can better characterize materials allowing for
- better utilization of available materials
- accommodation of new materials
- improved definition of existing layer proportion

- It uses material proportion that relates better with actual pavement performance
- It provides more reliable performance predictions
- It defines role of construction in a better way
- It accommodates environment and aging effect of materials in the pavement

- Pavement layer extends infinitely in the horizontal direction
- The bottom layer (usually the subgrade) extends infinitely downwards
- Materials are not stressed beyond their elastic ranges

- Material properties of each layer, like modulus of elasticity (), Poisson's ratio (),
- Pavement layer thicknesses, and
- Loading conditions which include the total wheel load () and load repetitions.

The outputs of the layered elastic model are the stresses, strains and deflections in the pavements.

**Stress**. The intensity of internally distributed forces experienced within the pavement structure at various points. Stress has units of force per unit area(pa)**Strain**. The unit displacement due to stress , usually expressed as a ratio of change in dimension to the original dimension (mm/mm )**Deflection**. The linear change in dimension. Deflection is expressed in units of length (mm)

- A set of dual tyres has a total load of 4090 kg, a contact radius a of 11.4 cm and a center to center tyre spacing of 34.3 cm. Find the ESWL by Boyd & Foster method for a depth of 34.3 cm. [Ans: 3369.3 kg]
- Calculate ESWL by equal stress criteria for a dual wheel assembly carrying 2044 kg each for a pavement thickness of 5, 15, 20, 25 and 30 cms. The distance between walls of the tyre is 11 cm. Use either graphical or functional methods. (Hint: P=2044kg, d=11cm, s=27cm). [Ans: 2044, 2760, 3000, 3230 and 4088]
- Let number of load repetition expected by 60kN standard axle is 1000, 120kN is 200 and 40 kN is 10000. Find the equivalent axle load using fatigue cracking as failure criteria according to IRC. Hint:

Prof. Tom V. Mathew 2009-08-03