Let’s talk traffic loading and volume

Traffic Loading and Volume

Chapter 6.1 & 6.2

Dr. Professor Christopher Barnes

Eneja Mushi M.Sc.

Pavement Analysis and Management

6.1 Design Procedures

• Traffic is the most important factor in pavement design. • When designing one should consider:

1. Load Magnitude2. Configuration of load 3. Load repetitions

• Three different procedures for considering vehicular and traffic effects in pavement design:

1. Fixed traffic 2. Fixed vehicle 3. Variable traffic

6.1.1 Fixed Traffic

• In fixed traffic, the thickness of pavement is governed by a single-wheel load

• Number of load repetitions is not considered as a variable. – If pavement is subjected to multiple wheels, they

must be converted to an equivalent single-wheel load so that design method based on single wheel can be applied.Method used in: Airport pavement, Highway pavement, no longer in use.

6.1.2 Fixed Vehicle

• The thickness pavement is governed by number of repetitions of a standard vehicle or axle load, usually 18kip single-axle load (SAL)

• IF more than one axle, convert to SAL by an Equivalent Axle Load Factor (EALF)

• # of repetitions of SAL or MAL must be multiplied by its EALF to obtain the equivalent effect SAL.

• The summation of equivalent effects of all axle loads = equivalent single-axle load (ESAL), which is the single traffic parameter for design purposes

• Most of the current design methods are based one the above concept!

6.1.3 Variable traffic and Vehicle

• Traffic and Vehicles are considered individually, no need to assign an equivalent factor for each axel load.

• Load can be divided into # of groups, stresses, strains & deflections of each group can determined separately and used in design.

• Best fit for mechanistic methods of design, where pavement responses can be evaluated by using a computer.

6.2 Equivalent Single-Wheel Load

• History: During WWII introduction of B-29 with Dual Wheel, up till then design was based on single wheel aircraft.

• New criteria need to be develop, time and money worked against it.

• As a result, relating theoretically the new loading conditions to an equivalent single wheel load so that the existing theory would work.

6.2 EQUIVALENT SINGLE-WHEEL LOAD

• ESWL depends on the criterion selected to compare SWL with MWL

• Studies were conducted In 1969 by Huang and 1970 by Gerrard and Harrison on single, dual and dual tandem wheels assuming that all wheels have the same radii. 1. Was found that use of different criteria, (stress, strain, deflection) is

important in determining ESWL2. ESWL increases as pavement thickness increases and modulus ration

increases or multiple-wheel spacing decreases • ESWL can be calculated theoretically or experimentally

measured stress, strain or deflection, or can be determined from pavement distress and performance conducted by WASHO and AASHO road test

6.2.1 Equal Vertical Stress Criterion

• In 1959 Boyd and Foster presented a semirational method for determine ESWL

6.2.1 Equal Vertical Stress Criterion

• ESWL varies with pavement thickness• For thickness smaller than ½ the clearance between

tires, ESWL = ½ of total load• For thickness greater that 200 % of c-c of tires,

ESWL= Total Load • Assuming a straight-line relationship between

pavement thickness and wheel load on logarithmic scales the ESWL for any intermediate thickness can be determined as follows.

6.2.1 Equal Vertical Stress Criterion

Pd = load on one of the dual tiresz = pavement thickness d = clerarance between dual tiresSd = center to center spacing between

dual tires

6.2.1 Equal Vertical Stress Criterion

• Vertical stress factor σz/q shown in the figure below can be used to find ESWL based on Boussinesq’s theory

6.2.1 Equal Vertical Stress Criterion

• Fig. below shows pavement of thickness z under single and dual wheels that have the same contact radius a.

6.2.1 Equal Vertical Stress Criterion

In the above fig. the maximum subgrade stress under single wheel occurs at point A with a stress factor σz/qs

qs =contact pressure under single wheelLocation of max. stress under dual wheels is not known

and can be determined by comparing the stresses at point 1 2 3.

The stress factor at each point can be obtained by superposition of the 2 wheels.

Maximum stress factor = σz/qd

qd = contact pressure under dual wheels.

6.2.1 Equal Vertical Stress Criterion

Following the above statements the formula defining the single and dual wheel stress factor is:

For the same contact radius, contact pressure is proportional to wheel load:

Ps = single wheel load, Pd = load on each of the duals

6.2.2 Equal Vertical Deflection Criterion

• Time showed that Boyd and Foster’s method was not safe.

• 1959 Foster and Ahlvin developed new method• Pavement system is considered as a homogeneous

half-space and the vertical deflection at a depth equal to the thickness of the pavement can be obtained from Boussinesq solutions

• A SWL that has the same contact radius as the one of dual wheels and results in a maximum deflection equal to that caused by the dual wheels in the ESWL (equal single wheel load)

6.2.2 Equal Vertical Deflection Criterion

• Deflection Factor F can be used to determine ESWL.

6.2.2 Equal Vertical Deflection Criterion

• Deflection of single and dual wheels, ws and wd =

Fs = deflection factor (of single wheel)at point A

Fd = deflection factor (of dual wheels) at point 1, 2, 3To obtain deflection factor (Fd) is obtained by

superposition of the duals

6.2.2 Equal Vertical Deflection Criterion

• To obtain the same deflection ws = wd or

• For the same contact radius, contact pressure is proportional to wheel load:

6.2.2 Equal Vertical Deflection Criterion

• Although Foster and Ahlvin method is superior to Boyd and Foster, their homogeneous half-space instead of a layered system is not logical from a theoretical viewpoint.

• Foster-Ahlvin method is still unsafe because, some of the pavements with thickness greater than those obtained by the method were considered inadequate or on the borderline, because ESWL for layered systems is greater than that for a homogeneous half-space.

6.2.2 Equal Vertical Deflection Criterion

• 1968 Huang suggested the use of layered theory and presented a chart for determining ESWL based on the interface deflection of the two layered systems as shown in the next slid.

a = contact radius Load factor h1 = pavement thickness E1/E2 = modulus ratio Sd = dual spacing

6.2.2 Equal Vertical Deflection Criterion

6.2.2 Equal Vertical Deflection Criterion

Comparing eq. 6.6 and 6.7b we get eq. 6.8

6.2.2 Equal Vertical Deflection Criterion

• ESWL can be determined from the deflection factors presented in the figure below

6.2.2 Equal Vertical Deflection Criterion

• But the use of the chart shown in Figure 6.4 is much quicker. The chart is based on a dual spacing Sd of 48in (1.22m).

• If actual spacing is different it must be changed to 48 in and the values of a and h1 have to be changed proportionally.

• As long as Sd/a and h1/a remain the same, the load factor will be the same.

• The upper chart is for a contact radius of 6 in and the lower chart is for a contact radius of 16 in.

• The load factor for any other contact radius can be obtained by a straight-line interpolation

6.2.2 Equal Vertical Deflection Criterion

• You can determine a` and h`1 from Sd h1 and a

• Using h’1 as the pavement thickness find load factors L1 and L2 from the chart

6.2.3 Equal Tensile Strain Criterion

• Conversion factors presented in figures below can be used to determine ESWL

6.2.3 Equal Tension Strain Criterion

• Tensile strain e at the bottom of layer 1 under a single-wheel load is:

• qs = contact pressure of a single wheel

6.2.3 Equal Tension Strain Criterion

• The tensile strain under dual or dual-tandem wheels is

qd = contact pressure of dual or dual-tandem wheels

6.2.4 Criterion Based on Equal Contact Pressure

• The above analysis of ESWL are based on:Assumption 1: Single wheel has the same contact

radius as each of the dual wheelAssumption 2: Single wheel has a different contact

radius but the same contact pressure as the dual wheels. In this case solution is much more complicated.

6.2.4 Criterion Based on Equal Contact Pressure

• To obtain equal deflection ws = wd or

Because

And

6.2.4 Criterion Based on Equal Contact Pressure

• For equal contact radius, contact pressure is proportional to the wheel load

If Pd and q are given, ad can be computed

6.2.4 Criterion Based an Equal Contact Pressure

In 1968 Huang compared the ESWL based on = radius with that based on equal contact pressure for a variety of case.

Found that: Unless the pavement is extremely thin and the modulus ratio close to unity, the difference between the two methods are not significant

6.2.4 Criterion Based an Equal Contact Pressure

• Two-layer interface deflections base on = contact pressure were also used by the Asphalt institute to compute the ESWL for full-depth asphalt pavement.

• This procedure is applicable for small aircrafts.

6.2.5 Criterion Based on Equivalent Contact Radius

• The 2 methods studied up till now were:– Equal contact radius – Equal contact pressure

• In 1993 Ioannides and Khazanovich proposed the use of an equivalent contact radius to determin the load equivalency (equivalent single axle radius ESAR),

6.2.5 Criterion Based on Equivalent Contact Radius

• The basic concept is to: Determine a single wheel load with an equivalent radius that would give the same response as dual-wheel assembly.

• They found (though statistical regression techniques) that the maximum bending stress due to dual tires in the interior of a concrete slab would be the same as a single tire with the equivalent radius

6.2.5 Criterion Based on Equivalent Contact Radius

• aeq = equivalent tire contact pressure• a = contact radius of each of the dual tires• S = c-c spacing between the dual