3  Loads

One of the primary functions of a pavement is load distribution.  Therefore, in order to adequately design a pavement something must be known about the expected loads it will encounter.  Loads, the vehicle forces exerted on the pavement (e.g., by trucks, heavy machinery, airplanes), can be characterized by the following parameters:   

• Tire loads

• Axle and tire configurations

• Repetition of loads

• Distribution of traffic across the pavement

• Vehicle speed

Loads, along with the environment, damage pavement over time.  The simplest pavement structural model asserts that each individual load inflicts a certain amount of unrecoverable damage.  This damage is cumulative over the life of the pavement and when it reaches some maximum value the pavement is considered to have reached the end of its useful service life. 

Therefore, pavement structural design requires a quantification of all expected loads a pavement will encounter over its design life.  This quantification is usually done in one of two ways: 

1. Equivalent single axle loads (ESALs).  This approach converts wheel loads of various magnitudes and repetitions ("mixed traffic") to an equivalent number of "standard" or "equivalent" loads. 

2. Load spectra.  This approach characterizes loads directly by number of axles, configuration and weight.  It does not involve conversion to equivalent values.  Structural design calculations using load spectra are generally more complex than those using ESALs.

Both approaches use the same type and quality of data but the load spectra approach has the potential to be more accurate in its load characterization. 

3.1  Tire Loads

Tire loads are the fundamental loads at the actual tire-pavement contact points.  For most pavement analyses, it is assumed that the tire load is uniformly applied over a circular area.  Also, it is generally assumed that tire inflation and contact pressures are the same (this is not exactly true, but adequate for approximations).  The following equation relates the radius of tire contact to tire inflation pressure and the total tire load:

States generally limit the allowable load per inch width of tire.  Based on a slightly dated survey (Sharma, Hallin and Mahoney, 1983), this tire load limitation varies  from a high of 140 N/mm (800 lbs/inch) to a low of 79 N/mm (450 lbs/inch).

Figure 4.14: FHWA Class 9 Five-Axle Tractor – Semi trailer (18 Tires Total) A typical tire load is 18.9 kN (4,250 lbs) with an inflation pressure of 689 kPa (100 psi.)

3.2  Axle and Tire Configurations

While the tire contact pressure and area is of vital concern in pavement performance, the number of contact points per vehicle and their spacing is also critical.  As tire loads get closer together their influence areas on the pavement begin to overlap, at which point the design characteristic of concern is no longer the single isolated tire load but rather the combined effect of all the interacting tire loads.  Therefore, axle and tire arrangements are quite important.

3.2.1  Descriptions

Tire-axle combinations are typically described as (see Figure 4.15):

• Single axle — single tire  (truck steering axles, etc.)

• Single axle — dual tires

• Tandem axle — single tires (see Figure 4.16)

• Tandem axle — dual tires

Single Axle with Single Tires	Single Axle with Dual Tires
Tandem Axles with Single Tires	Tandem Axles with Dual Tires

Figure 4.15: Tire-Axle Combinations (from Mahoney, 1984)

Figure 4.16: Tandem Drive Axle on a Tractor Frame During Manufacturing

3.2.2  Typical Axle Load Limits

Federal and State laws establish maximum axle and gross vehicle weights to limit pavement damage.  The range of weight limits in the U.S. vary a bit based on various Federal and State laws.  Figure 4.17 shows the range of maximum limits for single axle, tandem axle and gross vehicle weight (GVW) established by the states and the FHWA.

Figure 4.17: Range of Allowable Axle and Truck Weights in the U.S.
(based on data from USDOT, 2000)

Although each state and the FHWA have established maximum axle-tire load combinations, there are other restrictions as well.  One of the most common is the FHWA bridge formula (sometimes called the Federal Bridge Formula B).

3.3  Repetitions of Wheel Loads

Although it is not too difficult to determine the wheel and axle loads for an individual vehicle, it becomes quite complicated to determine the number and types of wheel/axle loads that a particular pavement will be subject to over its entire design life.  Furthermore, it is not the wheel load but rather the damage to the pavement caused by the wheel load that is of primary concern.  There are currently two basic methods for characterizing wheel load repetitions: 

1.  Equivalent single axle load (ESAL).  Based on AASHO Road Test results, the most common approach is to convert wheel loads of various magnitudes and repetitions ("mixed traffic") to an equivalent number of "standard" or "equivalent" loads.  The most commonly used equivalent load in the U.S. is the 80 kN (18,000 lbs) equivalent single axle load (normally designated ESAL).   
2. Load spectra.  The 2002 Guide for the Design of New and Rehabilitated Pavement Structures (NCHRP 1-37A) essentially does away with the ESAL and determines loading directly from axle configurations and weights.  This is a more precise characterization of traffic but relies on the same input data used to calculate ESALs. A typical load spectrum input would be in the form of a table that shows the relative axle weight frequencies for each common axle combination (e.g. single axle, tandem axle, tridem axle, quad axle) over a given time period (see Figure 4.18).  Often, load spectra data can be obtained from weight-in-motion stations.

Figure 4.18: Example Load Spectra Input Screen from NCHRP 1-37A

Typically, designers must not only calculate ESALs or load spectra for various vehicles but also must forecast the expected number of ESALs or load spectra a pavement will encounter over its entire design life. This information then helps determine the structural design. Highway design in most states is based on the ESAL traffic input anticipated over a future 10 to 50 year period.

3.4       Traffic Distribution

Along with load type and repetitions, the load distributions across a particular pavement must be estimated.  For instance, on a 6-lane interstate highway (3 lanes in each direction) the total number of loads is probably not distributed exactly equally in both directions.  Often one direction carries more loads than the other.  Furthermore, within that one direction, not all lanes carry the same loading.  Typically, the outer most lane carries the most trucks and therefore is subjected to the heaviest loading.  Therefore, pavement structural design should account for these types of unequal load distribution.  Typically, this is accounted for by selecting a "design lane" for a particular pavement.  The loads expected in the design lane are either (1) directly counted or (2) calculated from the cumulative two-direction loads by applying factors for directional distribution and lane distribution.   The 1993 AASHTO Guide offers the following basic equation:

3.5  Vehicle Speed

Although current design practices do not necessarily account for vehicle speed, it does influence pavement loading.  In general, slower speeds and stop conditions allow a particular load to be applied to a given pavement area for a longer period of time resulting in greater damage.  For HMA pavements this behavior is sometimes evident at bus stops (where heavy buses stop and sit while loading/unloading passengers) and intersection approaches (where traffic stops and waits to pass through the intersection) when mix design or structural design have been inadequate.  In flexible pavement design, Superpave accounts for vehicle speed indirectly by applying a design pavement temperature adjustment for slow-moving or stopped vehicles.

3.6       The ESAL Equations

ESALs indicate the relative damage to a pavement structure due to various axle loads (e.g., the normal mixed traffic condition).  Recall that wheel loads of various magnitudes and repetitions ("mixed traffic") can be converted to an equivalent number of "standard" loads.  The most common standard load is the 80 kN (18,000 lbs) ESAL.  The two standard U.S. ESAL equations (one each for flexible and rigid pavements) are derived from the AASHO Road Test results.  Both these equations involve the same basic format, however the exponents are slightly different.

The equation outputs are load equivalency factors (LEFs) or ESAL factors.  This factor relates various axle load combinations to the standard 80 kN (18,000 lbs) single axle load.  It should be noted that ESALs as calculated by the ESAL equations are dependent upon the pavement type (flexible or rigid) and the pavement structure (structural number for flexible and slab depth for rigid).  As a rule-of-thumb, the 1993 AASHTO Design Guide, Part III, Chapter 5, Paragraph 5.2.3 recommends the use of a multiplier of 1.5 to convert flexible ESALs to rigid ESALs (or a multiplier of 0.67 to convert rigid ESALs to flexible ESALs).  Using load spectra (as proposed in the 2002 Guide for the Design of New and Rehabilitated Pavement Structures) will eliminate the need for flexible-rigid ESAL conversions.  Table 4.5 shows some typical LEFs for various axle-load combinations.

 Table 4.5: Some Typical Load Equivalency Factors

3.6.1  Generalized Fourth Power Law

The AASHTO load equivalency equation is quite cumbersome and certainly not easy to remember.  Therefore, as a rule-of-thumb, the damage caused by a particular load is roughly related to the load by a power of four (for reasonably strong pavement surfaces).  For example, given a flexible pavement with SN = 3.0 and p_t = 2.5: 

1. A 18,000 lb (80 kN) single axle, LEF =1.0
2. A 30,000 lb (133 kN) single axle, LEF = 7.9
3. Comparing the two, the ratio is: 7.9/1.0 = 7.9
4. Using the fourth power rule-of-thumb:

Thus, the two estimates are approximately equal.

 General Observations Based On Load Equivalency Factors

1. The relationship between axle weight and inflicted pavement damage is not linear but exponential.  For instance, a 44.4 kN (10,000 lbs) single axle needs to be applied to a pavement structure more than 12 times to inflict the same damage caused by one repetition of an 80 kN (18,000 lbs) single axle.  Similarly, a 97.8 kN (22,000 lbs) single axle needs to be repeated less than half the number of times of an 80 kN (18,000 lbs) single axle to have an equivalent effect. 

   • An 80 kN (18,000 lbs) single axle does over 3,000 times more damage to a pavement than an 8.9 kN (2,000 lbs) single axle (1.000/0.0003 ≈ 3,333). 

   • A 133.3 kN (30,000 lbs) single axle does about 67 times more damage than a 44.4 kN (10,000 lbs) single axle (7.9/0.118 ≈ 67). 

   • A 133.3 kN (30,000 lb) single axle does about 11 times more damage than a 133.3 kN (30,000 lb) tandem axle (7.9/0.703 ≈ 11).

   • Heavy trucks and buses are responsible for a majority of pavement damage.  Considering that a typical automobile weighs between 2,000 and 7,000 lbs (curb weight), even a fully loaded large passenger van will only generate about 0.003 ESALs while a fully loaded tractor-semi trailer can generate up to about 3 ESALs (depending upon pavement type, structure and terminal serviceability).

2. Determining the LEF for each axle load combination on a particular roadway is possible through the use of weigh-in-motion equipment.  However, typically this type of detailed information is not available for design.  Therefore, many agencies average their LEFs over the whole state or over different regions within the state.  They then use a standard "truck factor" for design which is simply the average number of ESALs per truck.  Thus, an ESAL determination would involved counting the number of trucks and multiplying by the truck factor.

   • This method allows for ESAL estimations without detailed traffic measurements, which is often appropriate for low volume roads and frequently must be used for lack of a better alternative for high volume roads.

   • When using this method, there is no guarantee that the assumed truck factor is an accurate representation of the trucks encountered on the particular roadway in question.

3.6.2  Estimating ESALs

A basic element in pavement design is estimating the ESALs a specific pavement will encounter over its design life.  This helps determine the pavement structural design (as well as the HMA mix design in the case of Superpave).  This is done by forecasting the traffic the pavement will be subjected to over its design life then converting the traffic to a specific number of ESALs based on its makeup.  A typical ESAL estimate consists of:

1. Traffic count.  A traffic count is used as a starting point for ESAL estimation.  Most urban areas have some amount of historical traffic count records. If not, simple traffic tube counts are relatively inexpensive and quick.  In some cases, designers may have to use extremely approximate estimates if no count data can be obtained.
2. A count or estimate of the number of heavy vehicles. This usually requires some sort of vehicle classification within the traffic count.  The simplest classifications divide vehicles into two categories: (1) heavy trucks and (2) others.  Other, more elaborate schemes can also be used such as the FHWA's vehicle classification.

3. An estimated traffic (and heavy vehicle) growth rate over the design life of the pavement.  A growth rate estimate is required to convert a single year traffic count into the total traffic experienced over the pavement design life.  Typically, multiplying the original traffic count by the pavement design life (in years) will grossly underestimate total ESALs.  For example, Interstate 5 at mile post 176.35 (near Shoreline, Washington) has experienced a growth from about 200,000 ESALs per year in 1965 (original construction) to about 1,000,000 ESALs per year in 1994.  Thus, over a 30 year period, the ESALs per year have increased by a factor of five or an annual growth rate of about six percent. 

4. Select appropriate LEFs to convert truck traffic to ESALs.  Different regions may experience different types of loads.  For instance, a particular area may experience a high number of trucks but they may be mostly empty thus lowering their LEF.  For instance, the statewide LEF for Washington State is about 1.028 ESALs/truck.  However, this may be drastically different from local LEFs.

5. An ESAL estimate.  An ESAL estimate can be made based on the preceding steps.  Depending upon circumstances these estimates may vary widely.  Figure 4.19 shows an example of a pavement that was built for an estimated ESAL loading but is experiencing a much higher loading due to a marked increase in bus traffic.

Figure 4.19: Resulting Damage from a Marked Increase in ESALs

3.7  Load Spectra

The 2002 Guide for the Design of New and Rehabilitated Pavement Structures (NCHRP 1-37A) has gone away from the ESAL approach and adopted a load spectra approach.  In essence, the load spectra approach uses the same traffic data that the ESAL approach uses only it does not convert the loads into ESALs – it maintains the data by axle configuration and weight.  This information can then be used with a series of mechanistic-empirical equations to develop a pavement structural design.  Some key advantages of the load spectra approach are: 

1.      It is compatible with the FHWA's Traffic Monitoring Guide (TMG) and thus many agencies are already collecting the appropriate data. 

2.      It offers a hierarchical approach to traffic data input depending upon the users needs and resources.  There are three levels of potential input:  

·        Level 1 Inputs – Use of volume/classification and axle load spectra data directly related to the project.

·        Level 2 Inputs – Use of regional axle load spectra data and project-related volume/classification data.

·        Level 3 Inputs – Use of regional or default classification and axle load spectra data. 

3.      It already includes information on traffic distribution including directional, lane and temporal distribution (if needed) as well as traffic growth rates.

3.8  Summary

Loading is a fundamental pavement design parameter.  In order to fully characterize a load, the following parameters should be known: 

• Tire loads

• Axle and tire configurations

• Repetition of loads

• Distribution of traffic across the pavement

• Vehicle speed

Pavement damage caused by a particular load is roughly related to the load by about a power of four (for reasonably strong surfaces).  This means that, generally speaking, a vehicle weighing twice as much as another (and having the same axle/tire arrangement) will cause 16 times as much damage to the pavement. 

Given the number and types of vehicles in the world today, there are many different types of loads and load configurations.  The most common load characterization approach is to convert all loads into an equivalent number of  80 kN (18,000 lbs) axle loads (ESALs).  ESALs can then be used in pavement structural design.  The 2002 Guide for the Design of New and Rehabilitated Pavement Structures dispenses with ESAL calculations and deals directly with traffic load spectra, however the general load vs. damage concepts are the same.  Loads work in conjunction with materials, subgrade and the environment to determine pavement design inputs.