ESAL_D Equation

The predicted traffic loading to be furnished by the planning group is the cumulative 18-KIP ESAL axle applications expected on the design lane.

The designer must factor the project traffic forecast by direction and by lanes (if more than two lanes). Equation 8-2 on is used to determine the traffic in the design lane for the design period:

Where:

\(ESAL_{D}\) =The number of accumulated 18-KIP Equivalent Single Axle Loads in the design lane for the design period..

\(i\) = The year for which the calculation is made. When i = 1, all the variables apply to year 1. Some of the variables remain constant while others, such as AADT, L_F, and T₂₄, may change from year to year. Other factors may change when changes in the system occur. Such changes include parallel roads, shopping centers, truck terminals, etc.

\(n\) = The number of years the design is expected to last. (e.g., 10, 20, …).

\(AADT_i\) = Annual Average Daily Traffic for year i.

\(T\) = Percent heavy trucks during a 24-hour period. Trucks with six tires or more are considered in the calculations (Class 4-13).

\(D_F\) = Directional Distribution Factor. Use 1.0 if one-way traffic is counted or 0.5 for two-way traffic. This value is not to be confused with the Directional Factor (D) used for planning capacity computations.

\(L_F\) = Lane Factor converts directional trucks to the design lane trucks. Lane factors can be adjusted to account for unique features known to the designer such as roadways with designated truck lanes. L_F values can be determined from Table 8-1.

\(E_F\) = Equivalency Factor is the damage caused by one average heavy truck measured in 18-KIP ESALs. These factors should be provided by the Planning Department for each project. They will be reviewed annually and updated if needed by FDOT TDA Office based on WIM data. An example of E_F (E₈₀) values for different types of facilities is shown in Table 8-2.

Directional Distribution Factor (D_F)

Since the number of trucks represents the total for all lanes and both directions of travel, this number must be distributed by direction and by lanes for design purposes. Two-way directional distribution is usually made by assigning 0.5 (50 percent) of the traffic to each direction. One- ways are assigned 1.0 (100 percent).

Although D_F is generally 0.5 (50 percent) for most roadways, there are instances where more weight may be moving in one direction than the other. In such cases, the side with heavier vehicles should be designed for a greater number of ESAL units. For example, D_F may be assigned as 0.7 to account for trucks heavily loaded in one direction. (In practice, both directions of an undivided road would probably be designed for the heavier traffic.)

Lane Factor (L_F)

The L_F is calculated by using the Portland Cement Concrete Pavement Evaluation System (COPES) equation as described in NCHRP No. 277, Transportation Research Board (TRB), September 1986, as shown in Equation 8-3.

Where:

\(L_F\) = Proportion of all one directional trucks in the design lane.

\(LV\) = 0 if the number of lanes in one direction is 2.

\(LV\) = 1 if the number of lanes in one direction is 3 or more.

\(L_n\) = Natural Logarithm.

Assume: One-Way AADT = 25,000 and One-Way Lanes = 3 (meaning LV = 1)

\(L_{F}=1.567-0.0826\times{ln(25000)}-0.12368\times{1}\)

\(L_{F}=1.567-0.0826\times{10.127}-0.12368=1.567-0.836-0.12368\)

\(L_{F}=0.607\)

Load Equivalency Factor (E_F or E₈₀)

The results of the AASHTO Road Test have shown that the damaging effect of the passage of an axle of any mass (commonly called load) can be represented by a number of 18-KIP ESALs (E_F). For example, on flexible pavement, four applications of a 12-KIP single axle were required to cause the same damage (or reduction in serviceability) as one application of an 18-KIP single axle. One 24-KIP axle caused pavement damage equal to three 18-KIP axles. The determination of design ESALs is a very important consideration for the design of pavement structures.

A load equivalency factor represents the ratio of the number of repetitions of an 18-KIP single axle load necessary to cause the same reduction in the Present Serviceability Index (PSI) as one application of any axle load and axle number and configuration (single, tandem, tridem) (see Equation 8-4).

Different axle loads and axle configurations are converted to equivalent damage factors and averaged over the mixed traffic stream to give a load equivalency factor E_F for the average truck in the stream. This factor is available as a feature of TLFS. E_F values used in 18-KIP ESAL calculations can be obtained from TDA Office. To calculate the damage factor using TLFS, it is necessary to select either flexible or rigid E_F factors. The rigid E_F is based on 12-inch-thick pavement with a Terminal Serviceability Index (PT) of 2.5. The flexible E_F is based on a structural number of 5 with a Terminal Serviceability Index (PT) of 2.5.

It should be noted that load equivalency factors are functions of the pavement parameters, type (rigid or flexible) and thickness. These pavement factors will usually give results that are sufficiently accurate for design purposes, even though the final design may be somewhat different.

When more accurate results are desired and the computed design parameter is appreciably different from the assumed value, the new value should be assumed, the design 18-KIP traffic load (ESAL_D) should be recomputed, and the structural design determined for the new ESAL_D. The procedure should be continued until the assumed and computed values are as close as desired. Table 8-2 show some example equivalency factors for different types of facilities as suggested by the FDOT Rigid Pavement Design Manual and Flexible Pavement Design Manual.

Source:
FDOT Topic #625-010-006 Rigid Pavement Design Manual
FDOT Topic #625-010-002 Flexible Pavement Design Manual