U.S. Department of Transportation
Federal Highway Administration
1200 New Jersey Avenue, SE
Washington, DC 20590
2023664000
Federal Highway Administration Research and Technology
Coordinating, Developing, and Delivering Highway Transportation Innovations
This report is an archived publication and may contain dated technical, contact, and link information 

Publication Number: FHWAHRT05152
Date: February 2006 

Guidelines for Review and Evaluation of Backcalculation ResultsChapter 3. Forwardcalculation SpreadsheetsOverviewUsing the forward calculation principles outlined in the preceding sections, four generic forward calculation spreadsheets are provided, as follows:
Please note, however, that there are several constraints to using these spreadsheets. One constraint is that they are presently formatted for seven deflection readings. Accordingly, if your FWD generates more than seven deflection readings, the analyst should only paste in data for the seven most appropriate sensor positions obtained, depending on the units and type of pavement, etc. Before using the provided forward calculation spreadsheets, the following constraints should be noted: Notes on the FWD Deflection Data For flexible pavements, three of the seven chosen deflection readings must be positioned either at 0, 8, and 12 inches or 0, 200, and 300 mm. Further, these three must be ordered as the first three of the seven deflection positions selected. For rigid pavements, four of the chosen seven deflection readings must be positioned either at 0, 12, 24, and 36 inches or at 0, 300, 600, and 900 mm. Furthermore, these four must be the first, third, fifth, and sixth of the seven deflection positions selected. The use of these critical positions makes it possible to calculate either the AREA_{12} term or the AREA_{36} term for AC or PCC pavements, respectively. The appropriate AREA term is, in turn, used in the calculation of the bound surface course stiffness. The remaining sensor positions should be chosen such that they span the region in the deflection basin where one of these is approximately onehalf of the center deflection reading, for all lines of FWD input data. This enables proper use of the Hogg model for forward calculating the effective subgrade modulus and the depth to the effective hard layer. Although any dropbydrop FWD data may be used as input, to improve the random accuracy of the deflection readings, it is recommended that averages of multiple drops are used, especially in the case of rigid pavements or flexible pavements where the asphalt temperature is very low. This is important because the basin will be very flat, and the method is highly sensitive to very small errors in any of the AREA terms used for forward calculation of the bound surface course. Determine the Pavement Layer Structures for Forwardcalculation When using the forward calculation techniques, the operator must forward calculate elastic moduli for up to three layers for each deflection basin. Given that requirement, the pavement system being analyzed must be divided or combined into a two or threelayer structure, as follows:
For rigid pavements, the uppermost base layer below the PCC slab was considered the base layer. Using the Forwardcalculation SpreadsheetsThe four forward calculation spreadsheets provided are selfexplanatory in almost all circumstances. For firsttime users, the following steps should be carried out when using any of these spreadsheets:
What To Do With the Results of Back and ForwardcalculationAfter either back or forward calculation has been carried out to the satisfaction of the analyst, all values (or averages and coefficients of variance thereof) should be checked for reasonableness before using these data for pavement design purposes. Table 3 provides a broad range of modulus values for various pavement materials that may be considered reasonable. When using the broad ranges shown in Table 3, common sense should be exercised as well. For example, the range for asphaltbound surface courses covers a very broad temperature range, with the higher parts of the range shown covering colder pavement temperatures (down to freezing) and the lower part covering temperatures as high as 45° C (~ 115° F). If the analyst feels that either back or forward calculation resulted in any modulus values outside of the ranges shown in Table 3, or any other appropriate ranges, these should be rejected as either unrealistic or unreasonable. If both methods produced values within the ranges shown in Table 3, the pairs of values may be compared (or corresponded) and designated as recommended in Table 4. As can be seen in Table 4 and with the variability of in situ materials in mind, it is felt that an acceptable correspondence between back and forward calculated moduli can be considered to be within a factor of 1.5 (times or divided by) the screening value calculated through forward calculation. (Again, this is as long as both values are still within the reasonable ranges shown in Table 3.) In such a case, either value may be selected for pavement design purposes. Consider as well that the subgrade modulus back calculated through the Hogg model as presented herein is usually lower than that obtained through classical Backcalculation. This is mainly because the Hogg model only calculates the effective subgrade modulus under the load plate and to a finite depth, as indicated in the forward calculation spreadsheet output. Backcalculation, in most cases, assumes that the subgrade extends to an infinite (or even a fixed finite) depth, and is the same at all deflection basin offset distances (sensors #2 through #7 or more), including under the load plate (sensor #1). As a result, in the LTPP database, for example, the forward calculated subgrade modulus was around half of the back calculated subgrade modulus, on average. Therefore, if one uses the traditional AASHTO design formula, where the design subgrade modulus is assumed to be onethird that of the back calculated modulus, then the forward calculated subgrade moduli should not be divided by three, or the design will be far too conservative. It is not recommended that some of the modulus values from Backcalculation and some of the values from forward calculation be used for the design of a single uniform section, but rather the entire set of either back calculated or forward calculated values should be used, depending on the reasonableness of the values obtained. Microsoft^{®} Excel spreadsheets have been prepared containing all formulae used in phase I of this study. All forward calculation input quantities are totally transparent to those who wish to use the methodology, whether for screening or in rehabilitation design. To this end, four spreadsheets are availabletwo for asphaltbound surfaces (using SI and U.S. Customary units) and two for cementbound surfaces (SI and U.S. Customary). These spreadsheets can be obtained by contacting LTPP Customer Support Services: by phone at 2024933035 or by email at ltppinfo@fhwa.dot.gov. Table 3. Reasonable ranges for various pavement layers from the LTPP database.
Table 4. Flagging codes used to screen the back calculated LTPP database.
FHWAHRT05152

Topics: research, infrastructure, pavements and materials Keywords: research, infrastructure, pavements and materials,Pavements, LTPP, FWD, deflection data, elastic modulus, Backcalculation, forward calculation, screening of pavement moduli. TRT Terms: research, facilities, transportation, highway facilities, roads, parts of roads, pavements Updated: 04/23/2012
