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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: FHWA-HRT-05-150
Date: February 2006

Review of The Long-Term Pavement Performance (LTPP) Backcalculation Results

Chapter 7. Summary, Conclusions, and Recommendations


This report presents the results of a study that uses forwardcalculation techniques to screen the backcalculated computed parameter files in the LTPP database. The two different forwardcalculation techniques developed appear to produce reasonable results, both for screening and for estimates of moduli—one for the subgrade and one for the bound surface course layer. In addition, for flexible pavements a relationship developed by Dorman and Metcalf was used for estimates of the modulus of the unbound base course(s). For rigid pavements, a set of ratios relating the modulus of the concrete layer to the base layer was used, very similar to the method in part of the LTPP database covering backcalculation of rigid pavement systems.

The entire set of computed parameter tables of backcalculated pavement layer data was screened with appropriate forwardcalculated moduli. These data cover all available AC and PCC sections where backcalculation was carried out, including both level E and nonlevel E (Release 16.0—All QC Levels, July 2003 Upload). These computations were divided into two parts: a layered-elastic backcalculation approach using the MODCOMP computer program and a backcalculation approach developed specifically for rigid pavement systems using slab-on-dense-liquid and slab-on-elastic solid theory.

Some percentage of the backcalculated flexible pavement layered elastic moduli in the LTPP database derived from MODCOMP were assumed, or fixed, based on engineering judgment and to facilitate the backcalculation process. These values were not screened, but rather left unchanged as they exist in the existing tables with an associated “Y” flag. An even larger percentage of the backcalculated (and some of the forwardcalculated) data were considered to be not within a reasonable range according to the values presented in Table 14. For easy reference, this table is reproduced in this section as Table 17. Records containing moduli outside of the ranges shown in Table 17 were not further screened. Instead, they were flagged (using an “N” data cell, as appropriate) as not reasonable. All remaining records were then screened using the corresponding forwardcalculated moduli. Four different correspondence flags associated with each screened data record have been designated (see Table 15):

0 = Acceptable: The backcalculated value is within a factor of 1.5 of the forwardcalculated value.
1 = Marginal: The backcalculated value is within a factor of 2.0 of the forwardcalculated value (not 0).
2 = Questionable: The backcalculated value is within a factor of 3.0 of the forwardcalculated value (not 0 or 1).
3 = Unacceptable: The backcalculated value is greater than 3 times or less than ? times the forwardcalculated value.

Table 17. Reasonable ranges for various pavement layers in the LTPP database (same as Table 14).
  LTPP Code Reasonable Range
MPa psi
min max min Max
Base Materials
Asphalt-Treated Mixture, not Permeable Asphalt-Treated Base (PATB) 321 700 25,000 101,500 3,625,000
Gravel, Uncrushed 302 50 750 7,250 108,750
Crushed Stone 303 100 1,500 14,500 217,500
Crushed Gravel 304 75 1,000 10,875 145,000
Sand 306 40 500 5,800 72,500
Soil-Aggregate Mixture (predominantly fine grained) 307 50 700 7,250 101,500
Soil-Aggregate Mixture (predominantly coarse grained) 308 60 800 8,700 116,000
Fine Grained Soil or Base 309 35 450  5,100  65,000
Hot-Mixed AC 319 700 25,000 101,500 3,625,000
Sand Asphalt 320 700 25,000 101,500 3,625,000
Dense-Graded, Cold-Laid, Central
Plant Mix AC
323 700 25,000 101,500 3,625,000
Open-Graded, Hot-Laid, Central
Plant Mix AC
325 350 3,500 50,750 507,500
Cement-Aggregate Mixture 331 2,000 20,000 290,000 2,900,000
Econocrete 332 3,500 35,000 507,500 5,075,000
Lean Concrete 334 4,500 45,000 652,500 6,525,000
Soil Cement 339 1,000 7,000 145,000 1,015,000
Open-Graded, Cold-Laid, In-Place Mix AC 327 200 3,000 29,000 435,000
Limerock; Caliche 337 150 1,500 21,750 217,500
Other—Treated Base (TB) 350 400 8,000 58,000 1,160,000
Bound Surface Courses
Concrete Surface (uncracked)   10,000 70,000 1,450,000 10,150,000
AC Surface (>0 OC–<45 OC, not alligatored)   700 25,000 101,500 3,625,000
Unbound Subgrades
Any unbound type   15 650 2,175 94,250

Evaluation of the Rigid Pavement Backcalculated Data Derived from Slab-on-Dense-Liquid and Slab-on-Elastic-Solid Foundation Models

By and large, the screening process produced a set of excellent relationships for the rigid pavement data, essentially based on two-layer slab-on-elastic-solid and slab-on-dense-liquid models, modified as mentioned above for the base layer by using appropriate ratio-based formulas. For all structural layers, nearly 95 percent of all records screened were labeled with a flag of “0,” or acceptable, while most of the few remaining nonzero flags were “1,” or marginal.

Evaluation of the Backcalculated Data Derived from Layered Elastic Analysis

For the flexible pavement data and for the rigid pavement data using layered elastic theory (all generated through the MODCOMP backcalculation program), the screening process produced some data tables with fairly good agreement between the two analysis methods and many tables with relatively poor agreement between the back- and forwardcalculated moduli.

By way of background, for backcalculation involving more than two unknown layers, in most backcalculation programs, the modulus values are effectively derived from the bottom up. This factor is also true for the MODCOMP program. As a result, when a small error occurs in the lowest unknown layer—the subgrade—the compensating layer effect will inevitably occur, by alternately under- and over-estimating the moduli of the succeeding (overlying) layers. In these cases, by the time the fourth or fifth layer from the bottom is adjusted through the iteration process—the bound surface course—the necessary compensation for an incorrect subgrade modulus has taken place and a reasonable result has generally been obtained in spite of alternating too-high and too-low results in the intermediate layers beneath the surface course. The compensating layer effect appears to be mainly associated with distressed pavements that usually do not follow the rules and assumptions made of linear or even nonlinear layered elastic theory. On the other hand, with homogeneous, undistressed, and well-defined pavement structures, backcalculation often appears to work quite well. This observation is especially true for interior slab concrete tests—although only when a two-unknown layer system is used (plus a hard layer at some depth, if present).

Accordingly, the backcalculated asphalt and concrete surface course moduli using MODCOMP resulted in the best correspondence to the forwardcalculated moduli of all layers analyzed. For the asphalt moduli, better than 70 percent of the correspondence screened values (for both the point- and the section-data) were acceptable (flag = 0). For the concrete moduli at the point data level using MODCOMP, better than 60 percent of the screened data using a bonded condition in forwardcalculation were acceptable (flag = 0), while more than 80 percent of these data were acceptable assuming an unbonded condition between the PCC surface and the base course, when compared to the forwardcalculated values for rigid pavements. At the section level for the concrete modulus derived from MODCOMP, better than 90 percent of the backcalculated screened data were acceptable, with a correspondence flag of “0.”

For the subgrade layer, the correspondence between back- and forwardcalculated moduli using MODCOMP (both linear and nonlinear) was somewhat poorer than with the asphalt layer. However, these results are principally from the methodology, not the correctness (or lack thereof) of each method. Forwardcalculation uses the center deflection and the shape of the deflection bowl to characterize the subgrade stiffness under the load plate to a finite depth, as defined by the shape of the deflection bowl. Backcalculation uses one or more of the outer geophones to characterize the subgrade stiffness at that particular distance from the load, assuming it will also have the same stiffness under the load plate. Often this does not appear to be the case—hence, the compensating layer effect. In other instances, in particular with concrete or a very stiff AC pavements, a horizontally constant subgrade modulus appears to be a more reasonable assumption.

Consequently, only about 40 percent of the correspondence screened records for flexible pavement subgrades were classified as acceptable (flag = 0). The results of screening the subgrade section tables as well as the nonlinear version of MODCOMP were similar. On the other hand, most of the bias between the two methods was in the same direction—the backcalculated subgrade moduli from MODCOMP were generally higher than those from forwardcalculation. For the concrete sections, the correspondence between the two approaches was somewhat better, with about 50 percent of these being classified as acceptable, with a correspondence flag = 0. In all unacceptable cases, MODCOMP versus forwardcalculation produced divergent results that were about equally divided between marginal, questionable, and unacceptable (flag = 1, 2, or 3, respectively).

For the base layer using the MODCOMP backcalculation program, many of the backcalculated moduli (and some of the forwardcalculated moduli from the use of the Dorman and Metcalf relationship) were not reasonable according to the broad ranges given in Table 17. Of the remaining values that were screened using the correspondence flags, only between 30 and 40 percent of the data resulted in an acceptable flag of “0,” with the remainder once again divided more or less evenly among marginal, questionable, and unacceptable (corresponding flags = 1, 2, or 3, respectively).

The Microsoft® Excel spreadsheets containing all formulae used in phase I of this study have been provided to FHWA, so all forwardcalculation 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 available—two for asphalt-bound surfaces (using SI and U.S. Customary units) and two for cement-bound surfaces (SI and U.S. Customary). These spreadsheets can be obtained by contacting LTPP Customer Support Services: by phone at 202– 493–3035 or by e-mail at ltppinfo@fhwa.dot.gov. A publication entitled Guidelines for Review and Evaluation of Backcalculation Results (FHWA-HRT-05-152) is also available from FHWA for those wishing to use these spreadsheets.


This report presents the results of a study that used forwardcalculation techniques to screen the entire set of backcalculated computed parameter results in the LTPP database. Two parallel computed parameter data sets now exist: one existing set resulting from backcalculation and one newly created set resulting from forwardcalculation, for the same LTPP sections and using the same FWD input data. This choice does not mean that one method or the other is strictly right or wrong. They are, however, in many instances different.

As this report shows, backcalculation is more of an art than a science, although it is certainly rigorous and scientific in the sense that it can use the entire deflection basin to fairly accurately match up the theoretical and actual measured deflections with backcalculated modulus values. The user, however, must be aware of its limitations and assumptions, such as linear-elasticity, homogeneity, isotropic behavior, in addition to the assumption of being horizontally identical in stiffness for each structural layer beneath the width of the deflection basin, especially if a linear-elastic model is chosen for backcalculation. A skilled backcalculation analyst can deal with these potential shortfalls quite well by skillfully modeling the pavement system and by dealing with apparent or actual nonlinearity in a variety of ways.

For example, the analyst can assign a semirigid layer at some depth where the deflection basin suggests a possible stiff layer or bedrock, similar to how the Hogg model in forwardcalculation defines a depth to an apparent stiff layer, whether there actually is a very stiff layer or bedrock or not at that depth. Adjacent structural layers may also be combined to backcalculate an unknown layer modulus that would otherwise not influence the deflection basin enough to enable the derivation of a modulus value for a relatively thin structural layer. In other cases, a single, relatively thick pavement layer can be separated into two layers in the input file to characterize the apparent difference in material response as a function of depth within the pavement.

What would be most satisfying and give considerably more credibility to both backcalculated and forwardcalculated results is if they are both reasonable and correspond to one another (within reason) with a flag of “0” (i.e., within a factor of 1.5 of one another). For in situ layered-elastic properties of pavement systems, this level of correspondence can be considered reasonable and generally satisfactory for engineering purposes. When this correlation occurs, it can be maintained that the input assumptions for either approach were essentially correct and that either set of moduli may be used with confidence.

But what should be done when the correspondence flags between back- and forwardcalculation are 1, 2, or 3 (i.e., greater than a factor of 1.5 different from one another)? This situation means that both values are within a reasonable range according to Table 17 and are neither fixed nor assumed. It probably also means that the theoretical assumptions of one or the other, or both, methods are incorrect—or the method of choice is not being used wisely or correctly. Although forwardcalculation produced more stable results, globally, than the three- or more-layer backcalculation approach (using MODCOMP), backcalculated values cannot be categorically rejected, because they do offer a theoretically correct solution to a specific FWD deflection basin, however implausible they may appear. Accordingly, some of these cases may well be implausible, but there is still a possibilityhowever remote—that the values are in fact more or less correct, given the nature of in situ pavement materials and the often bizarre behavior of these materials under a load and under the influence of ever-changing environmental and other site-specific factors.

Now, however, the LTPP database user can be forewarned by the various flags and data quality checks as outlined in this report and assess whether to accept the values present in the existing backcalculated database (or the forwardcalculated parallel database), depending on the intended evaluation purpose.

In conclusion, the slab-on-elastic-solid or slab-on-dense-liquid models for backcalculation offer excellent correspondence with the rigid pavement forwardcalculation techniques, with very few values being labeled unreasonable. Accordingly, in the vast majority of cases, either (or both) may be used with a good degree of confidence.


Existing LTPP Backcalculation Data—Flagging and Addition of Forwardcalculation Data

As a remedial measure, it is recommended that the current LTPP backcalculated tables be retained as is, although with the various checks and flags added as outlined in this report. It is also recommended that the forwardcalculated values be appended to the computed parameter data tables, so that an LTPP database user can compare the two sets of values obtained from the same deflection basin. When these pairs of values pass both the reasonableness test and the acceptable (correspondence flag) test, then either (or both) may then be used with a greater degree of confidence than one or the other as a stand-alone value.

Future Analysis of the LTPP FWD Deflection Data—Conduct both Back- and Forwardcalculation

To date, only a limited percentage of the total volume of FWD load-deflection data have been processed through either back- or forwardcalculation. As this report documents, no single truth exists to determine or quantify actual in situ layered elastic moduli. The results obtained through backcalculation depend at least as much on how the program of choice is used than on the actual mechanics of how the program functions. Although forwardcalculation produces a unique set of values, these values are approximations, not cast-in-stone truth or baseline values. However, these approximations can certainly be used to guide the backcalculation program user to see if he/she is in the ballpark with answers obtained through any chosen method of load-deflection data analysis.

As a QA measure, it is further recommended that the entire FWD load-deflection database, where back- or forwardcalculation can be carried out, be reanalyzed in the case of the previously analyzed MODCOMP data along with the unanalyzed post-1998 data. Furthermore, since LTPP is a research project, it is not recommended that only one solution be offered as new or improved LTPP computed parameters, but rather two or more different solutions be provided to the LTPP database user. Forward- and backcalculation programs with different theoretical assumptions (for example, by comparing MODCOMP and forwardcalculation results) should be employed so that the LTPP database user can compare the values obtained for the same layer, test point, and test section.

Especially in the case of layered elastic backcalculation of three or more unknown layers, it is very important that each test section be handled on an individual basis by an experienced and savvy user of the selected backcalculation program. Even for an experienced analyst, this process will take some time, since each LTPP section should be carefully reviewed for discrepancies between the program’s input assumptions and actual deflection behavior. If MODCOMP (or any other backcalculation program) is selected for a second round of LTPP deflection data analysis, much more time will be necessary than for a typical batch processing of load-deflection data. For any layered elastic analysis using backcalculation, forwardcalculation as outlined herein may be used as a comparison and, if desired, to seed the backcalculation routine selected, as long as the forwardcalculated values are well within the reasonable ranges in Table 17. This table may be changed and updated as appropriate, for example by narrowing the range of reasonable asphalt layer moduli as a function of pavement temperature (if available), if new in situ modulus information is forthcoming about any of the materials listed in the table. Seeding with forwardcalculated values may well positively affect the backcalculated solutions, providing a more reasonable starting point for a good deflection basin fit and a more believable set of moduli in the output.

It will not be necessary to reanalyze or rescreen the back- or forwardcalculated values in the slab-on-elastic-solid or slab-on-dense-liquid database, since these two different approaches produced very similar results. It is recommended that experienced analysts carry out the same two approaches on the remaining rigid pavement data measured at interior slab locations using slab-on-dense-liquid and slab-on-elastic-solid theory for backcalculation.

Selection of Future LTPP FWD Data Analysis Tools—Backcalculation and Forwardcalculation

It is recommended that a second round of LTPP FWD deflection data analysis consist of the following steps:

  • Forwardcalculation of all LTPP sections—Use the methods as outlined in this report.
  • Backcalculation of the LTPP rigid pavement sections—Use slab-on-elastic-solid or slab-on-dense-liquid foundation analysis, as developed under the previous LTPP backcalculation project (FHWA-RD-01-113).
  • Backcalculation of the LTPP flexible pavement sections—Use a sound and user-friendly layered elastic backcalculation analysis program and seed values from forwardcalculation (provided these values are within reasonable ranges).

Recommended Actions to Improve Future Backcalculation Results

In the future, the forwardcalculated values can be used in the following ways to improve the backcalculation results:

  • The forwardcalculated values (if they are within a reasonable range) should be used to "seed" most backcalculation routines to assist in arriving at more reasonable and accurate backcalculated modulus values.

  • When a "flag" arises for any reason (reasonable ranges, large discrepancies with forwardcalculation, etc.), at the discretion of the analyst backcalculation can be modified and repeated to minimize these differences and/or mitigate the compensating layer effect, thereby improving the backcalculated database while leaving the forwardcalculated results in the database as well.

Notes on a Viable Alternative to Classic Multilayered Elastic Backcalculation

This section is based primarily on the knowledge and experience of the investigators of this task order, not an evaluation outcome of the project.

As an alternative to classic, multilayered backcalculation (e.g., MODCOMP, MODULUS, EVERCALC, etc.), some LTPP database processing time could be saved by using the proprietary ELMOD program, which is easier for a hands-off batch mode. This technique would still provide LTPP database users with the results of two different approaches using two methods (backcalculation with ELMOD and forwardcalculation as developed for this project) that are similar in some respects and dissimilar in others. The current version of ELMOD offers the user two internal processing engines—one using a deflection basin matching routine similar to traditional backcalculation and the other using the radius of curvature method, which is similar to the forwardcalculation routine for bound surface layers presented in this report. Based on our experience with ELMOD, the latter is more stable, and therefore more believable, because in many cases, layered elastic pavement systems (especially distressed pavement sections) generally do not follow the classical laws of homogeneity, isotropic properties, and horizontally constant moduli. Accordingly, both ELMOD approaches should be batch-processed so as to provide the LTPP database user with three comparable solutions—two from ELMOD and one from forwardcalculation. Traditional backcalculation (for example, using MODCOMP again) could also be added as a fourth set of values, as long as they are carried out more carefully and thoroughly than before, as mentioned previously.

The suggestion to consider the use of ELMOD, above, does not necessarily mean that ELMOD is better or more accurate than MODCOMP, EVERCALC, or MODULUS, etc. All of these traditional programs—as well as ELMOD and the forwardcalculation techniques presented in this report—produce approximations of in situ modulus values, at best. When using elastic layered theory on the vast quantity of LTPP data, ELMOD as a backcalculation engine would be both less costly and more efficient than most other backcalculation approaches known to the research team.

There may well be a public domain or other alternative to ELMOD, but the research team is not familiar with such an alternative. As far as is known, ELMOD is the only program that will both run deflection basin matching and radius of curvature or a similar method in one package.



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