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Publication Number: FHWA-HRT-12-023
Date: December 2012


Simplified Techniques for Evaluation and Interpretation of Pavement Deflections for Network-Level Analysis

CHAPTER 2 - Literature Review


An essential part of this project was to conduct an extensive literature search. While FWD load deflection data have long been used to carry out project-level analyses, using these data to conduct network-level surveys is performed less frequently. Nevertheless, the existing literature shows that several agencies are already using FWD data in their network-level pavement analysis procedures.

Some agencies have also developed procedures that may assist in the development of a simplified approach to using deflection data in a network-level analysis that links pavement structural parameters, determined through the use of FWD data to pavement performance.

A review of all available literature was duly conducted, including obtaining information from agencies outside the Unites States, to ascertain which agencies use deflection data, which approach they employ, and whether these particular approaches may be useful in the present study. All deflection parameters (measured or computed) included in this report refer to the Strategic Highway Research Program (SHRP) seven sensor positions.(2)

Literature Review Approach

Relevant literature references were reviewed on the following subjects to achieve the literature review objectives:

It is crucial to establish a reasonable body of knowledge on these topics to address the following:

Summary of Findings from Previous Studies

Table 1 provides a summary of potentially relevant agency practices for FWD data collection and use for network-level analyses identified during the literature review study (see the complete table of references in appendix A).

Table 1. Summary of useful practices for FWD use in network-level analyses.

Agency and Publication Test Point Spacing FWD Test Frequency FWD Sensor Positions Limiting Factors Basic Details of the PMS Approach

California Department of Transportation (Caltrans); "Test to Determine Overlay and Maintenance Requirements by Pavement Deflection Measurements"(3)




None; currently used for flexible and composite pavements only

Uses center deflection only, plus existing asphalt concrete (AC) or AC + portland cement concrete (PCC) layer thickness.

Federal Highway Administration (FHWA); Review of the LTPP Backcalculation Results(4)




None; may be used for flexible, composite, and rigid pavements alike

Uses Hogg model for subgrade modulus calculation. While it is possible that surface course stiffness can be derived using a related approach reported to FHWA by the authors, this is probably too complex and not worth the effort.

National Cooperative Highway Research Program (NCHRP); Project 10-48: Assessing Pavement Layer Condition Using Deflection Data(5)

Probably not studied

Probably not studied

SHRP positions, generally

None; all pavement types studied using LTPP database (flexible, rigid, and composite)

Uses easy-to-obtain deflection basin parameters and relates these parameters to observed pavement distresses.

FHWA; Temperature Predictions and Adjustment Factors for Asphalt Pavement





The adjustment for asphalt pavements for temperature-at-depth and center deflection adjustments for pavement temperature may be used to assist in the present study.

Kansas Department of Transportation (KDOT); "Network-Level Pavement Deflection Testing
and Structural Evaluation"(7)

A minimum of three tests per mile; five is preferred

One-third of network per year; however, one-fifth of network may be adequate

Unknown; probably unimportant

Flexible pavements only

Used data from one Kansas district on AC surfaces only (non-interstate), which is a similar approach to the current study. Based on the 1993 American Association of State Highway and Transportation Officials (AASHTO) Guide for Design of Pavement Structures.(8) The FWD, especially the center deflection value, added considerably to predictive capability of method used. Based on the concept of pavement structural evaluation (PSE). PSE was found to be twice as important to predict pavement performance as any other observable parameter. Recommended the use of Bayesian statistical models.

Alaska Department of Transportation (AkDOT); Modeling Flexible Pavement Reponse and Performance(9)

0.1 mi

After repaving

SHRP positions

No limits

Deflections are converted to layer moduli, which are then used to obtain stress/strain values under a standard equivalent single-axle load (ESAL). Transfer functions relate stress/strain to cracking in bound layers and permanent deformation in unbound layers.

Texas Department of Transportation (TxDOT); Incorporating a Structural Strength Index into the Texas Pavement Evaluation System (FHWA/TX-88/409-3F)(10)

0.5 mi

One recommended per year

1 ft

Flexible pavements less than 5.5 inches AC thickness

Structural strength index (SSI) varies from zero to 100 (weak to strong). Based on normalized basin parameters, such as outer deflections, surface curvature index (SCI), and center deflection under a 9,000-lb load. Can characterize subgrades and pavement structure independently in terms of relative stiffness. System based on statistical evaluation of deflections statewide.

TxDOT; Network-Level Deflection Data Collection for Rigid Pavement(11)

0.5 mi


1 ft

Rigid pavements

Not very useful from an analytical standpoint; mostly gives recommendations regarding field test procedures, estimated costs for testing and analysis, and reference to maximum allowable deflections for rigid pavements for network testing.

Virginia Department of Transportation (VDOT); Network-Level Pavement Evaluation of Virginia's Interstate System Using the Falling Weight Deflectometer (Report VTRC 08-R18)(12)

0.2 mi

4-5-year cycle

SHRP positions


Flexible pavements were analyzed by calculating the subgrade resilient modulus, the effective pavement modulus, and the effective structural number (SN). Rigid and composite pavements were analyzed by calculating the area under the deflection basin and the static modulus of subgrade reaction (k-value).

National Laboratory for Civil Engineering; Use of Deflections at Network Level in England for Programming and Other Purposes(13)

N/A; Used deflectograph, complemented by FWD

3-5 years


Flexible pavements only

Used Transport and Road Research Laboratory (TRRL) equations to calculate residual life and strengthening requirements based on deflection. The conclusion was that deflection does not increase with time and in some cases actually decreases due to an increase in pavement materials stiffness due to aging, etc. This approach was used until 2000.

South Africa; "Benchmarking the Structural Condition of Flexible Pavements with Deflection Bowl Parameters"(14)

0.2 km


300 mm typical

Flexible pavements only

Pavement is divided into three zones based on depth. Uses basin parameters to characterize base, middepth, and subgrade structural condition such as "sound," "warning," or "severe."

Association of Australian and New Zealand Road Transport and Traffic Authorities; Use of FWD in the Network Level Pavement Condition Survey(15)



0, 900, and 1,500 mm

Flexible and semi-rigid pavements

Uses adjusted SN as indicator for pavement bearing capacity. SN is calculated based on d0, d900, and d1500, in which d represents deflection and i is the distance from the center of the plate (0, 900 and 1,500 mm).

N/A = Not available.
1 mi = 1.61 km
1 inch = 25.4 mm
1 ft = 0.305 m
1 lb = 0.454 kg


Agencies Currently Utilizing Deflection Data for Network-Level Applications

Findings from the literature indicate that only five agencies use, or are planning to use, load deflection data directly within their PMS.

United Kingdom

The United Kingdom uses traveling deflectograph data, not FWD or dynamic load deflection data; therefore, these data are not applicable to the present study.(13,16) The traveling deflectograph does not correlate well with the FWD (or even the rolling wheel deflectometer (RWD)) due to the large differences in loading time and the Benkelman beam style apparatus involved, among other salient factors. While researchers in the United Kingdom have tried to supplement their traveling deflectograph data with FWD data, they discovered that the two do not correlate well, as expected; therefore, the FWD was dropped in favor of the traveling deflectograph. Interestingly, the old Caltrans traveling deflectograph, which was similar to the UK device, was dropped at least 30 years ago, first in favor of the Dynaflect® and later the FWD.


AkDOT uses a multiyear cycle for deflection readings based on ongoing pre-and post-rehabilitation projects. Their PMS approach using FWD data was only recently initiated.(9) It cannot be considered a simple process since back-calculation of sorts is currently used to determine remaining life. How well AkDOT's FWD evaluation procedure actually translates to pavement distresses, and therefore to pavement life expectancy, remains to be seen. Alaska's application of load deflection data within their PMS is relatively new. Accordingly, a few more years' worth of data will be needed to evaluate structural versus performance correlations. At the time this report was written, AkDOT gathered over 300 mi (483 km) of FWD data on the Parks Highway. These data were subsequently used as an example of how to incorporate the simplified methodology developed herein and will be shown later in this report.

Conversely, the methodology used to calculate the subgrade "seed" modulus using the AkDOT procedure is straightforward and immediately useable as a stand-alone parameter. Therefore, it can be used to correlate the subgrade modulus from the LTPP FWD database to see how well that particular approach (i.e., a nonlinear subgrade modulus model) relates to the various performance indicators in the mature LTPP database. The AkDOT procedure currently applies to flexible pavements only; however, rigid pavements may be investigated using the same subgrade modulus closed-form back-calculation process.


TxDOT currently uses deflection data in their PMS for flexible pavements only (district optional). (See references 10, 11, 17, and 18.) The publication Incorporating a Structural Strength Index into the Texas Pavement Evaluation System has been in use since its publication in 1988 in some of Texas's districts.(10) It is currently used for relatively thin asphalt-surfaced pavements in 4 of 13 districts in Texas - Fort Worth, Houston, San Antonio, and Pharr. It is expected that the entire State will soon use the newer process shown in table 1.(10)

In an older TxDOT method, network-level deflection basins were collected at selected locations in the State to determine averages and ranges for a variety of pavement thicknesses and subgrade types. Basin parameters were developed and used in lieu of a back-calculation approach due to the lack of pavement structural data (i.e., number of layers, layer thicknesses, and material types). The greatest drawback to this approach is that it does not provide an indication of remaining structural life or bearing capacity. This approach essentially uses two basin parameters: SCI and W7, which is the deflection measured 6 ft (1.83 m) from the FWD load center. SCI is the difference between the deflections measured at the center of the load plate and the deflection measured 12 inches (304.8 mm) from the load plate. From these two parameters, an SSI is determined from one of three tables: one for surface treated pavements, one for thin asphalt pavements, and one for intermediate and thick asphalt pavements. SSI is further adjusted for traffic and rainfall levels to arrive at a final SSI. SSI ranges from 100 for a 100 percent structurally adequate pavement to zero for a 100 percent structurally inadequate pavement (meaning zero percent adequacy). This approach allows the user to determine where the inadequacies lie, whether within the subgrade or somewhere within the pavement structural section itself, above the subgrade.


VDOT recently began using deflection data in their PMS, covering the entire network on a 4- to 5-year cycle for both flexible and rigid pavements.(12) The procedure is simple and straightforward. However, since it is relatively new, the current study will have to evaluate the relationship of Virginia's structural determination procedures to pavement performance data in the LTPP database.

In developing the VDOT method, a two-phase evaluation of a proposed network-level structural evaluation technique was carried out in 2007 and 2008. Both phases were restricted to interstate pavements. In phase I, only I-64 and I-77 were included in the study. The results looked promising, so phase II was initiated on the remainder of Virginia's interstate system. A final report was published in 2008, which concluded that network-level deflection testing could be used to address network needs in terms of rehabilitation strategies and funding management decisions.(12) The author further suggested that the network-level structural analysis should be expanded to include Virginia's primary network.

Pavement types in the study included flexible, rigid, and composite pavement structures. For flexible pavements, the analysis was conducted according to the 1993 AASHTO Guide for Design of Pavement Structures. (8) For rigid and composite pavements, the analysis was conducted according to the 1998 Supplement to the AASHTO Guide for Design of Pavement Structures: Part II - Rigid Pavement Design and Rigid Pavement Joint Design.(19)

For flexible pavements, the resilient modulus (Mr) is first calculated according to the 1993 AASHTO Guide for Design of Pavement Structures.(8) The effective pavement modulus (Ep) is calculated from the center deflection and subgrade modulus, also according to AASHTO procedures. Finally, an effective structural number (SNeff) is determined from Ep and the total pavement thickness above the subgrade.(8)

For rigid and composite pavements, the deflection basin AREA and the static modulus of subgrade reaction, k, are used to quantify overall structural condition.

A cumulative distribution curve of SNeffand Mr was developed for all flexible pavements in the study. Similar curves were developed for center deflections and deflection basin AREA for rigid pavements. These distribution curves are used to identify structurally weak areas of the network for further project-level investigation.

One factor that contributed to the overall success of this approach is the availability of pavement layer data (thicknesses, material types, etc.) in VDOT's Highway Traffic Record Information System database.(20) Also noted were rather high subgrade Mr in the cumulative distribution curves. The 50th percentile value of the subgrade stiffness was around 12,500 psi (86,125 kPa). This may have been due in part to the presence of rigid or semi-rigid layers in the subgrade, which the AASHTO method does not address, and in part due to the typical non-linear behavior of cohesive subgrades (with a lower effective modulus under the load than at increasing distances from the load). The 1993 AASHTO Guide for Design of Pavement Structures equations utilize the outer deflection sensors to characterize the subgrade modulus, not the true effective modulus of the subgrade under the load.(8)

South Africa

The Republic of South Africa uses FWD testing at 656-ft (200-m) intervals to ascertain the bearing capacity of three roadway "zones" or layers (surface, base, and subgrade). The methodology relies on direct deflection basin parameters, not back-calculation.(14) A benchmarking technique was developed to relate direct deflection values and basin parameters to the structural condition of the pavement at both the project and network levels. This benchmarking technique can be used in the absence of detailed information regarding pavement composition.

The South African method correlates FWD deflections to structural layers or zones within the pavement structure. These zones are numbered 1 through 3, where zone 1 corresponds to the materials closest to the load plate within the pavement structure, extending out to 11.7 inches (300 mm) in terms of the deflection basin (and probably somewhat less in terms of depth within the structure). In zone 2, the inflection point in the deflection basin occurs and generally lies from < 1 to 2 ft (< 0.305 to 0.61 m) in depth below the pavement surface. Zone 3 extends from approximately 2 to 6.5 ft (0.61 to 1.98 m) from the center of the load plate and thus represents the deepest layers in the pavement structure - primarily the subgrade.

In the South African method, the following deflection parameters and associated pavement structural zones are represented:

Calculation of RoC. RoC equals open parenthesis open parenthesis L squared closed parenthesis divided by two times D subscript zero times the quantity open parenthesis 1 minus D subscript 200 divided by D subscript zero closed parenthesis closed bracket.
Figure 1. Equation. Calculation of RoC

Calculation of BLI. BLI equals D subscript zero minus D subscript 300.
Figure 2. Equation. Calculation of BLI

MLI equals D subscript 300 minus D subscript 600.
Figure 3. Equation. Calculation of MLI

Calculation of LLI. LLI equals D subscript 600 minus D subscript 900.
Figure 4. Equation. Calculation of LLI

L = Diameter of the load plate of the FWD (mm).
D0 = Deflection at center of load plate (mm).
D200 = Deflection at 8 inches (200 mm) from the center of the load plate (mm).
D300 = Deflection at 12 inches (300 mm) from the center of the load plate (mm).
D600 = Deflection at 24 inches (600 mm) from the center of the load plate (mm).
D900 = Deflection at 36 inches (200 mm) from the center of the load plate (mm).

These deflection bowl parameters are related to a structural condition rating according to the structural condition and the type of base layer, as described in table 2, extracted from Horak's "Benchmarking the Structural Condition of Flexible Pavements with Deflection Bowl Parameters."(14)

The basin parameters LLI, MLI, and BLI are plotted against stationing for a particular roadway to facilitate the structural assessment procedure. This plot of structural condition is often used in conjunction with visual assessments to determine the type of rehabilitation required to restore the pavement to a good condition.



Table 2. Structural condition associated with deflection bowl parameters.(14)

Base Type Structural Condition Rating Deflection Bowl Parameters

Granular base


< 500

> 100

< 200

< 100

< 50








> 750

< 50

> 400

> 200

> 100

Cementitious base


< 200

> 150

< 100

< 50

< 40








> 400

< 80

> 300

> 100

> 80

Bituminous base


< 400

> 250

< 200

< 100

< 50








> 600

< 100

> 400

> 150

> 80

Note: These criteria can be adjusted to improve sensitivity of benchmarking.
1 mil = 25.4
1 ft = 0.305 m

The surface modulus is calculated at the various sensors and plotted against distance from the load plate to assess nonlinearity. The standard Boussinesq equations are used for this purpose. Points where the surface modulus increases with increasing distance from the load center are regarded as "stress softening." If the surface modulus is similar for all measured deflections, the subgrade is regarded as linear-elastic. Decreasing surface modulus with increasing distance from the load center indicates a "stress stiffening" subgrade.

Agencies Utilizing Deflection Data in a Manner Potentially Useful to Enhance Network-Level PMS Applications

In addition to the previously listed agencies that already utilize load deflection data within their PMS, the following agencies use deflection data with potential network-level PMS applications:

The following publications do not describe deflection data applications of specific agencies, but they are relevant to the scope of this project:

Identified Techniques for Simplified Evaluation and Analysis

Based on the literature review and summary of useful practices presented in table 1, a list of deflection techniques was created. Several techniques were considered to be applicable to the scope of this project and were selected for further analysis. The following techniques and equations were selected when applicable:

  1. D1, measured at the center of the load plate in millimeters. (See references 14, 3, 7, 15, and 21.)
  2. Direct deflection basin, D1 through D7, where Di is the deflection measured at sensor i = 1 through 7 according to SHRP's seven sensor positions. (2,21)
  3. Curvature index (CI)(see figure 5). (14,15,21)

    CI subscript i equals D subscript i minus D subscript i plus 1.
    Figure 5. Equation. Calculation of CIi

    Where Di is the deflection measured at sensor i = 1 through 7
  4. Shape indicator (F) (see figure 6). (21)

    F subscript i equals open parenthesis the quantity D subscript i minus 1 minus the quantity D subscript i plus 1divided by the quantity D subscript i closed parenthesis.
    Figure 6. Equation. Calculation of Fi

    Where i is the sensor 1 through 7.
  5. Slope variance (S) (see figure 7). (21)

    S subscript i equals D subscript 1 minus D subscript i.
    Figure 7. Equation. Calculation of Si.

  6. Reciprocal indicator (I) (see figure 8).(21)

    I subscript i equals 1 divided by D subscript i.
    Figure 8. Equation. Calculation of Ii

    Where i is the sensor 1 through 7.

  7. Rectangular area indicator (RA) (see figure 9).(21)

    RA equals the summation of D subscript i with values of i ranging from 1 to 7divided by D subscript i.
    Figure 9. Equation. Calculation of RA

    Where i is the sensor 1 through 7.

  8. Trapezoidal area indicator (TA) (see figure 10).(21)

    TA equals D subscript 1 plus D subscript 7 plus the summation of 2 times D subscript i with values of i ranging from 2 to 6 divided by D subscript i.
    Figure 10. Equation. Calculation of TA

    Where i is the sensor 1 through 7

  9. SNeff(see figure 11). (17,18,7)

    SN subscript eff equals 0.0045 times D times open parenthesis E subscript p closed parenthesis raised to the power of one-third
    Figure 11. Equation. Calculation of SNeff.

    Where D is the total pavement layer thickness above the subgrade (mm) and Ep is the effective pavement modulus, computed using the equation in figure 12.

    d subscript zero equals 1.5 times p times a times open bracket the sum of 1 divided by M subscript r times the square root of 1 plus open parenthesis D divided by a multiplied by the cube root of E subscript p divided by M subscript r closed parenthesis squared end cube root plus 1 minus open parenthesis 1 plus open parenthesis D divided by a closed parenthesis squared closed parenthesis raised to the power of negative 
one-half divided by the quantity E subscript p closed bracket
    Figure 12. Equation. Calculation of d0.

    Where d0 is deflection at the center of the load plate (mm), P is load plate pressure (MPa), a is load plate radius (mm), D is pavement layers thickness above subgrade (mm), and Mr is the resilient modulus, given by the following expression:

    M subscript r equals the quantity 2.4 times P divided by the quantity d subscript r times r.
    Figure 13. Equation. Calculation of Mr.

    Where Mr is resilient modulus (MPa), P is applied load (kN), dr is deflection at a distance r from the center of the load (mm). r is chosen as the distance to the seventh sensor

  10. Deterministic-empirical back-calculation model (closed form solution) for effective subgrade modulus (Hogg model).(4)

    M subscript r equals the quantity 2.4 times P divided by the quantity d subscript r times r.E subscript zero equals I times open parenthesis 1 plus mu subscript zero closed parenthesis times open parenthesis 3 minus 4 times mu subscript zero closed parenthesis divided by 2 times open parenthesis 1 minus mu subscript zero closed parenthesis multiplied by the quantity open parenthesis S subscript zero divided by S closed parenthesis times the quantity open parenthesis p divided by delta subscript zero times l closed parenthesis.
    Figure 14. Equation. Calculation of E0.

    Where E0 is subgrade modulus (effective) (MPa), μ0 is Poisson's ratio for subgrade, S0 is the theoretical point load stiffness (MPa), S is the pavement stiffness (MPa), P is applied load (kPa), Δ0 is the deflection at center of load plate (mm), L is the characteristic length (mm), and I is the influence factor. (4)

  11. Radius of curvature, shown in figure 1 (page 14) for completeness. (14)
  12. Elmod, nonlinear subgrade parameters. (22)

    Calculation of Esg. E subscript sg equals C times open parenthesis sigma divided by sigma prime closed parenthesis raised to the power of n.
    Figure 15. Equation. Calculation of Esg.

    Figure 16. Equation. Calculation of n. n equals log open parenthesis E subscript zero times open parenthesis r times 1 closed parenthesis divided by E subscript zero open parenthesis r times 2 closed parenthesis closed parenthesis all divided by 2 times log open parenthesis r times 2 divided by r times 1 closed parenthesis
    Figure 16. Equation. Calculation of n.

    Figure 17. Equation. Calculation of C. C equals E subscript zero time open parenthesis r times 1 closed parenthesis minus E subscript zero times open parenthesis r times 2 closed parenthesis all divided by open parenthesis sigma subscript open parenthesis r times 1 closed parenthesis divided by sigma prime closed parenthesis raised to the power of n minus the quantity open parenthesis sigma subscript open parenthesis r times 2 closed parenthesis divided by sigma prime closed parenthesis raised to the power of n
    Figure 17. Equation. Calculation of C.

    Figure 18. Equation. Calculation of E0(r). E subscript zero open parenthesis r closed parenthesis equals open parenthesis1 minus u squared closed parenthesis times P divided by pi times r times open parenthesis d subscript r closed parenthesis.
    Figure 18. Equation. Calculation of E0(r).

    Figure 19. Equation. Calculation of  . Sigma subscript open parenthesis r closed parenthesis equals 3 times P divided by the quantity 2 times pi times R squared all times the quantity cosine cubed times theta.
    Figure 19. Equation. Calculation of σ(r)


Esg = Subgrade modulus (kPa).
C = A layer constant, n is a layer constant representing the nonlinearity of the subgrade.
σ = Principle stress (MPa).
σ' = Reference stress (14.5 psi (0.1 MPa)).
E0(r) = Surface modulus at distance r from load center (MPa).
r = Horizontal distance from load center (mm).
z = Vertical depth with respect to the pavement surface (mm).
σ(r) = Principle stress at depth z (assuming z = r).
μ = Poisson's Ratio, d(r) is deflection at distance r from load center (mm).
P = Applied load on pavement surface (MPa).
R = Distance to evaluation point (R2 = r2 + z2).
θ = Angle with respect to vertical axis through load center.

In addition to the parameters mentioned, the load transfer efficiency (LTE) value was calculated for rigid pavements. There are two ways of calculating LTE - in one method, the FWD test is performed at the slab before the joint (joint approach), and in the second method, the FWD test is performed at the slab after the joint (joint leave). An analysis of both was conducted, and the values were close to each other. Therefore, for simplification, only one LTE value was chosen. The option was for the first method with LTE at the joint approach because it does not require any modification on the configuration of the FWD. The LTE at joint approach is referred to as "LTEA" in this report and was calculated as the ratio of the deflection at the third sensor (12 inches (304.8 mm) from the center of the load) and the deflection at the center of the load.


Several successful techniques for use in network-level PMS applications were identified through the literature search. A few highway agencies have been using deflections as part of their network condition assessment. Among those, Texas, Virginia, and South African approaches were selected for further investigation in succeeding tasks with little or no modification. In addition, there were several techniques that could be utilized in the present study even though these techniques were not used in a network-level PMS. Combining all sources available, a list of potential applicable techniques that are relevant to the scope of this project was created as a result of the literature review and is shown in table 1. These deflection techniques formed the basis for the analyses carried out in this project.