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Section 4: FPS21 Modulus Inputs and Backcalculation Methodology

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4.1 Overview of Modulus Inputs

Each material layer used in the structure will have a modulus input that shall characterize the average seasonal stiffness of that material over the course of the year. The construction process, inherent material variability (initially and over time), and effects of environment (moisture and temperature) and traffic loading will typically introduce considerable variance about the average value. Modulus inputs for HMA are based on a temperature of 77°F.

Overestimating this material property can result in a structure with poor permanent deformation performance and may subject the surface to early fatigue, while underestimating can result in an uneconomical pavement.

Additionally, materials that have an average in situ modulus in one circumstance may have a different average modulus if placed in another environment. This is particularly true of unbound base material; the modulus can be significantly influenced by the confinement provided by the layers above or below, absence of paved shoulders, or by the amount of moisture infiltrating the structure if the materials are moisture susceptible.

In evaluating a design that consists of layers that were pre-existing (including the subgrade), the falling weight deflectometer (FWD) is indispensable in determining what stiffnesses (through backcalculation) these layers can contribute to the new structure. Proposed virgin and reclaimed material moduli will require knowledge by the designer (preferably through past use and subsequent evaluation), tempered by the specifics of the current project.

Studies conducted on perpetual pavements indicate that stone-on-stone designed Superpave hot-mixes and thick composite HMA structures, using any type of HMA, have much stiffer in-place moduli values than conventional thinner surfaced HMA structures. Laboratory and field testing continues on these mixes to establish stiffness-temperature curves and better define “design” stiffness values by type, if necessary.

All backcalculated material modulus values are manually entered into their respective fields (values are not read from the MODULUS backcalculation summary file).

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4.2 Virgin and Modified-in-Place Materials

Below is a partial listing of typical design moduli by material type for virgin or modified-in-place materials to be used in FPS 21. For materials not listed, contact CST-M&P for recommendations.

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Material Type

2014 Specifications

Design Modulus

Poisson’s Ratio


Seal Coat

Item 316

200 - 250 ksi


Considered in the structural design only when placed on the surface. Not considered when used as an underseal.

Limestone Rock Asphalt Pavement

Item 330

200 - 350 ksi


Material typically placed as asphalt stabilized base or surface for low volume roads.

Hot-Mix Cold-Laid ACP

Item 334

300 - 400 ksi



Dense-Graded Hot-Mix Asphalt

Item 340, 341

Combined HMA thickness:

≤ 4 in. use 500 ksi

> 4.0 in. use 650 ksi



Permeable Friction Course

Item 342

300 ksi


Thinness of the lift and high air voids do not allow significant contribution to the overall structural capacity.

Superpave Mixtures

Item 344

Combined HMA thickness:

≤ 4.0 in. use 650 ksi

4 in. < T ≤ 6 in. use 750 ksi

> 6.0 in. use 850 ksi



Stone-Matrix Asphalt

Item 346

Same as Item 344



Asphalt Treatment (base)

Item 292

250 - 400 ksi


Use Tex-126-E, “Molding, Testing, and Evaluating Bituminous Black Base Materials,” asphalt content.

Emulsified Asphalt Treatment (Base)

Item 314, various OTU special specs

50 - 250 ksi


Contact CST-M&P for assistance in establishing optimum emulsion concentration and recommendations for adding cement or other filler material.

Flexible Base

Item 247

If historic data not available, modulus shall be no greater than 3-4 times the subgrade modulus or use FPS default, whichever is lower. Typical range 40-70 ksi.


In general, a finer graded base will have lower moduli than one that is a coarser gradation. As angularity and soundness of particles decrease, modulus will decrease to the lower end of the scale. Limiting the minus 200 clay fraction will improve resistance to moisture damage.

Lime Treated Base

Item 260, 263

60 - 75 ksi

0.30 - 0.35

Use Tex-121-E, “Soil-Lime Testing,” to establish optimum lime content. Long-term stiffness improvement will depend on concentration used and affinity of base material to undergo permanent chemical bonding.

Cement Treated Base

Item 275, 276

80 - 150 ksi

0.25 - 0.30

Use Tex-120-E, “Soil-Cement Testing,” to establish optimum cement content. For Item 276, a minimum 7-day unconfined compressive strength of 300 psi is established for Class L stabilized base. TTI research indicates that higher strengths can lead to detrimental shrinkage cracking. Micro cracking is encouraged for higher strengths. Also, very stiff, stabilized bases are not modeled effectively in FPS 21. Higher design moduli shall not be used.

Fly Ash or Lime-Fly Ash Treated Base

Item 265

60 - 75 ksi


Use Tex-127-E, “Lime Fly-Ash Compressive Strength Test Methods,” to establish optimum fly ash or lime fly ash content.

Lime or Cement Treated Subgrade

Item 260, 275

30 - 45 ksi


Use Tex-121-E or Tex-120-E, Parts 1, to establish optimum lime or cement content. Long-term stiffness improvement will depend on concentration used and affinity of subgrade material to undergo permanent chemical bonding. For cases when a subgrade will be treated (2-3% lime) to provide a working platform for construction equipment and a platform to improve compactive effort of the overlying layers, this layer shall not be accounted for in the structural design.

Emulsified Asphalt Treatment (Subgrade)

Item 314, various special specs

15 - 25 ksi


Contact CST-M&P for assistance in establishing optimum emulsion concentration.



Priority should be to use the project-specific backcalculated subgrade modulus. Defaults by county are available in the FPS design program. Typical range is 8-20 ksi.

0.35 - 0.45

Use of a backcalculated modulus is preferred. FPS 21 defaults to the average county subgrade modulus taken from a limited number of tests. For new highway construction on a new right-of-way, deflection testing on an adjacent highway, or intersecting highways can provide data for backcalculation. Alternatively, elastic modulus correlations to field or laboratory derived CBR or the program default may be used. Wetter or more highly plastic materials warrant higher Poisson ratios.

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4.3 Backcalculation Methodology

This procedure is used to determine modulus values for in situ pavement materials when these materials are used as is (unmodified) in FPS design. TxDOT currently uses version 6.1 of the MODULUS software for backcalculation of deflection data collected by the FWD. Version 6.1 is comparable to version 6.0; the main difference is the ability to read current Dynatest R80 formatted data files that have GPS locations embedded. The software (v 6.1) and user’s manual (v 6.0) in PDF document format are available through the CST Engineering applications link to the TTI on-line pavement design training site. Also, basic operation and discussion of inputs, cautions, and example problems is presented in the Flexible Pavement Rehabilitation Strategies training course and Flexible Pavement Design workshop.

The raw deflection file, pavement layer thicknesses, layer Poisson ratios, probable layer moduli ranges, and asphalt temperatures at the time of testing are all required inputs to perform backcalculation. The backcalculation process works on the assumption that the pavement structure can be modeled as a linear-elastic layered system. If the parameters of layer thickness, deflection, and Poisson ratio are known, the modulus can be approximated. A likely range of “probable” layer moduli provided by the program user facilitates the process by forming the basis of a small internal database against which mathematically generated deflection bowls are compared to the actual measured deflection bowl by the software. Once a reasonable match is made, the moduli that allow this match are reported as the individual layer moduli. In addition, the program reports a depth to stiff layer or bedrock.

4.3.1. Backcalculation Limitations and Adjustments

There are precautions and limitations to the backcalculation procedure that the user must consider. In the end, engineering judgment will be needed to decide on the veracity of solutions generated. The following are some pointers when using MODULUS 6.1:

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  • The modulus for layers thinner than 3.0 in. cannot be backcalculated. This situation arises most often for thin-surfaced flexible pavements. The user must assign a reasonable modulus to this layer (minimum and maximum are input as the same value in the program) based on thickness, level of distress, temperature, etc.
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  • The surface layer is always the layer that the load plate is in contact with, so a thickness must be entered. Where the surface is a bituminous surface treatment, it is allowable to use a nominal thickness, such as 0.5 in., and assign a nominal modulus, such as 200 ksi. Alternatively, the surface treatment can be combined with the underlying layer as the “surface,” reducing the total number of layers by one. In determining the seed moduli range for the surface, MODULUS assumes the layer is HMA and automatically fills the min/max seed values in accordance with the temperature posted in the Asphalt Temp cell. Where non-bituminous materials are the surface during testing, the user must insert seed values commensurate with the type of material tested.
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  • The maximum number of layers for which the modulus can be backcalculated is four (one of which is always the natural subgrade) in MODULUS 6.1. For circumstances where more layers are known to exist, the user must either consolidate or ignore layers. Consolidation is recommended for materials that are more likely to have a similar modulus and shear strength properties (i.e., different types of HMA, or flex base over reclaimed base). Ignoring layers may be reasonable in certain cases where the material’s contribution to the overall stiffness of the structure is minimal (i.e., “foundation course,” or lime treated subgrade – constructed as a working platform).
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  • There are times when a more reasonable solution is obtained modeling your pavement structure as a 3-layer system, even if you know there are four layers present. This situation may develop for a number of reasons, such as variable stabilization (leaching), variable depth to bedrock, etc.
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  • A check of reasonableness in the solutions generated shall be made. Reasonableness is more related to the in-place stiffness characteristics of the layers being modeled and not necessarily to the size of the average errors reported by the software in comparing the mathematically generated bowls to the measured bowls. While the 4-layer solution will generally give lower overall errors, the backcalculated material moduli may be unrealistic with respect to the in-place material, and the variability of reported moduli may be excessive (coefficient of variation 100% or greater). When there is doubt of reasonableness, the user should perform backcalculation runs using both 3- and 4-layer solutions (employing guidelines given in the third bullet). Additional field testing, such as with the dynamic cone penetrometer (DCP) along with engineering judgment, is necessary to ensure a valid, reliable solution.
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  • A check of the MODULUS summary table shall be made to detect outliers that skew the average value reported. Outliers may be the result of full-depth patches (different pavement structure) or very weak areas.
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  • For the purpose of using MODULUS-reported values as input to FPS 21, adjustment of the average modulus shall be considered; otherwise the performance of any pavement design solution based on these inputs could be jeopardized. As a rule-of-thumb, consider removing values that exceed one standard deviation from the unadjusted average, and then re-average. This should always be done for modulus values that are much higher than values that are more typical for the section. Consideration can be given to eliminating very low values only if the intention is to include a bid item for repair of weak areas (i.e., Item 351, “Flexible Pavement Structure Repair,” or Item 354, “Planing and Texturing Pavement”) as part of the job.
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  • Shallow bedrock (typically less than 60 in. deep) will almost always result in underestimation of the subgrade modulus and overestimation of the flexible base modulus and produce very high average error (> 20%). The recommended workaround is to fix the depth to bedrock (DTB) at 120 in. or, alternatively, 240 in. if the solution using the program-generated DTB produces suspect subgrade/base moduli. Another clue that the default solution is suspect would be if the ratio of the flexible base modulus (unstabilized layers only) to the subgrade modulus is very high (> 5). If the user opts to fix the calculated DTB to a value in the 120- to 240-in. range, then this user-selected value must also be used in FPS 21 design.
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  • MODULUS can perceive a shallow DTB in high water table situations (water is incompressible) as can be the case in east Texas. It may be beneficial to override the program-generated DTB value by using a fixed value of 120 in. Again, check the generated subgrade/base moduli values for reasonableness.
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  • Soft upper subgrade can also lead to high errors in the backcalculation process. In these cases, use a 4-layer solution where the soft portion of the subgrade is modeled as the subbase layer (fix depth at 12 in.) to provide better fit and more realistic backcalculated values for the base and deep subgrade. A check can be made in MODULUS using the Boussinesq procedure to evaluate how the subgrade modulus varies with depth. Verification with a dynamic cone penetrometer (DCP) may be warranted.

4.3.2 Modulus Correction Factors

In addition to adjustments made to backcalculated average modulus values for outliers in the deflection data set, correction factors must be applied to backcalculated: HMA values

FPS 21 considers the modulus of bituminous materials only at the reference temperature of 77˚F. Since FWD data are rarely collected at the reference temperature, corrections must be made for FPS input. Two methods are suggested:

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  1. Use the formula CF = T2.81/200,000, where CF is the correction factor to be multiplied by the backcalculated HMA modulus (adjusted for outliers), and T is the average temperature over the time the FWD survey was made, or
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  3. Use the Modulus Temperature Correction Program (MTCP). MTCP can use the surface temperatures measured at each deflection location and, together with the previous day’s average temperature (available at weather underground, predict the in-pavement temperature and compute the temperature adjusted modulus. Again, outliers must be removed from the calculated average. Flexible Base values

Performance models in FPS 21 expect a 10.0-in. thick flexible base. For backcalculated moduli of base layers that have a different thickness, multiplication correction factors in the following table should be used:

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Corr. Factor










Similarly, if virgin base materials are to be used, consider applying the above correction factors to values suggested in Table 5-6 in establishing the FPS 21 modulus input.

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