Structural design of highway or airfield pavements or railroads involves assumption of key mechanistic parameter values such as resilient modulus, modulus of subgrade reaction, dynamic modulus, and track modulus. There is growing interest in mechanistic-based construction testing methods to field verify design-modulus assumptions. Here, Pavana Vennapusa, Ph.D., P.E. and David J. White, Ph.D., P.E. describe how Automated Plate Load Testing (APLT) overcomes common testing challenges to provide direct measure of the design-modulus values used in the design of highways, airfields, and railroads. The work comes from the GAP 2019 transportation engineering conference proceedings, published by Geosynthetica.


One of the key input parameters in designing highway or airfield pavements and railroads is the design modulus value. Because geo-materials exhibit non-linear behavior, there are many definitions for moduli values – elastic modulus, reload modulus, resilient modulus, secant modulus, modulus of subgrade reaction, etc. – and there are many factors that influence the moduli values (see Briaud 2001). Design equations, particularly for pavement thickness design, are typically calibrated for moduli values measured using a certain test and interpretation procedure. Depending on the design procedure chosen, it is important for designers to understand these factors to select the appropriate testing procedure for field verification of the design modulus value.

Plate load testing (PLT) is considered the long-standing “gold standard” test measurement for assessing in situ pavement foundation support conditions and railway subgrades. From the 1930s to the 1980s, the Bureau of Public Roads, U.S. Corps of Engineers, AASHTO, and several state agencies used PLT to determine the modulus of subgrade reaction k-value for airfield and highway applications, investigate concrete pavement behavior, and verify/calibrate design equations (see Teller and Sutherland 1943, U.S. Corps of Engineers 1943, AASHTO 1962). In the 1940s Bureau of Public Roads reported extensive field testing for the Arlington Experiment Farm in Virginia, which involved repeated load-unload plate load tests (Teller and Sutherland 1943). Railway subgrade support is also characterized using the k-value (see Selig and Lutenegger, 1991) and plays an important role in trackbed design and analysis for railways (McHenry and Rose 2012).

The pioneering efforts from the 1930s to the 1980s established PLT to determine the load-displacement relationship of foundation layers and a significant role in calibrating the pavement thickness design equations developed by the AASHTO, PCA, and Corps of Engineers. However, the manual PLT methods were time consuming because of significant setup times with heavy reaction loads often creating unsafe conditions. Also, without automation, producing reproducible results from manual plate load testing can be difficult because of operator bias, lack of control with maintaining and applying loads, etc., even for a static test. It is almost impractical to apply repeated loads at a controlled load pulse using manual methods.

Because of those limitations, the frequency at which these tests were conducted has diminished substantially. As a simplification, several agencies attempted to develop local empirical relationships between plate load test measurements from California bearing ratio, R-value, falling weight deflectometer (FWD) testing, and others. These empirical relationships, however, present significant uncertainties and poorly match the field conditions.

Realizing the very important role plate load testing plays in determining the design-moduli values and the limitations involved with the manual setups and the uncertainties associated with using empirical relationships, the modern automated plate load testing (APLT) system was developed. APLT is a state-of-the-art test device used to characterize a variety of in situ mechanistic performance parameter values for pavement and pavement foundation layers (White and Vennapusa 2017, White et al. 2019). APLT has been used successfully on over 80 projects across the United States, Canada, and Latin America on research and implementation projects.

MORE FROM GAP 2019: Development of a 3/4-Inch Minus Crushed Base Course Specification

In this paper, a summary of the various design modulus input parameters used in pavement and railway design are summarized along with the current state-of-the-practice testing methods and their limitations. Then, the APLT procedures to determine the different design moduli values are presented along with example results from field projects.


In this section, the key input parameters used in highway, airfield, and railroad design are described as background information along with the current state-of-the practice for measuring these properties.

2.1 Foundation Layer Resilient Modulus, Mr

For flexible pavement design, the main pavement foundation layer input parameters in the AASHTO (1972, 1986, and 1993) design guides for flexible pavement design are resilient modulus (Mr) of subgrade, structural layer coefficients (ai) for all layers above the subgrade including the base, subbase, and surface layers, and drainage coefficient (mi) for the base and subbase layers. Empirical relationships are presented therein for ai and moduli values for base and subbase layers, in addition to other properties such as California bearing ratio (CBR) and R-value.

In the mechanistic-empirical (ME) pavement design procedure (AASHTO 2015), the main pavement foundation layer input parameter for flexible pavement design is Mr. There are three design levels in AASHTO (2015). Level 1 includes selection of stress-dependent constitutive model parameters (k1, k2, and k3) or determining Mr at the anticipated field stresses, and the model parameters are typically determined from laboratory Mr testing (i.e., AASHTO T307). Level 2 includes empirical correlations to estimate Mr from surrogate measurements such as CBR, dynamic cone penetrometer (DCP) measurements, and R-value measurements. Level 3 includes using default or recommended Mr values based on the soil AASHTO classification.

For rigid pavement design, the key design input parameter for foundation layers in many of the rigid pavement design procedures (AASHTO 1972, 1986, 1993, 2008; PCA, 1984; FAA 2016) is the modulus of subgrade reaction (k-value), which is discussed in the following sub-section of this paper. One exception is the Level 1 design in the ME design procedure (AASHTO 2015), where Mr constitutive model parameters are needed. For Levels 2 and 3 ME design, the selected Mr values are converted to a k-value in the design software (AASHTO 2015).

The Mr parameter is a highly stress-dependent parameter, and most soils exhibit the effects of increasing stiffness with increasing bulk stress and decreasing stiffness with increasing shear stress. The results from a test that involves applying a series of cyclic deviator and confining stresses can be used to model the behavior using the “universal” model (AASHTO 2015) shown in Eq. (1):

where, Mr = resilient modulus (psi); Pa = atmospheric pressure (psi); θ = bulk stress (psi); τoct = octahedral shear stress (psi); and k1, k2, and k3= regression coefficients.

In ME design guide (AASHTO 2015), it is recommended that the Mr properties be determined using laboratory testing (AASHTO T-307) for new projects and using falling weight deflectometer (FWD) on rehabilitation projects. Laboratory testing provides a controlled set of measurements at different stress combinations to develop regression parameters used in the “universal” model (Eq. 1). However, due to the complexity of the laboratory triaxial test and often non-representative boundary conditions, Mr of pavement foundation materials is often obtained from empirical correlations between Mr and other properties such as soil classification, California Bearing Ratio (CBR) or Hveem R-value (i.e., Levels 2 and 3 in ME Design). As an example, the different empirical relationships available in the literature between CBR (determined from different test procedures including the dynamic cone penetrometer (DCP) penetration resistance (PR) values) and elastic modulus values are shown in Figure 1, which highlights the significant uncertainties associated with the estimated moduli values.

In situ Mr is also often estimated from non-destructive surrogate tests including the FWD or light weight deflectometer (LWD). In practice, the elastic moduli values calculated from these test devices based on peak deformations are often confused with Mr values which are based on resilient (i.e., recoverable) deformations. Limitations of these non-destructive surrogate tests is the lack of a conditioning stage prior to testing and limited ability to maintain a defined contact stress during unloading. During pavement construction, pavement foundation materials are subjected to relatively high loads from construction traffic and compaction equipment. In response to these loads, aggregate particles rearrange themselves resulting in higher density and stiffness. For this reason, it is important to apply conditioning load cycles prior to testing to determine in situ Mr, which is not possible with FWD testing. Once surface paving is complete, the pavement foundation below is confined by the overlying pavement layers. The response of a pavement foundation to subsequent repeated traffic loading is both nonlinear and stress-dependent and therefore the effect of confinement is an important condition to consider in a field based Mr test.

Figure 1 shows compares results from the literature on relationships between CBR and elastic modulus
Figure 1. Empirical relationships published in the literature between CBR and elastic or resilient modulus.

2.2 Foundation Layer Modulus of Subgrade Reaction, k-value

The subgrade k-value and the composite k-value which accounts for inclusion of base layer placed over the subgrade, are the key foundation layer input parameters in most of the rigid pavement design procedures and railway subgrades (AASHTO 1972, 1986, 1993, 2008; PCA 1984; FAA 2016; Selig and Lutenegger 1991; McHenry and Rose 2012). Selection of the k-values have significant implications on design, cost and future performance of the pavement section. Depending on the design method chosen, it is important to understand the corresponding k-values for which the design equations were originally calibrated. Darter et al. (1995) explained this history in detail. In brief, the Corps of Engineers defined k-values as the ratio of applied load corresponding to 0.05 in. of plate deformation, wherein the loads are applied incrementally like the procedure described in ASTM D1196 or AASHTO T-222 using a 30-in. diameter loading plate (Middlebrooks and Bertram 1942). This formed the basis of the PCA (1984) and the Corps of Engineers rigid pavement design procedures (U.S. Corps of Engineers, 2001).

On the other hand, the AASHTO road tests (Highway Research Board 1962) conducted in the late 1950s followed a test procedure that involved performing three loading/unloading cycles each at three stress levels (5, 10, and 15 psi) using a 30-in. diameter loading plate (9 loading cycles total). The k-values were then determined using two procedures. The first procedure involved determining the elastic k-value (kE) based on the rebound deformations for each loading cycle (excluding the permanent deformation) and then averaging the data for the nine cycles. The second procedure involved determining the gross k-value (kG) based on the total deformation produced for each load level (at the end of the three loading cycles), and then averaging the data for the three load levels. The AASHTO (1972) design guide states that only one value was used to represent AASHTO Road Test sections in developing the rigid pavement design equation and is based on the kG value. The later versions of the AASHTO design guide (AASHTO 1986, 1993) does not indicate whether to use kE or kG.

From the different procedures described above, the kE value results in a higher value compared to both the kG value and the k-value determined using the 0.05 in. deflection criteria per Corps of Engineers. The magnitude of difference between these, however, will depend on the stiffness of the material, degree of saturation, level of compaction, and stresses applied.

The k-value is typically determined using AASHTO T-222 or ASTM D1196 non-repetitive static PLT or AASHTO T-221 or ASTM D115 repetitive static PLT. As stated earlier, traditional manual methods of conducting PLT is time-consuming. Therefore, as a simplification, several agencies attempted to develop local empirical relationships between plate load test measurements from CBR, R-value, FWD testing, and others. These relationships also show significant variability depending on the relationship chosen (see Zhang et al. 2019).

2.3 Strain Modulus, Ev

Strain modulus (or also referred to as the deformation modulus) is a quality assurance parameter used in Europe to field evaluate the pavement foundation layers (ISSMGE 2005, ATB Vag 2005). The DIN 18134 (2001) standard for plate load test describes the procedure to calculate strain moduli (Ev) using different plate sizes ranging from 12 to 30 in. diameter. The test involves applying two loading cycles, where the load is applied in equal increments until either a target deformation criterion (0.20 in.) or a maximum stress of 72.5 psi, whichever occurs first, is achieved. The strain modulus (Ev) is calculated for the two loading cycles (referred to as Ev1 and Ev2), using the load-deformation curve and assuming a Poisson’s ratio and shape factor for the anticipated stress distribution beneath the plate. High-speed rail design and field quality assurance specifications also use the Ev value (see Zicha 1989; Rulens et al. 2009).

The manual setup for this test suffers the same limitations as the traditional static PLT methods described above for k-value tests, with time-consuming setup and need for heavy reaction loads creating unsafe working conditions.

2.4 Asphalt Concrete Layer Dynamic Modulus

Dynamic modulus of the AC layer is one of the key asphalt layer property that has a substantial impact on the designed pavement layer thickness using regression based methods such as AASHTO (1972, 1986, and 1993) or the ME based method (AASHTO 2008). For linear visco-elastic materials such as hot mix asphalt (HMA) mixtures, the stress-strain relationship under a continuous sinusoidal loading in the frequency domain is defined by its complex dynamic modulus (E*) (Dougan et al. 2003). In laboratory testing, the dynamic modulus is defined as the ratio of the amplitude of the sinusoidal stress at a given time (t) and the amplitude of the sinusoidal strain at the same time and frequency that results in a steady state response. Laboratory testing to determine dynamic modulus (AASHTO TP62) is repeated at different temperatures and frequencies, and the results are then used to develop a complex modulus master curve, which is one of the design inputs in the ME Design (AASHTO 2008). Master curves are constructed using the principle of time-temperature superposition, where data at various temperatures are shifted with respect to log of time until the curves merge into a single smooth function. The amount of shift required at each temperature required to form the master curve describes the temperature dependency of the material (Dougan et al. 2003).

In AASHTO (1972, 1986, and 1993) design procedures, the design expression for flexible pavement design to calculate the design equivalent single axle loads (ESAL) is developed based on a tire inflation pressure of 70 psi and a travel speed of 55 mph with a bias-ply design (AASHTO 1962). It must be noted that the tire pressures today are much higher than this (> 100 psi) and is not accounted for in that ESAL calculations (Timm et al. 2014). The asphalt layer property is considered using a structural layer coefficient (a1) to represent the relative contribution of each pavement layer in the design. The following empirical expression is used to estimate a1 using the asphalt layer modulus (EAC) in units of psi:

In the AASHTO (1993) design guide, Eq. 2 is intended to use for use with a maximum EAC of 450ksi, which corresponds to a1 = 0.44. According to Timm et al. (2014), 45% of the states in the U.S. use 0.44 for at least one paving layer, 28% of the states use less than 0.44, two states (Alabama and Washington) recently revised the coefficients to 0.54 and 0.50. The higher coefficients used by Alabama and Washington reflect modern advances in the materials and the construction procedures (Timm et al. 2014).

In the ME design guide (AASHTO 2008), it is recommended that the dynamic modulus is determined using laboratory testing for new projects and using falling weight deflectometer (FWD) on rehabilitation projects. Laboratory testing provides a controlled set of data at different frequencies and temperatures to develop the master curves required in design. The FWD field testing is a convenient and rapid test which involves dropping a series of dynamic loads (typically 3 to 4), obtaining a deflection basin, and back calculating the individual layer properties. However, it only provides a single value and is typically obtained at one stress, and the loading applied is not sinusoidal as performed in the laboratory. Further, FWD testing is only performed using a few loading cycles which is not the same as the laboratory testing where the sample is conditioned prior to testing using hundreds of loading cycles. Because the loading is not sinusoidal, a frequency-dependent dynamic modulus cannot be estimated and directly used in the ME design. For these reasons, FWD testing results present limitations when using the data as part of the design process.


The APLT technology uses modern control and data collection systems combined with advanced stress control capability to simultaneously measure stress-dependent elastic and permanent deformation, stress-dependent elastic and resilient modulus, and load-pulse and frequency-dependent responses. The APLT is used to perform static PLTs (e.g., AASHTO T222) which takes about 30 minutes to 4 hours depending on subgrade stiffness and cyclic/repetitive plate load tests (e.g. ASTM 1195) with up to 100 cycles (5 minutes), 1000 cycles (20 minutes), and 10,000+ cycles test (2+ hours) per test location. The cyclic test process uses a controlled load pulse duration and dwell time (e.g., as required in the laboratory AASHTO T307 Mr test methods) for selected cycle times depending on the field conditions and measurement requirements. The advantage of cyclic tests is that the modulus measurements better represent the true field modulus value. This finding is well documented in the literature and is considered a major short-coming of other testing methods that only apply a few cycles/dynamic load pulses on the foundation materials.

The APLT system has the capability to measure inputs to develop in-situ confining and deviator stress-dependent constitutive models used in the AASHTOWare® Pavement ME Design (AASHTO 2015). The result of this test is a direct field measure of the mechanistic response of the pavement foundation. This is the only such in-situ test to directly measure the stress-deflection response with confinement control. Confinement control can be applied to precisely duplicate the pavement-induced stress conditions. Because the APLT test system is automated, the test methods are highly repeatable and reproducible (i.e., no operator bias). Operators only need to input the desired loading conditions (cyclic stress levels, load pulse duration and dwell time, and number of cycles) which are then tightly controlled by the machine. An advanced fluid-power control system was designed to perform the test operations and meets or exceeds the applicable testing standards.

Figure 2 shows the operator station, controls, monitor, and plate load test setup with sensors and reference beam for down core hole and on surface (foundation layer) measurements with different plate size configurations. The results of cyclic deformation, permanent deformation, elastic modulus, stiffness, resilient modulus, cyclic stresses, and number of cycles are calculated in real-time and are available for reporting immediately.

Figure 2 shows four images that details the full APLT set up and key pieces of the equipment
Figure 2. (a) APLT equipment setup for testing over a core hole location on pavement, (b) downhole plate and reference beam setup, (c) plate setup with deformation measurements of plate and at 2r, 3r, and 4r from plate center axis, and (d) 30 in. diameter plate load test setup.

3.1 Modulus of Subgrade Reaction (k-value)

APLT can be used to perform automated static PLTs in accordance with the applicable AASTHO, ASTM, Army Corps of Engineers, and European test standards. APLT is configured with 6 in., 12 in., 18 in., 24 in., and 30 in. diameter loading plates. A 30-in. diameter plate setup is shown in Figure 1d. The test is automated to meet the applicable test methods and therefore can produce highly repeatable and reproducible test results with no operator bias in testing or interpretation of results.

An example of test results with a 30-in. diameter loading plate with two loading cycles is shown in Figure 3, with calculations shown to calculate k values (uncorrected and corrected for plate bending), per AASHTO T222. The graph shows stress versus deformation values for the two loading cycles along with plate rotation measurements. The stress versus deformation readings from each loading cycle are fit with a second order polynomial relationship, which shows a coefficient of determination (R2) of close to 1, demonstrating the quality of the data produced from the automated static PLT.

Figure 3 shows 30 in. diameter static plate load test results with a graph and numbers chart
Figure 3. Example results of 30 in. diameter static plate load test with two loading cycles, per AASHTO T222.

3.2 Composite Resilient Modulus (Mr -Comp)

Composite uncorrected resilient moduli values from APLT can be calculated using the modified Boussinesq’s elastic half space solution equation shown in Eq. (3):

where, Mr -comp is in situ composite resilient modulus, δ is the resilient deflection of plate during the unloading portion of the cycle (determined as the average of three measurements along the plate edge, i.e., at a radial distance r’ = r), v is the Poisson ratio (often assumed as 0.40), 𝜎0 is the cyclic stress, r is the radius of the plate, f is the shape factor selected based on the anticipated stress distribution beneath the plate (π/2 to 8/3).

3.3 Layered Analysis for Individual Layer Resilient Modulus

A layered analysis sensor kit (Figure 1c) setup with APLT measures the resilient deflections at radii of 12 in. (2r), 18 in. (3r), and 24 in. (4r) away from the plate center. The layered analysis measurement sensor kit provides average resilient deflections measured over one-third of the circumference of a circle at the selected radii. This method was designed to improve upon practices that use point measurements, which are often variable from point-to-point for unbound aggregate materials. Like the loading plate representing an integrated response of the material under the plate, the deflection basin circumference bars were designed to represent an integrated deflection basis response over a length of one-third the circumference.

MORE FROM GAP 2019: Permanent and Resilient Deformation Behavior of Geogrid-Stabilized and Unstabilized Pavement Bases

Using the deflection basin measurements, two and three-layered analysis can be performed to develop stress-dependent Mr values. The two-layered analysis is performed using the Odemark method of equivalent layer thickness approach (AASHTO 1993), while the three-layered analysis is performed using a proprietary back calculation analysis recently developed by Ingios (APLT-BACK). The program was developed through a numerical algorithm to solve an extended formulation of the linear-elastic analysis theory and details are provided in White et al. (2019b). The most significant advantage of the APLT-BACK program over the many back calculation programs that are currently available is that the program allows modeling the analysis for different stress distributions beneath the loading plate (i.e., uniform, parabolic, and inverse parabolic). The different stress distributions can be easily accounted for in the Mr-Comp calculations using the appropriate stress distribution factor (f) in Eq. 3, but most of the current backcalculation programs typically are only designed to solve a uniform stress distribution problem. The uniform stress distribution is true only for a flexible plate on cohesionless soil, but the assumption is not accurate because of the rigidity of the plate and the soil type can be either cohesive or cohesionless.

3.4 Determination of “Universal” Model Regression Parameters

The “universal” model regression parameters required for the ME design can be obtained in situ using APLT at different cyclic stresses like the AASHTO T-307 lab testing. The applied cyclic and contact stresses and the number of loading cycles are customized per project needs. Cyclic stresses can be varied between 2 psi and 150 psi using a 12-in. diameter loading plate. The data can then be analyzed to fit the model shown in Eq. (4), which is like the laboratory test based model shown in Eq. (1), except that the regression parameters are identified with an asterisk (*) to differentiate with the regression parameters obtained from laboratory testing:

where, In-situ Mr = resilient modulus determined in-situ (psi); Pa = atmospheric pressure (psi); θ = bulk stress (psi) = σ1 + σ2 + σ3 = applied cyclic stress (σcyclic) plus confining stress due to pavement layer based on the thickness of the pavement above the unbound foundation layer (confining stress = 1 to 2 psi if performed down in a core hole and 0 if performed at the surface with no pavement confinement); σ2 = Ko σ1; σ3 = σ2; Ko = coefficient of lateral earth pressure at rest = v/(1-v); v = Poisson’s ratio; τoct = octahedral shear stress (psi) = ; and and k1*, k2*, and k3*= regression coefficients.

An example of the universal model fit curves obtained from the IL Tri State Tollway project near O’Hare airport are shown in Figure 4 and the model parameters are summarized in Table 1. Results showed that the in situ Mr-comp values are sensitive to the applied cyclic stress and showed a “break-point stress (𝜎cyclic-BP)” at which point further increase in stress showed a decrease in Mr-comp values. Identification of this break-point stress is critical to pavement designers to model future pavement designs to limit permanent deformation and premature distress problems. Using the deflection basin measurements and layered analysis calculations performed on APLT measurements obtained at different cyclic stresses, “universal” model parameters can be obtained for both the top and bottom layers in a two-layered structure. Example test results of such a case with testing on a crushed aggregate base over natural subgrade is shown in Figure 5 along with the “universal” model parameters reported separately for each layer. Results showed a generally increasing trend with cyclic stress for the top base layer (granular material) and a generally decreasing trend with cyclic stress for the bottom subgrade layer (cohesive material).

Figure 4 shows cyclic stress vs in-situ composite Mr and universal model fit curves
Figure 4. Cyclic stress versus in situ composite Mr and universal model fit curves.
Table 1 summarizes the universal model regression parameters from a tollway project
Table 1. Summary of universal model regression parameters from IL Tri-State Tollway project.


Although convenient, with often much less upfront costs compared to direct measurement options, using the indirect methods and empiricism, introduce substantial risks because the estimated values may not match the actual field conditions. Adoption of more rigorous in situ field measurements has been limited by the ability to perform reliable and repeatable measurements. With development of modern APLT as described in this paper, it is not possible to obtain reliable and repeatable test measurements to field verify design moduli values such as stress-dependent resilient modulus (Mr) and modulus of subgrade reaction (k-value) for foundation layer materials, and stress and frequency dependent dynamic moduli values for asphalt pavement layer materials. Direct measurements reduce risk to both the owner and the contractor allowing for confidence in optimizing designs, materials, and construction practices and represent the current and future industry direction for implementation of broader direct measurement programs.

Figure 5 graphs cyclic stress vs Mr of base and subgrade layers. It also display a chart of the universal model parameters.
Figure 5. Cyclic stress versus in situ Mr of base and subgrade layers, and universal model parameters separately for each layer.


Pavana Vennapusa, Ph.D., P.E. and David J. White, Ph.D., P.E are with Ingios Geotechnics, Inc.


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