1 Introduction

Due to the combined effects of traffic loads and environmental factors, the performance of the pavement structure has gradually deteriorated over the years. The technical condition of the asphalt pavement, from the surface to the subgrade, has shown a continuous decline (Hernando et al. 2013, Bhandari et al. 2023, and Xiong et al. 2024). Different pavement sections may exhibit different levels of premature distress, including permanent deformations, cracking, and loose material beneath the pavement layers (Suh et al. 2018, Donev and Hoffmann 2020 and Dinegdae et al. 2023).

Over the past few decades, researchers around the world have used various methods to assess pavement distress and identify potential causes of surface problems (Lippmann 1986, Gerritsen et al. 1987, Perdomo and Nokes 1993, and Hasan et al. 2024).

To mitigate pavement distress caused by traffic and climatic conditions, considerable work has been devoted to determining and estimating appropriate pavement design parameters for each construction layer. These parameters are then incorporated into advanced pavement design software to improve overall pavement performance.

The determination of critical parameters for pavement design within the mechanistic method revolves primarily around the estimation of stiffness modulus (E) and Poisson’s ratio (υ). The stiffness modulus (Mr) serves as the central stiffness metric for pavement layers, denoting the unloading modulus within the hysteresis loop after numerous cycles of repeated loading, typically obtained by repeated load triaxial (RLT) testing. However, it is worth noting that modulus of elasticity tests for pavement materials are both relatively expensive and time-consuming, prompting research into a simpler and more reliable alternative testing technique for Mr (Pericleous and Metcalf 1996, Kim et al. 2001, Razouki and Kuttah 2004, Kuttah 2021).

Moreover, the evaluation of mechanical pavement properties has traditionally relied on falling weight deflectometer (FWD) tests (Nega et al. 2016, Gupta et al. 2023), a method involving the application of impulsive loads to a pavement surface with subsequent measurement of deflection responses. The load amplitudes and frequency content intend to provide pavement deformation levels similar to those induced by truck wheal loads in heavy urban traffic loading, and it can also produce a huge amount of deflection data in a short period (Bianchini and Bandini 2010). Traditionally, the FWD test is the most widely used non-destructive testing (NDT) instrument in the world due to its high test accuracy, repeatability, and similarity to real loading conditions in terms of magnitude and duration. The use of NDT equipment has led to the development of several parameters describing deflection basins. The usefulness of these parameters has been demonstrated in calculating the modulus of elasticity (E-modulus) of pavement layers and assessing the structural condition of the pavement (Kim et al. 2000 and Park 2001, Thummaluru and Guzzarlapudi 2022, Kuttah 2023, and Duddu et al. 2023).

However, in light of the significant time and resource expenditures associated with FWD tests as well, this study proposes a substitution with light weight deflectometer (LWD) tests. The LWD theory and the measured modulus have been extensively discussed in various studies, offering a potential alternative to the conventional FWD to assess the condition of unpaved roads, cycle paths, or unbound pavement materials.

This study effectively demonstrates the correlation between experimentally determined LWD deflections and theoretically estimated deflections using EraPave. EraPave is a back-calculation software based on theoretical analysis “using the Multi-Layer Elastic Theory “ adopted to model and predict deflections in this study. The primary focus is on determining the layer structural capacity and evaluating changes in the deformation moduli of the tested layers under diverse conditions, including varying moisture contents and applied dynamic loads.

In summary, this study navigates the complexities of pavement evaluation, proposing the substitution of FWD tests with LWD tests for specific test conditions. The utilization of VTI’s analytical tools (ERAPave) and consideration of alternative testing techniques (i.e., VTI’s multifunctional LWD) underscore the commitment to optimizing the assessment of pavement properties, in terms of layer structural capacity and the changes in the tested layer deformation moduli for different moisture contents and applied impulsive loads for different road construction materials tested in this study.

2 Tested Material Properties

2.1 Unbound Granular Material

For the granular base layer, a gravel material 0/32 has been selected to be tested in this study. The gradation of the tested base material is shown in Table 1 with the percentage passing.

Table 1 Particle size distribution of the tested unbound base material
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The compaction properties of the selected base material were determined by the modified Proctor test according to ASTM D1557 (2012). The test was carried out by compacting several CBR soil samples using a cylindrical mold with a diameter of 152.4 mm.

The results of the compaction tests showed that the compaction curve of the tested material is a one-and-a-half peak curve with two optimum water contents and two maximum dry densities. One of the maximum dry densities is on the dry side (at W = 0%) and the other is on the wet side (at around W = 6%). The maximum dry densities are 2.2 g/cm3 and 2.3 g/cm3 at 0% and 5.7% water content, respectively.

2.2 Sandy Soil

Commonly available sandy subgrade soil has also been tested in this study. The particle size distribution of this soil is shown in Table 2 below. According to ASTM D2487 (2017), the tested soil is classified as SP sand, indicating poorly graded sand.

Table 2 Particle size distribution of the tested sandy soil
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The specific gravity of the selected sandy soil was determined according to the guidelines of SS-EN 1097-6 (2013) and was found to be 2.664.

The modified Proctor test according to ASTM D1557 (2012) was used to assess compaction properties. The test involved compacting several soil samples using a cylindrical mold with a diameter of 152.4 mm. The results of the modified Proctor compaction tests on the selected sandy soil showed a maximum dry density of 1.72 g/cm3 at an optimum moisture content of 12%.

2.3 Silty Sand Soil

A silty sand subsoil was selected for testing in this study. A comprehensive series of laboratory tests were carried out on the selected soil to determine various physical properties, including particle size distribution, clay fraction, soil classification, specific gravity, fluid and plastic limits, and compaction characteristics.

The particle size distribution test for the selected soil was carried out according to the guidelines of SS-EN 933-1 (2004), and the results are presented in Table 3 below:

Table 3 Particle size distribution of the tested sandy soil
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The clay content in the soil was tested according to the VTI method for particle size distribution analysis with laser diffraction [10 nm–2 mm] and was found to be 5%.

According to Väg (2008), the tested soil is of material type 4A (mixed-grained soils with frost hazard class 3). According to SS-EN ISO 14688-2 (2004), the soil is classified as silty sand with 5% clay.

The specific gravity of the selected soil was tested according to SS-EN 1097-6 (2013), Appendix G, and was found to be 2.64. The liquid and plastic limits were determined at SGI (Swedish Geotechnical Institute) according to SS-EN ISO 17892-12 (2018). The test results showed a liquid limit (LL) of 18% and a plastic limit (PL) of 14.3%, resulting in a plasticity index of 3.7% for the tested soil. In this project, compaction properties were determined using the modified Proctor test according to ASTM D1557 (2012). The test was performed by compacting several soil samples using a cylindrical mold with a diameter of 152.4 mm. The soil samples were compacted at different water contents ranging from 0 to 16% to determine the water-density relationship. The results of the compaction tests showed that the tested soil has a maximum dry density of 2.03 g/cm3 at an optimum moisture content of about 8.2%.

2.4 Sandy Silty Clay Soil

A sandy silty clay subsoil was also chosen for this study. A series of laboratory tests were carried out on the selected soil to determine its physical properties, namely particle size distribution, clay and silt fractions, soil classification, specific gravity, fluid and plastic limits, compaction characteristics, and soil classification.

The particle size distribution test was carried out on the selected soil according to SS-EN 933-1 (2004); see Table 4.

Table 4 Particle size distribution of the tested sandy silty clay soil
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The clay content of the soil was tested by the sediment method at SGI (Swedish Geotechnical Institute), and the test results showed that the soil consisted of 37.5% clay particles (≤ 0.002 mm), fine content of 75.7% (clay and silt), sand content of 21.9%, and gravel content of 2.4%.

According to Väg (2008), the tested soil is of material type 5 (with frost hazard class 4). According to SS-EN ISO 14688-2 (2004), the soil is classified as sandy silty clay (see Fig. 6).

The specific gravity of the selected soil was tested according to Swedish Standard SS 027115 (1989) and found to be 2.65.

The fluid and plastic limits were determined at SGI according to Swedish Standard SS 027115 (1990) and Swedish Standard SS 027121 (1990), respectively. The test results showed a liquid limit (LL) of 37% and a plastic limit (PL) of 17.8% giving a plasticity index of 19.2%.

The compaction properties of the investigated soil were determined using the modified Proctor test according to ASTM D1557 (2012). The soil samples were compacted at different moisture contents ranging from between 7 and 27% to determine the water-density relationship.

3 Field Testing

The field LWD tests with the corresponding moisture content tests have been conducted on a large test pit of the compacted material under controlled conditions. The test pit was approximately 9.5 m long × 5 m wide × 1.5 m depth and was equipped with a concrete well with a water-discharging motor that was used to control the groundwater level during testing, as shown in Fig. 1.

Fig. 1
figure 1

The test pit used in the study

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The sandy soil was first compacted and tested in the test pit and then, once all the required field tests had been completed, the sandy soil was removed, and the base course material was placed in the test pit and compacted. Similarly, on completion of all the field tests relating to the gravel material, this was removed, and the silty sandy soil was placed and tested. Finally, when all tests on the silty sandy soil have been completed, the silty sandy clay is compacted and tested. The field test conditions of the LWD tests, with the corresponding water contents and applied contact pressures, carried out on each of the compacted materials are shown in Table 5.

Table 5 The field test conditions of the LWD tests, with the corresponding water contents and applied contact pressures
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4 Equipment Used and Working Principles

4.1 Light Weight Deflectometer (LWD) Test

The LWD serves as a modulus-based measurement tool with considerable potential for incorporation into the compaction control process (Fleming et al. 2007). It gauges deflection caused by a falling weight to estimate the dynamic deformation modulus (Evd). The calculation of Evd employs the elastic half-space theory for a one-layer system based on Boussinesq (1885), as shown in Eq. (1). This equation presupposes the test medium to be a linearly elastic, isotropic, homogeneous semi-infinite continuum. The determination of the modulus relies on two assumed parameters: the shape factor for the distribution of contact stress between the plate and the soil (A) and Poisson’s ratio (ν).

$$\mathrm E=2\mathrm k\left(1-\mathrm v^2\right)/{\mathrm{Ar}}_0$$
(1)

where k is the load (peak)/deformation (peak), ro is the plate radius, A is the stress distribution factor, and ν is the Poisson’s ratio.

The operating principle of the LWD is to measure the deflection caused by a falling weight of up to 20 kg, which is detected by integrated geophones (see Fig. 2). The LWD used in this study has a basic falling mass of 10 kg. During the test, the falling mass hits the plate and generates a load pulse of up to 7 kN, depending on the fall height.

Fig. 2
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The LWD used in the study

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The central deflection of the material surface under test is measured through a hole in the load plate using a high-precision seismic transducer (geophone). In addition, two further deflection geophones are positioned at 30 cm and 60 cm from the center line of the load. A 3-cm-diameter base plate was used for the field measurements in this study. Adjustment of the drop height is quick and easy using a moveable release handle, and the peak impact force is determined from actual load cell readings (see Fig. 2).

The data acquisition software is installed on a PC connected to the LWD. The modulus of deformation of the surface and/or plate (Evd) can be displayed on the PC screen in real-time, in addition to the time history graph from both the deflection sensors and the load sensor. For LWD in the field, Evd is calculated using Eq. 1, assuming A = 4 and ν = 0.35.

In addition, the deformation moduli measured by field LWD at 30 cm and 60 cm from the centerline of the drop load were calculated using Eq. (2) for stresses at eccentricity from the load centerline. The dynamic deflection of the subgrade and/or base material is determined by considering the media to be a semi-infinite elastic body and the load to be uniform over a circular area. This can be calculated mathematically as:

$$\mathrm{Evd}\;\mathrm{field}=\mathrm F^\ast\left(1-\mathrm v2\right)/\left(\mathrm\pi.\mathrm r.\mathrm{dr}\right)$$
(2)

where dr is the deflection at distance r from the center and F is the peak force.

4.2 Nuclear Density Gauge (NDG)

The nuclear density gauge (NDG) was used to determine the in situ moisture content of the tested soil in the test pit. The test method is useful as a rapid, non-destructive technique for in situ measurement of wet density and water content of soil and soil aggregates, and determination of dry density (ASTM D6938 2017).

5 Results and Discussion

5.1 In the Case of Unbound Granular Material (UGM)

The gravelly base layer was tested at various locations at relatively low moisture levels (about 3%) and higher moisture levels about 6.6% (after applying water) using a multi-functional LWD available at VTI.

The field LWD tests were carried out at three different drop heights by varying the drop height of the 10 kg drop weight to give 3 kN, 5 kN, and 7 kN applied loads, corresponding to approximately 42 kPa, 70 kPa, and 100 kPa vertical contact pressures, respectively.

The EraPave software was used to assess the structural condition of the pavements to predict the layer moduli using a back-calculation process based on deflection data measured by LWD tests.

A comparison of the average dynamic displacements at the surface of the gravel base layer, obtained using field LWD and those obtained using ERAPave, for different moisture contents and applied stress conditions is shown in Fig. 3. Note that the average dynamic displacement from the LWD test is the average for drops 4, 5, and 6 as is common practice for any conventional LWD test. These LWD data points are used in ERAPave as input deflections at 0, 30, and 60 cm intervals to determine the deflection range and corresponding layer modulus in ERAPave.

Fig. 3
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The deflections in the gravelly base course layer tested using the LWD test and the corresponding back calculation displacements in ERAPave

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In Fig. 3, it can be seen that the influence lines for displacement measurement with depth using ERAPave match very well the measured total displacements recorded by field LWD for all tested conditions.

The root mean square error (RMSE), see Fig. 3, reported for the compacted unbound layer varied from 0.46 to 3.51 for the compacted gravel base layer, demonstrating the considerable potential of LWD data. This suggests that LWD data can be effectively utilized as input in ERAPave to predict layer moduli for compacted gravel base layers under different water contents.

In terms of layer E-modulus, the back-calculated layer stiffnesses from ERAPave for the gravelly base layer was 86.1 MPa from the average for the points tested at 42, 70, and 100 kPa applied stress under 3% water content. A layer-modulus of 82.7 was obtained for the points tested at 100 kPa applied stress and 6.6% water content. Decreasing the E-moduli with increasing the water content is something expected.

5.2 For the Case of Sandy Soil

For the sandy soil, the LWD tests involved two drop height settings, resulting in applied loads of 3 kN and 5 kN (corresponding to vertical contact pressures of approximately 42 kPa and 70 kPa) for compacted sandy soil tested at 3% water content. For soil body tested at 9% water content, a single drop height setting was used, yielding an applied load of 3 kN (100 kPa applied stress).

To evaluate the structural condition and predict layer moduli of the compacted soil, the ERAPave software was employed for the case of the UGMs. Figure 4 illustrates a comparison of average dynamic displacements at the sandy soil surface obtained from both field LWD and the back-calculated displacement in ERAPave under varying moisture contents and applied stress conditions.

Fig. 4
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The deflections in the sandy soil layer tested using the LWD test and the corresponding back-calculated displacements in ERAPave

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LWD data points, representing averages for drops 4, 5, and 6, were utilized in ERAPave to determine the displacement range and corresponding layer modulus at 0, 30, and 60 cm intervals.

In Fig. 4, the calculated displacement using ERAPave matched well with the measured total displacements recorded by LWD for all tested conditions. The root mean square error (RMSE reported for the sandy subgrade layer varied from 1.1 for the 3% water content case under 42 kPa applied stress to 9.97 for the same water content but under 100 kPa applied stress. The RMSE value of 3.36 was reported for the case of higher water content (9%) and intermediate applied stress of 70 kPa.

Despite the variations in RMSE values, the LWD test data, as shown in Fig. 4, can be effectively employed as input in ERAPave to predict layer moduli for compacted sandy soil layers under the specified water contents and applied stresses.

Concerning layer E-modulus, back-calculated layer stiffnesses from ERAPave yielded an average E-layer modulus of 86.9 MPa for points tested at 42 kPa and 70 applied stresses under 3% water content. A layer modulus of 49.4 MPa was obtained for points tested at 100 kPa applied stress and 9% water content.

5.3 For the Case of Silty Sand Soil

The silty sand subgrade was also tested at various locations at three different moisture levels (namely 8%, 10%, and 15%) using the multi-functional LWD available at VTI.

The field LWD tests were carried out at three different drop heights by varying the drop height of the 10 kg drop weight to give applied loads of 1.6 kN, 3.3 kN, and 6.5 kN, corresponding to approximately 50 kPa, 100 kPa, and 200 kPa vertical contact pressures, respectively. The diameter of the LWD steel plate was 0.2 m for the tests conducted on the silty sand subgrade.

A comparison of the average dynamic displacements at the surface of the compacted silty sand layer obtained using field LWD and those obtained using ERAPave for different moisture contents and applied stress conditions is shown in Figs. 5, 6, and 7. Note that the average dynamic displacement from the LWD test is the average for drops 4, 5, and 6. These LWD data points are used in ERAPave as input deflections at 0, 30, and 60 cm intervals to determine the deflection range and corresponding layer modulus.

Fig. 5
figure 5

The deflections in the silty sand soil layer tested using the LWD test and the corresponding back-calculated displacements in ERAPave at 8% water content

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Fig. 6
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The deflections in the silty sand soil layer tested using the LWD test and the corresponding back-calculated displacements using ERAPave at 10% water content

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Fig. 7
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The deflections in the silty sand soil layer tested using the LWD test and the corresponding back-calculated displacements in ERAPave at 15% water content

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In Figs. 5, 6, and 7, it can be seen that the calculated displacement using ERAPave agrees well with the measured total displacements recorded by the field LWD for all conditions tested for different water contents.

The RMSE reported for the compacted silty sand layer, see Figs. 5, 6, and 7, varied from 1.85 for the lowest water content of 8% at the lowest applied stress of 50 kPa to 33.7 for the highest water content tested of 15% and the highest applied stress tested of 200 kPa. This means that for this type of soil, increasing the water content and applied stress has a negative effect on the calculated RMSE when using LWD data as input in ERAPave. The lowest water content and applied stresses result in a better match between the input displacements from the LWD tests and the back-calculated displacement from ERAPave, and hence a better prediction of the average layer modulus. This suggests that LWD data can also be used as input to ERAPave to predict layer moduli for compacted sandy soil layers under different water contents. Therefore, for the sandy soil case, the LWD input data should be used with caution for applied stresses greater than 50 kPa and higher water contents of around 15%.

In terms of the E-modulus of the layer, the back-calculated layer stiffnesses from ERAPave were 67.7 MPa, 57.8 MPa, and 48.3 MPa as an average for the points tested at 200, 100, and 50 kPa applied stress at 8%, 10%, and 15% water content, respectively.

5.4 For the Case of Sandy Silty Clay Soil

A sandy silty clay soil was also selected and tested at various locations at three different water content levels (namely 16%, 19%, and 24%) using the multi-functional LWD available at VTI.

The field LWD tests were carried out at three different drop heights by varying the drop height of the 10 kg drop weight to give applied loads of 1.7 kN, 2.6 kN, and 3.5 kN, corresponding to approximately 24 kPa, 37 kPa, and 50 kPa vertical contact pressures, respectively. The diameter of the LWD steel plate was 0.3 m for the tests conducted on the clayey subgrade.

A comparison of the average dynamic displacements at the surface of the compacted clay layer obtained using field LWD and those obtained using ERAPave for different water contents and applied stress conditions is shown in Fig. 6. Note that during the routine LWD measurements, the average dynamic deformation modules for the last three drops after the first three pre-test drops are usually considered (i.e., the Evd is taken as the average of the Evds measured for drops 4, 5, and 6). These LWD data points are used in ERAPave as input deflections at 0, 30, and 60 cm intervals to determine the deflection range and corresponding layer modulus in ERAPave.

In Figs. 8, 9, and 10, it can be seen that the calculated displacement using EraPave agrees very well with the measured total displacements recorded by the field LWD for all conditions tested.

Fig. 8
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The deflections in the sandy silty clay layer tested using the LWD test and the corresponding back-calculated displacements in ERAPave at 16% water content

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Fig. 9
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The deflections in the sandy silty clay layer tested using the LWD test and the corresponding back-calculated displacements in ERAPave at 19% water content

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Fig. 10
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The deflections in the sandy silty clay layer tested using the LWD test and the corresponding back-calculated displacements in ERAPave at 24% water content

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The RMSE reported for the compacted sandy silty clay layer, see Figs. 8, 9, and 10, varied from 0.88 for the lowest water content of 16% at the lowest applied stress of 24 kPa to 114.6 for the highest tested water content of 24% and the highest tested applied stress of 50 kPa. As in the case of the compacted silty sand layer, this means that for the clayey soil, increasing the water content and applied stress has a negative effect on the RMSE value when using LWD data as input in ERAPave. The lowest water content and applied stresses result in a better match between the input displacements from the LWD tests and the back-calculated displacement from ERAPave, and hence a better prediction of the average layer modulus. This suggests that LWD data can also be used as input to ERAPave to predict layer moduli for compacted clayey soils at water contents up to 24% and applied pressures up to 38 kPa. Note that the LWD input data should be used with caution for the combination of high-water contents of 19 to 24% and applied pressures close to 38 kPa.

In terms of the E modulus of the layer, the back-calculated layer stiffness moduli from ERAPave was 33 MPa as an average for the points tested at 24, 38, and 50 kPa applied stress under 16% water content. Layer moduli of 19 MPa and 17 MPa were recorded as averages for points tested at 19% and 24% water content, respectively.

It is also important to note that for all four materials tested, the predicted layer modulus from ERAPave, when adopting the LWD test data, reported a decrease in layer modulus with increasing water content for the same group of applied loads, which is well in line with documented general trends in the literature.

6 Conclusions and Recommendations

In the current study, a comprehensive evaluation of pavement materials through LWD tests and subsequent analysis with the ERAPave software yielded valuable insights into the structural behavior of diverse road construction materials. The results underscore the efficacy of LWD as an alternative to FWD tests and highlight its potential for optimizing pavement design processes and determining layer modulus. Based on the current study, layer moduli of 86.1 MPa and 82.7 MPa were estimated using ERAPave based on LWD tests carried out on unbound granular material (Gravel Base Layer) at 3% and 6.6% water content, respectively. For sandy soil, layer moduli of 86.9 MPa and 46.4 MPa were estimated at a water content of 3% and 9%, respectively. Layer moduli of 67.7 MPa, 57.8 MPa, and 48.3 MPa were estimated at 8%, 10%, and 15% water content, respectively, for the silty sand soil layer. Similarly, for sandy silty clay soil, layer moduli of 33 MPa, 19 MPa, and 17 MPa were recorded for points tested at 16%, 19%, and 24% water content, respectively.

These numeric conclusions affirm the suitability of LWD tests, coupled with the ERAPave analysis, as a robust methodology for predicting layer moduli across diverse pavement materials. The consistent trends of decreasing E-modulus with increasing water content align with established patterns in pavement engineering literature. The study advocates for the prudent use of LWD, especially in conditions of lower water content and applied stresses, to enhance the efficiency and accuracy of pavement evaluation practices.