Impact of vibration intensity and loose layer thickness on highway subgrade compaction performance based on field prototype tests

1 Introduction

Transportation infrastructure is an important foundation for national modernization and a key guarantee for implementing the strategy to build a strong transportation system and promote coordinated regional development (An et al., 2020; Smith et al., 2018). With the continuous expansion of China’s expressway network and the rapid growth of transportation demand, highway engineering is advancing toward higher standards, greater quality, and greater durability (Xu et al., 2022; Liu and Xiao, 2010). As a crucial component of the highway structural system, the engineering performance of the subgrade directly affects the service performance of the pavement structure and the overall operational safety of highways (Mahpour and El-Diraby, 2022). Under complex geological conditions and heavy traffic loads, subgrade compaction, as a key construction process for ensuring subgrade quality, has been widely applied in engineering practice by increasing the density of fill materials and improving particle contact conditions to enhance structural stiffness and stability (Anjan Kumar et al., 2016; Scott et al., 2020). Vibratory compaction has become the dominant construction method due to its high efficiency and strong adaptability; however, its effectiveness is influenced not only by the properties of the fill material but also by vibration intensity, loose layer thickness, and construction parameters (Zaman et al., 2010; Yan et al., 2014). Improper parameter matching may lead to insufficient compaction or energy waste. It may even induce disturbances to the subgrade structure, highlighting the urgent need to clarify the underlying mechanisms to guide engineering practice systematically.

At present, the evaluation of subgrade compaction quality still mainly relies on post-construction testing methods such as the sand replacement method (Wang et al., 2023), nuclear density gauge (Arulrajah et al., 2014), cutting ring method (Chang-Ning, 2017), water replacement method (Zhang et al., 2019), and portable falling weight deflectometer (Bu et al., 2023; Kim et al., 2007). Although these methods can reflect the final degree of compaction, they cannot characterize the dynamic evolution of the subgrade structural state during compaction and provide limited guidance for real-time optimization of construction parameters. In recent years, with the development of sensing technologies and signal analysis methods, dynamic analysis based on acceleration responses has gradually become an essential approach for investigating vibratory compaction behavior of subgrades (Liu et al., 2016; Mooney and Rinehart, 2007; Yang et al., 2020; Wang et al., 2024; Facas Norman et al., 2010). Existing studies have shown that subgrades exhibit pronounced time-domain, frequency-domain, and time–frequency response characteristics during vibratory compaction, which are closely related to the densification state of the fill material and the energy dissipation process. However, current research has mainly focused on laboratory tests (Ji et al., 2021; Arabali et al., 2018; Zvonaric et al., 2021), numerical simulations (Kim and Chun, 2016; Zhu et al., 2022; Ma et al., 2020), and artificial intelligence–based predictive models (Anjan Kumar et al., 2016; Minchin et al., 2008; Barman et al., 2016). At the same time, systematic investigations into the effects of vibration intensity and loose layer thickness under field-scale prototype conditions remain insufficient.

In view of this, this study conducted field-scale prototype vibratory compaction tests based on an actual highway project, using a sandstone weathered soil–rock mixture as the research material, to systematically investigate the dynamic response characteristics of the subgrade under different vibration intensities and loose layer thicknesses. Acceleration time-history analysis, Fourier transform (FFT), Hilbert–Huang transform (HHT), and marginal spectrum energy analysis were employed to characterize the near-surface dynamic response and vibration-energy distribution of the compacted layer from the perspectives of the time domain, frequency domain, and time–frequency–energy characteristics. The measured compaction degree obtained from sand replacement tests was also used as a conventional reference for comparison. The results are intended to provide experimental evidence for understanding the response characteristics of vibratory compaction and a reference for the selection of compaction parameters under similar field conditions.

2 Field-scale prototype test design

2.1 Engineering overview

The prototype test site was located on a section of an expressway in Ziyang County, Sichuan Province. The test area was approximately 100 m in length and 20 m in width (Figure 1). The fill material used in the field tests was obtained directly from the construction site and consisted predominantly of a soil–rock mixture formed from weathered sandstone. In terms of particle characteristics, the sandstone fraction was dominated by medium-to coarse-grained particles with predominantly angular or subangular shapes.

To quantitatively characterize the gradation of the fill material, particle-size distribution tests were conducted, and the resulting gradation curve is shown in Figure 2. The particle sizes ranged approximately from 0 to 60 mm, with a maximum particle size of approximately 60 mm. According to the particle-size distribution characteristics, the tested fill was classified as a coarse-grained soil. The uniformity coefficient (C _u) and curvature coefficient (C _c) were 29.3 and 1.0, respectively, indicating a relatively broad particle-size distribution. The principal physical, gradation, and compaction characteristics of the fill material are summarized in Table 1.

TABLE 1. Basic physical, gradation, and compaction characteristics of the tested fill material.

Heavy compaction tests were further conducted to determine the compaction characteristics of the fill material. The optimum moisture content was 8.8%, and the corresponding maximum dry density was 2.0 g/cm³. These parameters, together with the particle-size distribution, provide a quantitative characterization of the tested weathered sandstone fill.

The maximum particle size of approximately 60 mm is considerably smaller than the loose-layer thicknesses of 300 and 500 mm adopted in the field tests, corresponding to loose-layer-thickness-to-maximum-particle-size ratios of approximately 5.0 and 8.3, respectively. This relationship provides a basis for the selection of the two loose-layer thicknesses investigated in this study.

2.2 Test equipment

During subgrade filling and compaction, an XS2631J vibratory roller was selected as the primary compaction equipment to ensure the quality of the fill material. Its technical specifications are listed in Table 2. A high-performance dynamic signal acquisition system was employed during the tests, with a sampling frequency of 1000 Hz, to synchronously collect acceleration response signals from within the fill material and from the vibratory drum. An independent synchronous clock was used to ensure temporal consistency among multi-channel data. Triaxial acceleration sensors with a measurement range of 50 g were used; some were embedded in the subgrade fill, while others were rigidly mounted on the vibratory roller frame. All sensors were uniformly connected to the dynamic signal testing and analysis system via signal cables, enabling real-time acquisition and recording of acceleration data throughout the compaction process.

TABLE 2. Parameters of the vibratory roller.

2.3 Layout of measurement points

Four compaction lanes were arranged within the same test area under consistent basic field and measurement conditions, while the loose layer thickness and vibration mode were varied according to the designed test program. The overall layout is shown in Figure 3. The lanes were designated as Site1, Site2, Site3, and Site4. Along the direction of travel in each lane, five acceleration sensors were embedded at a uniform spacing of 2 m, with a consistent burial depth of 0.1 m. The three-directional acceleration time histories were collected to characterize the near-surface dynamic response and its spatial variation along the roller traveling direction. Because all embedded sensors were installed at the same depth, the present measurements were used to characterize the dynamic response of the near-surface portion of the compacted layer rather than the variation of vibration response with depth. Based on the sensor distribution, the test area was further divided into five zones, labeled a, b, c, d, and e, to facilitate comparative analysis of the dynamic responses at different locations.

2.4 Test program

This study focused on the vibratory compaction process of highway subgrades, with particular emphasis on the effects of vibration intensity and loose layer thickness on subgrade compaction performance. A total of four field test groups were designed around these influencing factors, with each pair forming a set of comparative working conditions. The detailed test schemes and parameter configurations are provided in Table 3.

TABLE 3. Test conditions.

High-amplitude vibration corresponds to an excitation force of 405 kN, a nominal vibration frequency of 27 Hz, and a nominal amplitude of 1.9 mm; low-amplitude vibration corresponds to an excitation force of 290 kN, a nominal vibration frequency of 32 Hz, and a nominal amplitude of 0.95 mm.

During the tests, the vibratory roller entered the test area from the left and initiated data acquisition. One round-trip movement of the roller, consisting of one forward pass and one return pass, was defined as one compaction cycle. Therefore, each compaction cycle corresponded to two compaction passes over a given sensor location. After completing one compaction cycle, the roller exited from the left side, and data acquisition was terminated. Upon completion of each test group, the sand replacement method was used to measure compaction in different zones, thereby providing a quantitative evaluation of subgrade compaction performance.

3 Analysis of test results

3.1 Compaction degree and statistical analysis

To quantitatively evaluate the compaction performance and spatial variability of the subgrade under different test conditions, sand replacement tests were conducted at multiple locations within each compaction lane after completion of the vibratory compaction process. Ten measurements were performed for each test condition. For the 50 cm low-amplitude condition, two measurements affected by field testing anomalies were excluded, leaving eight valid measurements for statistical analysis, while all ten measurements were retained for each of the other three conditions. These measurements were treated as spatial replicates to characterize the variability of the field compaction response. The statistical characteristics of the measured compaction degree are summarized in Table 4.

TABLE 4. Statistical characteristics of compaction degree under different test conditions.

As shown in Table 4, the mean compaction degree increased from 89.86% to 93.22% when the vibration mode changed from low amplitude to high amplitude at a loose layer thickness of 50 cm, corresponding to an increase of 3.36 percentage points. When the loose layer thickness was reduced to 30 cm, the mean compaction degree increased from 90.72% under the low-amplitude mode to 92.01% under the high-amplitude mode, corresponding to a smaller increase of 1.29 percentage points. This indicates that increasing vibration intensity produces a more pronounced improvement in compaction performance when the loose layer is relatively thick, whereas the difference between the two vibration modes becomes smaller at a reduced loose layer thickness.

The coefficients of variation under the four test conditions ranged from 1.67% to 4.44%, reflecting a certain degree of spatial variability associated with the field soil–rock mixture. The 50 cm low-amplitude condition exhibited the highest coefficient of variation, whereas the 50 cm high-amplitude condition showed the lowest value, indicating a comparatively more uniform compaction state under the latter condition.

To further quantify the effects of loose layer thickness and vibration mode, a two-way ANOVA based on Type II sums of squares was conducted, with loose layer thickness and vibration mode treated as the two influencing factors. At a significance level of 0.05, vibration mode exhibited a statistically significant overall effect on compaction degree (F = 6.303, p = 0.017). In contrast, the main effect of loose layer thickness was not statistically significant (F = 0.068, p = 0.796), and the interaction between loose layer thickness and vibration mode was also not statistically significant (F = 1.311, p = 0.260). These results indicate that, within the range of test conditions considered in this study, vibration intensity exerted a more pronounced overall influence on the measured compaction degree than loose layer thickness.

Overall, the statistical results are consistent with the subsequent dynamic-response analyses. For the relatively large loose layer thickness, increasing the vibration intensity is more beneficial for improving the compaction state, whereas at the smaller loose layer thickness, the difference in compaction degree between the low- and high-amplitude modes is reduced. The following sections further examine these differences from the perspectives of acceleration response, frequency-domain characteristics, and vibration-energy evolution.

The measured compaction degree increased from 89.86% to 93.22% as the vibration mode changed from low to high amplitude at a loose layer thickness of 50 cm, whereas the corresponding increase was from 90.72% to 92.01% at 30 cm. These measured trends were subsequently compared with the changes in acceleration, spectral amplitude, and energy-distribution characteristics.

3.2 Time-domain characteristics

To elucidate the acceleration response characteristics of the surface layer during subgrade compaction, Figures 4–7 present a comparative analysis of the acceleration time-history curves of the four test lanes in the X-direction (roller traveling direction) and the Z-direction (vertical excitation direction of the vibratory drum). Although three-directional acceleration signals were collected during the field tests, the subsequent analysis focuses on the X- and Z-direction responses because these two directions are directly associated with the roller traveling motion and the primary vibration excitation, respectively. In contrast, the Y-direction is perpendicular to the roller traveling direction in the horizontal plane and mainly reflects secondary lateral vibration; therefore, it was not included in the detailed analysis.

A total of 20 embedded acceleration sensors were originally arranged in the four test lanes, with five sensors in each lane. During the field tests, sensors A9 and A10 in Site2, A12 in Site3, and A17 in Site4 failed to provide valid acceleration records. Consequently, valid data were obtained from 16 of the 20 embedded sensors, corresponding to 80% of the originally arranged measurement points. The subsequent analyses were conducted using only complete and valid acceleration records. Representative measurement points used for the frequency-domain and energy analyses were selected from the valid sensors based on data completeness and their spatial correspondence within the designated test zones.

The prominent peaks observed in the time-history curves correspond to the moments when the vibratory drum passes over the measurement points. Their amplitudes reflect differences in the near-surface dynamic response of the compacted layer under different test conditions. By analyzing the peak characteristics and their spatial variations, the vibration-response characteristics of the near-surface fill can be quantitatively compared, providing a basis for the subsequent frequency-domain and energy analyses.

Based on the overall response characteristics, the acceleration time histories of the four test lanes exhibit high consistency and stability in the Z-direction, with amplitude variations mainly concentrated between 5 and 6 g, indicating a relatively uniform transmission of vibrational energy. This feature is closely related to the vibratory roller’s working mechanism, as the excitation force is primarily applied in the vertical direction, resulting in a more regular Z-direction response. In contrast, the acceleration time histories in the X-direction tend to exhibit more scattered instantaneous peaks, which can be attributed to particle rearrangement and densification of the soil–rock mixture along the traveling direction during compaction. This process is jointly influenced by various uncertain factors, such as soil reaction forces, interparticle friction, and interlocking effects, leading to greater randomness in the X-direction vibration response.

To analyze the influence of vibration intensity and loose layer thickness on the dynamic response characteristics within the subgrade, Figure 8 compares the peak acceleration responses in zones a and c under four independent test conditions. It should be noted that Site 1–Site 4 represent different combinations of loose layer thickness and vibration mode rather than successive stages of a continuous compaction process. Therefore, the differences in peak acceleration among the four test conditions are interpreted in terms of the effects of vibration intensity and loose layer thickness rather than as a temporal evolution of the compaction state.

At a loose layer thickness of 50 cm, the difference in Z-direction peak acceleration between the high- and low-amplitude vibration modes is relatively pronounced, indicating that vibration intensity has a pronounced influence on the dynamic response under this condition. The high-amplitude vibration mode provides greater excitation energy, which is more favorable for vibration transmission through the relatively thick loose layer. In contrast, when the loose layer thickness is reduced to 30 cm, the difference in Z-direction peak acceleration between the two vibration modes becomes smaller, indicating a reduced sensitivity of the dynamic response to vibration intensity at the smaller loose layer thickness.

Comparison of different loose layer thicknesses further shows that, under the low-amplitude vibration mode, the Z-direction peak acceleration for the 30 cm loose layer thickness is higher than that for the 50 cm loose layer thickness. This suggests that reducing the loose layer thickness facilitates the transmission of vibration energy under relatively low excitation intensity. Under the high-amplitude vibration mode, however, the difference in peak acceleration between the two loose layer thicknesses is relatively small, indicating that the influence of loose layer thickness on the dynamic response is weakened when the excitation intensity is relatively high.

In addition, Figure 8 shows that the peak acceleration responses in zones a and c exhibit generally consistent trends under the same test conditions, indicating good spatial comparability of the dynamic response within the test lanes. Therefore, representative measurement points were selected in the subsequent analysis to further investigate the effects of vibration intensity and loose layer thickness from the perspectives of frequency-domain characteristics and energy distribution.

3.3 FFT analysis

Acceleration time-history data from representative measurement points under different test conditions were selected for frequency-domain analysis. For each measurement point, the acceleration signal corresponding to the passage of the vibratory roller was selected from the recorded time history and directly processed using the fast Fourier transform (FFT). The sampling frequency was 1000 Hz. The resulting amplitude spectra were used to identify the dominant response frequency and the corresponding spectral amplitudes under different test conditions. The same signal-selection and FFT-processing procedure was applied consistently to all valid acceleration records to ensure comparability among the test conditions.

The resulting Fourier spectra are shown in Figure 9. Overall, the spectral response patterns under the high- and low-amplitude vibration modes are generally consistent, with the differences mainly reflected in the dominant response frequency and spectral amplitude.

Within the same vibration mode, the spectral response shapes for different loose layer thicknesses show good consistency. The vibratory roller operates at nominal frequencies of 27 Hz and 32 Hz under the high- and low-amplitude vibration modes, respectively. In contrast, the FFT spectra obtained from the acceleration responses measured within the subgrade fill exhibit dominant response frequencies of approximately 24 Hz under the high-amplitude mode and 27 Hz under the low-amplitude mode. The difference between the measured dominant response frequencies and the nominal vibration frequencies is attributed to the dynamic interaction between the vibratory drum and the soil–rock mixture during vibration transmission, including the effects of drum–subgrade contact, particle rearrangement, interparticle interaction, nonlinear deformation, and energy dissipation. Therefore, the frequencies identified from the FFT spectra represent the dominant response characteristics of the roller–subgrade system rather than the nominal excitation frequencies of the vibratory roller. In the low-amplitude vibration mode (Figures 9a,c), the second- and third-order harmonic components occur at approximately 55 Hz and 82 Hz, respectively. In the high-amplitude vibration mode (Figures 9b,d), the corresponding harmonic components occur at approximately 49 Hz and 73 Hz, respectively. These harmonic frequencies are approximately two and three times the corresponding dominant response frequency, indicating that the measured vibration responses retain clear and stable periodic characteristics and remain governed by the periodic excitation of the vibratory roller.

Further comparison of different loose layer thicknesses shows that, when the loose layer thickness is relatively large, the dominant spectral peak under the high-amplitude vibration mode is markedly higher than that under the low-amplitude mode. This indicates that the higher excitation level produces a stronger frequency-domain response under the 50 cm condition. The broader spectral distribution and lower dominant peak observed under the low-amplitude mode may be associated with greater vibration-energy loss within the near-surface compacted layer.

When the loose layer thickness is reduced to 30 cm, the dominant spectral peak under the low-amplitude vibration mode increases markedly and approaches, or in some cases slightly exceeds, that under the high-amplitude mode. Combined with the measured compaction degrees reported in Section 3.1, this response suggests that the 30 cm loose layer can achieve a relatively favorable compaction state even under the low-amplitude vibration mode. The observed spectral characteristics may reflect differences in particle rearrangement and contact conditions during compaction; however, these internal processes are inferred from the dynamic response rather than directly measured.

In addition, under the high-amplitude vibration mode, the differences in the dominant spectral peaks between the two loose layer thicknesses are relatively limited, indicating a lower sensitivity of the near-surface frequency response to loose layer thickness at the higher excitation level. Overall, higher compaction degrees are generally accompanied by larger dominant spectral peak amplitudes and a more concentrated spectral distribution. This trend is particularly evident in the Z-direction response and provides a useful frequency-domain indicator for comparing compaction responses under the investigated test conditions.

3.4 HHT analysis

To systematically reveal the energy distribution characteristics of subgrade dynamic responses under different vibration intensities and loose layer thicknesses, Hilbert–Huang transform (HHT) analysis was performed on the acceleration signals of zone A in both the X- and Z-directions to obtain the corresponding time–frequency spectra (Figures 10–13). Before the Hilbert transform, the measured acceleration signals were decomposed using empirical mode decomposition (EMD). Since EMD is an adaptive decomposition method, the number of intrinsic mode functions (IMFs) was not fixed in advance but was determined according to the characteristics of each signal. For the acceleration signals analyzed in this study, approximately 10–12 IMF components were generally obtained. During the EMD sifting process, the local maxima and minima of each signal were identified to construct the upper and lower envelopes, and the mean of the two envelopes was iteratively removed. A component was regarded as an IMF when the numbers of zero crossings and extrema differed by no more than one and the local mean of the upper and lower envelopes was approximately zero. The decomposition was continued until the residual became monotonic or could no longer be further decomposed into meaningful oscillatory components. The resulting IMF components were then subjected to the Hilbert transform to obtain the corresponding instantaneous amplitudes and instantaneous frequencies, from which the Hilbert time–frequency spectra were constructed. The same EMD–Hilbert processing procedure was applied to the acceleration signals under all test conditions.

The results indicate that energy is mainly concentrated during the time intervals when the vibratory roller passes over the sensors, exhibiting higher amplitudes and broader energy bands in the low-frequency range, with dominant frequencies primarily distributed between 10 and 40 Hz. As frequency increases, the energy amplitude under all conditions shows a gradual attenuation trend, indicating that the subgrade fill exhibits a weaker response to high-frequency vibration components and that vibrational energy is mainly concentrated in the low-frequency range.

From the perspective of directional characteristics, the energy bandwidth and amplitude of the time–frequency spectra in the Z-direction are generally greater than those in the X-direction, indicating that the vibration response is more concentrated in the vertical direction, which is consistent with the primary excitation direction of the vibratory drum. This directional difference is particularly pronounced under the low-amplitude vibration mode, suggesting that vertical vibration remains the dominant component of the near-surface dynamic response and energy distribution under the investigated test conditions.

Further comparison of different loose layer thicknesses shows that the difference in the Hilbert spectral response between the high- and low-amplitude vibration modes is more pronounced at a loose layer thickness of 50 cm. Under this condition, the Hilbert spectral amplitude under the high-amplitude vibration mode is higher than that under the low-amplitude mode. When the loose layer thickness is reduced to 30 cm, the spectral responses under the two vibration modes become closer, and the low-amplitude mode also exhibits relatively concentrated energy within the dominant frequency range. Combined with the measured compaction degrees reported in Section 3.1, these characteristics suggest that the 30 cm loose layer can achieve a relatively favorable compaction state even under the low-amplitude vibration mode.

Under the same low-amplitude vibration mode, reducing the loose layer thickness results in higher instantaneous amplitudes and a more concentrated Hilbert spectral distribution. This response may be associated with reduced vibration-energy loss in the near-surface portion of the compacted layer. From a physical perspective, such behavior may be related to changes in particle rearrangement and interparticle contact conditions as the compaction state improves.

In contrast, under the high-amplitude vibration mode, the differences in the Hilbert spectral response between the two loose layer thicknesses are relatively small. This observation suggests that the higher excitation level reduces the sensitivity of the near-surface dynamic response to changes in loose layer thickness. The relatively concentrated spectral response may be associated with a more stable macroscopic compaction state.

3.5 Marginal spectrum energy analysis

To further characterize the frequency-dependent energy distribution of the near-surface vibration response under different vibration intensities and loose layer thicknesses, marginal spectrum analysis was performed based on the Hilbert spectrum obtained from the HHT analysis. For a Hilbert spectrum H(ω,t), the marginal spectrum h(ω) is defined by Equation 1:where (H (ω,t)) denotes the Hilbert spectrum, (ω) is the angular frequency, and (T) represents the duration of the selected acceleration-signal segment. The marginal spectrum reflects the cumulative contribution of each frequency component over the selected time interval.

h ω = ∫ 0 T H ω , t d t (1)

To further quantify the overall spectral-energy level, the marginal spectrum was integrated over the analyzed frequency range, as shown in Equation 2:where (h(ω)) is the marginal spectrum and (E) represents the integrated marginal-spectrum energy index.

E = ∫ ω h ω d ω (2)

The same signal-selection criterion, time interval, frequency range, and processing procedure were applied to all valid acceleration records to ensure comparability among the different test conditions.

Based on the above procedure, the marginal spectrum curves in both the X- and Z-directions generally exhibit a dominant low-frequency peak followed by gradual attenuation toward higher frequencies, indicating that the near-surface vibration response is mainly concentrated within the dominant low-frequency band. Under the same test conditions, the marginal spectrum amplitudes at different measurement points in the Z-direction are relatively close, reflecting good consistency in the vertical dynamic response. In contrast, the X-direction marginal spectra exhibit larger differences and more pronounced fluctuations across the frequency range. This behavior is attributed to the combined effects of vibratory excitation, roller advancement, and interparticle interactions in the horizontal direction, which result in greater spatial variability of the near-surface vibration response.

At the same loose layer thickness, the vibration mode has a pronounced influence on the marginal spectrum response. When the loose layer thickness is 50 cm, the marginal spectrum amplitudes under the high-amplitude vibration mode are generally higher than those under the low-amplitude vibration mode, indicating a greater vibration-energy input under the higher excitation level. The corresponding increase in marginal spectral energy may be associated with reduced relative energy loss during vibration transmission and a greater proportion of the input energy contributing to the dynamic response of the compacted layer. When the loose layer thickness decreases to 30 cm, the marginal spectrum responses under the two vibration modes become closer. This behavior may indicate that the thinner loose layer is more favorable for developing a relatively stable compaction state even under the low-amplitude vibration mode, resulting in a more concentrated response within the dominant frequency band.

From the perspective of a single vibration mode, the marginal spectrum response under the high-amplitude vibration mode shows relatively limited differences between the two loose layer thicknesses, suggesting that the influence of loose layer thickness on the near-surface dynamic response is reduced when the excitation intensity is relatively high. In contrast, under the low-amplitude vibration mode, the marginal spectrum response is more sensitive to changes in loose layer thickness. As the loose layer thickness decreases, the marginal spectral response becomes more concentrated within the dominant frequency range, which, together with the measured compaction results, suggests a more favorable compaction state under the 30 cm condition. The resulting marginal spectrum energy curves under the four test conditions are shown in Figures 14–17.

4 Conclusion

Based on the field-scale prototype tests and dynamic response analyses, the effects of vibration intensity and loose layer thickness on subgrade compaction performance were investigated, and the following conclusions can be drawn:

• A combination of acceleration time-history analysis, Fourier transform (FFT), Hilbert–Huang transform (HHT), and marginal spectrum energy analysis was used to characterize the dynamic response of the subgrade from the perspectives of the time domain, frequency domain, and time–frequency–energy characteristics. This multi-perspective analysis provides a basis for comparing compaction responses under different field test conditions.
• Vibration intensity and loose layer thickness affect the near-surface dynamic response and energy characteristics of the compacted layer in different ways. Statistical analysis indicates that vibration mode has a more pronounced influence on compaction degree, while no significant interaction between vibration mode and loose layer thickness was identified. For relatively large loose layer thicknesses, increasing vibration intensity produces a stronger dynamic response, whereas the difference between the two vibration modes becomes smaller as the loose layer thickness decreases.
• Improvements in compaction performance are generally accompanied by increases in the dominant spectral peak amplitude, greater concentration of the vibration response within the low-frequency range, and changes in marginal spectral energy. These dynamic-response characteristics can provide a reference for evaluating compaction behavior and selecting vibratory compaction parameters under field conditions similar to those investigated in this study.

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Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fbuil.2026.1946274/full#supplementary-material

Supplementary material Supplementary material at the source

Footnotes

Edited by: Sujit Kumar Dash, Indian Institute of Technology Kharagpur, India

Reviewed by: Zhuoling He, Southwest Jiaotong University, China

Ruihan Li, Southwest Jiaotong University, China