The test construction waste soil (Figure 1) belongs to the argillaceous siltstone obtained from the Jinhua South Interchange section of the expressway in Zhejiang. Physical properties of argillaceous siltstone were summarized in Table 1. The particle size distribution of this argillaceous siltstone was as shown in Figure 2.

The wet argillaceous siltstone was adjusted to the target moisture content by weighing and water spraying, and sealed in a plastic bag to make the argillaceous siltstone evenly wet for 24 h, and then the moisture content was measured and averaged. The argillaceous siltstone is divided into five layers, and the cylindrical specimen (Figure 3) with a diameter of 100 mm and a height of 200 mm is made by uniform static pressure on the hydraulic universal testing machine. After demoulding, the specimens were wrapped with cling film and allowed to stand for 48 h to make the humidity uniform, and then the dynamic triaxial test was carried out (Zhang et al., 2024).

In this test, Dynatriax100/14 automatic triaxial test system was used to carry out dynamic triaxial test on construction waste soil subgrade filler, and permanent deformation properties of construction waste soil subgrade filler was studied. The maximum dynamic load provided by the device is 14 kN, the loading frequency is up to 10 Hz, and the test range of dynamic displacement is 30 mm. The cyclic load of this test is applied in the form of half-sine wave (Xin et al., 2021; Zhang et al., 2021), the loading frequency is 1 Hz, the loading time is 0.2 s, and the intermittent time is 0.8 s. The test termination condition adopts the double control index of strain and vibration. If the axial strain reaches 5%, the test is terminated. Otherwise, the test will be terminated when the total number of vibrations reaches 10,000 (Zhang et al., 2020; Zhang et al., 2024). The dynamic triaxial test scheme is shown in Table 2 w/OMC is the ratio of water content (w) to optimal moisture content (OMC). The above tests were carried out at about 20°C.

The influence of water content on permanent deformation of construction waste soil subgrade filler was analyzed under confining pressure of 60 kPa and dynamic stress amplitude of 130 kPa. The permanent deformation test results of construction waste soil subgrade filler under different water content were shown in Figure 5.

It can be seen from Figure 5 that the permanent deformation of the sample increases with the increase of water content. At the same time, the permanent deformation of the sample under different water content accumulates rapidly in the early stage of loading, and the growth rate of permanent deformation gradually slows down after about 2000 cycles of cyclic loading, and the difference of permanent deformation change amplitude caused by different water content gradually decreases, indicating that the permanent deformation accumulation of subgrade filler under long-term cyclic loading is affected by the combined effect of water content and cyclic loading times. A similar rule was found in the study of Zhang et al. (2024). In order to facilitate the analysis, the permanent deformation value generated by 10,000 cycles of loading was used as the comparison standard. Compared with the case of water content of 1.0 OMC, the permanent deformation of the specimen with water content of 1.2 OMC increased by 28%, and the permanent deformation of the specimen with water content of 0.8 OMC decreased by 8%. It shows that a small change in water content can cause the permanent deformation of subgrade filler to increase exponentially. In view of this, attention should be paid to the waterproof and drainage problems of subgrade engineering during the operation period. The sand cushion and sand wrapping edge moisture control technology based on the idea of capillary barrier can be used to prevent or delay the wetting of subgrade to ensure strength.

The influence of confining pressure on permanent deformation of construction waste soil subgrade filler was analyzed under water content of 1.2 OMC and dynamic stress amplitude of 130 kPa. The permanent deformation test results of construction waste soil subgrade filler under different confining pressure were shown in Figure 6.

It can be seen from Figure 6 that the permanent deformation of the sample decreases with the increase of confining pressure. Confining pressure has a significant effect on the permanent deformation of subgrade filler. The research shows that although higher confining pressure can enhance the ability of subgrade filler to resist deformation, its permanent deformation characteristics are still affected by factors such as dynamic stress amplitude and water content. It can be seen from the permanent deformation curve that in the previous loading stage, the confining pressure has a great influence on the cumulative axial strain increment, while in the subsequent loading stage, the influence is not so significant. The increase of confining pressure helps to limit the slip between soil particles and keep the sample in a compressed state. Under the action of confining pressure, the permanent deformation development speed of the sample is significantly slowed down, and with the increase of confining pressure amplitude, the slowing effect is more obvious. Similar results were found in the study of Zhou et al. (2022) and Huang et al. (2023). Taking the permanent deformation value generated by 10,000 cycles of cyclic loading as the comparison standard, compared with the case of confining pressure of 60 kPa, the permanent deformation of clay specimens with confining pressure of 90 kPa and 120 kPa is reduced by 30% and 40% respectively. At the same time, it is found that when the confining pressure increases from 60 kPa to 90 kPa, the cumulative rate of permanent deformation of the sample is significantly slowed down. The enhancement of confinement effect caused by the increase of confining pressure makes the permanent deformation transition from plastic creep to plastic stable state under cyclic loading. This shows that confining pressure plays a key role in controlling the permanent deformation of subgrade filler, and has important reference value for engineering design and construction.

The influence of confining pressure on permanent deformation of construction waste soil subgrade filler was analyzed under water content of 1.2 OMC and confining pressure of 60 kPa. The permanent deformation test results of construction waste soil subgrade filler under different dynamic stress amplitude were shown in Figure 7.

It can be seen from Figure 7 that the larger the dynamic stress amplitude, the greater the permanent deformation of the specimen. When the dynamic stress amplitude is at a low level, the permanent deformation of the specimen tends to be stable after a small amount of cyclic loading. It can be found that the permanent deformation of the specimen under the dynamic stress amplitude of 30 kPa and 70 kPa enters a stable state after about 2000 times of loading. When the dynamic stress amplitude reaches 130 kPa, the permanent deformation of the specimen continues to accumulate with the number of cyclic loading, showing plastic creep characteristics. Nie et al. (2020) and Wang et al. (2024) also found a similar phenomenon. Taking the permanent deformation value generated by 10,000 cycles of cyclic loading as the comparison standard, compared with the case of dynamic stress amplitude of 40 kPa, the permanent deformation of clay specimens with dynamic stress amplitude of 70 kPa and 130 kPa increased by 100% and 263%, respectively. This shows that the permanent deformation of subgrade soil in the dynamic influence area of subgrade, especially in the shallow area of subgrade which is significantly affected by dynamic load, will increase significantly with the increase of vehicle axle load. Therefore, it is necessary to strictly control the overload phenomenon in the road engineering during the operation period to ensure that the dynamic deformation of the subgrade is within a reasonable range.

Under cyclic loading, the cumulative strain ε _p of the soil gradually increases with the increase of the number of loading N. This cumulative deformation usually shows that in the initial stage, the cumulative deformation increases rapidly. With the increase of loading times, the cumulative deformation growth gradually slows down. Finally, the cumulative deformation tends to a stable value. This deformation characteristic can be described by an exponential decay function (Ma et al., 2023; Liu et al., 2025).

It is assumed that the relationship between the permanent deformation increment ε _p caused by each loading and the current stress level σ and the loading times N can be expressed as the following permanent deformation increment expression Equation 1: ε p = f σ , N (1)

According to the elastic-plastic behavior and experience of materials, the following forms Equation 2 can be used: ε p = k · σ n · 1 − e − β N (2)

Where, k is the material constant, reflecting the plastic deformation ability of the material; σ is the stress during the loading; n is the stress sensitivity index, reflecting the nonlinear dependence of deformation on stress; β is the loading cycle influence coefficient, reflecting the cumulative effect of loading cycles on the increase in deformation.

In addition to the influence of loading times, confining pressure, dynamic stress amplitude and water content on plastic deformation can not be ignored. Therefore, by adding these factors, the prediction model of permanent deformation of subgrade filling in Formula 3 is finally proposed. ε p N = k · σ o c t σ a t m n w w O M C m · 1 − e − β N (3)

Where, σ _oct is body stress, σ _oct = (σ ₁+2σ ₃)/3; σ _atm is the reference stress, generally at atmospheric pressure (100 kPa); w is the moisture content; w _omc is the optimal moisture content; m is the parameter.

The fitting values of the parameters under different test conditions are shown in Table 3. The fitting results are shown in Figure 8.

According to the analysis results of Table 3 and Figure 8, the proposed prediction model shows excellent agreement with the actual test data when calculating the deformation curve. The fitting correlation coefficient of the model is more than 0.9, which fully proves the rationality and reliability of the model. The model can capture the dynamic changes of test data with high precision, thus providing a powerful tool for predicting the deformation behavior of subgrade soil under cyclic loading. In addition, a significant feature of the proposed prediction model is that it comprehensively considers many key factors such as dynamic stress amplitude, confining pressure and water content. This comprehensive consideration of multiple factors makes the model not only accurately reflect the deformation law of soil under the influence of a single factor, but also more comprehensively describe the complex deformation behavior under the combined action of multiple factors. Therefore, the model has high practical value in practical engineering applications, which can help engineers predict and control the deformation of subgrade soil more accurately, so as to optimize the design and improve the safety and economy of the project.

In order to verify the applicability and accuracy of the proposed mechanical model of permanent deformation of subgrade filler, the test data of subgrade filler in this paper and other subgrade fillers in the existing literature are used to verify the model. The permanent deformation test data of different subgrade fillers of Li et al. (2021), He et al. (2023), Zhang et al. (2024) and Liu et al. (2025) are used for verification, as shown in Table 4. Comparison between measured and predicted values is shown in Figure 9.

According to Table 4 and Figure 9, the proposed prediction model shows high accuracy in predicting the permanent deformation of different types of subgrade fillers. The good agreement between the calculated values and the experimental results verifies the effectiveness of the model in predicting the permanent deformation of subgrade fillers. In addition, the proposed prediction model is verified by selecting the test data of other subgrade fillers in the existing literature. The results further show that the model is not only suitable for specific subgrade fillers, but also has a wide range of applications. The excellent prediction accuracy of the model means that it can be used as an important tool in the engineering design and construction process to help engineers and researchers more accurately predict and control the permanent deformation of subgrade fillers under cyclic loading. This is essential to ensure the long-term stability and durability of road engineering, especially in the face of complex traffic loads and environmental conditions. The wide applicability of the model also shows that it can be adjusted and optimized according to the geological conditions and filling characteristics of different regions to meet different engineering requirements. This flexibility makes the proposed model a powerful analytical tool that can be applied to different engineering projects around the world.