Study on the Permanent Deformation and Dynamic Stress–Strain of Coarse-Grained Subgrade Filler under Cyclic Loading

Abstract

Using coal gangue as a subgrade filler will produce good benefits, and its application prospects are very broad. It is of great engineering and scientific value to study the improvement method and dynamic characteristics of coal gangue subgrade filler under traffic load. Combining the properties of coal gangue material, fly ash and lime and soil were added to improve the bearing behavior of coal gangue subgrade filler. Then, a compaction test was carried out using the principle of orthogonal experimental design. By analyzing the compaction test results, the optimal proportion of each additive was obtained. A large-scale dynamic triaxial test was carried out with the proportion of each admixture in the maximum dry density group in the compaction test. Based on the dynamic triaxial test results, the effect of confining pressure on the permanent strain was analyzed, the analysis model of permanent deformation and cycle number of traffic loading was proposed, and the correctness of the model was verified. In addition, a modified Hardin–Drnevich model was established, which can describe the dynamic stress–dynamic strain curve of coal gangue subgrade filler under traffic load, and then, the dynamic modulus and damping ratio were analyzed.

1. Introduction

Coarse-grained filler is widely used in subgrade structures due to its excellent compaction performance, high filling density, and high shear strength [1,2]. Due to the dispersed behavior of coarse-grained filler, the subgrade has become the weakest and most unstable structure in the entire road structure and has become the main factor leading to road deformation. Vehicle load has the characteristics of low frequency and low amplitude and is a long-term cyclic load. Although the stress level of the vehicle load is much lower than the static shear strength of the subgrade filler, under the effect of many load cycles, the subgrade filler will produce excessive permanent deformation, leading to the loss of functionality of the subgrade structure and damage, thereby causing engineering problems such as road unevenness and uneven settlement [3].

Coal gangue consists of a large number of crushed rock particles and fine particles whose properties are very close to that of soil, which is a good coarse-grained filler material. Using coal gangue as a subgrade filler will produce good benefits, and its application prospects are very broad. Therefore, it is of great engineering and scientific value to study the improvement method and dynamic characteristics of coal gangue subgrade filler under traffic load. Zhang et al. [4,5] investigated the permanent deformation of coal gangue subgrade filler and established a unified analysis model under traffic cyclic loading. This model can describe plastic shakedown, plastic creep, and incremental collapse [6,7] types using a unified relationship, providing important application value for the study of permanent deformation. There are few investigations in the study of the dynamic characteristics of coal gangue subgrade filler, but the study of the dynamic properties of other coarse-grained subgrade fillers can provide this article with good reference value. He et al. [8] studied the relationship between the permanent deformation of coarse-grained soil and the stress level, compaction degree, moisture content, and loading frequency under cyclic loading triaxle testing and found that permanent deformation increases with the increase in partial stress and moisture content and decreases with the increase in compaction degree.

To study the permanent deformation and dynamic properties of coarse-grained subgrade filler, two types of methods have been proposed [9,10]. The first approach is to develop an analysis model to predict the relationship between permanent deformation and loading cycles [11,12,13,14,15,16]. The purpose of this method is to calculate the deformation of the coarse-grained subgrade filler. The second emphasizes quantitative evaluation of the developing tendency to permanent deformation [17]. In addition, the particle breakage of coarse-grained subgrade filler under different loads has also received attention from many scholars [18,19,20].

At present, there is still a lack of clear understanding of the permanent deformation and dynamic stress–strain of coarse-grained subgrade filler under cyclic loading. Therefore, this project improved coal gangue subgrade filler by adding fly ash, lime, water, soil, and other materials, and we conducted an in-depth study on its dynamic characteristics under traffic cyclic load.

2. Materials

2.1. Material Sampling

The coarse-grained subgrade filler used in this test is coal gangue (a solid waste derived from a coal mine located in Xiangtan City of Hunan Province, China). Coal gangue accumulated in the mining area is displayed in Figure 1. Coal gangue is a mixture of various types of crushed stones and fine-grained soil. Currently, the amount of emissions and required storage area are huge, but the utilization rate is relatively low. Piled-up coal gangue results in many environmental issues. For example, a large area of land is occupied, air pollution is brought about by dust, water pollution is induced by heavy metals, and geological disasters led by coal gangue mountains have been generated [4,21]. Hence, the extensive use of accumulated coal gangue is an urgent issue that needs to be addressed.

The crushed stone materials used in the construction of subgrade filler need to be obtained from nearby quarries. The predatory mining of quarries has a significant impact on the surrounding ecological environment. If coal gangue that meets the road use requirements within the scope of highway construction can be used instead of crushed stone materials, this can not only reduce the problem of coal gangue accumulation and the impact of quarries on the surrounding ecology and reduce the cost of highway construction but also achieve significant economic, social, and environmental benefits. The use of coal gangue as subgrade filler material has obvious advantages. First, there are no special requirements for the type and quality of coal gangue, and there are no strict restrictions on the content of harmful components. Multiple types of coal gangue can be applied. Second, the application of coal gangue in subgrade engineering has the advantages of high consumption, no need for special treatment, and no need for special technical means. Using it as subgrade material is an effective way to extensively utilize coal industry waste, effectively reduce coal gangue accumulation, and save road construction costs. Therefore, coal gangue has broad application prospects as subgrade filler material. For instance, the Benghuai Expressway, Hehuaifu Expressway, Qinglan Expressway, and Pingdingshan Linru Expressway have all used coal gangue as subgrade filler [21].

2.2. Properties of the Material

In order to eliminate the influence of initial moisture content, the coal gangue was transported to the laboratory and fully dried in a drying box for later use. The liquid limit, plastic limit, and CBR are 0.1231, 0.2911, and 0.2325, respectively.

An X-ray diffractometer was used to analyze the mineral composition of the coal gangue. The test results are shown in Figure 2. The main mineral composition of coal gangue was determined as follows: quartz 41.24%, calcite 26.57%, illite 15.31%, kaolinite 11.43%, chlorite 4.11%, feldspar 1.02%, and other 0.32%.

3. Tests

3.1. Compaction Test Plan

Combined with the inherent properties of coal gangue material, the mechanical properties of coal gangue can be improved by adding material. Because coarse-grained subgrade filler includes many coarse particles and the content of fine particles is small, to make the grade of coarse-grained subgrade filler more uniform and ensure that the coarse particles take on the role of the skeleton, clay soil was added for improvement, and the soil content was 0%, 4%, 8%, and 12%. Considering that coal gangue has many oxides of Si, Al, Ca, and other elements, by adding fly ash and lime, it can be activated when exposed to water to improve its bearing capacity. Meanwhile, considering costs, only a small amount of lime and fly ash should be added. Therefore, the fly ash content should be 0%, 2%, 4%, and 6%, the lime content should be 0%, 3%, 6%, and 9%, and the water content should be 0%, 6%, 12%, and 18%. Based on the principle of orthogonal experimental design, a four-factor and four-level orthogonal table was used to design the compaction test scheme (shown in

Table 1. Compaction test plan.

Number	Fly Ash%	Lime%	Water%	Soil%
1	0	0	0	0
2	0	3	5	6
3	0	6	10	12
4	0	9	15	18
5	2	0	5	12
6	2	3	0	18
7	2	6	15	0
8	2	9	10	6
9	4	0	10	18
10	4	3	15	12
11	4	6	0	6
12	4	9	5	0
13	6	0	15	6
14	6	3	10	0
15	6	6	5	18
16	6	9	0	12

).

Based on the experimental plan in Table 1, the dry density of the sample was obtained using a heavy compactor.

3.2. Large-Scale Dynamic Triaxial Test Scheme

Dry density is an indicator of the density of the sample, and the higher the dry density, the denser the sample under this condition. Therefore, based on the dry density determined using the above compaction test as the control index, a large-scale triaxial test was carried out with the proportion of each admixture in the maximum dry density group. The compaction degree was 96%, and the generation of a large triaxial sample was controlled by the dry density. The device uses a sine wave to simulate traffic load to carry out dynamic characteristic tests, and the dynamic loading frequency was set at 1 Hz. The large-scale triaxial test of coal gangue subgrade filler requires the preparation of nearly 80 kg of test material for each sample, which has a long test period, high costs, and difficulty in sample production. Therefore, the large-scale dynamic test was carried out on the basis of the maximum dry density group of admixture proportion.

The loading methods of large-scale dynamic triaxial tests can be divided into two categories. The first type of loading is as follows: combined with the actual traffic load, the axial dynamic load amplitude is 200 kPa, the traffic cyclic load is 30,000 times, and the confining pressures are 25 kPa, 50 kPa, 100 kPa, 150 kPa, 200 kPa, and 300 kPa. The tests were repeated three times under each test condition, and a total of 18 groups of tests were carried out in this test. This experiment is mainly used to study the variation in permanent deformation of samples under different confining pressure conditions. The second type of loading method is as follows: the dynamic amplitude of the axial load of the same sample is successively taken as 50 kPa, 70 kPa, 90 kPa, and so on. The confining pressures of different samples were taken as 25 kPa, 50 kPa, 100 kPa, 150 kPa, and 200 kPa until the loading failure of the samples, and the tests were repeated three times under each test condition. A total of 18 groups of tests were carried out in this test, which was mainly used to study the dynamic constitutive model of the samples under traffic load and the changes in relevant dynamic parameters.

3.3. Analytical Methods

The methods in these tests were carried out with reference to JTG3430-2020 [22] highway geotechnical test regulations.

First of all, the coal gangue and each admixture were prepared according to the scheme shown in Table 1. Then, the coal gangue was fully stirred, and then, the coal gangue was sealed and placed for more than 6 h to make full contact. Then, the dry density index of the sample was obtained using the heavy compaction test (Figure 3). The heavy compactor is shown in Figure 3a, and the experimental equipment parameters are as follows: hammer mass of 4.5 kg, hammer drop height of 45 cm (Figure 3b), inner diameter and height of the sample cylinder of 15.2 cm and 17 cm, respectively, sample volume of 2177 cm³ (Figure 3c), compacted in three layers with 98 blows per layer, and maximum particle size of 40 cm. The dry density after the experiment was obtained using Equation (1):

$${\rho }_d=\frac{\rho }{1+0.01\omega }$$

(1)

where ρ_d is the dry density (g/cm³); ρ is the wet density (g/cm³); and ω is the moisture content (%).

The large-scale dynamic triaxial test was conducted using a large dynamic and static triaxial test instrument, as shown in Figure 4. The experimental steps included sample preparation, saturation, consolidation, and loading. The detailed test steps are as follows: first, during sample preparation, the sample size was $\varphi$300 mm × 600 mm, and the sample was prepared using the dry packing method. The coarse-grained subgrade filler was divided into five equal parts for preparation and then each particle part was mixed thoroughly and evenly. The layered vibration method was used to compact each layer of particles to a given height. After each layer of particles was compacted, the surface became rough, and then, the next layer of particles was compacted. During the manual compaction process, the particles were gently pressed with a compaction hammer, and the position of the particles was continuously adjusted through dynamic disturbance to achieve the goal of compaction, avoiding particle breakage as much as possible during the compaction process. By controlling the mass and height of each layer of particles, the goal of controlling the compaction degree of the sample was achieved. Second, during sample saturation, once sample preparation was complete, the sample in the pressure chamber was placed into the loading device. The sample was saturated using the reverse pressure saturation method, and then, the saturation of the sample was checked using the B-value. When the B-value was greater than 0.95, the sample was considered to have reached the saturation requirement. Third, during sample consolidation, the consolidation of the sample was carried out using the method of isobaric consolidation, during which the water inside the sample was discharged through a volumetric tube. Once consolidation was complete, the sample was loaded. Fourth, during sample loading, when the sample reached the given cycle numbers or the accumulated axial strain of the sample reached 15%, it was considered that the sample had been damaged.

4. Test Results and Analysis

4.1. Hydration Effect Analysis

Through the above compaction test, the maximum dry density of the samples of each group was obtained, and the maximum dry density of the samples of the eighth group was obtained, that is, the proportion of each additive was 2% fly ash, 9% lime, 10% water, and 6% soil, and the maximum dry density was 2.27 g/cm³.

The reasons for this phenomenon are explained as follows: the above analysis of coal gangue materials shows that the materials in this study contain a large number of compounds of Si, Al, Ca, and other elements, and the coal gangue containing these substances will undergo hydration reactions in the presence of water after adding fly ash and lime, thereby generating calcium hydroxide, calcium silicate hydrate, calcium aluminate hydrate, and carbonate crystals. The structure of the sample is continuously improved with the progress of the hydration reaction so that the strength and water stability of the sample are continuously improved and the compaction effect and bearing performance of the sample are enhanced.

4.2. Analysis of the Permanent Deformation of Coal Gangue Samples under Traffic Load

Traffic load acts on the subgrade for a long time, and researchers and those involved in construction tend to pay more attention to the long-term permanent deformation of the subgrade rather than paying special attention to the deformation of each cyclic load application process. Therefore, the permanent deformation of coal gangue subgrade filler after a large-scale dynamic triaxial test is studied in this section.

Typical samples before and after the large-scale triaxial test are shown in Figure 5. It can be seen that during the loading process, the sample is subjected to traffic load and confining pressure, and the upper and lower parts of the sample are squeezed to the middle, resulting in the failure mode of the sample mainly in the form of the middle bulge.

The curves of the permanent strain of coal gangue subgrade filler and the number of traffic cyclic loads under different confining pressure conditions are shown in Figure 6. It can be seen from Figure 6 that the relationship between the axial permanent strain of coal gangue and the number of vibration times of cyclic loads under traffic cyclic loads can be divided into three parts: first, the rapid increase stage. With the increase in cycle times, the curve presents an approximate linear increase. Then comes the slow growth stage, where the degree of curve growth gradually becomes slow, and with the increase in the number of cycles, curve growth gradually decreases. Finally, in the basic stability stage, the permanent strain basically tends to no longer change, and the curve changes very little.

As shown in Figure 6, when the confining pressure increases from 25 kPa to 300 kPa, the permanent deformation of coal gangue samples decreases by 2.37%, 1.62%, 0.90%, 0.35%, and 0.23% in turn. Therefore, the influence of confining pressure on the permanent strain of the sample is significant, and the permanent strain of the sample gradually decreases with the increase in confining pressure. When the confining pressure is low, the increase in confining pressure leads to a large reduction in the permanent deformation of the sample, but when the confining pressure is high, the increase in confining pressure leads to a small reduction in the permanent deformation of the sample.

Regression analysis of the relationship between the permanent strain of coal gangue samples under cyclic traffic loading and vibration times under cyclic load found that the following model can be used to express it:

$$\epsilon =\alpha N^{\beta }$$

(2)

where ε is the permanent strain (%) of the coal gangue sample; N is the vibration number of traffic cyclic load; and α and β are the fitting parameters of the model.

Figure 7 shows the comparison between the above model and the test results, and

Table 2. Model parameters.

Confining Pressure	$\mathit{\alpha }$	$\mathit{\beta }$	R2
25 kPa	1.9733	0.1113	0.9886
50 kPa	2.4815	0.042	0.9712
100 kPa	1.1731	0.0593	0.9807
150 kPa	0.2349	0.1617	0.9762
200 kPa	0.4016	0.0793	0.9773
300 kPa	0.2816	0.0837	0.9524

shows the model parameters. It can be seen from Figure 7 and Table 2 that the permanent deformation calculation model established in this paper can suitably describe the relationship between the permanent deformation of coal gangue subgrade filler and the vibration number of traffic cyclic load.

4.3. Dynamic Constitutive Analysis of Coal Gangue Filler under Traffic Load

Figure 8 shows the dynamic stress–dynamic strain relationship curve of the coal gangue subgrade filler under traffic load. It can be seen from the figure that the dynamic stress of the sample increases with the increase in dynamic strain. The greater the confining pressure, the greater the dynamic stress when the specimen is destroyed.

In order to further analyze the dynamic constitutive relationship of coal gangue samples under traffic load, the Hardin–Drnevich model was introduced to analyze the dynamic constitutive relationship of coal gangue subgrade filler, and its expression is as follows:

$${\sigma }_d=\frac{{\epsilon }_d}{\frac{1}{E_{d\mathit{max}}}+\frac{{\epsilon }_d}{{\sigma }_{d\mathit{max}}}}$$

(3)

where ${\sigma }_{dmax}$ is the maximum dynamic stress, $E_{dmax}$ is the maximum dynamic modulus, ${\sigma }_d$ is dynamic stress, and ${\epsilon }_d$ is the dynamic strain.

According to the changes in the curve in Figure 8, it can be seen that the dynamic stress–dynamic strain relationship of the sample does not present a good hyperbolic type, so it does not fully conform to the Hardin–Drnevich model in Equation (2), and it needs to be modified. The following correction coefficients were introduced:

$${\gamma }_h=\frac{{\gamma }_d}{{\gamma }_r}\beta$$

(4)

$$\beta =1+a{e}^{-b\frac{{\gamma }_d}{{\gamma }_r}}$$

(5)

The expression of the Hardin–Drnevich model in the shear state is as follows:

$$\frac{{\tau }_d}{{\tau }_{d\mathit{max}}}=\frac{\frac{{\gamma }_d}{{\gamma }_r}}{1+\left|\frac{{\gamma }_d}{{\gamma }_r}\right|}$$

(6)

where ${\tau }_d$ is shear stress under dynamic force; ${\gamma }_d$ is the shear strain under dynamic force; ${\tau }_{d\mathit{max}}$ is the maximum dynamic shear stress; ${\gamma }_r$ is the reference strain, ${\gamma }_r={\tau }_{dmax}/G_{dmax}$, $G_{dmax}$ is the maximum dynamic shear modulus; and β, a, and b are correction coefficients.

By replacing ${\gamma }_d/ {\gamma }_r$ in Equation (6) with ${\gamma }_h$, the modified Hardin–Drnevich model can be obtained from Equations (3)–(6) as follows:

$${\sigma }_d=\frac{{\epsilon }_d{E}_{d\mathit{max}}\left(1+a{e}^{-b\frac{{\epsilon }_d{E}_{d\mathit{max}}}{{\sigma }_{d\mathit{max}}}}\right)}{1+\left|\frac{{\epsilon }_d{E}_{d\mathit{max}}\left(1+a{e}^{-b\frac{{\epsilon }_d{E}_{d\mathit{max}}}{{\sigma }_{d\mathit{max}}}}\right)}{{\sigma }_{d\mathit{max}}}\right|}$$

(7)

Figure 9 shows the comparison between the revised Hardin–Drnevich model and the test data. It can be seen from the figure that the revised model can suitably describe the dynamic stress–dynamic strain relationship curve of coal gangue subgrade filler under traffic load, thus verifying the correctness of the derived model.

Dynamic shear modulus is an important parameter for the analysis of the dynamic characteristics of subgrade filler. The calculation method is as follows:

$$G_d=\frac{G_{d\mathit{max}}}{1+\frac{{\gamma }_d}{{\gamma }_r}}$$

(8)

Combined with the modified Hardin–Drnevich model, its expression is as follows:

$$E_d=\frac{E_{d\mathit{max}}}{1+{\gamma }_h}=\frac{E_{d\mathit{max}}}{1+\frac{{\epsilon }_d{E}_{d\mathit{max}}\left(1+a{e}^{-b\frac{{\epsilon }_d{E}_{d\mathit{max}}}{{\sigma }_{d\mathit{max}}}}\right)}{{\sigma }_{d\mathit{max}}}}$$

(9)

The dynamic modulus of the sample was calculated using Equation (9). Figure 10 shows the variation law of the dynamic modulus of coal gangue samples under dynamic traffic load. It can be concluded from the figure that the dynamic modulus decreases with the increase in dynamic strain and increases with the increase in confining pressure.

The damping ratio can reflect the energy loss during cyclic loading. The calculation method is as follows:

$$\lambda =\frac{1}{4\pi }\frac{\mathsf{\Delta }W}{W}$$

(10)

where $\lambda$ is the damping ratio; $\mathsf{\Delta }W$ is the energy loss under a single cycle load; and $W$ is the total energy.

The damping ratio of the sample was calculated from Equation (10). Figure 11 shows the variation law of the damping ratio of the sample. It can be seen from the figure that the damping ratio shows a decreasing variation law with the increase in dynamic strain and confining pressure.

5. Conclusions

(1) Combining the properties of coal gangue material, fly ash, lime, and soil were added to improve the bearing behavior of coal gangue subgrade filler. Then, a compaction test was carried out using the principle of orthogonal experimental design. By analyzing the compaction test results, the optimal proportion of each additive was obtained.

(2) A large-scale dynamic triaxial test was carried out with the proportion of each admixture in the maximum dry density group in the compaction test. Based on the dynamic triaxial test results, the effect of confining pressure on the permanent strain was analyzed, the analysis model of permanent deformation and cycle numbers of traffic loading was proposed, and the correctness of the model was verified.

(3) The dynamic stress of the sample increases with the increase in the dynamic strain; the greater the confining pressure, the greater the dynamic stress when the specimen is destroyed. A modified Hardin–Drnevich model was established, which can describe the dynamic stress–dynamic strain curve of coal gangue subgrade filler under traffic load.

(4) The dynamic modulus of coal gangue samples under traffic load decreases with the increase in dynamic strain and increases with the increase in confining pressure. The damping ratio decreases with the increase in dynamic strain and confining pressure.