J. Cent. South Univ. (2020) 27: 2043-2053

DOI: https://doi.org/10.1007/s11771-020-4429-4

Experimental study of dynamic resilient modulus of subgrade soils under coupling of freeze–thaw cycles and dynamic load

ZHAO Yang(赵阳)^{1, 2}, LU Zheng(卢正)^{1, 3}, YAO Hai-lin(姚海林)¹,GU Fan(顾凡)^{4, 5}, DUAN Ya-hui(段亚辉)⁶

1. State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil

Mechanics, Chinese Academy of Sciences, Wuhan 430071, China;

2. University of Chinese Academy of Sciences, Beijing 100049, China;

3. Hubei Key Laboratory of Geo-Environmental Engineering, Wuhan 430071, China;

4. National Engineering Laboratory of Highway Maintenance Technology, Changsha University of Science & Technology, Changsha 410114, China;

5. National Center for Asphalt Technology, Auburn University, Auburn 36830, USA;

6. School of Urban Construction, Wuchang University of Technology, Wuhan 430023, China

Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2020

Abstract: Although the dynamic properties of subgrade soils in seasonally frozen areas have already been studied, few researchers have considered the influence of shallow groundwater during the freeze–thaw (F–T) cycles. So a multifunctional F–T cycle system was developed to imitate the groundwater recharge in the subgrade during the freezing process and a large number of dynamic triaxial experiments were conducted after the F–T cycles. Some significant factors including the F–T cycle number, compaction degree, confining pressure, cyclic deviator stress, loading frequency, and water content were investigated for the resilient modulus of soils. The experimental results indicated that the dynamic resilient modulus of the subgrade was negatively correlated with the cyclic deviator stress, F–T cycle number, and initial water content, whereas the degree of compaction, confining pressure, and loading frequency could enhance the resilient modulus. Furthermore, a modified model considering the F–T cycle number and stress state was established to predict the dynamic resilient modulus. The calculated results of this modified model were very close to the experimental results. Consequently, calculation of the resilient modulus for F–T cycles considering the dynamic load was appropriate. This study provides reference for research focusing on F–T cycles with groundwater supply and the dynamic resilient moduli of subgrade soils in seasonally frozen areas.

Key words: dynamic resilient modulus; freeze–thaw cycles; dynamic load; dynamic triaxial test; prediction model

Cite this article as: ZHAO Yang, LU Zheng, YAO Hai-lin, GU Fan, DUAN Ya-hui. Experimental study of dynamic resilient modulus of subgrade soils under coupling of freeze–thaw cycles and dynamic load [J]. Journal of Central South University, 2020, 27(7): 2043-2053. DOI: https://doi.org/10.1007/s11771-020-4429-4.

1 Introduction

As an important index in the design of subgrade structures, the dynamic resilient modulus describes typically the mechanical properties of subgrade under traffic load [1]. Since SEED et al [2] proposed this concept, numerous experiments have been performed to determine the dynamic resilient modulus of soils. For example, LIU et al [3] and BLACKMORE et al [4] conducted many experiments to investigate the effects of the degree of compaction, stress level, and moisture content on the resilient modulus. The increment of confining pressure and degree of compaction can contribute to higher dynamic resilient modulus. By contrast, it decreases with increasing moisture content and axial stress. Furthermore, the effect of temperature on dynamic resilient modulus has been studied by CHRIST et al [5]. Many scholars, with the exception of experimental research, studied the prediction model of resilient modulus. Experimental methods, models with stress, and models including the matric suction are the main categories of resilient modulus models [1, 6]. YAO et al [7] proposed a new prediction model that considers stress and matric suction and mitigates the nonuniformity of bulk stress. Moreover, BHUVANESHWARI et al [8], KALOOP et al [8], and PATEL et al [10] developed many prediction models for different soil categories.

These above-mentioned contents do not involve the impact of the freeze-thaw (F-T) tests. However, F-T cycles are the indispensable factor for studying the subgrade in the seasonally frozen area. Based on the experiments of F-T cycles in closed system, ISHIKAWA et al [11] studied the effect of dynamic resilient modulus of in-service pavement. The experiment results indicated that F-T cycles can damage the pavement structures and the service life seriously. QI et al [12] claimed that the resilient modulus of compacted soils was reduced obviously after F–T cycles. LU et al [13] proposed the cement can improve the frost resistance of expansive soils and conducted several groups of experiments to study the resilient modulus of modified expansive soils after F-T tests. TIAN et al [14] claimed that F-T cycles and stress levels had a considerable impact on dynamic resilient modulus and proposed a model that could be used for coarse-grained materials to predict dynamic resilient modulus.

Many researchers have investigated the resilient modulus of compacted soils by considering and neglecting F-T cycles. The studies that considered F-T cycles were mainly conducted in closed systems. However, the groundwater supply is a substantial factor in the study of F-T cycles of subgrade [15]. In engineering practice, subgrade often contains shallow groundwater during the freezing process. Therefore, for determining the resilient moduli of compacted subgrade soil under coupled F-T cycles (open system) and dynamic loads, the multifunctional F-T system (open system) was developed, which can simulate the water supply of groundwater. The influence of F-T cycles, stress level, and soil physical state on the dynamic resilient modulus of the subgrade compacted soils was studied by conducting the F-T cycle test and dynamic triaxial tests. Finally, a modified model predicting the resilient modulus was proposed and verified by experimental data.

2 Experiment

2.1 Materials

The soil specimens originated from the Songhua River, China. Table 1 shows the physical indexes of the soil specimens. According to JTG E40-2007 [16], the soil type is low liquid-limit clay.

Table 1 Basic physical properties of soil

All soil samples were dried and sieved (2 mm grid). Subsequently, the air-drying moisture content was determined, and the final soil samples were prepared based on the required soil amount and target water content. Samples with three different water contents (12.6%, 14.6% and 16.6%) and three different compaction degrees (93%, 95% and 97%) with cylindrical forms (height of 76 mm, diameter of 38 mm) were prepared. Then, the soil samples used for the F-T cycles and dynamic triaxial tests were sealed airtightly in plastic wrap and place in a constant temperature and humidity chamber.

2.2 Test apparatus

The multifunctional F-T system (open system) developed by the research team can be used to simulate the F-T cycles of subgrade soil in the natural environment; that is, external water is supplied during the freezing process. The F-T cycle system consists of four parts: sample cylinder and thermal insulation device, temperature control system, supplementary water supply system, and monitoring and data acquisition system. The special device of this F-T cycle system is the supplementary water supply system, which consists of four Markov bottles that are connected to the bottom of the soil samples by silicone tubes. Furthermore, the water surface in the Markov bottles is at the same height as the bottom of the soil specimens; thus, water can be supplied without pressure. During the tests, Markov bottles supply the soil samples with external water; the water valve is closed during the thawing process. So, it can simulate the situation of groundwater supplying in the F-T cycles of subgrade. The SPAX-2000 produced by the American GCTS Company was used to perform dynamic triaxial tests on the remolded soil specimens after the F-T tests. The test apparatuses are shown in Figure 1.

Figure 1 Dynamic triaxial test system

2.3 Test procedures

The following numbers of test cycles were applied in the experiments: N_FT=0, N_FT=1, N_FT=3, N_FT=5 and N_FT=7, where N_FT is the number of F-T cycles. During the F-T cycles, the soil specimens were in a chamber that maintained the temperature between -30 to 30 °C according to the temperature statistics of a local meteorological bureau at the Songhua River mainstream in Northeast China. The F-T cycle number must be confirmed based on the multifunctional F-T system (open system) before conducting the F-T tests. The experiments lasted for 8 h (frozen) and 4 h (thawed), respectively.

The remolded soil specimens after F-T tests were taken for the dynamic triaxial test. The dynamic resilient modulus test procedure schedule is shown in Table 2, and the corresponding loading sequence is shown in Table 3 by referring to Ref. [17]. The loading sequence includes two steps: preloading and testing. Preloading eliminates incomplete contact between the soil samples and the platform of the device. Subsequently, the corresponding half plus load was applied (Table 3).

Table 2 Test procedure for determining dynamic resilient modulus

Table 3 Loading sequence

After conducting the dynamic resilient modulus test, the data of last five sets were extracted to figure up the resilient modulus of samples by Eq. (1):

                               (1)

where M_R is the dynamic resilient modulus, MPa; σ_d is the cyclic deviator stress, kPa; and ε_R is the average resilient strain for the last 5 cycles of each loading sequence.

3 Results and discussion

3.1 Influence of F-T cycles

Due to the volume of data, the soil specimens with 1 Hz loading frequency, 93% degree of compaction, and 12.6% initial moisture content were chosen for the investigation, as shown in Figure 2. The test data correspond to an average of four parallel specimens, and the standard deviations of the data are indicated by error bars in Figure 2. The coefficient of variation is below 15%. From the experimental data as a whole, dynamic resilient modulus declines as the N_FT growing. When N_FT increases from zero to one, the dynamic resilient modulus decreases sharply and decreases by 27.3%,60.0%, 55.8% and 53.1% on average under different confining stresses. Hence, the resilient modulus is mainly affected by the first F-T cycle. The value of resilient modulus gradually tends to a certain range after three F-T cycles. The reasons are as follows: much moisture migrates to the frozen zone when the soil samples experience F-T cycles with external water replenishment, which causes the volume of the specimens to expand. The frost heave is higher than the thawing settlement after the melting process, which causes the dynamic resilient modulus to decrease sharply. However, the porosity of the soil samples stabilizes with increasing number of cycles. In this case, the mechanical properties and physical state of the specimens after multiple F-T cycles stabilize. WANG et al [18] demonstrated that soil samples with a higher compaction degree after many F-T cycles tend to be loose, whereas soil specimens with a lower compaction degree tend to be dense. Part of the data of soil specimens under seven F-T cycles is greater than the value under five F-T cycles in this study. The phenomenon may be due to the lower compaction degree. But it still needs future research to verify this view.

Figure 2 Variation in dynamic resilient modulus versus N_FT:

3.2 Influence of initial moisture content

Most researchers have concentrated on studying the impact of F-T on moisture content in closed systems. Therefore, the water content distribution of soil specimens after F-T tests in an open system should be determined before conducting dynamic triaxial tests. The distributions of the moisture content along the height direction after various F-T cycles in an open and a closed system are shown in Figure 3, respectively. Compared with that of the closed system, the water content of soil specimens under several F-T cycles in the opened system changes greatly. The lower part of soil samples in which initial moisture content is 14.6% and compaction degree is 95%, after a single F-T cycle, reaches the saturated state in opened system, while the soil specimens reach the saturated state or the oversaturated state as N_FT=3. In addition, the quantity of water migration in the opened system is much larger than the value in the closed system. Overall samples in closed system have not been reached the saturated state.

Figure 3 Distribution of moisture content along height direction after F-T cycles in opened system and closed systems:

The distribution of the water content along the height direction of soil specimens with various initial moisture contents after 3 F-T cycles (opened system and closed system) with k=0.95 is shown in Figure 4. As shown, the water content of soil specimens along the height direction stabilizes after the F-T in opened system. By contrast, the water content after F-T cycles in the closed system forms a moisture gradient due to the water migration.

Figure 4 Moisture content distribution of compacted soil in open and closed systems:

After the above test results analyzed, the soil samples after F-T cycles in opened-system were conducted to dynamic triaxial experiments. Figure 5 presents the experimental data of resilient modulus changing with the initial moisture content under different degree of compaction. The soil specimens were used for this evaluation with the N_FT of three, confining pressure of 60 kPa, and loading frequency of 1 Hz. It’s obvious that the growth of initial water content contributes to lessening of dynamic resilient modulus and the attenuation rate on the left part of the optimum moisture content is slightly larger than that on the right part. On the basis of the experimental results of 93% degree of compaction, the resilient modulus declines by 21.15%, as cyclic deviator stress is 30 kPa and initial moisture content increases from 12.6% to 14.6%. The reduction rate of dynamic resilient modulus is 6.5% when the initial moisture content increases from 14.6% to 16.6%. The soil samples with various initial moisture contents approach the saturated or oversaturated state after several F-T tests. Owing to the higher initial moisture content, after multiple F-T cycles, the soil specimens are more likely to reach the saturated state. Furthermore, their resilient modulus approaches the values of saturated soil samples. Therefore, the attenuation rate of dynamic resilient modulus decreases in the opened system, as initial moisture content increases.

Figure 5 Variation in dynamic resilient modulus versus initial moisture content:

3.3 Influence of compaction degree

For the soil specimens discussed in this section, the N_FT was three, confining pressure was 60 kPa, and loading frequency was 1 Hz. As Figure 6 shown, dynamic resilient modulus increases in varying degrees and the growth rate declines slightly with the enhance of compaction degree. The results of the specimens with a cyclic deviator stress of 40 kPa are discussed herein. The average growth rates of the dynamic resilient moduli are 68.1% and 20.3% when the compaction degree increases gradually, respectively. This is because soil samples with relatively low compaction degree have higher porosity, which causes greater structural damage in the samples after several F-T cycles. By contrast, the soil samples with relatively high compaction degrees exhibit few pores. The lower porosity hinders the migration of water during the F-T cycles. After thawing, the porosity increases slightly, which causes weak damage to the structure of the compacted soil and is slightly influenced by the F-T cycles.

3.4 Influence of cyclic deviator stress and loading frequency

The test data for the soil specimens with one F-T cycle, 95% compaction degree, and 12.6% initial moisture content are shown in Figure 7. The cyclic deviator stress and resilient modulus have negative correlation, and the attenuation rate is approximately constant. At a confining pressure of 30 kPa, the dynamic resilient modulus decreases by 12.8%, 14.3% and 13.7% with increasing cyclic deviator stress at a loading frequency of 1 Hz. The loading frequency is another factor that affects the dynamic resilient modulus. The higher the loading frequency, the greater is the dynamic resilient modulus. The reason for the change in the resilient modulus is that the particle structure of the soil is easily affected by the dynamic load. The structure of soil is damaged and rearranged by the cyclic deviator stress, which results in a decrease of dynamic resilient modulus.

Figure 6 Variation in dynamic resilient modulus versus compaction degree:

Figure 7 Variation in dynamic resilient modulus versus dynamic stress:

3.5 Influence of confining pressure

The loading frequency, compaction degree, and water content of the soil specimens used for evaluation are 1 Hz, 93% and 12.6%, respectively. As Figure 8 shows, resilient modulus arises with the enhance of confining pressure under different N_FT cycles, while the growth rate decreases in different degrees. Regarding the soil samples with one F-T cycle, the average increases in the dynamic resilient modulus are 35.42%, 24.84% and 17.36% when confining pressure gradually arises from 15 to 60 kPa. The volume increases, the porosity increases, and the resistance to deformation decreases after the specimens subjected to several F-T tests, because of the relatively small confining pressures. By contrast, the higher confining pressure limits the previously mentioned deformation, which increases the dynamic resilient modulus and decreases the porosity. However, the porosity cannot be eliminated because the confining pressure increases to a certain value. Thus, the porosity reduction rate decreases slightly.

Figure 8 Variation in dynamic resilient modulus versus confining stress:

4 Modification of prediction model for resilient modulus

Many researchers have developed many prediction models for the resilient modulus. The more applicable models are the composite models, which can be mainly classified into the Uzan model, octahedral shear stress model, UT-Austin model [19], and Ni model. These models include mainly the effect of the stress and do not consider the F-T cycles. However, experimental results demonstrate that F-T tests in opened system have a significant influence on the dynamic resilient modulus. Therefore, the F-T cycles were considered and modified based on the UT-Austin model [19] in this study. The equation of the modified model is as follows:

                       (2)

where N is N_FT, and k₁, k₂, k₃ and k₄ are the corresponding fitting coefficients.

Based on a fit of the test data at 1 Hz according to Eq. (2), the calculated results are shown in Table 4. The first number of the soil sample name indicates the initial moisture content, and the second number represents the compaction degree.

According to Table 4, the modified model exhibits a good fit. However, Eq. (2) doesn’t reflect the effect of stress level and soils physical state on the dynamic resilient modulus. Therefore, the test data are examined again with Eq. (2) and Table 4: lnk₁, k₂, k₃ and k₄ can be calculated by polynomial fitting with the compaction degree and initial moisture content. The fitted expressions are as follows:

Table 4 Fitting results

       (3)

       (4)

       (5)

            (6)

where A₁₁–A₄₅ are the fitting coefficients of the experimental result: A₁₁=-2997, A₁₂=66.65, A₁₃= -19.34, A₁₄=-0.3742, A₁₅=-0.2677, A₁₆=-0.203, A₂₁=-343.1, A₂₂=7.348, A₂₃=-0.6536, A₂₄= -0.03873, A₂₅=-0.000235, A₂₆=0.02125, A₃₁=-324, A₃₂=6.989, A₃₃=-0.9367, A₃₄=-0.03729, A₃₅= 0.006242, A₃₆=0.01085, A₄₁=2114, A₄₂=-75.85, A₄₃=176.7, A₄₄=0.5653, A₄₅=-1.853.

Based on Eqs. (2)-(6) mentioned above and experimental data, the modified model was verified and analyzed. The calculations for the dynamic resilient modulus at 12.6% initial water content, 93% degree of compaction, and 60 kPa confining pressure are shown in Figure 9(a). Figure 9(b) presents the calculation results of dynamic resilient modulus of soil samples with initial moisture modulus of 12.6%, compaction degree of 93% and F-T cycles. Evidently, the modified prediction model represents low liquid-limit clay very well.

5 Conclusions

1) The dynamic resilient modulus was greatly influenced by the first F-T cycle. It decreases by 27.3%, 60.0%, 55.8% and 53.1% on average at the different confining stresses and stabilizes after three F-T cycles.

2) The particular variation in the moisture content depends on whether water is supplied during the freezing process, which causes an imbalance in the attenuation rate.

Figurre 9 Model verification:

3) The compaction degree and confining pressure can enhance the dynamic resilient in varying degrees but the cyclic deviator stress is just the opposite. The rate of change in dynamic resilient modulus presents different forms.

4) A modified model considering the F-T cycles was developed based on the experimental results. The model represents low liquid-limit clay well. Nevertheless, further research will be conducted to study its applicability to other soil types.

5) This study does the dynamic triaxial tests after F-T cycles instead of during F-T cycles. There may be some experimental errors during the tests. So, the multifunctional F-T system should be improved in recent years, which can be conducted the dynamic triaxial tests during the F–T cycles.

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(Edited by ZHENG Yu-tong)

中文导读

冻融循环和动荷载耦合作用下路基土动回弹模量试验

摘要：为了考虑浅层地下水在路基土冻融循环过程中的影响，自主研发了多功能冻融循环试验系统，模拟冻结过程中路基土存在地下水补给的工况，并对冻融循环后的试样进行大量动三轴试验。系统研究了冻融循环次数、压实度、围压、循环偏应力、加载频率、初始含水率对土体动回弹模量的影响。结果表明，路基土动回弹模量随着循环偏应力、冻融循环次数、初始含水率的增加而减小，相反，随着压实度、围压、加载频率的增加而增加。此外，基于试验数据建立了考虑冻融循环和应力状态的动回弹模量修正预估模型，模型计算结果表明，修正的预估模型具有较高的精度。本研究可为地下水补给工况下的冻融循环研究和路基土动回弹模量研究提供相应参考。

关键词：动回弹模量；冻融循环；动荷载；动三轴试验；预估模型

Foundation item: Projects(41672312, 41972294) supported by the National Natural Science Foundation of China; Project(2017CFA056) supported by the Outstanding Youth Foundation of Hubei Province, China; Project(KFJ170104) supported by the Changsha University of Science & Technology via Open Fund of National Engineering Laboratory of Highway Maintenance Technology, China

Received date: 2020-03-21; Accepted date: 2020-04-05

Corresponding author: LU Zheng, PhD, Professor; Tel: +86-13469993948; E-mail: zlu@whrsm.ac.cn; ORCID: 0000-0003-3226-6535; DUAN Ya-hui, PhD, Professor; Tel: +86-13907156177; E-mail: 2336004327@qq.com; ORCID: 0000-0002- 6455-1915