Junhui Peng,Huiren Hu,Junhui Zhang

National Engineering Research Center of Highway Maintenance Technology,Changsha University of Science and Technology,Changsha,410114,China

Keywords:Subgrade soil Soil-water characteristic curve (SWCC)Overburden stress Degree of compaction Prediction mode

ABSTRACT The subgrade soil is generally in saturated or unsaturated condition.To analyze complex thermo-hydromechanical-chemical (THMC) behaviors of subgrade,it is essential to determine the soil-water characteristic curve(SWCC)that represents the relationship between matric suction and moisture content.In this study,a full-automatic rapid stress-dependent SWCC pressure-plate extractor was developed.Then,the influences of overburden stress and degree of compaction on the SWCC of subgrade soil such as high liquid limit silt (MH) and low liquid limit clay (CL) were analyzed.Accordingly,a new model taking into account the influences of overburden stress and degree of compaction based on the well-known Van Genuchten (VG) SWCC fitting model was presented and validated.The results show that with the increase of the degree of compaction and overburden stress,the saturated moisture content of subgrade soil decreases,while the air-entry value increases and the transition section curve becomes flat.The influences of the degree of compaction and overburden stress on the SWCC of MH is greater than that of CL.Meanwhile,there was a satisfactory agreement between the prediction and measurement,indicating a good performance of the new model for predicting the SWCC.

1.Introduction

The soil is generally in saturated or unsaturated condition for subgrade due to the influence of groundwater.Scholars have found that matric suction exists in unsaturated soils.Environmental and climatic conditions such as infiltration of rainwater,evaporation,etc.(Zhang et al.,2020a,b)lead to the variation of moisture content,which changes the proportion of soil particles,water and air in soil,and then alters the surface tension of the water-air interface,resulting in the change of matric suction.Different matric suctions have different influences on the complex thermo-hydromechanical-chemical (THMC) behaviors for subgrade (Zhang et al.,2020c,d).To assess the influence of external environment on THMC behaviors of subgrade,soil-water characteristic curve(SWCC),which represents the relationship between matric suction and moisture content (or degree of saturation) and reflects the water holding capacity of the soil,is developed.Taking the capillary phenomenon of subgrade soil as an example,groundwater will migrate to the area of unsaturated subgrade because of the existence of matric suction.This phenomenon can be described by solving the seepage governing equation using the SWCC.Overall,it is essential to investigate the SWCC for the understanding of THMC behaviors of subgrade under environmental conditions.

In general,there are two remarkable characteristics for subgrade soil:overburden stress and degree of compaction.Due to the geostatic stress,the pavement structure load,traffic load and other actions,the subgrade soil is subjected to a stress state anytime.The variation of the soil pore structure and soil-water-air contact surface resulting from overburden stresses can lead to the change of SWCC.Many researchers have studied the SWCC of unsaturated soil under different overburden stresses.Ng and Pang (2000a,b)introduced the concept of stress-related SWCC and applied it for the development of stress-related SWCC instrument.The results showed that the overburden stress has a significant effect on SWCC,and the greater the overburden stress,the greater the air-entry value.Li and Vanapalli (2022) adopted the developed models to predict the SWCC for coarse-and fine-grained soils with consideration of the influence of stress state,which can be used in numerical modeling of complex coupled hydro-mechanical problems.Meanwhile,the subgrade is designed and built according to the degree of compaction,and the pore size and distribution can change with depth.The influence of the degree of compaction on SWCC of soils has been reported by several investigators.Zhou et al.(2012) introduced a simple approach to quantify the effect of degree of compaction on the SWCC,based on an incremental relationship between the degree of saturation and the initial void ratio.Zhao et al.(2017) investigated the effects of the degree of compaction on the water retention properties of a compacted infilled joint soil from Beihetan (China).Chen et al.(2019) conducted an experimental investigation of the microstructure of a coarse-grained soil used in high-speed railway track bed at various degrees of compaction and proposed a novel SWCC model considering the degree of compaction.In summary,previous studies have investigated the influence of degree of compaction or the overburden stress on SWCC,and indicated that these influences are significant.However,few studies have considered the influence of both factors on the SWCC,and the corresponding SWCC model has not been proposed.Therefore,to provide a more reasonable SWCC used to reveal the THMC performance of subgrade,it is necessary to take into account the joint influence of the degree of compaction and overburden stress and to develop a new SWCC model.

To date,efforts have been made by researchers to obtain reliable,affordable,easily performed testing methods for SWCC,such as centrifuge method (Li et al.,2020),pressure-plate (Richards,1948),filter paper method (Mohammed et al.,2021),etc.These methods face a common problem that the test process is lengthy to obtain the SWCC,since it is required a long time to complete waterair equilibrium for every level of matric suction (Gee et al.,2002;Dexter et al.,2012).Subsequently,some scholars attempted to give a new test method to shorten testing time.Wayllace and Lu(2012)proposed an instantaneous water release and inhalation method,namely one-step flow method that integrates physical experiment and numerical inversion to test SWCC under dry and wet conditions,resulting in short test time.Wang et al.(2015) reduced the cross-sectional area of the specimens to decrease the test time.Adel et al.(2020) developed a continuous pressure automatic determination system suitable for remolded soil and unchanged soil,which can be continuously,directly and accurately measure SWCC in a short time.The time required for drying and wetting SWCC is less than 10% of the conventional multi-step flow method.These methods presented in the literature shorten the testing time by improving the existing instruments combined with the theoretical model,or the test conditions.The pressure-plate extractor based on the principle of axial translation serves as a reliable method in establishing the SWCC,which is not appropriate to use these methods to shorten the time due to the complexity of these methods and the risk of precision reduction.The long testing time of the pressure-plate extractor is determined by the inability of ceramic plate to drain quickly enough to reach the water-air equilibrium.Based on this,the researchers began to try to improve it with a fiber membrane which can pass through water quickly and cannot pass through air under the special range of air pressure.Nishimura et al.(2011),Hong et al.(2016),Wang et al.(2017),and Habasimbi and Nishimura (2019) developed a series of new instruments to measure SWCC using microporous membranes instead of ceramic plate.The SWCCs of different soils were tested by the new instruments,and the results showed that the equilibrium time required for SWCC measurement by using the new instruments with good performance was much shorter than that required using conventional methods.However,these instruments cannot apply a vertical stress to the specimen and thus cannot readily study the influence of stress state on the SWCC.Ng and Pang (2000a,b) developed a stress-dependent SWCC pressure-plate extractor to study the influence of stress state on the SWCC.This instrument also faces the same problem of long testing time.Overall,the existing pressure-plate extractor cannot meet the requirements of both applying overburden stress and rapid testing.

Therefore,to short testing time and apply stress when investigating the influences of overburden stress and degree of compaction on the SWCC,a full-automatic rapid stress-dependent SWCC pressure-plate extractor is developed.Then,the influences of overburden stress and degree of compaction on the soil-water characteristics of high liquid limit silt (MH) and low liquid limit clay (CL) in China are investigated using the developed apparatus.In addition,based on the van Genuchten(1980)model(VG model),a new model for SWCC taking into account the overburden stress and degree of compaction is proposed and validated.

2.Materials and methods

2.1.Modified pressure-plate extractor for SWCC

As one of the testing methods of SWCC,the pressure-plate extractor uses the axial translation technology to obtain the relationship between the matric suction and moisture content by increasing the pore gas pressure and controlling the water flow in the soil.This method is more accurate and reliable than other test methods (Ng and Pang,2000a;Lu and Likos,2004).But the conventional pressure-plate extractor cannot meet the requirements of both applying the overburden stress and rapid testing.To solve this problem,a modified pressure-plate extractor for SWCC was developed.

Firstly,the permeability of ceramic plate used by the conventional pressure-plate extractor is very low,about 1×10-11m/s.This means that it takes a long time to achieve water and air balance in the specimen.It is common to takes 1-2 months to complete a SWCC.Hence,an extractor for faster testing SWCC of unsaturated soil under one-dimensional stress conditions needs to be developed for saving time.

Hydrophilic fiber film is composed of glucose,basically cellulosic biomass,which is chemically stable and inert.It has good hydrophilicity and water flux.Moreover,it possesses good antishrinkage performance,which can avoid film damage in the test process.The maximum air-entry value of hydrophilic fiber film can reach 400 kPa,which means that the most obvious variation of SWCC can be tested,and the film can be used to determine SWCC of subgrade.The water-air equilibrium time required in the SWCC test is much less than that of the conventional ceramic plate,due to the thin thickness,good hydrophilicity and water flux.The membrane flux,which refers to the amount of fluid passing through a unit area in a unit time and reflects the permeability of the film,is defined as 1.528 × 10-3m/s under a pressure of 24 inches of mercury.In this paper,the hydrophilic fiber film was used instead of the ceramic plate to greatly reduce the overall testing time.Specifications of hydrophilic fiber film and ceramic plate are summarized in Table 1.To support the soil specimen and protect the hydrophilic fiber film at the bottom of the device,a special dense permeable stone with the same diameter and thickness as the ceramic plate was designed(as shown in Fig.1),and the porosity is 0.3.

Fig.1.Schematic diagram of hydrophilic fiber film and dense permeable stone.

Table 1Specifications of hydrophilic fiber film and ceramic plate.

Then,vertical load is applied to the soil specimen inside the pressure chamber through a loading rod to realize the application of overburden stress(refers to Ng and Pang,2000a,b).Meanwhile,to ensure a constant overburden stress during the test,a pressure sensor is set in the loading rod and linked to the control system,which can adjust the overburden stress on the soil specimen in real time.

Further,to facilitate the operation of apparatus and avoid the test error caused by manual operation,the test automation is also emphasized when developing the apparatus.A fully automated control system was built,which consist of control software in industrial computer and a series of sensors.The air pressure,overburden stress,scour of bubbles,environment humidity and others can precisely be controlled by this system and the water volume can be recorded automatically.

Finally,based on the above ideas to solve these problems and the early research of ours project team(Peng,2021;Zhang,2021),a new SWCC pressure-plate extractor was developed (Fig.2),which has a high degree of automation,short testing time and application of vertical load.

Fig.2.Schematic diagram of modified stress-dependent SWCC pressure-plate extractor.

The whole equipment consists of a pressure chamber system,a axial pressure system,an automatic water volume measurement system,a constant temperature and humidity system,and an automatic control system,which are illustrated as follows:

(1) The pressure chamber system is used to place the soil specimen and provide a matric suction control environment by adjusting the air pressure to reach the preset matric suction,namely,air pressure in the system is equal to the matric suction.A combination of hydrophilic fiber membrane and dense permeable stone (Fig.1) is placed at the bottom of the soil specimen to enable rapid SWCC testing.

(2) Vertical load is applied by the axial pressure system on the soil specimen inside the pressure chamber system through the loading rod to investigate the effects of stress state on the SWCC of the subgrade soil.

(3) The automatic water volume measurement system can record the change of moisture content inside the soil specimen during the test,so as to obtain the moisture content of the soil specimen under the action of various levels of matric suction.

(4) Constant temperature and humidity are realized by the external humidifier and air conditioner to reduce the influence of external climatic factors on the test results.The water mist produced by the humidifier is transmitted to the transparent cover through the pipeline.At the same time,the air conditioning in the laboratory is set to control the constant temperature.

(5) The automatic control system is realized by touchable industrial computer,which can control the air pressure,vertical stress,and the frequency of automatic scour of bubbles,and can also record changes of moisture content of soil specimen,vertical displacement,and matric suction.When the suction of each level reaches equilibrium,the moisture content versus matric suction curve of soil specimen,namely SWCC,can be calculated and drawn.

2.2.Test material and specimen preparation

MH and CL are often used as subgrade filler.In this paper,these kinds of soil specimens,MH and CL,were obtained from Changsha and Shanghai in China,respectively.According to the Chinese testing standard JTG 3430-2020 (2020),sieve analysis,Atterberg limits,specific gravity,and standard Proctor (light compaction)tests were performed.The particle size distribution curves are shown in Fig.3,and the other results are summarized in Table 2.

Fig.3.Particle size distribution curves of MH and CL.

Table 2Index properties of the two common subgrade soils.

2.3.Experimental program

To evaluate the influence of overburden stress on SWCC,different stress states were applied to the specimens.Taking the common subgrade with 5 m high as an example,the unit weight of soil is about 18 kN/m3,and the geostatic stress calculated is equal to 90 kPa.Therefore,fouroverburden stresses,0 kPa,40kPa,80kPa and 120 kPa,were chosen in this paper.Meanwhile,the degree of compaction when filling the subgrade is often set to 93%,96%,or even larger values,according to the design requirements.Two extreme states,i.e.dense and relatively loose,were considered in this work.The degrees of compaction of 90%,93%,96%and 99%were chosen.Details of the experimental program are summarized in Table 3.

Table 3Summary of the testing program for determining SWCC.

Table 4Model parameters of SWCC of MH.

Table 5Model parameters of SWCC of CL.

2.4.Testing procedures

The modified extractor was employed to test the SWCC of the specimens with various stresses and degrees of compaction. Initially,soils obtained from the field were air-dried,crushed and sieved using a 2 mm sieve.It was then oven-dried at 105°C for 24 h prior to the preparation of a re-compacted soil specimen.Water was added to obtain the optimum moisture content of soils(Table 2),and was mixed with the soil thoroughly.Subsequently,the soils were kept in a plastic bag for moisture equilibrium for about 48 h in a temperature-and moisture-controlled room.According to the volume of oedometer ring with 61.8 mm diameter and 20 mm high and the maximum dry density of specimens,the total mass required for a soil specimen with the desired degrees of compaction (Table 3) can be calculated.The soil was divided into two equal parts and statically re-compacted using universal testing machine in an oedometer.Re-compacted soil specimens were then submerged in deaired water inside a desiccator subjected to a vacuum for about 24 h to ensure full saturation.Meanwhile,the hydrophilic fiber film and the dense permeable stone were saturated in a vacuum saturator for 24 h.The saturated specimen was then placed on the hydrophilic fiber film at the top of dense permeable stone,and the equipment was sealed to complete the installation.The target overburden pressure (Table 3) was applied on the soil specimen through the loading rod (Fig.2).The air pressure was increased to the target matric suction value by the pressure chamber system (Fig.2).The specimen was subjected to an increasing matric suction in a series of steps(Table 3)to test the SWCC.As the matric suction increased,water was expelled from the soil specimen and tested by the automatic water volume measurement system (Fig.2).Generally,3-5 h are required to achieve water-air equilibrium at a given matric suction,but the conventional method takes 1-2 d (Ng and Pang,2000a).After the equilibrium was reached,change of water volume in the specimen precisely tested every hour should not exceed 0.006 mL as the standard for equilibrium.After the required maximum suction was achieved,complete test process was ended.

3.Results and discussion

3.1.Verification of the test results by the modified extractor

To verify the accuracy of the SWCC results tested by the modified stress-dependent pressure-plate extractor,the SWCC of MH was investigated considering different degrees of compaction and neglecting the overburden stress by using the modified and conventional extractors,respectively.The tests S1,S5,S9 and S13(Table 3)were chosen,and the obtained results are shown in Fig.4 and analyzed in detail.The moisture content,which is the ratio of water volume to the total volume of soil when it is fully saturated,decreases with the increase of matric suction whether using the modified extractor or the conventional method.Meanwhile,the higher the degree of compaction,the lower the saturated volume moisture content,and the more obvious the correlation of SWCC with the degree of compaction.This is because the soil becomes more compact,and thus the pores become smaller with the increase of degree of compaction (Zhang et al.,2020c).Further,the error of moisture content tested by two methods under the same level of matric suction is very small,and the maximum relative error is only 1.4%.It is easily understood that the SWCCs tested by the modified and conventional extractors are basically consistent.On the other hand,the water-air equilibrium time at each level of matric suction tested by the modified extractor varies from 2 h to 4 h.When the matric suction is less than 300 kPa,it takes about 1-2 d to obtain the SWCC,while the conventional extractor requires 7-15 d to obtain the SWCC and about 1-2 months to balance water and air at each level of matric suction (Ng and Pang,2000a).Accordingly,the modified extractor can save the testing time.

Fig.4.Testing results using the modified and conventional extractors.

Fig.5.Stress-dependent SWCC of MH for different degrees of compaction: (a) 90%,(b) 93%,(c) 96%,and (d) 99%.

3.2.Effect of overburden stress on SWCC

To investigate the influence of the overburden stress,four kinds of overburden stresses,i.e.0 kPa,40 kPa,80 kPa and 120 kPa,are chosen to test the SWCC of MH and CL with different degrees of compaction using the modified stress-dependent pressure-plate extractor.The results are shown in Figs.5 and 6,respectively.It can be seen that the overburden stress has a significant influence on the SWCC.Compared to the low overburden stress,the SWCC of soil with the high overburden stress exhibits a greater air-entry value,at which the volumetric moisture content starts to decrease significantly.The saturated moisture content becomes lower with the increasing overburden stress,which can be explained by the decrease of pore volume ratio.Moreover,the loss rate of moisture content is faster at the high level of matric suction,leading to the flatter SWCC.This is because the overburden stress will compress the soil and make the soil pore smaller,which make the air more difficult to enter the specimen,and less water will be discharged slowly in the process of drainage.

Meanwhile,it is clear that there is a substantial difference in influences of overburden stress on the SWCC of MH and CL.With the increase of overburden stress,the moisture content of MH at the same level of matric suction and degree of compaction changes more significantly than that of CL.The change rate of moisture content in MH gradually decreases with the increase of overburden stress,but the rate is basically the same for CL.Taking the testing results of soils with the degree of compaction of 90%and the matric suction of 0 kPa as example,the moisture content decreases by 13.3% for MH (Figs.5a) and 7.9% for CL (Fig.6a) when the overburden stress varies from 0 kPa to 120 kPa.This is likely to be caused by the larger content of fine particles in MH compared to that in CL (Table 2),and the fine particles are more easily redistributed in the soil specimen under vertical loading.These indicate that the influence of stress state on the SWCC of MH is greater.

Fig.6.Stress-dependent SWCC of CL for different degrees of compaction: (a) 90%,(b) 93%,(c) 96%,and (d) 99%.

Fig.7.The degree of compaction-dependent SWCC of MH for different overburden stresses: (a) 0 kPa,(b) 40 kPa,(c) 80 kPa,and (d) 120 kPa.

Fig.8.The degree of compaction-dependent SWCC of CL for different overburden stress: (a) 0 kPa,(b) 40 kPa,(c) 80 kPa,and (d) 120 kPa.

3.3.Effect of the degree of compaction on SWCC

The SWCCs of MH and CL under different overburden stresses and degrees of compaction are depicted in Figs.7 and 8,respectively.The degree of compaction also has a significant impact on the SWCC of subgrade soil.The saturated volumetric moisture content becomes smaller as the degree of compaction increases,while the air-entry value increases and the SWCC becomes flatter,which is similar to the effect of overburden stress on the SWCC.This is because the subgrade soil also has different pore size distributions under different degrees of compaction.When the degree of compaction is small,the soil has many large-size pores,and it is easy for air to enter and exit the soil,so that the soil is prone to absorb water and expel water.On the contrary,the larger the degree of compaction,the smaller the internal pores of the soil,and the larger the capillary suction.It is difficult for air to enter the soil,and for water absorption or drainage,so that the water holding characteristic of the soil is relatively strong.Similar phenomenon was also reported by Ng and Pang (2000b).Notably,the change of moisture content is small when the degree of compaction varies from 90% to 96%,whereas there is a significant difference for the moisture content when the degree of compaction varies from 96%to 99%.Of course,this phenomenon becomes discernible as the overburden stress increases.

3.4.Establishment and verification of prediction model for SWCC related to the overburden stress and degree of compaction

To describe the relationship between the matric suction and moisture content of unsaturated soil for calculating complex THMC behaviors of subgrade,expressions for continuous explicit functions are required.Subsequently,continuous prediction models for SWCC were proposed based on test data and the physical mechanism between soil,water and gas.A large number of prediction models have been proposed and applied,and some are widely used,such as the models proposed by Gardner(1958),Brooks and Corey(1964),van Genuchten (1980),and Fredlund and Xing (1994),which are presented as follows.

3.4.1.Gardner’s model

This model is a single-parameter model with exponential form,which is often used to solve the analytical solutions related to unsaturated soil because of its simple form (Lu and Likos,2004).The expression is as follows:

whereθis the moisture content of soil;θrandθsare the residual and saturated moisture contents,respectively;βis the soil pore size distribution parameter representing the rate of reduction in the moisture content as the pressure headhbecomes greater;andh=-ψ/(ρg),in whichψis the matric suction,ρis the density of water (ρ=1000 kg/m3),andgis the gravitational acceleration(g=9.8 N/kg).

3.4.2.Brooks and Corey’s model

Brooks and Corey(1964)analyzed a large number of test data on moisture content and matric suction,and proposed a SWCC model related to the pore size distribution indexλ:

wherehais the air-entry value.

3.4.3.VG model

van Genuchten (1980) proposed a three-parameter mathematical model for fitting the SWCC,namely VG model:

whereais a parameter related to the air-entry value;andmis a parameter related to the residual moisture content at the end of the curve,andm=1-1/n.

3.4.4.Fredlund and Xing’s model

Based on the VG model,Fredlund and Xing (1994) proposed a new SWCC model considering the pore size distribution:

wherehris the matric suction under residual moisture content.

Each model has its applicable conditions,including soil type,soil particle diameter,mineral composition,pore size and distribution,stress state,size,etc.The selection of model has a great impact on the prediction accuracy of SWCC.Modifying the parameters on the basis of the existing model is a common approach to improve the prediction model of SWCC so that it can consider the impact of different conditions.Based on Fredlund and Xing (1994)’s model,Zhang et al.(2020c)established a relationship between the vertical stress and the SWCC model by expressing the parameters of the Fredlund and Xing’s model with the quadratic function of stress,and obtained a new SWCC model to consider the influence of overburden stress.This paper refers to this research idea,and develops a new model based on the VG model by taking into account the overburden stress and the degree of compaction.

Firstly,VG model was used to fit the test data of moisture content and matric suction for MH and CL under different degrees of compaction and overburden stresses (Figs.5 and 6),and the fitting parameters are shown in Tables 4 and 5.As the degree of compaction and overburden stress increase,theavalue decreases,and the air-entry value increases,which can be attributed to increasing soil density and the difficulty for air to enter the soil.The transition section of the SWCC becomes flat,and thenvalue becomes small with the increases of degree of compaction and overburden stress.The saturated volumetric moisture contentθsalso becomes small under large degree of compaction and overburden stress.These results imply that there is a good correlation between the overburden stress and the degree of compaction and these parameters.

Then,the functional relationship between the model parameters and the degree of compaction and overburden stress was explored.After trying a variety of functional forms,it was found that the parametersa,nandθscan be redefined as the expressions of the degree of compaction and overburden stress in the form of power functions:

where K is the degree of compaction;σ is the overburden stress;Pais the atmospheric pressure,andPa=101.3 kPa;andai,niandsi(i=0,1,2) are the fitting parameters.

The fitting parameters of VG model for MH and CL obtained using Eq.(5) are shown in Table 6.The smallest correlation coefficientR2is 0.92,indicating that the functional expressions have a high fitting correlation.The functional expression can be used to describe the prediction model of SWCC related to the overburden stress and the degree of compaction.The new model’s parameters for MH and CL can be respectively expressed as

Table 6Fitting parameters of VG model for MH and CL obtained using Eq.(5).

To discuss the correctness and applicability of the new model,the test results from Yao (2018) were chosen based on the matric suction and moisture content under different overburden stresses(0 kPa,30 kPa,60 kPa and 90 kPa)and degrees of compaction(85%,90%and 95%)for granite residual soil(GRS).Firstly,VG model was used to fit SWCC test data of GRS under different degrees of compaction and overburden stresses,and the fitting parameters are summarized in Table 7.Then,the fitting parameters of VG model for GRS were obtained using Eq.(5),as shown in Table 8.The function expression has a high fitting correlation and can be used to describe the prediction model of SWCC related to the overburden stress and the degree of compaction.The new model’s parameters for GRS can be expressed as

Table 7Model parameters of SWCC of GRS.

Table 8Fitting parameters of VG model for GRS obtained using Eq.(5).

The SWCC prediction model for GRS considering the overburden stress and degree of compaction can be obtained by substituting Eq.(8) into Eq.(3).The new model is used to calculate the moisture content under different levels of matric suction,degree of compaction and overburden stress.The calculated and tested results are shown in Fig.9.Although the new model is less correlated than the VG model(Table 7),it is found that the smallest correlation coefficientR2is 0.96 when the degree of compaction is 85%and the overburden stress is 60 kPa.This shows that the new model still has a good prediction performance.

Fig.9.Comparison of tested and calculated values: (a) 85%,(b) 90%,and (c) 95%.

Overall,the new model considering the degree of compaction and overburden stress has a good performance for SWCC.Further,the model makes it possible to consider the influence of the degree of compaction and overburden stress on the subgrade performance.Taking the water migration of subgrade as example,the degree of compaction is determined by the requirement of design and the overburden stress is calculated by considering the pavement structure,soil moisture content and soil density.Then,the SWCC of subgrade at each position can be obtained by using the new model,and the humidity migration of subgrade under the influence of external environment can be obtained by solving the seepage governing equation.

4.Conclusions

In this paper,the SWCCs of subgrade soil under different degrees of compaction and overburden stresses are experimentally determined using a newly modified SWCC pressure-plate extractor.A new prediction model of SWCC related to the degree of compaction and overburden stress is established and validated.The main conclusions are as follows:

(1) In order to reasonably and rapidly test SWCC of subgrade considering the degree of compaction and overburden stress,a full-automatic rapid stress-dependent SWCC pressureplate extractor was developed.Compared to the conventional pressure-plate extractor,the accuracy of the test results of the novel extractor was verified and a better performance was achieved,such as saving about 95% of the test time,higher degree of automation,application of vertical load,and so on.

(2) The degree of compaction and overburden stress have a significant influence on the SWCC for subgrade soils.As the degree of compaction and overburden stress increase,the saturated moisture content of subgrade soil decreases,the airentry value increases and the SWCC becomes flatter.Especially,there is a phenomenon that the change rate of moisture content is small when the degree of compaction varies from 90% to 96%,but there is a significant difference for the moisture content when the degree of compaction increases from 96%to 99%.However,this phenomenon becomes less obvious as the overburden stress increases.Meanwhile,the influences of the degree of compaction and overburden stress on the SWCC of MH are greater than that of CL in terms of the moisture content,air-entry value and so on.

(3) By analyzing the relationship between VG model parametersa,nandθs,and the degree of compaction and overburden stress,the VG model was improved,and a SWCC prediction model considering the degree of compaction and overburden stress was established.The new model has a high fitting correlation (R2＞0.9) and is applicable for many kinds of soils.This model makes it possible to consider the influence of the degree of compaction and overburden stress on the subgrade performance such as water migration and resilient modulus.

(4) There are some interesting ideas which can be explored in the future work based on this study.To comprehensively reveal the influence of degree of compaction and overburden stress on the SWCC,different subgrade fillers such as silt,sand and construction and demolition wastes are worth exploring using the new extractor and SWCC model developed in this study.Meanwhile,the microscopic mechanism of the influence of the degree of compaction and overburden stress on the subgrade soil SWCC can be revealed from the microscopic perspective by applying some microscopic testing equipment such as computed tomography (CT),scanning electron microscope (SEM),and so on.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was supported by the National Natural Science Foundation of China(Grant No.52208419),Science and Technology Innovation Program of Hunan Province,China (Grant No.2022RC1030),and Project of Scientific Research of Hunan Provincial Department of Education,China (Grant No.21C0187).