J. Cent. South Univ. (2017) 24: 875-890

DOI: 10.1007/s11771-017-3490-0

Dynamic behavior of new cutting subgrade structure of expensive soil under train loads coupling with service environment

QIU Ming-ming(邱明明)¹, YANG Guo-lin(杨果林)¹, SHEN Quan(申权)¹, YANG Xiao(杨啸)²,

WANG Gang(王刚)¹, LIN Yu-liang(林宇亮)¹

1. School of Civil Engineering, Central South University, Changsha 410075, China;

2. Department of Civil Engineering, Monash University, Clayton VIC 3800, Australia

Central South University Press and Springer-Verlag Berlin Heidelberg 2017

Abstract: Expansive soil is sensitive to dry and wet environment change. And the volume deformation and inflation pressure of expansive soil may induce to cause the deformation failure of roadbed or many other adverse effects. Aimed at a high-speed railway engineering practice in the newly built Yun-Gui high-speed railway expansive soil section in China, indoor vibration test on a full-scaled new cutting subgrade model is carried out. Based on the established track-subgrade-foundation of expansive soil system dynamic model test platform, dynamic behavior of new cutting subgrade structure under train loads coupling with extreme service environment (dry, raining, and groundwater level rising) is analyzed comparatively. The results show that the subgrade dynamic response is significantly influenced by service conditions and the dynamic response of subgrade gradually becomes stable with the increasing vibration times under various service environment conditions. The vertical dynamic soil stress is related with the depth in an approximate exponential function, and the curves of vertical dynamic soil stress present a “Z” shape distribution along transverse distance. The peak value of dynamic soil stress appears below the rail, and it increases more obviously near the roadbed surface. However, the peak value of dynamic soil stress is little affected outside 5.0 m of center line. The vibration velocity and acceleration are in a quadratic curve with an increase in depth, and the raining and groundwater level rising increase both the vibration velocity and the acceleration. The vertical deformations at different depths are differently affected by service environment in roadbed. The deformation of roadbed increases sharply when the water gets in the foundation of expansive soil, and more than 60% of the total deformation of roadbed occurs in expansive soil foundation. The laid waterproofing and drainage structure layer, which weakens the dynamic stress and improves the track regularity, presents a positive effect on the control deformation of roadbed surface. An improved empirical formula is then proposed to predict the dynamic stress of ballasted tracks subgrade of expansive soil.

Key words: high-speed railway; full-scale model testing; dynamic response; expansive soil; service environment; new subgrade structure

1 Introduction

With the rapid development of high-speed railway in China, many engineering problems about expansive soil are sprouting out, which provides great developmental momentum and severe challenges for the further study of expansive soil or its related engineering. Expansive soil is a kind of special soil because the expansive soil has distinctive features of swelling, disintegrating, softening by absorbing water, shrinking and cracking by losing water and repeated changing, and it is mainly composed of strong hydrophilic clay mineral (montmorilonite) and mixed-layer clay mineral [1-5]. Some scholars carried out research on the expansive soil strength testing [6], degradation behavior under dry-wet cycles [7, 8], mesostructure [9], and evolvement rules to grasp the characteristics of expansive soil. The results show that expansive soil is sensitive to moisture-change, and it is very bad for the structure safety and stability in expansive soil areas due to the swelling-shrinking deformation and strength degradation of expansive soil. Accordingly, it is critical to reasonably control moisture status of subgrade, which has optimal deformation coordination performance and waterproofing and drainage effects of the railway subgrade engineering in expansive soil areas.

The composite waterproof structure layer of “Two fabrics and one membrane” is applied to expansive soil cutting subgrade areas of Nanning-Kunming railway. However, the field survey showed that the defects appeared at the waterproofing sections of geotextil in service such as subsidence, proof drainage and mud pumping [5], which seriously affects normal transport of railway and traffic safety. And therefore, the treatment effect is not ideal when adopting traditional flexible waterproofing to handle subgrade of expansive soil. The newly built Yun-Gui high-speed railway is alongside with the Nanning-Kunming line, and the line will encounter much cutting of expansive soil (rock). For ensuring construction safety of Yun-Gui railway and long-term dynamic stability of cutting subgrade, the waterproofing and drainage structure layer and the new subgrade structure are designed based on the characteristics of expansive soil as well as the disease mechanism of subgrade to solve technical problems of newly built Yun-Gui high-speed railway in expansive soil areas.

Many scholars put forward train vibration loads simulation [10, 11], elastic theory solutions [12-15], numerical simulation analysis [16-18], model test [19-22] and field test [23-26] to study dynamic response and influence factors for high-speed railway subgrade. COSTA et al [12] considered the nonlinearity of soil to analyze the dynamic response of high-speed railway subgrade. SHAN et al [16] adopted numerical simulation method to establish three- dimensional dynamic model of ballasted track-subgrade system for discussing the effect of train load and speed on the dynamic characteristics of soil subgrade. BIAN et al [22] used model test method to study the characteristics of vibration velocity and dynamic soil stress of ballastless high-speed railway under moving train loads, and an improved empirical calculation formula is then proposed to determine the dynamic soil stress of ballastless high-speed railway. YANG et al [23] got the change rules of velocity and acceleration with depth under dry and wet service environment by studying the dynamic characteristics of fully-enclosed cutting subgrade of high-speed railway in expansive soil areas based on field test method. The results show that the varieties of structure type and its parameters have a significant impact on the dynamic performance of subgrade, and understanding the dynamic soil stresses level and load transfer mechanism of each structure layer is the fundamental assurance for subgrade structure design and deformation control of high-speed railway. Compared the new subgrade structure with traditional subgrade structure under moving train loads, the dynamic response has large differences because of the direct effect of waterproofing structure layer. A special study is required on the dynamic interaction of track-new subgrade structure-foundation of expansive soil under train vibration loads and extreme service environment conditions, which is of great significance to understand stress level and dynamic behaviors of new subgrade structure.

Physical model testing in laboratory, as an effective alternative to field measurement, provides valuable data to study the dynamic behavior of track-substructure interaction under train loads. In this work, based on current research results and the typical design section of new cutting subgrade structure in medium-strong expansive soil areas, the full-scale vibration test model of new cutting subgrade structure is established to study the distribution, the attenuation laws of dynamic response and dynamic stress under train load coupling with service environment. An empirical formula is then proposed to predict the dynamic stress beneath the ballasted tracks of expansive soil while taking the effect of soil depth into account. The characteristics of velocity, acceleration and vertical deformation are analyzed. The research results are applied to new Yun-Gui high-speed railway project construction and provide the reference for the similar engineering practice.

2 Engineering situation

The Yun-Gui high-speed railway, north from Kunming, Yunnan province and south to Nanning, Guangxi province, about 710.3 km long, is a newly-built ballasted double-track railway and national Ι level in China. The segment of Nanning to Baise is designed as a double-line ballasted track with a design speed of 250 km/h. The segment of Baise to Kunming is a double-line ballasted track designed by 200 km/h with a reservation of 250 km/h passenger condition. The segment of expansive soil (or rock) is inevitable along the line, and its length is about 129.7 km that accounts for 18.3% of the total line. The length of expansive soil roadbed segment (include station) is about 66.2 km that accounts for 9.3% of total line. There is weak, medium and strong expansive soil along the line with a discontinuous distribution. The region belongs to subtropical humid monsoon climate zone. So, the rainfall and evaporation are large, and the characteristics of seasonal and dry-wet circulation are obvious all year.

2.1 New cutting subgrade structure design

Ballasted tracks subgrade of high-speed railway consists of surface layer and bottom layer [27], and the subgrade surface and bottom layer thickness are dependent with design speed. When the design speed is less than 200 km/h, the structure thicknesses of subgrade surface and bottom layer are 0.6 m and 1.9 m respectively. When the design speed is more than 250 km/h, the structure thicknesses of subgrade surface and bottom layer are 0.7 m and 2.3 m, respectively. In general, the graded broken rock is used as the filling of subgrade surface layer, and the A, B stuffing or improved soil is used as the filling of subgrade bottom layer. The subgrade structure need to be enhanced for the performance of waterproof and impervious in special geological conditions, and the composite geomembrane or composite waterproofing and drainage plate is deployed in subgrade, which is the commonly used method in the railway engineering.

According to the construction demand of Yun-Gui railway line in expansion soil areas, the cement-based composite material of semi-rigid waterproof is researched for the subgrade structure, which has reasonable deformation coordination performance and waterproofing and drainage effects. It is applied to cutting subgrade structure of expansive soil for its full-enclosed waterproof quality. Through the bottom of the subgrade surface layer, a structure layer of waterproofing and drainage is laid to prevent surface water into bottom layer of subgrade and foundation, as well as to adapt to the deformation of expansive soil foundation. The diagram of new type cutting subgrade structure is shown in Fig. 1. Among them, the type of foundation soil is medium-strong expansive soil. The subgrade structures are downwards as follows: 0.70 m subgrade surface layer (0.65 m graded broken rock and 0.05 m medium-coarse sand), 0.20 m waterproofing and drainage structure (modified cement-based composite materials), and subgrade bottom layer (or replacement layer, A, B stuffing, the thickness as the case may be and the recommended value is 0.50-2.30 m). In order to ensure the reliability of subgrade structure, and to combine with the distribution features of expansive soil, there are blind-drains at the bottom of two lateral sides to strengthen the waterproofing and drainage. The draining of cutting slope mainly depends on horizontal cracks and drainage system to discharge rainwater and groundwater into the lateral drain and blind-drains.

2.2 Mechanics performance test on waterproof structure layer

The characteristics of lower-middle elastic modulus, strong anti-permeability and high toughness are required for the waterproof structure layer to perform deformation coordination as well as waterproof impervious behavior. Consequently, the material of new type waterproof structure layer is developed by optimizing the proportions among the various components including the sand, the soil, the rubber, the emulsified asphalt, the cement and the fiber, in which, the sand and the soil are used as skeleton system; the rubber and the emulsified asphalt are used as modified components; and the cement and the fiber mixed system are used as reinforcement components. Based on the above six kinds of material compositions, different material specimens are produced with different mixing ratios and different sizes and the specimens of modified cement-based composite materials are tested under different conditions to obtain the physical and mechanical parameters, such as density, compressive strength, elastic modulus, stress-strain relationship. The main parameters of the specimen are listed in Table 1.

Figure 2 shows the stress-strain relationship curve of composite material under different test conditions. The analysis results show that the stress-strain relationship curves present little difference under 0.15×10⁶ times, 1.00×10⁶ times and 2.00×10⁶ times fatigue loading test. The inner structure of composite material is not damaged by long-term fatigue loading, and it shows that the material has strong anti-fatigue performance. The peak value of stress reduces by 0.3 MPa compared to baseline group under coupling functions of the soaking and the long-term dynamic loading. The maximum value of dynamic load induced by train is 98.8 kPa in the actual service process of new waterproof structure layer, and it is only 1/8 compared with the experimental value of long-term dynamic loading. So, the new type composite materials can meet the basic requirements under long-term soaking and actual train loads. At the same time, the disadvantages of the traditional compound material of earthwork waterproof including the deformation, the damage and joint problems in construction can be well avoided because of the construction convenient and excellent continuity of the new type material of waterproof.

Fig. 1 Sketch of new cutting subgrade structure (Unit: m)

Table 1 Main mechanic indexes of waterproof structure layer

Fig. 2 Relation of stress-stain

3 Track-subgrade-foundation system model testing

3.1 Full-scale testing model design

The typical design section of new cutting subgrade of medium-strong expansive soil is selected based on the Yun-Gui railway engineering in expansion soil areas. A portion of a full-scale track-subgrade-foundation system model for a high-speed railway is built in the steel box following the Chinese high-speed railway design code. The inner dimensions of the steel box are 9.2 m long, 2.0 m wide and 4.6 m high. The subgrade is composed of several substructures which are downwards named as 0.7 m subgrade surface layer, 0.2 m waterproofing and drainage structure layer, and 0.6 m subgrade bottom layer. The test model is shown in Fig. 3. The soil pressure sensor, velocity sensor, acceleration sensor and soil strain sensor are embedded in the roadbed to investigate the dynamic behavior of new cutting subgrade structure under train loads coupling with service environment conditions(dry, raining, and groundwater level rising). The full-scale test model is established according with the actual engineering condition to ensure that the design specifications of test model are almost identical to a section of the newly built Yun-Gui high-speed railway in China and the size. The type and their construction quality of each structure of track-subgrade-foundation system test model are also consistent with the construction site.

Fig. 3 Full-scale model testing of track-subgrade-foundation (Unit: m):

The subgrade structure layer is composed of subgrade surface layer, waterproofing and drainage structure layer and subgrade bottom layer. The position relationship of structure layer is shown in Fig. 1. Based on filling gradually and vibrant-tamp method, the surface layer of subgrade is a layer graded broken with 0.7 m in thickness to support the ballast bed, and the bottom layer of subgrade is 0.6 m thick-layer filled by A, B stuffing below the waterproofing and drainage structure layer. These two layers are required to have appropriate strength and stiffness, which are usually represented by the density ρ, the moisture content ω, the compaction coefficient k, the subgrade reaction k₃₀ and the dynamic deformation modulus E_vd. These parameters are used to control the construction quality of the railway substructure following the Chinese high-speed railway design code (TB10621-2009). The waterproofing and drainage structure layer is a layer with 0.2 m in thickness constructed by modified cement-based compound materials by using integral-laying method. Its main parameters of physical and mechanical are listed in Table 1. The foundation (nature subsoil) is composed of medium-strong expansive soil following the test section of Yun-Gui high-speed railway, which is filled by gradually method. The density is used to control the construction quality of fill soil. The physical parameters of the medium-strong expansive soil are summarized in Table 2.

3.2 Testing components layout

The soil pressure sensor, velocity sensor, acceleration sensor, soil strain sensor and moisture sensor are arranged in layers and embedded in the roadbed model to investigate the dynamic behavior characteristics of substructure under train loads. The position of monitoring sites and the layout of sensor are shown in Fig. 4, and the sensor parameters are listed in Table 3.

3.3 Train loads and loading system

The track structure is composed of double rails, fasteners, sleeper and ballast bed. The dynamic loadings induced by rail-wheel interaction first transfer to the track structure via sleeper, then to the substructure. In this process, the sleepers play a role in transforming train loads on the rail surface into vertical vibration loads on the sleeper surface at each fastener’s position. The train vibration loads are simulated following the CRH2-type high-speed train, in which, the wheelbase of bogie is 2.5 m; the vehicle length is 17.5 m; the train speed is 250 km/h; and then the train load frequency are 27.8 Hz and 4.0 Hz. The loading frequency value of 4.0 Hz is selected because the substructure of high-speed railway mainly reflects low frequency vibration induced by the train loads. Use the equipment weight to simulate the static rail-wheel loads P_j caused by train axle load in the roadbed surface. The additional dynamic rail-wheel load △P induced by train’s movement is simulated by adopting sinusoidal stress variations. The maximum dynamic axial forces of roadbed and stress amplitude are expressed by P_dl and σ_dl, with P_dl=380.0 kN and σ_dl=98.8 kPa, so we have Eq. (1) as a response to the load conditions in model tests.

                      (1)

where P_j is static rail-wheel load (kN); △P is additional dynamic rail-wheel load (kN); f is frequency (Hz); and t is time (s).

Table 2 Main physic-mechanic indexes of expansive soil

Fig. 4 Arrangement measuring instruments (Unit: m)

Table 3 Specification of each transducer for model test

In the indoor model testing, the loading system (MTS) in laboratory, which consists of reaction frame, actuators and distribution girder, is used to generate equivalent vertical loadings at the track structure for simulating the dynamic excitations due to high-speed train's movements. The maximum and minimum values for loading are 380 kN and 20 kN. Sine wave is performed with a load frequency of f=4.0 Hz. The static rail-wheel loads is determined as 200 kN (P_j=200 kN), and the additional dynamic rail-wheel loads is 180 kN (△P=180 kN). The time-history curve of loading and loading system is shown in Fig. 5.

Fig. 5 Dynamic loading system of train:

3.4 Service environment simulation and testing process

In the process of vibration test, the three service conditions including dry, raining, and groundwater level rising are simulated to study the dynamic interaction of track-subgrade-foundation under train loads. There are 1.0×10⁶ times excitation vibration for each service condition, and 3.0×10⁶ times in all. The specific process of test is as follows:

Step 1: The testing model is performed with 1.0×10⁶ times vibration under the dry condition after construction, and the data are recorded from the model test.

Step 2: The values for the rain-speed and rainfall are 29.8 mm/d and 3.68 m³ following the observed rainfall of Baise section of the Yun-Gui high-speed railway. The water supply network is installed above the roadbed model for simulating rainfall, and the soil strain sensor and moisture sensor are arranged in layers and embedded in the roadbed model to monitor the dynamic behavior of subgrade and underlying expansive soil due to rainfall. The testing model is performed another 1.0×10⁶ times vibration after rainfall, and the data are recorded in the test.

Step 3: The developed sequential water injection system is installed in roadbed for simulating groundwater level rising or surface water infiltrating. The water is injected into the roadbed simultaneously using a bottom-up approach, and the data are got from the moisture sensor to monitor the dynamic changes of groundwater level and saturation of expansive soil. The testing model is excited with 1.0×10⁶ times vibration again after water injection. Record the data in the test at the same time.

4 Test results and discussion

4.1 Distribution characteristic of dynamic soil stress

Figure 6 shows the curves of dynamic soil stress at different depths of subgrade with the increasing vibration times under different service environment conditions. The dynamic soil stress of subgrade showed fluctuation greatly under the same service condition at the beginning of the vibration. However, the dynamic soil stress gradually became stable after a number of vibrations. The dynamic soil stress of subgrade is significantly influenced by service conditions. The raining and groundwater level rising increases the soil stress in subgrade. Additionally, the dynamic soil stress decreases with an increase in depth from the roadbed surface. The dynamic soil stress is little influenced by service conditions when the depth from roadbed surface is larger than 2.3 m. After the subgrade model is excited with 1.0×10⁶ times vibrations under three service conditions, the dynamic soil stresses from the roadbed surface are 32.0 kPa, 37.0 kPa and 39.3 kPa at a depth of 0.2 m, increased by 15.6% and 22.8% under the conditions of the rising of raining and groundwater level compared with the dry condition. The dynamic soil stress shows fluctuation greatly with vibration times at the bottom of waterproof structure layer because the waterproof structure layer has semi-rigid characteristics.

Fig. 6 Curves of dynamic soil stress with vibration times under different service conditions (A, B, C and D correspond to sensors located under roadbed surface 0.2, 0.9, 1.5 and 2.2 m; same as in following)

The phenomenon reflects that the waterproof structure layer performs strong adaptability and coordination ability, and it can significantly improve the regularity of track.

Figure 7 shows the attenuation curves of dynamic soil stress of subgrade with depths under the track center. The curve is fitted by hyperbola function and exponential function, as shown in Table 4. Combined with Fig. 7 and Table 4, the relation between the dynamic soil stress and the depth is approximately in exponential function. The dynamic soil stress attenuate mainly occurs within 1.0 m depth from roadbed surface. And it decreases by more than 50% at the waterproof structure layer location (see Fig. 7(b)). Under three service environment conditions, the dynamic soil stresses from the roadbed surface are 32.0, 37.0 and 39.3 kPa at a depth of 0.2 m, and the dynamic soil stress are 14.0, 16.0 and 18.0 kPa at bottom of waterproof structure layer. Compared with the dynamic soil stresses of roadbed surface, the dynamic soil stress of lowest-layer of waterproof structure are reduced by 56.3%, 56.8%and 54.2%, respectively, which shows that the new-type waterproof structure layer has effects on energy dissipation, and it can accelerate attenuation of dynamic soil stress.

Fig. 7 Curves of dynamic soil stress with depths:

The field test data available in references are summarized in Table 5. It shows that the strength values of dynamic soil stress at the roadbed surface range from 50.0 to 100.0 kPa for ballasted tracks [15, 29, 30]. The larger dynamic soil stress will lead to soil particles breakage and further accumulated deformation. So, the parameters of dynamic soil stress strength at the roadbed surface and accumulated deformation are not only used to design subgrade structure rationally, but also used in operational safety and later maintenance for ballasted railway. For describing the attenuation characteristics of subgrade dynamic soil stress with depths below the track structure, the attenuation coefficient λ is introduced here as the ratio of the dynamic soil stress σ(z) at any depth to the dynamic soil stress σ(z) of roadbed surface. The attenuation coefficients λ with depths from the roadbed surface for ballasted based on the field measurements and the current model testing data are shown in Fig. 8. The figure clearly indicates that the dynamic soil stress attenuation mainly occurs in the superstructure layer of roadbed (ballast bed, subgrade surface layer), and the dynamic soil stress from the roadbed surface in the ballasted tracks decreases by more than 80% at a depth of 3.0 m. The dynamic soil stress attenuates much faster in new subgrade structure by adding waterproof structure layer than in traditional subgrade structure. And dynamic soil stress from the roadbed surface in the ballasted tracks decreases by about 80% at a depth of 1.5 m. The attenuation curves of No. 1 and No. 2 are lower limits and upper limits, the fitting result by exponential function is between them, and the calculation result by elastic theory can be seen approximate lower limit when empirical data are really lacking. Combined with Fig. 8 and Table 4, the fitting attenuation curve of dynamic soil stress with depths from the roadbed surface by exponential function is more consistent with the test results and the average goodness- of-fit R² reaches 0.992. So, the relationship between the dynamic soil stress and depth can be expressed by the exponential function, which are expressed by

Table 4 Fitting equations between dynamic soil stress and depth

Table 5 Dynamic stress measured at roadbed surface in ballasted

                        (2)

Fig. 8 Comparison between attenuation coefficients of dynamic stress

where σ(z) is dynamic stress any soil depth; σ(z₀) is dynamic stress of roadbed surface; λ is the attenuation coefficient of dynamic stress; a and b are fitting coefficients; z is the depth from roadbed surface (m).

Based on the calculation formula predicting dynamic stress at the roadbed surface in code for design of ballasted high-speed railway in China [27], the dynamic stress with depth from the roadbed surface under train loads in expansive soil areas can be determined by

               (3)

where σ(z₀) is dynamic stress of roadbed surface (kPa); λ is the attenuation coefficient of dynamic stress; P is the axle load of trains (kN); v is train speed (km/h); α is the speed coefficient, and α=0.004 is recommended for a high-speed railway when the train speed v reaches 200-250 km/h, and α=0.003 is recommended for a high-speed railway when the train speed v reaches 300-350 km/h, and (1+αv) is defined as the dynamic impact factor with an upper limit of 1.9 when it is passenger railway line; z is the depth from roadbed surface (m).

Figure 9 shows the distribution laws of vertical dynamic soil stress in the transverse testing section under different service environment conditions. The curve of vertical dynamic soil stress presents a “Z” shape distribution along transverse distance under the vibration loads, and the peak value of dynamic soil stress appears below the rail. The single-peak characteristics are more obvious near roadbed surface. The dynamic soil stress is greatly affected by the vibration loads within 5.0 m distance from the center line with an average value of 5.0 kPa. While under three different service environment conditions, the dynamic soil stresses from the roadbed surface are 40.0, 41.0 and 43.0 kPa at a depth of 0.2 m below the rail, and the values of dynamic soil stress increase by 2.5% and 7.5% with the rising of raining and groundwater level compared with dry condition. It is shown that the dynamic performance of subgrade is significantly influenced by service conditions, and the moisture change of expansive soil is the key factor that affects the magnitude and distribution of dynamic soil stress. Consequently, the measures of enhancing waterproofing and drainage measures and maintaining the moisture stability of expansive soil foundation is crucial to ensure the long-term dynamic stability of subgrade.

Fig. 9 Distribution curves of dynamic soil stress with lateral distance: (Section 1 is at 0.2 m depth from roadbed surface; Section 2 is bottom of waterproof structure layer; Section 3 is bottom of subgrade structure layer; the same as in the following)

4.2 Distribution characteristic of vibration velocity

Figure 10 shows the curves of vibration velocity at different depths of subgrade with the increase in vibration times under different service environment conditions. The conclusions from the figure are as follows: 1) Under dry condition, the vibration velocity of subgrade shows fluctuation greatly at the beginning of the vibration, which is mainly because the stuffing and velocity sensor are constantly adjusted and coupled under the dynamic loading. However, the vibration velocity gradually becomes stable after vibration reaches 0.5×10⁶ times, and the vibration velocities are 9.0, 7.8, 6.4 and 2.6 mm/s at the different depths. 2) Under raining condition, the vibration velocity shows fluctuation greatly at the beginning of the vibration and it obviously increases under dynamic loading, but it does not present apparent change under the bottom layer of subgrade. The stable values of velocity are 10.0, 9.5, 7.2 and 2.0 mm/s at the different depths, and they increase by 11.1%, 21.8%, 12.5% and -23.1% compared with the dry condition, respectively. 3) Groundwater level rising leads to the hopping increasing state of the vibration velocity at the beginning of the vibration. The velocity gradually becomes stable after 0.3×10⁶ times vibration, with the values of 10.5, 10.0, 8.1 and 2.1 mm/s at the different depths which increase by 16.7%, 28.2%, 26.6% and -19.2% compared with the dry condition. The primary reasons for that hopping change are as follows. On one hand, excess pore-water pressure will be produced in layers by dynamic loading when water infiltrating into the subgrade. It is the increased stiffness of structure and the weakened energy dissipation of roadbed structure in the macroscopic that leads to the increase of vibration velocity. The vibration velocity gradually decreases with the excess pore-water pressure dissipation, and finally it tends to be steady. On the other hand, the deformation of expansive soil foundation is complex and asynchronous. The dynamic loading coupling with service environment would eventually make the behavior of subgrade be coordinated with service environment constantly. The raining and groundwater level rising causes vibration velocity to increase in subgrade, and the velocity volatility of subgrade surface layer is more evident than that of waterproof structure layer. The phenomenon shows that the new-type waterproof structure layer has better energy dissipation and diffusion effect on the vibration velocity, and the volatility of velocity is attenuated and spread out above the waterproof structure layer.

Fig. 10 Curves of vibration velocity with vibration times under different service conditions

Figure 11 shows the attenuation curves of vibration velocity of subgrade with depths under the track center. It can be seen from Fig. 11 that the vibration velocity is significantly influenced by service environment conditions above the bottom layer of subgrade and the relations between vibration velocity and depth are approximate parabola function, as shown in Table 6. Under three service environment conditions, the vibration velocities from the roadbed surface are 9.0, 10.0 and 10.5 mm/s at a depth of 0.2 m below the rail and the vibration velocities are 7.8, 9.5 and 10.0 mm/s at bottom of waterproof structure layer, which shows that the raining and groundwater level rising causes vibration velocity to increase, and it is most affected by the groundwater level rising.

Fig. 11 Curves of vibration velocity with depths

Table 6 Fitting equations between velocity and depth

Figure 12 shows the distribution laws of vibration velocity on the transverse testing section under different service environment conditions. The distribution laws of vibration velocity alone the transverse are the same under the three service environment conditions (dry, raining, and groundwater level rising), and the vibration velocity increases firstly, and then decreases along the horizontal distance, and finally it tends to be stable. The peak value of vibration velocity appears below the rail. The raining and groundwater level rising can lend to its increase in substructure. Corresponding with the foregoing three service environment conditions, the vibration velocities from the roadbed surface are 9.5, 11.3 and 11.5 mm/s at a depth of 0.2 m under the rail, and the vibration velocities increase by 18.9% and 21.1% by raining and groundwater level rising compared with dry condition, respectively.

Fig. 12 Distribution curves of vibration velocity with lateral distance:

4.3 Distribution characteristic of vibration acceleration

Figure 13 shows the curves of vibration acceleration at different depths of subgrade with the vibration times increasing under different service environment conditions. The conclusions from the figure are as follows: 1) Under dry condition, the vibration acceleration of subgrade shows great fluctuation at the beginning of the vibration, but it gradually becomes stable after 0.2×10⁶ times vibration, and the vibration accelerations are 0.20, 0.17, 0.14 and 0.08 m/s² at the different depths. 2) Under raining condition, the vibration accelerations increase obviously under dynamic loading, when the vibration accelerations are stable after a number of vibration times, and their values are 0.27, 0.23, 0.19 and 0.09 m/s² at the different depths, which increase by 35.0%, 35.3%, 35.7% and 12.5% compared with the dry condition. 3) Groundwater level rising leads to the hopping increasing state of the vibration acceleration at the beginning of the vibration, and the acceleration gradually becomes stable after vibration 0.5×10⁶ times, whose values are 0.29, 0.25, 0.21 and 0.12 m/s² at the different depths, and they increase by 45.0%, 47.1%, 50.0% and 50.0% compared with the dry condition, respectively.

Fig. 13 Curves of vibration acceleration with vibration times under different service conditions

Figure 14 shows the attenuation curves of vibration acceleration of subgrade at different depths under the track center. Under different service environment conditions, the relation between vibration acceleration and depth is approximate in parabola function (see Table 7), and its magnitude and distribution are significantly influenced by service conditions. The vibration accelerations from the roadbed surface are 0.20, 0.27 and 0.29 m/s² at the depth of 0.2 m. Compared with the dry condition, the vibration accelerations increase by 35.0% and 45.0% by raining and groundwater level rising, respectively. The vibration accelerations are 0.17, 0.23 and 0.25 m/s² at bottom of waterproof structure layer. Compared with the dry condition, the vibration accelerations increase by 35.3% and 47.1% by raining and groundwater level rising, respectively. This shows that the raining and groundwater level rising cause vibration velocity to increase above the bottom layer of subgrade, and waterproofing and drainage measures are required enhancing to reduce the diseases of roadbed and to ensure the long-term stability of subgrade.

Fig. 14 Curves of vibration acceleration with depths

Table 7 Fitting equations between acceleration and depth

Figure 15 shows the distribution laws of vibration acceleration on the transverse testing section under different service environment conditions. The distribution laws of vibration acceleration along the transverse are the same as these under the three service environment conditions (dry, raining, and groundwater level rising), and the peak value of vibration velocity appears below the rail. The vibration acceleration decreases with an increase in the horizontal distance from the central line, and the average value of vibration acceleration is less than 0.05 m/s² outside 5.0 m from central line. Corresponding with the foregoing three service environment conditions, the vibration accelerations from the roadbed surface are 0.18, 0.25 and 0.30 m/s² at a depth of 0.2 m under the rail, and increase by 38.9% and 66.7% by raining and groundwater level rising compared with dry condition, respectively. This shows that the raining and groundwater level rising cause vibration acceleration to increase in subgrade structure layer and it is extremely detrimental to the long-term dynamic stability of subgrade.

Fig. 15 Distribution curves of vibration acceleration with lateral distance:

4.4 Analysis of subgrade deformation

Figure 16 shows the vertical deformation curves of subgrade directly below the track with the vibration times increasing under different service environment conditions (dry, raining, groundwater level rising). The conclusions from the figure are as follows: 1) Under dry condition, the relation between the deformation of roadbed surface and foundation surface and vibration times is increasingly linear, and the maximum deformation of roadbed surface is -2.72 mm. Among them, the deformation of foundation is -2.19 mm, which is about 80.5% of the total deformation; the deformation of subgrade is -0.53 mm, which is about 19.5% of the total deformation. So, the post-construction settlement of subgrade control is mainly affected by foundation settlement, and the strengthen foundation treatment measures should be taken to reduce the post-construction settlement in actual engineering. 2) Under raining condition, the settlement of roadbed greatly increases at the beginning of the vibration; the total settlement of roadbed is -23.58 mm under the rail. Among them, the deformation of foundation is -16.66 mm, which is about 70.7% of the total deformation; and the deformation of subgrade is -6.92 mm, which is about 29.3% of the total deformation. The deformations of roadbed surface and foundation surface reduce by 2.72 mm and 2.56 mm respectively after 1.0×10⁶ times vibration, which indicates obvious swelling deformation in roadbed. The main reason is that the swelling deformations of expansive soil foundation push the roadbed upward due to the water infiltrating into the expansive soil by wall of model box and hidden leakage points. 3) When groundwater level rises, there will be obvious swelling deformation of expansive soil foundation with the moisture content increasing, which rapidly reduces the deformation of roadbed surface and foundation surface. The deformation gradually becomes stable after vibration 2.7×10⁶ times and the deformations of roadbed surface and foundation surface are 9.92 mm and 7.34 mm, respectively. This shows that there is obvious swelling deformation and swelling pressure when water infiltrating into the expansive soil. It often causes non-uniform deformation of subgrade structure and creak of waterproof structure. Consequently, in expansive soil areas, reinforcing the waterproofing and drainage measures and deformation coordination performance of subgrade has positive effects on improving the adaptability and stability of subgrade structure.

Fig. 16 Curves of subgrade deformation with vibration times under different service conditions

4.5 Waterproof effect testing of subgrade structure

In the process of vibration test, the moisture sensor is arranged in subgrade structure to monitor the moisture changes under dynamic loading, and the depths of moisture sensor from the roadbed surface are 0.2, 0.9, 1.7, 2.2 and 2.7 m, respectively. Since the trial has ended, the curves of moisture with depths under three different service environment conditions are shown in Fig. 17. The relation between moisture and depth is increasingly linear under dry condition; the moisture of subgrade surface layer increases quickly under raining condition, but the moisture (Precision of moisture sensor: ±3%) is almost constant below the waterproof structure layer, which shows that the rainwater is isolated in subgrade surface layer due to waterproof structure layer. It is not into foundation of expansive soil. When groundwater level rises, the moisture increases obviously under the waterproof structure layer, but the moisture is stable in the waterproof structure layer, which means that the groundwater is isolated below the waterproof structure layer. With the tests above, the new-type waterproof structure layer can keep excellent waterproof and impermeable effects.

Fig. 17 Moisture changes with depth under different service conditions

The surface layer of subgrade is excavated and checked after 3.0×10⁶ times model test under three different service environment conditions and the appearance of waterproof structure layer is shown in Fig. 18. By on-site closely examining, the waterproof structure layer has not introduced any crack damage and leakage, which verifies that the waterproof structure layer has strong anti-permeability and anti-fatigue performance under dynamic cyclic loading.

Fig.18 Appearance of waterproof layer after model tests:

5 Verification of service result based on field test data

The scheme will be applied and popularized to newly built Yun-Gui railway engineering. To further ensure the construction quality of Yun-Gui railway and to validate the service performance of new-type waterproof structure layer, two cutting subgrade sections of medium-weak and medium-strong expansive soil are selected for field testing. The two service conditions of dry and soaking are simulated to study the performance of waterproof and anti-fatigue of new-type waterproof structure layer under dynamic cycle loads, and test results are as follows.

The moisture sensor is arranged on the interface of subgrade structure to monitor the moisture changes under dynamic loading. The measured results of medium-weak and medium-strong expansive soil test model are shown in Tables 8 and 9. The measured data show that the moisture increases obviously above the waterproof structure layer when water infiltrating into the subgrade surface layer, but the moisture is stable under the waterproof structure layer. This shows that the new-type waterproof structure layer can effectively prevent the surface water from immersing, and present excellent waterproof behavior in medium-weak and medium- strong expansive soil areas.

Table 8 Monitoring data of moisture in section DK161+840

Table 9 Monitoring data of moisture in section DK205+542

In order to verify the anti-fatigue performance of waterproof structure layer under service environment conditions coupling with dynamic loading, the surface layer of subgrade is excavated after 2.0×10⁶ times field vibration test on each section, and checked for cracks and leakage points of waterproof structure layer. The appearance of waterproof structure layer is shown in Fig. 19. Results of check show that the waterproof structure layer does not induce any crack damages and leakages. Consequently, the waterproof structure layer can meet the basic requirements of waterproof, impermeabilityand anti-fatigue, which provides a guarantee for construction quality and long-term dynamic stability of the newly built Yun-Gui railway.

Fig. 19 Appearance of waterproof layer after in-situ tests:

6 Conclusions

1) The subgrade dynamic responses with vibration times and then becomes stable under different service environment conditions, and the raining and groundwater level rising cause dynamic soil stress to increase. The relation between dynamic soil stress and depth is approximate in exponential function, and the new waterproof structure layer can accelerate attenuation of dynamic soil stress. The curves of dynamic soil stress present a “Z” shape distribution along transverse distance. The peak value of dynamic soil stress appears below the track, and the peak characteristics are more obvious close to the roadbed surface. And it is little affected outside the center line 5.0 m. An improved empirical formula is then proposed to predict the dynamic soil stress of ballast track subgrade of expansive soil.

2) Under the same service environment condition, the velocity and acceleration of subgrade show a greater volatility at the beginning of excitation test, but it gradually becomes stable with the increase of vibration times, and it represents a quadratic curve with an increase in the depth. The distribution of new subgrade velocity and acceleration are significantly influenced by service environment conditions, especially the influence of groundwater level. The influence of the raining and dry is relative weak. The velocity and acceleration of subgrade increase with the increasing of moisture content in expansive soil, which means that a waterproofing and drainage measure should be specially taken in actual project to reduce the diseases of roadbed and ensure the long-term stability of subgrade.

3) The service environment conditions have different effects on the vertical deformation of different depth location in roadbed. The deformation of roadbed increases sharply when the water gets into the foundation of expansive soil. There is obvious swelling deformation with the increasing of moisture content in expansive soil, and it is the swelling deformation that causes the uplift deformation of roadbed. Because more than 60% of the total deformation of subgrade occurs in expansive soil foundation, reinforcing swelling-shrinkage deformation control of expansive soil and laying waterproofing and drainage structure layer has positive effects on deformation control of roadbed surface as well as the track regularity improvement.

4) The new-type waterproof structure layer can meet requirements of waterproof, impermeability, anti- vibration and impact-absorbing. It can effectively prevent the water from impregnation under raining and groundwater level rising, and it can maintain strong anti-permeability and anti-fatigue performance under coupling function of soaking and long-term dynamic cyclic loading. It presents better energy dissipation and diffusion effect on the train vibration load and is useful to improve the ride performance and long-term dynamic stability of railway track.

5) The full-scale model testing provides a better understanding on the dynamic behavior of subgrade structure under train loads, and improves design method for high-speed railways subgrade structure in expansive soil areas.

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(Edited by YANG Hua)

Cite this article as: QIU Ming-ming, YANG Guo-lin, SHEN Quan, YANG Xiao, WANG Gang, LIN Yu-liang. Dynamic behavior of new cutting subgrade structure of expensive soil under train loads coupling with service environment [J]. Journal of Central South University, 2017, 24(4): 875-890. DOI: 10.1007/s11771-017-3490-0.

Foundation item: Projects(51478484, 51308551, 51678571) supported by the National Natural Science Foundation of China; Project(2016zzts063) supported by Fundamental Research Funds for the Central Universities, China

Received date: 2015-09-14; Accepted date: 2016-03-22

Corresponding author: QIU Ming-ming, PhD; Tel: +86-15116159345; E-mail: sxdfqiuming@163.com