Experimental study on the shear stiffness and damping ratio of the coarsegrained soil against geogrid interface
Aijun Chen^{1} , Chunhui Su^{2} , Junhua Chen^{3} , Xianyuan Tang^{4} , Zhaoyao Yuan^{5}
^{1, 2, 3, 4, 5}School of Architecture and Transportation Engineering, Guilin University of Electronic Technology, No. 1 Jinji Road, Qixing District, Guilin, 541004, China
^{2}Corresponding author
Journal of Vibroengineering, Vol. 22, Issue 7, 2020, p. 16061617.
https://doi.org/10.21595/jve.2020.21204
Received 2 December 2019; received in revised form 7 June 2020; accepted 14 June 2020; published 7 November 2020
Geosyntheticreinforced soil structures are mostly used to retain subgrade slope of highway and railway. For the design and performance analyses of geosyntheticreinforced soil structures under repeated loading, such as those induced by compaction, traffic and earthquakes, the understanding of cyclic soil–geosynthetic interface behaviour is of great interest. Nevertheless, experimental data concerning this type of behaviour are very scarce. A laboratory study was carried out and is described in this paper. This paper presents the behaviour of an interface between a coarsegrained soil and a geogrid under cyclic loading conditions. A largescale direct shear test device able to perform displacementcontrolled cyclic tests was used. The results obtained are presented and discussed, especially the effects of the displacement amplitude and normal stress on the shear stiffness and damping ratio are investigated. The dynamic response parameters of the soilgeosynthetic interface are greatly affected by the number of cycles, and the variations in the two parameters with the number of cycles are related to the normal stress and the shear displacement amplitude. when at large displacements, the damping ratio decreases first and then stabilizes with the number of cycles. However, at small displacement, the shear stiffness and damping ratio are all decrease somewhat at the initial stage of cyclic shearing. As the experimental materials used in this study are relatively single, and further experimental research should be carried out in the future. The shear parameters of interface in this study can provide reference for the design of reinforced soil structure.
 The dynamic response parameters of the soilgeosynthetic interface are greatly affected by the number of cycles.
 The variations of shear stiffness and damping ratio with the number of cycles are related to the normal stress and the shear displacement amplitude.
 When at large displacements, the damping ratio decreases first and then stabilizes with the number of cycles.
 When at small displacement, the shear stiffness and damping ratio are all decrease somewhat at the initial stage of cyclic shearing.
Keywords: cyclic shearing; geogrid; coarsegrained soil; shear stiffness; damping ratio.
1. Introduction
With regard to highway and railway subgrade engineering, geosynthetics are often used to enhance the stability of subgrade slopes. Reinforced soil structures in practice bear not only static loads such as gravity but also dynamic loads such as earthquakes, wave loads and traffic loads. The properties of the soilgeosynthetics interface under static loading may be studied by monotonic direct shear tests and pullout tests. Under dynamic loading, the soilgeosynthetic interface is subjected to cyclic shear action, and the cyclic direct shear test is used to study the interfacial shear behavior under cyclic shear. Due to the different loadings, the interfacial characteristics must be different for static loads and dynamic loads. Research on the dynamic shear properties of the soilgeosynthetic interface will help understand the interaction principle of the interface and improve the accuracy of the stability analysis of reinforced soil structures under dynamic loads.
The mechanical properties of the interface between the soil and geosynthetics have an important influence on the stability and durability of reinforced soil structures. Over recent decades, many researchers have investigated the shear properties of the interface under static loads [1, 2]. Liu et al., [3] studied the model regarding the effect of the grid transverse rib on the interface shear strength under a static load. Many scholars [47] carried out a series of tests to evaluate the impacts of the normal stress, shear speed and material properties on the shear strength of the interface. Khoury et al., [8] researched the properties of the interface between unsaturated soil and geosynthetics, using modified direct shear equipment, and proposed an elasticplastic constitutive model to characterize the unsaturated soilreinforcement interface properties. Anubhav et al., [9] studied the properties of the soilgeotextile interface with different textures, proposing a nonlinear constitutive model to characterize the interface properties. Lee et al., [10] and Choudhary et al., [11] conducted largescale direct shear tests to study the impacts of the particle diameter and the type of geosynthetic on the interface shear properties. Bergado et al., [12] obtained the values of the interface friction angle of the geomembranesoil interface under dry and wet conditions by conducting largescale direct shear tests. Vangla et al., [13] and Punetha et al., [14] recorded the movement of soil particles and the stretcher strain of geotextiles by taking photos and using scanning electron microscopy (SEM) in shear tests.
For the interaction between geosynthetics and soil under a dynamic load, Zhang et al., [15] developed a largescale 3D testing machine for the soilstructure interface that was adopted to study the cyclic mechanical properties of the contact surface. Mortara et al., [16] studied the impact of cyclic shear on the strength properties of the contact surface between the soil and structure by performing a series of cyclic shear tests. Nye et al., [17] studied the shear properties of the claygeosynthetics interface by implementing monotonic direct shear and cyclic direct shear tests. Fox et al., [18] studied the damage properties of geotextiles under dynamic loading with a series of static and dynamic direct shear tests. Vieira et al., [19] compared the results of loadcontrolled and displacementcontrolled shear tests by conducting monotonic and cyclic direct shear tests. Liu et al., [20] studied the impacts of different geotechnical materials and cyclic loading on the interface shear stiffness and damping ratio by adopting a largescale multifunctional interface shear apparatus, but the number of cycles was only 10, which made it difficult to fully reflect the actual loading condition of the reinforced soil structure.
Some scholars have utilized multiple methods and means, including direct shear tests, pullout tests and inclined plane tests, to obtain the properties of the soilgeosynthetic interface under various working conditions. Zimmie et al., [21] studied the dynamic properties of various soilgeosynthetic interfaces using direct shear tests and shaking table tests, which revealed the major properties of the dynamic friction angle in the interface. Kamalzare et al., [22] investigated the static properties of the soilgeosynthetic interface of different geosynthetics by adopting largescale shear tests, showing that the interface strength characteristics of different geosynthetics are significantly different. DE et al., [23] and Chen et al., [24] conducted a series of direct shear and centrifuge model tests to study the dynamic properties of eight soilgeosynthetic interfaces. By using plane tests, Lopes et al., [25] investigated the interface properties of multiple geosynthetics, demonstrating a significant impact of the type and structure of the geosynthetic on the interface friction angle. In addition, Deng et al., [26] and Zhao et al., [2729] carried out theoretical research on the mechanical properties of relevant geotechnical materials and obtained some valuable conclusions.
In studying the characteristics of the soilgeosynthetic interface of reinforced soil structures under dynamic loads, the cyclic shear stiffness and damping ratio are often used to characterize the dynamic response parameters of reinforced soil structures. However, there has been no comprehensive study on the shear stiffness and damping ratio of the soilgeosynthetic interface in previous studies, especially the number of shear cycles used in the existing research results, which are too few to reflect the real behavior of actual engineering under dynamic action. In this paper, the large amplitude cyclic shear test and small amplitude cyclic shear test are carried out, and the variations in the shear stiffness and damping ratio under different dynamic loads for geogrids against coarsegrained soil interfaces has been obtained, which can provide effective parameters for the stability analysis of reinforced soil structure.
2. Materials and apparatus
2.1. Materials
A coarsegrained soil adopted as the testing soil is a mixture of clay and graded gravel. The grain size distribution curve of the soil is presented in Fig. 1, and the physical properties of the clay are shown in Table 1. Fig. 1 reveals that the content of finegrained group less than 0.075 mm is only about 16 %, so it can be judged that the soil material belongs to sandy soil, which is a good kind of subgrade filler. The test geogrid is bidirectional, and its technical parameters are shown in Table 2.
Table 1. Physical indices of testing clay
Specific gravity  Liquid limit (%)  Plastic limit (%)  Plastic index 
2.75  36.1  20.2  15.9 
Table 2. Technical indexes of the geogrid
Quality per unit area (g/m^{2})  Aperture size (mm)  Rib width (mm)  Ultimate tensile strength (kN/m)  Ultimate elongation (%) 
310  15  10  90  4 
Fig. 1. Grain size distribution curve of the soil
Fig. 2. Largescale direct shear apparatus
2.2. Description of the apparatus
This test adopts a largescale dynamicstatic direct shear apparatus (as shown in Fig. 2), and the length, width, and thickness of the upper and lower shear boxes are 500 mm×500 mm×150 mm. The maximum particle size of the soil in the direct shear test is 48 mm. The geogrids are fastened on the top of the lower shear box via a fixture before the shear test. When shearing the interface, the upper shear box is fixed while the lower box moves horizontally. The maximum horizontal shear displacement can reach 300 mm, with shearing rates from 0.01 mm/s to 2 mm/s. The maximum vertical displacement is 200 mm, and the maximum normal loading is 600 kN. Due to the same size of the upper and lower shear boxes, the vertical stress remains unchanged by changing the vertical loads. The horizontal and vertical displacements during the shearing process are measured using the displacement sensor and automatically read by the computer.
In addition, the large direct shear tester, equipped with an auxiliary soil sample loading and unloading device, is adequate to make the large soil samples and to load and unload the shear box faster.
3. Test procedure
3.1. Test methods
Cyclic shear tests consist of large and smalldisplacement amplitude shears for the soilgeosynthetics interfaces. The cyclic shear test of large displacement amplitude adopts the vertical stress/100 kPa, the shear displacement amplitude / 10 mm, 20 mm and 40 mm respectively, and the shear rate / 0.8 mm/ s. The small displacement amplitude cyclic shear test adopts the vertical stress / 100 kPa, 200 kPa and 300 kPa, the shear displacement amplitude / 2 mm, and the shear rate / 0.8 mm/s. Parameters considered for conducting the experiment under both largedisplacement and smalldisplacement amplitude shear are tabulated in Table 3 and Table 4 respectively.
Table 3. Test parameters of the largedisplacement amplitude shear
Frequency (Hz)  Normal stress (kPa)  Number of cycles  Displacement amplitude (mm) 
0.02  100  200  10 
0.01  100  100  20 
0.005  100  50  40 
Table 4. Test parameters of the smalldisplacement amplitude shear
Frequency (Hz)  Normal stress (kPa)  Number of cycles  Displacement amplitude (mm) 
0.1  100  1000  2 
0.1  200  1000  2 
0.1  300  1000  2 
3.2. Specimen preparation
The soil is compacted in three layers 250 mm in height. For easy compaction and installation of the geogrids, the thicknesses of the top and bottom layers are both 100 mm, and those of the middle layers are 50 mm, with a 90 % degree of compaction. When compacting specimens, the soil in the bottom layer is placed in the lower shear box and hammered to 100 mm in height. Then, the upper shear box is lifted and fixed on the lower shear box with screws; subsequently, the soil for the second layer is weighed and placed in the shear box. When the soil samples in the first and second layers stand at 150 mm in height, the upper shear box is removed, and the geogrid is fastened on the top of the lower shear box with clamps. Finally, the upper shear box is lifted and fastened, and the third layer of soil is placed into the box and compacted to 250 mm in height. The installed geogrid is shown in Fig. 3.
Fig. 3. Geogrid in the interface
4. Shear stiffness and damping ratio
The stiffness and damping ratio of soils are often used for dynamic response analysis. Nye et al., [17] revised the method of calculating the stiffness and damping ratio and used it to describe the dynamic characteristics of the sandconcrete interface. Fox et al., [18] applied it to a dynamic response analysis of the geomembranegeotextile interface. Choudhary et al., [11] and Punetha et al., [14] applied the stiffness and damping ratio to a dynamic shear analysis of the soilgeosynthetics interface. In this paper, the shear stiffness and damping ratio are used to describe the cyclic shear behavior of the reinforced soil interface by a similar method. Fig. 3 presents the calculation process for the shear stiffness and damping ratio in a single hysteretic loop [17]. Considering the asymmetry of the same hysteretic loop in two shear directions, the shear stiffness $K$ in the hysteretic loop is calculated as follows:
In the formula, ${K}_{1}$ and ${K}_{2}$ are the shear stiffnesses in the two shear directions, and are the peak shear stresses in the two shear directions, and $\mathrm{\Delta}a$ is the shear displacement amplitude. Similarly, the damping ratio $D$ is calculated as follows:
In the formula, ${D}_{1}$ and ${D}_{2}$ are the damping ratios in two shear directions, $A$ is the area of the whole hysteresis loop, and ${A}_{1}$ and ${A}_{2}$ are the shaded areas in Fig. 4.
Fig. 4. Calculation of the secant shear stiffness and damping ratio from the hysteresis loop
Fig. 5. Singleloop curve of the shear stressshear displacement
5. Experimental results and analyses
5.1. Characteristics of the interface shear strength
Fig. 5 presents the single curve of the shear stress versus shear displacement at a displacement amplitude of 10 mm, and the hysteresis curves of the shear stressshear displacement during the first 50 cycles are shown in Fig. 6 (the initial loading curve in the first cycle is not included). As shown in Fig. 5, the curve of the shear stressshear displacement consists of four stages: positive loading, reverse unloading, reverse loading and positive unloading, which circulate clockwise. The positive loading starts from the shear displacement of 0 mm, and the shear stress increases with shear displacement and reaches the peak value at the same time when the displacement is maximum. The reverse unloading curve is initially steep, as the shear stress decreases rapidly with a decrease in displacement, and the later unloading curve is parallel with the positive loading curve. The reverse loading curve is parallel with the positive loading curve, as the shear stress increases with the shear displacement. The positive unloading curve is initially steep and then tends to be gentle. While the forward loading, the increase of the displacement between soil particles and grid results in the increase of interface friction gradually, but the soil particles do not turn over completely; at the initial stage of the reverse unloading, the shear stress decreases rapidly to 0 due to the repositioning of soil particles, and when the shear displacement is 0, the negative shear stress has been generated, thus completing the half cycle. So does the other half cycle.
Fig. 6. Curves of the shear stress versus shear displacement
a) Displacement amplitude of 10 mm
b) Displacement amplitude of 20 mm
c) Displacement amplitude of 40 mm
Fig. 6 shows that the larger the shear displacement amplitude is, the more moderate the initial positive loading and reverse loading curve trends, which means that a smaller load is needed for displacements from 0 to the semi amplitude value than for other displacements. In addition, the greater the displacement amplitudes are, the greater the load variation during the unloading stage. This is because the greater the displacement amplitude is, the greater the damage to the soilgeosynthetic interface, especially the damage caused by the breaking of the geogrid ribs.
5.2. Normal deformation of the interface
Fig. 7 presents the curve of the normal displacementshear displacement for the shear displacement amplitude of 20 mm. As shown in Fig. 9(a), it is evident that the specimen has a distinct normal displacement, which means that volumetric deformation occurs in the soilgeosynthetic interface. With the increase in cycles, the normal displacement of a single cycle decreases gradually, and the accumulated normal displacement becomes larger. Fig. 9(b) shows that during the single shear cycle, the specimen alternately produces shear contraction and dilatancy, i.e., loading shear results in dilatancy, and unloading shear produces contraction. The shear contraction of a single cycle is greater than the shear dilatancy; however, the contractive behavior is superimposed on the dilative behavior, so the sample contracts as a result of the induced cycling. Under loading shear, the soil particles in the soilgeosynthetic interface climb and move to generate shear expansion. Under unloading shear, soil particles in the soilgeosynthetic interface are rearranged to become tense and generate shear shrinkage under the vertical stress.
Fig. 7. Curves of the normal displacementshear displacement
a) Fifty shear cycles
b) Single shear cycle
5.3. Interface shear stiffness and damping ratio
5.3.1. Influence of the number of cycles
When reinforced soil structures are subjected to longterm dynamic loads, the soilgeosynthetic interface undergoes thousands of shearing cycles. However, the number of soilgeosynthetic interface shear cycles in existing research results is only 1040 [17, 19, 20]. As the number of shear cycles has a significant effect on the soilgeosynthetic interface characteristics, it is necessary to carry out more shearing cycles to obtain them. In this paper, 1000 shearing cycles were carried out for the coarsegrained soil against the geogrid interface, and the variations in the shear stiffness and damping ratio with cycles under two normal stresses (200 kPa and 300 kPa) are shown in Fig. 8 and Fig. 9, respectively.
Fig. 8 shows that the shear stiffness decreases with the number of cycles at the small displacement amplitude (2 mm). The shear stiffness decreases sharply during the first 50 cycles, then decreases slowly and does not stabilize completely after 1000 cycles.
Fig. 9 shows that the development of the damping ratio varies greatly with the cycle number for different normal stresses. During the first 200 cycles, the damping ratio decreases with the number of cycles, and the rate of reduction is fast first and then slow. After 200 cycles, the damping ratio is basically stable between 0.18 and 0.19 under a normal stress of 200 kPa. Under a normal stress of 300 kPa, the damping ratio increases with the number of cycles, but the growth rate is slow first and then fast, and the damping ratio increases stepwise and exceeds the initial value after 500 cycles.
Analyzing Fig. 8 and Fig. 9, the influence of the cycle number on the shear stiffness and damping ratio is obvious. Even if the cycle number reaches 1000, the parameters of the interface characteristics are still not stable. Moreover, the variations in the shear stiffness and damping ratio with the cycle number are closely related to the displacement amplitude and normal stress. That is, under different shear conditions, the development law of the interface parameters with the cycle number varies. To fully obtain the dynamic response of the reinforced soil structure, shear tests should be conducted under various working conditions and with a large number of cycles.
Fig. 8. Change in the shear stiffness with shear cycles
Fig. 9. Change in the damping ratio with shear cycles
5.3.2. Influence of the displacement amplitude
The variations in the shear stiffness and damping ratio with cycle numbers at different shear displacement amplitudes (10 mm, 20 mm, 40 mm) are obtained by cyclic shear tests; the results are shown in Fig. 10 and Fig. 11 (normal stress is 100 kPa).
Fig. 10. Shear stiffness at different displacement
Fig. 11. Damping ratio at different displacement
It can be seen that the shear stiffness increases with the number of cycles during the initial stage of cyclic shear. The shear stiffness at displacement amplitudes of 20 mm and 40 mm decreases slightly and tends to be stable after 10 cycles, but the shear stiffness at the displacement amplitude of 10 mm does not decrease significantly and stabilizes above 2900 kPa/mm, which shows that the interface exhibits shear hardening during cyclic shear. Similar behavior was observed by Vieira et.al., [19]. For the same number of cycles, the shear stiffness at the displacement amplitude of 40 mm is greater than 4700 kPa/mm, and the shear stiffness at displacement amplitudes of 20 mm and 10 mm is less than 3000 kPa/mm. The shear stiffness at a displacement amplitude of 40 mm is much larger than that at the other two amplitudes, which indicates that the shear stiffness easily increases when the displacement amplitude rises. The interface shear strength of coarsegrained soil against a geogrid includes (i) resistance of the geogrid ribs, (ii) sliding friction between the soil particles and the geogrid ribs, and (iii) friction and interlocking of the soil particles. At a large shear displacement amplitude, the adjustment of the soil particles is sufficient, and the increase in the soil compactness leads to an increase in the interlocking force of the soil particles, so the shear stiffness increases to a certain extent during the initial stage of cycles. After 10 cycles, the compactness of the soil will not increase, and the interlocking force of the soil particles will remain stable. However, an overly large displacement amplitude may lead to the fracturing of the transverse rib, and the resistance of the transverse rib will decrease accordingly. Therefore, the shear stiffness at a displacement amplitude of 40 mm will decrease after 10 cycles.
Fig. 11 shows that during the initial stage of cyclic shear, the damping ratio at different displacement amplitudes decreases sharply with the cycle number but no longer decreases significantly after 15 cycles and tends to be stable. Liu et. al., [20] carried out cyclic shear tests on a geogridsand interface at displacement amplitudes of 1 mm, 3 mm and 5 mm (10 cycles), and it was found that the interfacial damping ratio did not change significantly with the cycle number, which is different from the conclusion of this paper. The reason is that the displacement amplitude is too small and the number of cycles is too few, which leads to little change in the damping ratio. Comparing the damping ratios at different displacement amplitudes, the damping ratios at the displacement amplitude of 10 mm are significantly smaller than those at the other two amplitudes, and the damping ratios at the displacement amplitude of 40 mm are slightly larger than those at the amplitude of 20 mm. For example, when the cycle number is 5, the damping ratios at amplitudes of 10 mm, 20 mm and 40 mm are 0.28, 0.36 and 0.40, respectively, indicating that the larger the displacement amplitude is, the greater the damping ratio. The damping ratio is a parameter characterizing the speed of energy dissipation of reinforced soil structures subjected to dynamic loading. Figure 8 illustrates that cyclic shear will cause the energy dissipation rate of the interface to be fast and then slow, after which the dissipation rate will tend to be stable. The larger the displacement amplitude is, the faster the energy decay. These conclusions are consistent with those of Liu et al., [20].
5.3.3. Influence of normal stress
The relationship between the shear stiffness and damping ratio with the cycle number under different normal stresses (100 kPa, 200 kPa and 300 kPa) is obtained by cyclic shear at a small displacement amplitude of 2 mm, as shown in Fig. 12 and Fig. 13.
Fig. 12. Shear stiffness under different normal stresses
Fig. 13. Damping ratio under different normal stresses
Fig. 12 shows that the shear stiffness under different normal stresses decreases with the number of cycles, decreases rapidly during the initial stage of the shearing cycle, and then decreases slowly after 15 cycles. The shear stiffness under normal stresses of 200 kPa and 300 kPa decreases stepwise, which indicates that the soilgeosynthetic interface presents shear softening at small displacement amplitudes, which is completely contrary to the shear hardening shown in Fig. 10, and the main reason is that the shear displacement amplitude is different. When the displacement amplitude is small (e.g., 2 mm), the position of the soil particles near the interface does not adjust sufficiently. Because the soil is denser before shearing, the soil particles near the interface are loosened by cyclic shearing, which leads to a decrease in soil compactness. Therefore, the reduction in the cohesive force between the soil particles results in shear softening. The shear stiffness under a normal stress of 100 kPa is significantly lower than that under the other two normal stresses at the same cycle number. The shear stiffness under a normal stress of 300 kPa is slightly greater than that of 200 kPa, which indicates that the larger the normal stress, the greater the shear stiffness is. Relevant studies show that the shear strengths of the soilgeosynthetic interface and pure soil both coincide with the MohrCoulomb theorem, so an increase in the normal stress will inevitably lead to an increase in the shear stiffness [10].
Fig. 13 shows that the damping ratio decreases with the cycle number during the first 30 cycles under different normal stresses and then gradually stabilizes without any significant decrease. During the first 100 cycles, the damping ratio under a normal stress of 100 kPa is obviously smaller than that under the other two normal stresses with the same cycle number, and the damping ratio under 200 kPa is slightly larger than that under 300 kPa. Combined with Fig. 6, when the cycle number exceeds 400, the damping ratio under 300 kPa increases gradually and is larger than that under 200 kPa, which indicates that the greater the normal stress is, the faster the energy dissipation of the interface. LIU et.al., [20]studied the cyclic shear behavior of the geogridsand interface and found that the damping ratio tended to be the same with the number of cycles under different normal stresses, which is different from the conclusion of this paper. The reasons for this difference lie in the following: (1) different soil samples are used in the cyclic shear tests, and the properties of sand and coarsegrained soil are quite different; (2) the number of shear cycles differs greatly, and the results obtained in reference [20] using 10 cyclic shear tests may be unilateral and partial; (3) the normal stresses of cyclic shear are different, and the normal stresses (30 kPa, 60 kPa and 90 kPa) of reference [20] are less than those of this paper.
6. Conclusions
The largescale cyclic direct shear tests are carried out to obtain the shear stiffness and damping ratio of the reinforced soil interface, and the law of the parameters with number of cycles under different shear displacement and vertical stress is analyzed. The main conclusions drawn are as follows: (1) The shape of the hysteretic curves at different displacement amplitudes is different. The deformation of the soilgeosynthetic interface shows shear dilatancy under loading and shear contraction under unloading during cyclic shear, and the overall deformation of the specimen after cyclic shear is shear contraction; (2) With the increase of the number of cycles, the shear stiffness decreases and tends to be stable, but the change of the damping ratio is related to vertical stress; (3) The larger the displacement amplitude is, the larger the shear stiffness and damping ratio are; the larger the vertical stress is, the larger the shear stiffness and damping ratio are.
It should be noted that this study has discussed only the performance of coarsegrained soil against geogrid interface, and it is difficult to provide comprehensive guidance for engineering practice. Therefore, more large scale cyclic shear tests of different types of reinforcement materials and soil should be carried out in the future.
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