Field study on vibration characteristics of geocell-reinforced aeolian sand subgrades

Abstract

Constructing highways in deserts is expensive due to the difficulty of acquiring materials; utilizing aeolian sand effectively has become a problem, especially in the Xinjiang region, where the desert widely occurs. This paper aims to investigate the vibration response of a geocell-reinforced aeolian sand subgrade under traffic loading based on field tests of highways in deserts. The vibration acceleration response of geocell-reinforced aeolian sand and gravelly soil upper roadbed structures is tested. The field test results illustrate the effects of dynamic loading on geocell-reinforced aeolian sand roadbeds, and the thickness substitution ratio between geocell-reinforced aeolian sand roadbeds and conventional gravelly soil roadbeds is determined and verified based on the vibration acceleration monitoring values. The results show that the vibration response induced by the test vehicle is concentrated within the 30 Hz frequency band, and the higher the vibration frequency, the faster the vertical decay in the road. The vibration damping capacity of the reinforced aeolian sand roadbed is better than that of the gravelly soil roadbed; when replacing the gravelly soil roadbed with the reinforced aeolian sand roadbed, the substitution ratio is 0.31–0.42. It is verified that half thickness of gravel soil on roadbeds can be replaced by geocell-reinforced aeolian sand under different working conditions. The results of this study can provide reference data for the design of highway subgrades in deserts.

Introduction

With the construction of the core area of the Silk Road Economic Belt in Xinjiang, many highways in deserts have been built in rapid succession. The S21 Awu Highway Project is the most essential and convenient channel between Urumqi and northern Xinjiang, with a total length of 342.5 km and a 120 km/h design speed. This project is vital for enhancing the connection between Urumqi and Altay, shortening the interregional distance, and promoting regional economic and social development. In the design and construction of highways in deserts, gravelly soil is generally chosen as the upper roadbed filler to transfer vehicle loads. In desert areas, the long transportation distance of raw materials and construction difficulties make the upper roadbeds of highways in deserts expensive to build. Due to its low surface activity, looseness, obvious non-plasticity, notable non-hydrophilicity, and high collapsibility, aeolian sand is unsuitable for direct use as an upper roadbed filler on desert expressways^1,2,3. Therefore, using reinforced aeolian sand instead of gravelly soil as the upper roadbed filler is economically feasible.

Geosynthetics have been widely used in highway engineering, with geocells utilized primarily for load-bearing and reinforcement purposes⁴. On the other hand, considering that aeolian sand particles are small and non-cohesive, reinforcing them with three-dimensional geosynthetics is more effective^5,6,7. Geocells have the advantages of being lightweight and having high strength, convenient transportation, and easy construction. Geocells save road construction materials and optimize road performance by increasing the strength, stiffness, and durability of the structural layer to reduce the thickness of the subgrade^8,9,10,11,12. After geocell reinforcement, roads can carry higher traffic volumes. The geocell's reinforcement mechanism indicates that it can be used as a reinforcing element within the soil to promote stress redistribution and limit soil deformation. The closed geocell around the reinforced soil has a lateral restraining effect, and there is a friction effect between the geocell and the soil in the generation of relative displacement, which significantly improves the roadbed's bearing capacity^13,14,15,16. In addition, geocells have the advantages of light weight and high strength, convenient transportation and easy construction. Therefore, the use of geocells to reinforce aeolian sand is an ideal means to enhance the performance of aeolian sand.

Many scholars have used various experiments and numerical simulations to illustrate the enhancement of highway performance using geocells^17,18,19. Particularly, there have been many studies on the static properties of geocell-reinforced aeolian sands. For example, Singh²⁰ conducted plate loading tests using geocell-reinforced and unreinforced sand and compared the results from these laboratory tests with field test results. The experimental results showed that geocell reinforcement significantly increased the strength and stiffness of the sand. Using a large-scale triaxial test, Song²¹ demonstrated that geocells were more effective than loose sandy soils in reinforcing compacted sandy soils. Using a block resonance test, Hasthi and Hegde²² found that the use of geocell-reinforced aeolian sand resulted in a 61% reduction in the displacement amplitude. Nevertheless, these findings only reflect the static properties of geocell-reinforced aeolian sand and do not consider the dynamic response of the subgrade under traffic loading. Therefore, more mobile wheel load field tests are needed to investigate the effect of geosynthetic reinforcement in the subgrade.

Since the state of geosynthetic reinforcement under actual conditions needs to be considered in practical applications, compared with the results of laboratory and unpaved tests, the results of field tests are more reliable for highway practice. For instance, White²³ showed that the lateral confinement effect of geomaterials on the fill under dynamic loading can improve its performance. At the same time, axle weight and vehicle speed are the main factors affecting the dynamic response of the railroad subgrade. Latha et al.²⁴ investigated the effect of geosynthetic reinforcement on increasing bearing capacity and reducing rutting depth through systematic field tests. Their test results showed that the geotextile effectively increased the number of vehicle passes from 17 to 100, and the rut depth of the geotextile-reinforced section was significantly smaller than that of the unreinforced section. Pokharel²⁵ conducted a large-scale traffic test of geocell reinforcement of weak roadbeds. The geocell reinforcement reduced the deformation of the subgrade and the roadbed, saved 13 cm of subgrade material, and increased the service life by 3.5 times. Yang et al.²⁶ conducted a large-scale traffic test on a geocell-reinforced weak subgrade. Through geocell reinforcement, the subgrade and subgrade deformation decreased, 13 cm of subgrade material was saved, and the service life increased by 3.5 cm. In addition, Imjai et al.²⁷ investigated the effectiveness of geosynthetics for reinforcing flexible pavements through a foot-scale field test in which the geosynthetics were placed at different depths to measure the structural response in the field. The results showed that the vertical static stresses in the subgrade were reduced by 66%, and the dynamic stresses were decreased by 72%. Geosynthetic reinforcement significantly reduced the vertical stresses transmitted to the subgrade and the roadbed. Singh et al.²⁸ investigated the performance of geosynthetics for the reinforcement of unpaved roads using mobile wheel load tests. The test results showed that the surface deformation was reduced by 44.89% in the geotextile-reinforced test section and 28.57% in the geogrid-reinforced test section. Luo²⁹ compared the dynamic deformation modulus of geocell-reinforced and unreinforced roadbeds using a roadbed reinforcement test and suggested that geocell-reinforced roadbeds can increase the dynamic deformation modulus by 27% and reduce the soil pressure by 30.1 to 37.2%. In addition, geocell reinforcement can reduce the surface bending subsidence of the roadbeds by 26.4 to 29.2%. The above research shows that the dynamic response of subgrades determines the critical dynamic characteristics and working properties, which is important for designing subgrade structures and reducing project costs^30,31.

Several scholars have carried out field test studies on the dynamic and static structural properties of geosynthetic-reinforced soils. Due to the limitations of the test conditions, conventional field tests for traffic loading can only be carried out on unpaved roads, which cannot accurately express the dynamic properties of the road when it is in service. Because the state of geosynthetic reinforcement under natural conditions needs to be considered in practical applications, field tests are more reliable for highway practice than are laboratory and unpaved road tests. At present, there is still a lack of field tests on the dynamic characterization of geocell-reinforced aeolian sand; therefore, the actual reinforcing effect of geocell-reinforced aeolian sand under the action of a driving load cannot be effectively illustrated, which affects the further promotion of geocell-reinforced aeolian sand in highways in deserts. This paper investigates the vibration attenuation performance of geocell-reinforced aeolian sand roadbeds under a moving wheel load test. Two road test sections were constructed in the field to achieve this goal, with geocell-reinforced aeolian sand and gravelly soil as the upper roadbed. The mobile wheel load performance of the geocell-reinforced aeolian sand test section was compared with that of the gravelly soil test section. The vibration acceleration index was used to evaluate the vibration attenuation of geocell-reinforced aeolian sand, and the bearing capacity index of aeolian sand was verified to determine the proportion of geocell-reinforced aeolian sand replacing gravelly soil. This paper aims to verify the effectiveness of geocell-reinforced aeolian sand replacing traditional gravel soil in roadbed fill by studying the dynamic characteristics of aeolian sand roadbeds under vehicle dynamic loading. The research results can provide a design basis for constructing highways in deserts.

Field testing

Case study description

The field test site is located in the hinterland of the Gurbantunggut Desert along the S21 line, namely, the first highway in the deserts within the Xinjiang Uygur Autonomous Region. The total length is 342.5 km, and the design speed is 120 km/h. The test section of this study is selected from Huanghuagou to Urumqi, K233 + 600 to K233 + 750, with a total length of 150 m. This section is a separated subgrade, and the width of one side is 13.25 m. Two schemes are designed for this test section to compare the vibration characteristics of geocell-reinforced aeolian sand and gravelly soils as the upper roadbed. Scheme 1 entails the use of woven fabric + gravelly soil to fill the upper roadbed. Through dynamic triaxial tests of reinforced and unreinforced aeolian sand, it is found that the hysteresis curve of geocell-reinforced aeolian sand is denser and the plastic deformation is smaller, which indicates that the geocell can better restrict the development of the soil plastic zone³². Therefore, Scheme 2 involves the use of woven fabric and geocell-reinforced aeolian sand to fill the upper roadbed. The gravelly soil and aeolian sand filler were taken from the local area, and the grading curves of the two filler materials are shown in Fig. 1. The thickness of the asphalt layer was 12 cm, the cement-stabilized gravel subgrade was 36 cm, and the thickness of the natural gravel subbase was 18 cm in both scenarios. The physical properties of the gravelly soil and aeolian sand are shown in Table 1. The geogrid used in the field test is a plug-in integral high-strength geocell, and the material is polypropylene resin. To ensure that the strip and the connection point exhibit high strength and consistent strength matching, the grid belt connection is interwoven by U-shaped steel nails. The U-shaped nails exhibit a diameter greater than 2.5 mm, and they are subjected to galvanized anti-corrosion treatment. The physical and mechanical parameters of the polypropylene resin geocells are shown in Table 2.

Figure 1

The grading curves of the filler scale.

Table 1 Physical property indices of the fillers.

Table 2 Physical and mechanical parameters of the geocell.

Monitoring program

The reinforcing effect of geocells on aeolian sand roadbeds under traffic load conditions is reflected explicitly in the performance and spatial attenuation of dynamic stress, dynamic velocity, and dynamic acceleration at different locations when the test vehicle passes through the test section. The vibration acceleration is closely related to the vehicle's driving speed, loading, and material properties of the subgrade. Vibration acceleration is an essential parameter for determining the effect of energy generated by vehicle loading on road structures³³. To study the spatial attenuation trend of the vibration acceleration along the vertical direction of the geocell-reinforced aeolian sand subgrade and the traditional gravel soil subgrade, the vibration reduction performance levels of these two different forms of subgrade structures were compared, and the sensor layout was consistent between the two subgrades. Five monitoring points were established in the sections of the two roadbeds, which were evenly arranged on the surface of the pavement, between the pavement and the upper roadbed, between the upper and lower roadbeds, and within the aeolian sand roadbed. Due to the varying thicknesses of the roadbed structures, the buried depth of the sensor differs. The layout depths of geocell reinforced aeolian sand roadbed sensors are 0 m, 0.66 m, 0.81 m, 1.26 m and 1.71 m respectively. The depth of gravel soil roadbed sensors is 0 m, 0.66 m, 0.96 m, 1.41 m and 1.86 m respectively. The layout position is shown in Fig. 2. Measurement was conducted by a pressure point vibration accelerometer, model JMCZ-2091, with a range of 1 to 1.4 kHz, an acceleration up to 100g, a charge sensitivity of 2060 PC/g, and the signal output as the voltage output. A standard vibration source that can generate 10 cm/s² acceleration was used for calibration and scaling before burial. JMCZ-2091 vibration accelerometers were placed along the vertical direction during road construction. After the sensors were pre-buried at predetermined positions in the test section, the surrounding aeolian sand was compacted via jump tamping. The acquisition analyzer is a sixteen-channel dynamic acquisition module modeled as JMDY-1016, which can collect the dynamic acceleration value of the measurement point in real time and directly convert it into a time curve.

Figure 2

Diagrammatic drawing of sensor placement.

Test program

The test program mainly considers the effects of vehicle type, weight, and speed. Based on available statistics on highway traffic volume data and representative vehicle types^34,35, the dynamic acceleration test takes three different types of vehicles, namely, two-axle trucks, three-axle trucks, and buses, to pass through the test and control sections of the geocell-aeolian sand subgrade at different speeds (Fig. 3). The mass of the trucks was controlled by loading them with aeolian sand before the test. Prior to the test, the quality of the different models was accurately measured, and the error was controlled within 1% to ensure the rigor of the test. The test was designed for 60 working conditions. These working conditions are listed in Table 3. In addition, to ensure that the test vehicle can pass through the range of 20 m before and after the test section at a uniform speed, there is 1 km in front of the test section for the vehicle to accelerate in advance. During the test, the rear wheel center track line overlapped with the marking line directly above the sensor. The test was repeated in 3 groups for each working condition, and the data with similar excitation were selected from the test results.

Figure 3

Preparation and testing arrangements at the site: (a) geocell laying; (b) aeolian sand filling; (c) two-axle truck; and (d) three-axle truck.

Table 3 Test conditions.

Field test results and analysis

Vibration analysis of the upper roadbed on gravelly soil

When a vehicle passes on the gravelly soil upper roadbed, accelerometer G1 records the vertical acceleration-time diagrams of different models passing at different speeds when unloaded (Fig. 4). In the graphs, the different colored curves represent the different driving speeds of the test vehicles. As the vehicle travel time and the distance from the monitoring point change, the collected response acceleration signals first increase and then decrease, with apparent peaks. The waveforms of passenger cars and trucks are different, and the waveforms of the two-axle and three-axle trucks are similar. In addition, a smaller peak occurs before the peak when the passenger car passes at a driving speed of 20 km/h. When traveling at a slower speed, the front and rear axles of the test vehicle act on the test section separately. The axle load of the rear axle is more significant than that of the front axle, so two wave peaks are formed with a large front and a small back. At faster speeds, the front and rear axles are closer in time, so they overlap into a single peak.

Figure 4

Time–history characteristics under different traffic loads: (a) Buggy; (b) two-axle truck; and (c) three-axle truck.

Figure 5 shows the frequency domain characteristics of the vertical attenuation of the excitation of an unladen two-axle truck passing over a gravelly soil upper roadbed road at 20 km/h. While a vehicle travels along the road, the wheels of the vehicle travel on the road with a specific frequency and amplitude of bouncing due to the unevenness of the road surface. The vertical vibration is mainly caused by the excitation generated by the vehicle body bumps. As shown in Fig. 5, the vibration response shows a trend of attenuation with increasing depth, and the vibration frequency ranges from 0 to 50 Hz, with the main components concentrated from 0 to 30 Hz. This indicates that the vibration caused by the vehicle traveling on the site is mainly low-frequency. Spectral analysis revealed that the high-frequency and low-frequency vibration attenuation speeds are slow during the vibration attenuation process. This is because the high-frequency vibration in the propagation process is fast; due to the large soil body damping effect, the attenuation speed is more rapid. Low-frequency vibration attenuation is slower, so the propagation distance is greater than that of high-frequency vibration. In addition, as the depth of the monitoring point increases, the amplitude of the acceleration signal decreases significantly, which shows that the monitoring results are reliable.

Figure 5

Frequency domain features along the depth direction.

Characteristics of the vibration acceleration amplitude with vehicle speed and vehicle weight

The changes in the vibration acceleration amplitude with vehicle speed and weight are shown in Fig. 6. The vibration response caused by a passenger car is highly sensitive to changes in speed; the vibration acceleration amplitude of the passenger car at a speed of 20 km/h is 3.9 times greater than that at a speed of 120 km/h. For a 2.7 t passenger car, the speed increased from 20 to 60 km/h, and the acceleration amplitude of the subgrade increased from 0.32 to 0.44 cm/s², which is an increase of 28%. For a 10 t two-axle truck, the speed increased from 20 to 60 km/h, and the acceleration magnitude of the road surface increased from 0.77 to 1.04 cm/s², which is an increase of 26%. For a 16 t three-axle truck, the speed increased from 10 to 30 km/h, and the acceleration magnitude of the road surface increased from 2.79 to 3.46 cm/s², which is an increase of 19%. The above analysis demonstrates that the vibration acceleration decreases with increasing depth when different vehicles pass at varying speeds, and there is a mutation point in the process of reducing the vibration acceleration under most working conditions. With increasing vehicle speed and vehicle weight, the acceleration at different depths of the subgrade increases, and the closer to the vibration source, the more significant the acceleration change is. This indicates that the change in the vehicle speed and vehicle weight influences the attenuation characteristics of acceleration along the depth direction of the subgrade. Since the tests were conducted on the same test section with the same pavement structure, flatness, and inherent vibration characteristics, it can be seen that the increase in speed affects road vibration.

Figure 6

The curve of vibration acceleration with vehicle speed and vehicle weight: (a) buggy; (b) two-axle truck; (c) three-axle truck; and (d) both trucks.

The impact of changing the test vehicle load on the road vibration response is also pronounced, and the vibration response of the two-axle truck is more sensitive to changes in vehicle weight. For every 1 t increase in the weight of a two-axle truck, the vibration velocity amplitude increases by 0.16 cm/s², with an average increase of 15%, and for every 1 t increase in the weight of a three-axle truck, the vibration velocity amplitude increases by 0.04 cm/s², with an average increase of 1.8%. When the vehicle weight is 15 t, the vibration response of the three-axle truck is slightly greater than that of the two-axle truck, which is caused by the superposition of the same vibration source of the rear two axles³⁶.

Vibration attenuation laws for different upper roadbed structures

The vibration attenuation laws of different roadbed forms are significantly different. Therefore, the dynamic characteristics of roadbed structures under different vehicle weights, speeds, and models have specific research value. Figure 7 shows the vibration attenuation curves of two-axle and three-axle trucks with a vehicle weight of 16 t. For two-axle and three-axle trucks with the same mass, the vibration acceleration amplitude in the vertical direction shows a different attenuation trend. The attenuation of two-axle and three-axle trucks is closer on the geocell-reinforced aeolian sand side. The attenuation is most apparent in the geocell-reinforced aeolian sand layer, with an attenuation rate above 20%. On the gravelly soil side, the vibration attenuations of the two-axle and three-axle trucks are more disparate. The attenuation rate of the two-axle truck in the gravelly soil layer is 15%, and the attenuation rate of the three-axle truck in the gravelly soil layer is only 6%.

Figure 7

Vibration attenuation curves of different vehicle models with a weight of 16 t.

Figure 8 shows the vibration attenuation curves of passenger cars and trucks at different speeds. Due to the lower axle weight of the passenger car, road vibration in the pavement structure at the loss of larger, transmitted to the roadbed when the vibration acceleration amplitude is reduced to 0.2 cm/s² or less. The decrease is greater than 60%, with the maximum decrease reaching 87%. For two- and three-axle trucks under different driving speed conditions, the vibration acceleration decreases with increasing depth. On the geocell-reinforced aeolian sand side, the attenuation rate of vibration acceleration in the geocell-reinforced aeolian sand layer increased significantly. However, the attenuation rate of the vibration acceleration on the gravelly soil side does not show any particular change in the gravelly soil layer. The vibration attenuation of the geocell-reinforced aeolian sand layer is greater than that of the gravelly soil layer.

Figure 8

Vibration attenuation curves at different speeds: (a) buses and (b) two-axle and three-axle trucks.

Figure 9 illustrates the vibration response attenuation curves for different vehicle weights. The vibration attenuation of both upper roadbed structures becomes more pronounced as the vehicle weight increases. Additionally, vehicle weight affects geocell-reinforced aeolian sand slightly more than gravelly soil. A combination of the results in Figs. 8 and 9 reveals that changing the vehicle weight and driving speed has an effect on the attenuation of vibration in the road structure. In addition, the attenuation rate of the vibration acceleration of the geocell-reinforced aeolian sand upper roadbed is greater than that of the gravelly soil upper roadbed under different working conditions. This is because the polypropylene resin geocell improves the dynamic elastic modulus as well as the damping of the aeolian sand; therefore, it changes the compression and deformation properties of the aeolian sand under traffic loading, restricts the lateral deformation of the soil, inhibits the development of the shear zone in the soil, and strengthens the load-bearing capacity of the soil, thus improving the vibration suppression performance³⁷.

Figure 9

Vibration response attenuation curves under different vehicle weights: (a) two-axle truck and (b) three-axle truck.

Analysis of the vibration attenuation effect of different upper roadbeds

To analyze the attenuation of vibration acceleration in different upper roadbeds under traffic loading, the proportion of vibration acceleration attenuation per unit height is defined as the dynamic acceleration attenuation coefficient ${K}_{a}$:

$${K}_{a}=\frac{{a}_{u}-{a}_{d}}{{a}_{u}\Delta h}$$

(1)

where ${a}_{u}$ is the vibration acceleration of the upper layer, ${a}_{d}$ is the vibration acceleration of the lower layer, and $\Delta h$ is the height difference between the upper and lower layers.

According to the above equation, the attenuation coefficients of the dynamic acceleration of roadbeds under different working conditions can be calculated (Fig. 10). The attenuation coefficients of gravelly soils at different test speeds are much lower than those of geocell-reinforced aeolian sand, and the influence of the driving speed on the attenuation coefficient is small. Under the most unfavorable working conditions, the driving speed of the bus is 120 km/h. Under the most unfavorable working conditions, the driving speed of a two-axle truck and three-axle truck is 60 km/h, and the average attenuation coefficient of geocell-reinforced aeolian sand at this time is 3.2 times that of gravelly soil. Figure 10b shows that the attenuation coefficient of the vibration acceleration increases with increasing vehicle weight, and the increase in the gravelly soil is slightly greater than that in the geocell-reinforced aeolian sand. This is because gravelly soils under heavy loads produce greater micro-deformation, consuming a portion of the energy into internal energy, and the nature of vibration transfer is the transfer of energy. Hence, the attenuation coefficient of the gravelly soil is more significant. The most unfavorable working condition of a two-axle truck occurs when the truck weight is 22 t. The most unfavorable working condition of a three-axle truck occurs when the truck weight is 52 t.

Figure 10

Attenuation coefficient curves for different vehicle (a) speeds and (b) weights.

Discussion

This paper mainly explores the influence of geocell-reinforced aeolian sand upper roadbeds on the vibration response of aeolian sand subgrades to show that the dynamic characteristics of geocell-reinforced aeolian sand subgrades are better than those of traditional subgrade forms. The results of this study can provide practical reference data for highways in deserts at the design and construction stages. In addition, by comparing the attenuation coefficients of the most unfavorable working conditions, the thickness of geocell-reinforced aeolian sand needed to replace the traditional gravelly soil upper roadbed can be calculated.

An analysis of the vibration attenuation effect of different upper roadbeds shows that the impact of geocell-reinforced aeolian sand changes with changing test vehicle mass and speed; the most unfavorable working conditions for two-axle trucks are a truck weight of 22 t and a traveling speed of 60 km/h. The most unfavorable working conditions for three-axle trucks are a truck weight of 52 t and a traveling speed of 60 km/h.

Considering the different test models and upper roadbeds, the field data are normalized to compare the vibration attenuation laws under other working conditions. The normalization process is as follows:

$$A=\frac{{a}_{i}}{{a}_{0}}$$

(2)

where ${a}_{i}$ is the vibration acceleration amplitude of the measurement point and ${a}_{0}$ is the vibration acceleration amplitude of the road measurement point.

The attenuation curves of the vibration acceleration at each measurement point under the most unfavorable working conditions of different test vehicles and the attenuation curves after normalization are shown in Fig. 11. Figure 11 shows that under the most unfavorable working conditions, the vibration attenuation effect of geocell-reinforced aeolian sand on the vibration acceleration is greater than that of a road surface, gravelly soil, or aeolian sand. This occurs because the vertical tendons in the three-dimensional cellular side-limiting structure of the geocell play a role in the lateral restraint of the soil body as well as generate a profound foundation effect; this substantially increases the apparent cohesion of the soil body and the integrity of the structural layer, thus increasing the attenuation of vibration acceleration³⁸.

Figure 11

Normalized attenuation curve: (a) attenuation curve and (b) normalized curve.

The substitution ratio of the geocell-reinforced aeolian sand upper roadbed to the gravelly soil upper roadbed can be calculated based on the vibration attenuation coefficient as follows:

$$C=\frac{{h}_{t}}{{h}_{l}}=\frac{{K}_{al}}{{K}_{at}}$$

(3)

where C is the proportion of substitution, ${h}_{l}$ is the thickness of the gravelly soil upper roadbed, ${h}_{t}$ is the thickness of the equal-proportion substitution of the geocell-reinforced aeolian sand upper roadbed, ${K}_{al}$ is the vibration attenuation coefficient of the gravelly soil, and ${K}_{at}$ is the vibration attenuation coefficient of the geocell-reinforced aeolian sand.

Figure 12 shows the variation curve of the substitution ratio with vehicle weight, which shows that the substitution ratio increases with increasing vehicle weight. This finding also confirms the need to increase the thickness of geocell-reinforced aeolian sand under heavy load conditions. Under the action of two-axle trucks, the substitution ratio is in the range of 0.18–0.42. Under the action of three-axle trucks, the substitution ratio is in the range of 0.15–0.31. The substitution ratio used in the field is 0.5, which can theoretically satisfy the vibration acceleration requirements in all the test cases.

Figure 12

Geocell-reinforced aeolian sand replacement gravel/soil ratio curve.

Finally, the substitution ratios between the geocell-reinforced aeolian sand upper roadbed and the gravelly soil upper roadbed are calculated. When the highway subgrade filling height is low, the bearing capacity of the roadbed material does not meet the allowable bearing capacity requirements because the traffic load is not effectively spread through the subgrade. Theoretically, the sum of the dynamic stress and static stress attenuated by each working layer of the subgrade should meet the requirements of the allowable bearing capacity of the subgrade holding layer as follows:

$$\sigma ={\sigma }_{S}+{\sigma }_{D}\le \left[{f}_{0}\right]$$

(4)

where ${\sigma }_{D}$ is the dynamic stress value (kPa) at the top of the bearing layer; ${\sigma }_{S}$ is the static stress value (kPa) at the top of the bearing layer; and $\left[{f}_{0}\right]$ is the allowable bearing capacity of the bearing layer (kPa).

The static stress is the sum of the stress of the test vehicle axle load and each structural layer as follows:

$${\sigma }_{s}={\sigma }_{0}+\sum {\gamma }_{i}{h}_{i}$$

(5)

The dynamic stress can be calculated by combining the parameters of the vibration accelerometer as follows:

$${\sigma }_{D}=\phi a$$

(6)

where $\phi$ is the instrument parameter, which is 356 according to the field situation.

The ultimate bearing capacity of single-layer geocell reinforced aeolian sand measured by static load test is 456 kPa³⁹, and the measured value is basically consistent with the previous studies⁴⁰. In addition, according to the calculation formula of bearing capacity of geocell reinforced foundation studied by Li Chi⁴⁰ and Lei Shengyou⁴¹ (Eqs. 7–9), the calculation is carried out according to the parameters in static load test:

$$ p_{u}{\prime} = p_{u} + \Delta p_{u} $$

(7)

where p_u is the bearing capacity of pure aeolian sand foundation calculated according to Terzaghi formula; Δp_u is the increment of bearing capacity of aeolian sand foundation after geocell reinforcement.

$$ p_{u} = 0.4\gamma bN_{r} + qN_{q} + 1.2cN_{c} $$

(8)

where γ is the gravity of aeolian sand, the value is 16.4 kN/m³; the bearing capacity coefficient N_r is 93.16; b is the width of the loading plate in the static load test, the value is 0.3 m; q is the overlying load, because the thickness of the overlying soil is 0, the value of q is 0; The cohesion is small, the value is 0; the calculation can be obtained as 178.87 kPa.

$$ \Delta p = \left( {\gamma s + \frac{T}{r}} \right)N_{q} + \frac{4T\sin \beta }{b} $$

(9)

where T is the tension of the geocell, the single-layer tension is 15 kN; s is the final settlement, the value is 0.045 m; r is the radius of the round on both sides of the foundation, generally 3 m; β is the angle between the tension and the horizontal plane, and β is 12.68° calculated by the settlement; The bearing capacity coefficient N_q is 40; After calculation, the incremental value of bearing capacity is 250.75 kPa. According to the above calculation, the bearing capacity of single-layer geocell reinforced aeolian sand subgrade is 429.62 kPa.

To ensure safety, the allowable bearing capacity $\left[{f}_{0}\right]$ is taken as 380 kPa, and according to the literature⁴², and the actual measurement, the average rear wheel static stress σ₀ of a 22 t vehicle can be calculated as 108 kPa. The average rear wheel static stress σ₀ of a 52-t vehicle is 201 kPa. An assessment of the load-carrying capacity for the most unfavorable conditions is provided in Table 4.

Table 4 Checking table of the bearing capacity under the most unfavorable conditions.

The most unfavorable working condition is when the ratio of the vibration attenuation coefficient of gravel soil to the vibration attenuation coefficient of geocell-reinforced aeolian sand is the smallest, i.e., the substitution thickness is the largest, so the substitution ratio under the most unfavorable working condition is the maximum value. The most unfavorable working conditions are when the test vehicle weight is the greatest; then, the static stress generated by the vehicle is also the largest. When the most unfavorable working conditions are satisfied, other working conditions can be introduced. Therefore, we can verify the reasonableness of the substitution ratio by calculating the load-carrying capacity under the most unfavorable working conditions.

In this paper, the dynamic characteristics of the geocell-reinforced aeolian sand subgrade under traffic load conditions are investigated. The results show that the damping capacity of the geocell-reinforced aeolian sand roadbed is greater than that of the traditional gravel soil roadbed. The obtained conclusion is similar to that reported in previous studies. Gao et al.⁴³ conducted a field test by embedding a vibration velocity measuring device inside a geocell-reinforced aeolian sand roadbed. The results indicated that the attenuation of the vibration velocity of the geocell-reinforced aeolian sand roadbed is less than that of gravel soil, but the attenuation curve is smoother. In addition, the depth of the working area of the geocell-reinforced aeolian sand subgrade is smaller, which also shows that the dynamic attenuation characteristics of the geocell-reinforced aeolian sand roadbed are better than those of gravel soil. Ya⁴⁴ used ABAQUS to study the dynamic stress attenuation of geocell-reinforced aeolian sand subgrade and the deformation of the geocell under traffic load conditions. When a vehicle travels over the geocell, the geocell will be deflected and is tilted, and the deformation will gradually recover after the vehicle leaves. Through the analysis of the dynamic stress attenuation coefficient, it is shown that the geocell-reinforced aeolian sand roadbed reduces the vibration, improves the long-term service performance of the roadbed, and homogenizes and reduces the peak stress. In addition, there will be a net effect after the geocell-reinforced aeolian sand roadbed is applied, which reduces the settlement. In this paper, the dynamic response of the geocell-reinforced aeolian sand subgrade is studied by the field test method, and valuable results are obtained. However, there are still shortcomings in this research. Next, numerical simulation, microscopic mechanism and field test results should be combined to study the mechanism of action between the geocell and aeolian sand.

Conclusion

In this study, moving wheel load tests were carried out on roadbeds composed of two structures, namely, a geocell-reinforced aeolian sand upper roadbed and a gravelly soil upper roadbed, to assess the effect of the vibration response of a subgrade with geocell-reinforced aeolian sand. The attenuation coefficients of the two forms of subgrades were also compared to derive a thickness replacement formula for the conventional gravelly soil upper roadbed and the geocell-reinforced aeolian sand roadbed. Based on the above analysis, the conclusions are summarized as follows. The test vehicle's vibration response is mainly dominated by low-frequency vibration, and the vibration frequency is concentrated within 30 Hz. Spectral analysis reveals that during the vibration decay process, the high-frequency vibration in the road structure decays fast vertically, and the low-frequency vibration decays slowly. The vibration acceleration amplitude increases with the increase in the vehicle speed and vehicle weight. When the vibration sources are closer, the acceleration is superimposed, increasing the amplitude. The attenuation effect on the vibration of the geocell-reinforced aeolian sand upper roadbed and gravelly soil upper roadbed increases with increasing vehicle weight, in which the degree of increase in gravelly soil is slightly greater than that in geocell-reinforced aeolian sand. The mobile wheel load field test results reveal that in the different models, the effects of vehicle weight, driving speed, and geocell-reinforced aeolian sand on the vibration attenuation ability are greater than those of the gravelly soil, and under other working conditions, one-half the thickness of the geocell-reinforced aeolian sand upper roadbed can be used instead of the gravelly soil upper roadbed. In addition, considering the most unfavorable conditions, the attenuation coefficients are compared to calculate the thickness substitution ratio of the geocell-reinforced sand roadbed and the traditional gravel soil roadbed under different conditions. Notably, half of the thickness of the geocell-reinforced sand layer roadbed can be used to replace the traditional gravel soil roadbed.