Introduction

Geocell reinforcement paved the way for using locally available inferior materials in the road construction. Geocell is an interconnection of cells that form a honeycomb pattern, which provides confinement to the inferior material and laterally distributes the load. It reduces the load transferred to the layer below (subgrade layer). When a load is applied, the geocell reinforcement holds the infill material in cells from being displaced by hoop action in the cell walls, thereby increasing the shear strength of the composite system [1]. In addition to the hoop action, the surrounding cells provide passive resistance, and friction offered by geocell wall and infill material further contribute towards the reduction of stress, thus, increasing the bearing capacity of the layer beneath the geocell-reinforced layer [2]. In unpaved roads, the geocell reinforces the unbound aggregates and reduces the deformation. The geocell reinforcement aids in reducing the thickness of the base layers [3, 4]. In unpaved and low-volume roads, a significant amount of traffic load is carried by the base layers, which requires either a thicker base layer or a high strength base material. Geocell is believed to be a suitable alternative for the low-volume roads, because it reduces the need for a thicker base layer or high-quality base materials.

Numerous studies were performed in the past decade on the geocell reinforcement. These studies can be classified as employing the geocell as a building foundation support [1, 5,6,7,8,9,10,11,12], railroad subgrade or base improvement [13,14,15,16,17], and base or subgrade improvement in roads [18,19,20,21,22,23,24,25,26,27,28]. All these studies documented the benefit of geocell and its working principles. However, there were limited studies on designing roads with geocell reinforcement. Pokharel (2010) developed a design method using geocell for low-volume roads with no surface layers, which were a modification of unpaved roads design with planar geosynthetics [29]. The proposed model was based on limited test data (geocell from one manufacturer and four base materials), and its applicability on a different type of material (other than tested) is questionable. The other available design method was developed by Presto Geosystem (2008), in which the main design criterion is the friction angle between the infill and geocell wall. The proposed method does not consider the quality of infill material in the geocell and is based solely on the type of material sand, silt, and stone. Recent studies [2, 3] worked towards the design methods. However, the proposed models are either not based on extensive laboratory tests or field studies.

Developing a design method for low-volume roads needs robust laboratory testing, numerical analysis, parametric study, and refined quality data. The primary objective of this study is to present laboratory testing, refinement of the laboratory data, and calibration and validation of the developed FEM model. Also, this study evaluated the working principles of geocell. This manuscript provides useful information to the blooming researchers in developing the lab as well as FEM modeling. The detailed discussion on the laboratory evaluation and FEM is included in the following sections.

Test Setup and FEM

Since the purpose of this study is to perform groundwork for the design, a laboratory test setup is developed along with representative FEM. Therefore, the laboratory test setup and FEM had similar dimensions and boundary conditions.

Laboratory Setup

A rectangular steel tank 1.5 m × 1.2 m × 0.9 m was fabricated to simulate a field pavement section in the laboratory, as shown in the schematic in Fig. 1a. This tank can accommodate multiple pavement layers (subgrade, geocell-reinforced or geocell-unreinforced base layer, and a base layer on top as a cover). The length and width of the box were chosen based on the preliminary study with a focus to minimize the influence of the box boundary on the measured test results and considering the typical geocell sizes available for reinforcement.

Fig. 1
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a Laboratory setup and b FEM quarter model

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A height of 915 mm was chosen to accommodate 610 mm of subgrade and 305 mm of base layers. The base layer thickness was selected based on the height of the geocell available in the market and the recommended cover thickness (by geocell manufacturers and researchers), and typical base thickness used in low-volume roads within Texas. The commonly available geocell sizes are 76, 100, 150, and 200 mm. Even though manufacturers recommended a minimum cover thickness of 50 mm, the published literature [7,8,9] suggests the use of cover thickness ranging from 25 to 152 mm for various applications. By considering the combination of geocell and cover thickness, the maximum anticipated base layer thickness will be 305 mm.

Once the base layer thickness is selected, a preliminary pavement analysis was performed to evaluate the vertical stress distribution in the subgrade using the linear elastic multi-layer model (BISAR [37]). In the analysis, various combinations of base modulus and thicknesses, and subgrade modulus were used. The results indicated that even for the weaker base and subgrade modulus, the vertical stresses in subgrade faded in less than 610 mm. Hence, a 610 mm subgrade layer is considered, such that the box boundary will not influence the stress distribution.

Based on the published literature, the geocell acts like a semi-rigid beam that means the stress is distributed over a wider area. If the box size is restricted to only 915 mm, then it can accommodate only two geocell pockets on each side. If the geocell acts like a beam, then the portion of the load may be absorbed by the box. Hence, this study selected the box dimensions of 1.2 m × 1.5 m, which allowed placement of 3–4 geocell pockets, thus, minimizing the influence of the box boundary.

Materials

In this study, a lower modulus base material is reinforced with a 152 mm high geocell. Subgrade and base materials were obtained from the side of a low-volume road in Texas. The material properties are shown in Table 1 along with the test procedure followed for obtaining material properties. Each pocket of geocell, under stretched conditions, has a longitudinal length of 234 mm, the transversal length of 203 mm, a height of 150 mm, and a thickness of 1 mm. This study used only 101 mm as cover thickness; however, it is necessary to evaluate the required optimum cover thickness above geocell in a future study, as suggested by Tafreshi and Dawson 2010 [1].

Table 1 Material properties
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Testing, Data Collection, and Refinement

Two samples were prepared one with geocell reinforcement and the other one without any reinforcement. In both samples, the subgrade of 610 mm thickness was placed. In Sample 1 (unreinforced base), the base layer of 254 mm was placed on top of the subgrade. In Sample 2 (geocell-reinforced), a base layer of 152 mm reinforced with the geocell layer is overlaid on top of the subgrade, followed by 101 mm of the cover layer (unreinforced base). Subgrade and base layers are compacted to a minimum of 95% of MDD in 152 mm layers. The compaction was performed using a plate vibrator.

A cyclic loading pattern was applied at the center of the tank using a 305 mm-diameter 25 mm-thick steel plate to replicate the pavement loading (shown in Fig. 2). A 12.5 mm rubber padding was glued to the bottom of the loading plate to simulate the tire flexibility. Ideally, a 0.1 s of loading followed by a rest period of 0.9 s is preferred for simulating traffic loading. However, the loading signal was modified as 0.2 s of loading and 1.0 s of rest due to limitation of the MTS® loading system. Figure 2 shows the planned and achieved loading. In the laboratory evaluation, 20,000 load cycles of 551 kPa, 5000 cycles of 689 kPa, and 5000 cycles of 827 kPa were applied. The tests performed at higher stresses were to evaluate the effectiveness of geocell under high loads.

Fig. 2
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Load cycle

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In this study, the benefits of the geocell reinforcement were estimated by comparing its performance with an unreinforced sample. Pressure cells (230 mm diameter and 6 mm height) and strain gauges were used to monitor the response of the geocell. The stress distribution beneath geocell was evaluated by placing three pressure cells on top of the subgrade (placed at the center below three consecutive geocell pockets), as shown in Fig. 3a. Strain gages were glued and adequately protected to monitor the hoop strains developed in the geocells. 120 Ω strain gages were selected based on its sensitivity as well as its suitability with the data acquisition system. A half-bridge strain gage circuit was selected to enhance the signal-to-noise ratio.

Fig. 3
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Laboratory instrumentation locations and FEM stress and strain locations

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To collect data from the transducers and loading system, two data acquisition systems were used. The MTS® loading system has a built-in data acquisition system that records the load and vertical deformation on the sample. This data acquisition system can collect data at a frequency of 100 data points/s. The stresses and strains from instrumented sections were recorded through LMS ® data acquisition system, which can record 16 locations (strain gages and pressure cells) at a time. The data were acquired at a frequency of 128 data points/s. Before applying the cyclic load on the prepared sample, an initial reading of all electronics was obtained to make sure that the transducers are properly functioning. The initial reading is considered as the datum, and the data collected during the testing are adjusted accordingly.

Since load and deformation transducers generate electronic signals, the transducers tend to measure electronic noise, as well, which can be cyclic or noncyclic. Since each test is performed for 20,000 load cycles, and each load cycle is around 1.3 s, more than 3 million data points from each channel (strain gages, pressure cells, and load cell) were collected, based on data sampling frequency. Therefore, the data need to be reduced, and noise needs to be minimized without altering the waveform of the applied load (cyclic pulse). In this study, a Kernel regression (nonparametric regression) [30] is used that provides an effective means by which complex displacement/pressure patterns occurring over a wide range of values can be captured. Also, a commonly used moving average method was used for data reduction. Kernel smoothing utilizes locally weighted averages of the data defined by a Kernel. The reduced data are summarized in Fig. 4 using two methods, and the results suggest that the moving average shifts not only the waveform, it is also inefficient in reducing the data points.

Fig. 4
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Reduction of data and noise removal using kernel regression

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Finite-Element Modeling (FEM)

A three-dimensional FEM was developed to simulate the behavior of reinforced pavement layers and for comparison with the laboratory test results. To perform FEM, a commercially available finite-element program LS-DYNA was selected, because this program allows dynamic FEM and includes a wide list of material and contact models/algorithms. Moreover, the program can also be installed on the High-Performance Cluster (HPC) that reduces the simulation time. Although FEM can identify the level of reinforcement provided by the geocell, the generation of mesh for FEM is complicated due to several factors like the interaction between geocell and adjacent soil, transfer of load, and confinement provided by the geocell, among others.

Additionally, the modeling of geocell required a significant number of elements and nodes to model the honeycomb shape of geocell [5], which also requires significant computational time. A quarter model was used to reduce the number of elements as conditions of symmetry exist in the finite-element model, as shown in Fig. 1b. Modeling the geocell using a rhomboidal pattern is less complex as opposed to the pseudo-sinusoidal honeycomb pattern and has been used in different studies [15, 26].

Many researchers modeled the geocell and infill material as a composite material using a finite-element or finite-difference methods [10,11,12, 28]. Some researchers [5, 6, 15, 21, 26] modeled them as a separate material. In the geocell-reinforced base layer, the infill material (linear elastic or plastic) and geocell (elastic) respond differently to loading. Also, the working mechanism of each material is different. Thus, the geocell-reinforced layer is modeled, such that the behavior of infill material and geocell is evaluated separately. In this study, the Federal Highway Administration (FHWA, USA) Soil Constitutive Model was used for modeling base, subgrade, and geocell pocket infill material. This model is a modified Mohr–Coulomb model available in LS-DYNA that was extended to include excess pore-water effects, strain softening, strain hardening, strain-rate effects, and elements’ deletion [31, 32]. These enhancements to the standard soil material models were made to increase the accuracy, robustness, and ease of use for highway applications. The properties of each material were determined using Tex-117-E Test Procedure for Triaxial Compression for Soil and Base Materials following the recommendations of Reid et al. [32] and Saleh and Edwards [33] for samples collected at different sites. Geocell was modeled as a linear elastic material with a density of 950 kg/m3, Poisson’s ratio of 0.45, and elastic modulus of 414 MPa. It was desired to design the FEM with a reinforced layer that allows the expansion of the geocell panels. For this purpose, boundary conditions were removed just for the geocell-reinforced base layer, while the other layers were restrained from lateral movement. The subgrade bottom is restrained from vertical movement. While evaluating the material constitutive models for simulating the geomaterials, it was found that instability did not occur due to the removal of lateral constraints on the nodes at the edge of the reinforced base layer. Discrete elements were used as a contact type between geocell and adjacent base material. The selection of contact type was presented in detail by Inti et al. [18]. The loading pattern similar to the one shown in Fig. 2 is applied. Instead of using 20,000 load cycles, only 100 cycles were applied, because the responses in the laboratory are almost constant after 100 cycles of the load, thus minimizing computational time.

Results and Discussion

The test results from FEM are included in Figs. 5, 6, and 7, while FEM and laboratory result comparisons are included in Figs. 8 and 9. The influence of higher stress on geocell performance is included in Fig. 10.

Fig. 5
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Vertical stress distribution contours obtained from FEM

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Fig. 6
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Vertical stress along the depth at the center of loading plate

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Fig. 7
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a Hoop stress on geocell. b Representation of geocell under load. c Hoop stress contours on geocell wall

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Fig. 8
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Vertical stress on subgrade top. a Laboratory. b Finite-element modeling (FEM)

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Fig. 9
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Strains on the geocell pockets: a FEM and b laboratory testing

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Fig. 10
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Performance of geocell at higher loads

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The vertical stress distribution contours, observed in unreinforced and geocell-reinforced samples, are shown in Fig. 5. The geocell-reinforced layer facilitated the reduction of vertical stress on the subgrade top by absorbing a portion of applied stress (Fig. 5b), which resulted in lower stress on subgrade, thus increasing its bearing capacity. The vertical stress along the center of the loading plate is presented in Fig. 6. It is observed that the stress is reduced below the loading from the point geocell-reinforced layer started and its effectiveness increased with depth.

The hoop stresses developed in the geocell (below the loading plate) are shown in Fig. 7. The magnitude of stress on geocell is higher than the applied load, indicating that the geocell is effectively absorbing the applied load. The hoop stress is not constant within the geocell pocket (Fig. 7c) as anticipated. The hoop stress is maximum on the bottom part of the geocell (Fig. 7a) and at the center of the cell rather than at joint, which is often assumed as the weakest spot in the geocell. Similar trends in hoop stress distribution were observed by the study conducted by Saride et al. (2017); however, that study used a monotonic load, whereas this study was performed using a cyclic (repeated) dynamic load. This indicates that the increase in the height of geocell will provide more benefits provided that the infill material is sufficiently compacted with an increase in the height of geocell.

The vertical stresses obtained from the laboratory tests and FEM are shown in Fig. 8. The FEM was calibrated by comparing the stresses with multi-layer model BISAR. The vertical stresses were matched with the stress analysis of the same sections using BISAR and compared with both the laboratory and FEM unreinforced pavement sections. It is visible from Fig. 8a that the BISAR and laboratory results closely matched for unreinforced sections, indicating that the transducers and data analysis are performing as per the theory. The FEM analysis estimated slightly higher stresses in comparison to BISAR estimation. Although higher, the difference in stresses is less than 10%. In both laboratory test results and FEM, the stress on subgrade below the loading plate was reduced by around 69 kPa, which is close to 30%. The stress reduction is much higher outside the loading plate, i.e., after the edge of the loaded geocell pocket. The stress distribution curve of the geocell-reinforced layer neither resembles a flexible pavement nor a rigid pavement but a combination of both.

The hoop strains recorded on the consecutive geocell pockets from the loading plate are shown in Fig. 9. Significant difference in strain values is observed FEM and laboratory. For instance, the hoop strains observed in first geocell pocket in FEM were 4500 microstrains, whereas the lab testing showed only 1200 microstrains. In FEM, the base material inside geocell is assumed as isotropic and geocell as a linear elastic, which might not be the case in the laboratory sample. It is evident from the strain graphs in Fig. 9a that there is a more elastic recovery in FEM than the laboratory testing. It can be noted that the first geocell pocket below load is taking the considerable load and transferring minimal to the subsequent cells.

The influence of the increase in stresses is summarized in Fig. 10. Geocell is effective in reducing the stresses even when the pavement is subjected to higher loads. This analysis is performed, because often, the low-volume roads are subjected to higher loads due to agricultural equipment movement in Texas. Although the geocell pocket beneath the load plate showed some reduction in stresses on subgrade, the percentage reduction of stresses lessened with increasing load which is contrary to the researcher’s expectation; it is hypothesized through this observation that when geocell is subjected to higher loads, the geocell channelizes the load acting as a conduit, resulting in higher stresses than expected. When greater loads are expected, then using geocell of higher height, multiple layers of geocell or a taller cover over geocell may be required.

Closure

  • This paper presented the laboratory setup, FEM, laboratory data refinement, and analysis of results that can be used for developing a design method for roadways reinforced with geocell.

  • The geocell-reinforced layer reduced the vertical stress on the subgrade by acting as a semi-rigid layer. Even at higher loading pressures of 689 and 827 kPa, the geocell reinforcement worked efficiently.

  • Comparison between reinforced and unreinforced sections, in both FEM and laboratory results, indicated that the geocell layer reduced the vertical stress on the subgrade nearly by 30%. However, in this study, only one type of subgrade, base, and geocell are tested. In the future, the study should be expanded by incorporating various combinations of base and subgrade materials and thicknesses.

  • Even though the FEM and laboratory test results agree with stress distribution, the FEM model needs further refinement to match the hoop stresses estimated from the laboratory tests.